Skip to content

M
mathematica
Commit ffa3296f authored by himyss's avatar himyss
Browse files
Options

data added

parents
Show whitespace changes
Inline Side-by-side
Showing with 3056 additions and 0 deletions
3Energy (2).nb 0 → 100644
View file @ ffa3296f
This source diff could not be displayed because it is too large. You can view the blob instead.
deutron.nb 0 → 100644
View file @ ffa3296f
(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 13.0' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
NotebookDataLength[ 95200, 2289]
NotebookOptionsPosition[ 89553, 2191]
NotebookOutlinePosition[ 89981, 2208]
CellTagsIndexPosition[ 89938, 2205]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
RowBox[{
RowBox[{"(*", " ", "Input", " ", "*)"}], " ", "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"kProton", " ", "=", " ",
SqrtBox[
RowBox[{"2", "*", "2.225", "*",
FractionBox[
RowBox[{"939.565", "*", "938.272"}],
RowBox[{"938.272", "+", "939.565"}]]}]]}], ";"}],
"\[IndentingNewLine]",
RowBox[{
RowBox[{"radCh", " ", "=", " ", "2.1421"}], ";"}]}]}]], "Input",
CellChangeTimes->{{3.866683779231073*^9, 3.866683807571497*^9}, {
3.8666838393818808`*^9, 3.8666838923039827`*^9}, {3.8666847300789223`*^9,
3.8666848011687326`*^9}, {3.866684835937563*^9, 3.8666848506595507`*^9}, {
3.866685313816524*^9, 3.866685351704863*^9}, {3.866689549776765*^9,
3.866689552977665*^9}, {3.866691101712513*^9, 3.866691105512731*^9}, {
3.866691177671338*^9, 3.866691183519827*^9}, {3.866691222726439*^9,
3.8666912265676317`*^9}, {3.8666912841399517`*^9, 3.866691327721827*^9}, {
3.8666913674365187`*^9, 3.866691379354693*^9}, {3.866692223786235*^9,
3.866692243517498*^9}, {3.86669234088623*^9, 3.866692356098913*^9}, {
3.8666925244941597`*^9, 3.8666925247684307`*^9}, {3.866789171218506*^9,
3.866789284836467*^9}, {3.866789484746875*^9, 3.8667895047278633`*^9},
3.866791544874084*^9, {3.867203881456174*^9, 3.867203891918221*^9}, {
3.86859415931714*^9, 3.868594159600313*^9}, {3.868594205588904*^9,
3.8685942118497667`*^9}},
CellLabel->"In[45]:=",ExpressionUUID->"15f55500-85b0-49bd-b8c0-7ea00f0e2245"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"(*", " ",
RowBox[{
"\:041d\:0430\:0439\:0434\:0451\:043c", " ",
"\:0440\:0430\:0434\:0438\:0443\:0441"}], " ", "*)"}], " ",
"\[IndentingNewLine]",
RowBox[{"Solve", "[",
RowBox[{
RowBox[{
RowBox[{
RowBox[{
SuperscriptBox["radii", "2"], "/", "4"}], " ", "+", " ", "0.64", " ",
"-", "0.125"}], "==",
SuperscriptBox["radCh", "2"]}], ",", "radii", ",",
RowBox[{"Assumptions", "\[Rule]",
RowBox[{"{",
RowBox[{"radii", ">", "0"}], "}"}]}]}], "]"}]}]], "Input",
CellChangeTimes->{{3.8672039064993887`*^9, 3.867204004483068*^9}, {
3.8672040350457573`*^9, 3.867204051044759*^9}, {3.868594165302346*^9,
3.8685941958762693`*^9}},
CellLabel->"In[47]:=",ExpressionUUID->"f1c72a75-7ee7-46f9-a8f7-4cd49fd00c7a"],
Cell[BoxData[
RowBox[{"{",
RowBox[{"{",
RowBox[{"radii", "\[Rule]", "4.036628499131423`"}], "}"}], "}"}]], "Output",\
CellChangeTimes->{3.86738855414594*^9, 3.867475734034484*^9,
3.868362805408889*^9, 3.868364543237402*^9, 3.868418704643059*^9,
3.8684296801198797`*^9, 3.868503326763413*^9, 3.86851076684522*^9,
3.868591730457405*^9, 3.8685945085451393`*^9, 3.868595755218032*^9,
3.86859955362208*^9, 3.8695655152900333`*^9, 3.869628019580538*^9},
CellLabel->"Out[47]=",ExpressionUUID->"787a36b5-5ebb-450b-97f8-6a66d36d74d3"]
}, Open ]],
Cell[BoxData[
RowBox[{
RowBox[{"(*", " ",
RowBox[{
"\:0418\:0441\:043f\:043e\:043b\:044c\:0437\:0443\:0435\:043c", " ",
"\:0442\:0430\:043a\:043e\:0435", " ",
"\:043f\:0440\:0435\:0434\:0441\:0442\:0430\:0432\:043b\:0435\:043d\:0438\
\:0435", " ", "\:0432\:043e\:043b\:043d\:043e\:0432\:043e\:0439", " ",
"\:0444\:0443\:043d\:043a\:0446\:0438\:0438"}], " ", "*)"}],
"\[IndentingNewLine]",
RowBox[{
RowBox[{"fl1", "[",
RowBox[{"k_", ",", "q_", ",", "r_"}], "]"}], " ", ":=", " ",
RowBox[{
RowBox[{"Exp", "[",
RowBox[{
RowBox[{"-", "k"}], "*", "r"}], "]"}], " ", "-", " ",
RowBox[{"Exp", "[",
RowBox[{
RowBox[{"-", "q"}], "*", "r"}], "]"}]}]}]}]], "Input",
CellChangeTimes->{{3.866787316082055*^9, 3.866787385489438*^9},
3.866789623085449*^9, {3.8667897202033997`*^9, 3.866789728514553*^9}, {
3.868594244912619*^9, 3.86859426617033*^9}, {3.868599535129788*^9,
3.868599540788164*^9}},
CellLabel->"In[48]:=",ExpressionUUID->"40ae1148-daf9-4e15-8762-688f07195dad"],
Cell[BoxData[
RowBox[{
RowBox[{"(*", " ",
RowBox[{
"\:041d\:043e\:0440\:043c\:0438\:0440\:0443\:0435\:043c", " ",
"\:0432\:043e\:043b\:043d\:043e\:0432\:0443\:044e", " ",
"\:0444\:0443\:043d\:043a\:0446\:0438\:044e"}], " ", "*)"}],
"\[IndentingNewLine]",
RowBox[{
RowBox[{"Norm1", "[",
RowBox[{"k_", ",", "q_"}], "]"}], " ", ":=", " ",
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{
RowBox[{"fl1", "[",
RowBox[{"k", ",", "q", ",", "r"}], "]"}], "^", "2"}], ",",
RowBox[{"{",
RowBox[{"r", ",", "0", ",", "Infinity"}], "}"}], ",",
RowBox[{"Assumptions", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"k", ">", "0"}], ",",
RowBox[{"q", ">", "0"}]}], "}"}]}]}], "]"}]}]}]], "Input",
CellChangeTimes->{{3.866787389630982*^9, 3.866787451078424*^9}, {
3.86678748396309*^9, 3.866787512998473*^9}, {3.868365116728319*^9,
3.868365119682788*^9}, {3.868594293307797*^9, 3.868594304549119*^9}, {
3.868599541924264*^9, 3.8685995475331373`*^9}},
CellLabel->"In[49]:=",ExpressionUUID->"7a2bcc4d-5447-48d1-ac24-841589704be5"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Simplify", "[",
RowBox[{"Norm1", "[",
RowBox[{"k", ",", "q"}], "]"}], "]"}]], "Input",
CellChangeTimes->{{3.86860390507694*^9, 3.868603917141555*^9}},
CellLabel->"In[50]:=",ExpressionUUID->"b71993bf-44b9-4b50-90b9-025a29b6f35d"],
Cell[BoxData[
RowBox[{
FractionBox["1", "2"], " ",
RowBox[{"(",
RowBox[{
FractionBox["1", "k"], "+",
FractionBox["1", "q"], "-",
FractionBox["4",
RowBox[{"k", "+", "q"}]]}], ")"}]}]], "Output",
CellChangeTimes->{{3.868603908548182*^9, 3.8686039184646873`*^9},
3.869565521238338*^9, 3.869625957956542*^9, 3.869628024261294*^9},
CellLabel->"Out[50]=",ExpressionUUID->"36448c3c-ed58-4b87-bca0-c6f7044cd75e"]
}, Open ]],
Cell[BoxData[
RowBox[{
RowBox[{"PsiD", "[",
RowBox[{"k_", ",", "q_", ",", "r_"}], "]"}], ":=", " ",
FractionBox[
RowBox[{"fl1", "[",
RowBox[{"k", ",", "q", ",", "r"}], "]"}],
SqrtBox[
RowBox[{"Norm1", "[",
RowBox[{"k", ",", "q"}], "]"}]]]}]], "Input",
CellChangeTimes->{{3.866790998002054*^9, 3.8667910749768953`*^9}, {
3.866791375415957*^9, 3.866791421868765*^9}, {3.866791549994028*^9,
3.866791550606978*^9}, {3.8672042627726517`*^9, 3.867204264059602*^9},
3.868423974748228*^9, {3.868510732445642*^9, 3.86851075423566*^9}, {
3.868591785188673*^9, 3.868591787116836*^9}, {3.868591945385953*^9,
3.868591945528491*^9}, {3.8685920653683558`*^9, 3.868592065938489*^9}, {
3.868592200352151*^9, 3.868592220304749*^9}, {3.868592933204508*^9,
3.868592937488298*^9}, {3.868594321890065*^9, 3.868594328109784*^9}},
CellLabel->"In[51]:=",ExpressionUUID->"ed029352-16a6-45e1-b42a-177020211247"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"\[IndentingNewLine]",
RowBox[{"PsiD", "[",
RowBox[{"k", ",", "q", ",", "r"}], "]"}]}]], "Input",
CellChangeTimes->{{3.8685984536355467`*^9, 3.868598456868614*^9}},
CellLabel->"In[52]:=",ExpressionUUID->"1508f981-ab16-4888-9c9d-70043439577a"],
Cell[BoxData[
FractionBox[
RowBox[{
SqrtBox["2"], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["\[ExponentialE]",
RowBox[{
RowBox[{"-", "k"}], " ", "r"}]], "-",
SuperscriptBox["\[ExponentialE]",
RowBox[{
RowBox[{"-", "q"}], " ", "r"}]]}], ")"}]}],
SqrtBox[
RowBox[{
FractionBox["1", "k"], "+",
FractionBox["1", "q"], "-",
FractionBox["4",
RowBox[{"k", "+", "q"}]]}]]]], "Output",
CellChangeTimes->{3.868598458698038*^9, 3.8685995629995413`*^9,
3.869565525592538*^9, 3.869625962223899*^9, 3.8696280292131033`*^9},
CellLabel->"Out[52]=",ExpressionUUID->"d7839f75-9aed-4efb-95bf-f0aa05801eb8"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"(*", " ",
RowBox[{
RowBox[{
"\:041f\:0440\:043e\:0432\:0435\:0440\:0438\:043c", " ",
"\:043d\:043e\:0440\:043c\:0438\:0440\:043e\:0432\:043a\:0443"}], ",",
" ",
RowBox[{
RowBox[{
"\:0432\:0435\:0437\:0434\:0435", " ", "\:0433\:0434\:0435", " ",
"\:0443", " ", "\:043d\:0430\:0441", " ",
"\:0438\:043c\:043f\:0443\:043b\:044c\:0441\:044b", " ",
"\:0434\:043e\:043c\:043d\:043e\:0436\:0430\:0435\:043c", " ",
"\:043d\:0430", " ",
"\:043a\:043e\:044d\:0444\:0444\:0438\:0446\:0438\:0435\:043d\:0442",
" ",
RowBox[{"1", "/", "hc"}]}], "==",
RowBox[{
RowBox[{"1", "/", "197.327"}], " ", "\:0434\:043b\:044f", " ",
"\:0440\:0430\:0437\:043c\:0435\:0440\:043d\:043e\:0441\:0442\:0438"}]}]\
}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{"Integrate", "[",
RowBox[{
SuperscriptBox[
RowBox[{"(",
FractionBox[
RowBox[{
SqrtBox["2"], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["\[ExponentialE]",
RowBox[{
RowBox[{"-", "k"}], " ", "r"}]], "-",
SuperscriptBox["\[ExponentialE]",
RowBox[{
RowBox[{"-", "q"}], " ", "r"}]]}], ")"}]}],
SqrtBox[
RowBox[{
FractionBox["1", "k"], "+",
FractionBox["1", "q"], "-",
FractionBox["4",
RowBox[{"k", "+", "q"}]]}]]], ")"}], "2"], ",",
RowBox[{"{",
RowBox[{"r", ",", "0", ",", "Infinity"}], "}"}], ",",
RowBox[{"Assumptions", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"k", ">", "0"}], ",",
RowBox[{"q", ">", "0"}]}], "}"}]}]}], "]"}]}]], "Input",
CellChangeTimes->{{3.86738924390305*^9, 3.867389265162883*^9},
3.868592069790248*^9, 3.868592175306278*^9, {3.868592227741321*^9,
3.868592228962371*^9}, {3.8685922770324097`*^9, 3.8685922831167917`*^9}, {
3.8685929499135513`*^9, 3.868592952952462*^9}, {3.868594341632305*^9,
3.868594381115343*^9}, {3.868594497762939*^9, 3.868594504907331*^9}, {
3.868594547173224*^9, 3.868594552292612*^9}, {3.868598275497266*^9,
3.868598275773817*^9}, 3.8685994674679527`*^9, {3.868599511457546*^9,
3.868599518423562*^9}},
CellLabel->"In[53]:=",ExpressionUUID->"cd919aeb-3101-4893-8360-ca90a34b5f8a"],
Cell[BoxData["1"], "Output",
CellChangeTimes->{
3.867389267153965*^9, 3.8674757368662777`*^9, 3.868362822870886*^9,
3.868364534825906*^9, 3.868364571308099*^9, 3.8683646862164707`*^9,
3.868418724949291*^9, 3.868424003660665*^9, 3.8684240538961067`*^9,
3.868429726397519*^9, 3.868503338909972*^9, {3.868510760161477*^9,
3.8685107836324863`*^9}, 3.868591740324675*^9, 3.8685919503322763`*^9,
3.868592286450618*^9, 3.8685929550022717`*^9, {3.868594532156452*^9,
3.868594555136402*^9}, 3.868595763986228*^9, 3.868598253224373*^9,
3.86859952158809*^9, 3.868599567371044*^9, 3.8695655289855413`*^9,
3.869628033543208*^9},
CellLabel->"Out[53]=",ExpressionUUID->"b0e60b84-1f1f-4268-863d-06c8900b3b0b"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"(*", " ",
RowBox[{
"\:041f\:043e\:0438\:0441\:043a", " ", "q", " ", "\:043a\:0430\:043a", " ",
"\:0441\:0440\:0435\:0434\:043d\:0435\:0435", " ",
SuperscriptBox["r", "2"]}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{
SuperscriptBox[
RowBox[{"PsiD", "[",
RowBox[{
FractionBox["kProton", "197.327"], ",",
FractionBox["q", "197.327"], ",", "rad"}], "]"}], "2"], "*",
SuperscriptBox["rad", "2"]}], ",",
RowBox[{"{",
RowBox[{"rad", ",", "0", ",", "Infinity"}], "}"}]}], "]"}], "-",
SuperscriptBox["4.04", "2"]}], ",",
RowBox[{"{",
RowBox[{"q", ",", "225", ",", "230"}], "}"}]}], "]"}], "*)"}],
"\[IndentingNewLine]",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{
RowBox[{
SuperscriptBox[
RowBox[{"(",
FractionBox[
RowBox[{
SqrtBox["2"], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["\[ExponentialE]",
RowBox[{
RowBox[{"-", "k"}], " ", "r"}]], "-",
SuperscriptBox["\[ExponentialE]",
RowBox[{"-",
FractionBox[
RowBox[{"q", " ", "r"}], "197.327"]}]]}], ")"}]}],
SqrtBox[
RowBox[{
FractionBox["1", "k"], "+",
FractionBox["197.327", "q"], "-",
FractionBox["4",
RowBox[{"k", "+",
FractionBox["q", "197.327"]}]]}]]], ")"}], "2"], "*",
SuperscriptBox["r", "2"]}], "/.",
RowBox[{"k", "->", " ",
FractionBox["kProton", "197.327"]}]}], " ", ",",
RowBox[{"{",
RowBox[{"r", ",", "0", ",", "Infinity"}], "}"}]}], "]"}], "-",
SuperscriptBox["4.04", "2"]}], ",",
RowBox[{"{",
RowBox[{"q", ",", "225", ",", "230"}], "}"}]}], "]"}]}]], "Input",
CellChangeTimes->{
3.8685946768723087`*^9, {3.868594803071945*^9, 3.868594825178236*^9}, {
3.8685995856506357`*^9, 3.868599618767168*^9}, {3.8685997043552017`*^9,
3.868599788228649*^9}, {3.8685998237866592`*^9, 3.868599944132773*^9}},
CellLabel->"In[54]:=",ExpressionUUID->"d1262ffb-87ed-4322-8f05-1b89384f8939"],
Cell[BoxData[
GraphicsBox[{{{}, {},
TagBox[
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwd0nkw3GcYB/BtjTREjJK4j90444hbxZFXZKRIpClCXW3dpnZtJcYV18Zi
3Ueomw2ydv0coSuo442SwxGt2JWhwRBJHKkRolPi6Pv2j2ee+czzxzPPM19K
AN01+HMSieSCCveAZxYkEplqR5JLCbCfgUCKo1cggc2eFCsVQgBTyWSF/+cD
/PVJCJSBuJ0Jdm/o6ZJRCISdc8lB2F8ffLbSC4FjPfPoGfa6PiuvBoJzSS8O
CynIDvGO84EQ7JpGHKirI3s0l7I2BgB1yaIyWwvZezHy281+wF65Gt1zFpll
KGIk0g+2iyO9X+ojO9NSNxT7wBmm9oKlEXJIYritWi+QHtO996Mp8k6ETrHZ
b2DOHYqMWyDf0alKt+gBT5kBdG0r5POzon623eCmhJu8ky0yxVnF4EYX2J0W
+LfaIS8fLXG8HoKLu/UrM5eQr7gqy9A7AXeQEbtzGTnv9Ev3TD5YG9/kujsj
m8lMuhT8CjYMW2TjXZCPf8zX43aA58I9jdfXkTMp/LHmdjBG8bSxcUeWfOfq
8PAByHpMKvTxRNbSzNC71wY0m63TB7yRrVr6qW0tgLE21P3ODznH2stlgQDd
4XPZ7v7I0i/Slld4QPKuaFh7EPIeX1N9vxFoSd9mCEKRXw15vjHiAAUBw9o6
HHm6ryAONIDnfwtNwiKQz+VppdLrALvF0jQtEjk6eViOxwbfPNAXvIlCLpbV
N4mrBlA8okMiFjmsuHd1qRyIc+2MY24juw9mcki/gKh1Ss9kEnLZ8PFM4yLA
Tr+etMVA5uaYTznlgsYgqWWPNOQ/lTVPlKcBeoVKBoOFXCCkSc4mAI/o86ZV
2cgkemp8JQ0olLxN3svDpsp9MlOC1ScWxdSKkO023vrb0uD+MNUsowTZqEKG
cpgIlacdqjrLkOW9Qzm66dA31+CkoBJZh1jNMcqFMRkcVYta5M3oYz+FFEG3
GSrt+zrkqpTg9q0SdN6w7+h95PHOfw9GyuEiV/eGFg/f+zg5MK8axlnPZzk2
I68o+Rey2PC9lLp/axv+V+T+d/Q6SL7QGTXbgfcFWvmYN8CoLz0K/+nEeSxN
EN26D+u1Wdc8enAeVv46mGqEd0u+cEroQw4y33Qu4UHlqiXPLOyEKBNyNQ82
1PWHlGGLX6buNPAgv+0Wk489wH5Sy+dBwcgCfI+9YS77cYoHZQ+7LPz6kRXX
yZXSTbAsJEzjwgD23PJSfhMk0y6ZXsXOYSp0lTZB7i1Ve29s1UcO2bVNsCdF
8EM09ug207StCc5W2FW2Yj+5VpM60QSV/pCXVoPY8zZnThKwQbhNNsC2mljb
OUVA/VcThtbYFa4FI8oEtFllunhiUxV//1mfgL4iH1j52DmNjwauEHBZbLy0
GnsT6BW5EZAq1cghsDtoucE+BExU8Rt+ih2daSkRTsBjGpZTQuyiGMbCTQLm
6cosvca2/zTYEU9AWeONzQ/YWaf20u4QsOarkaMj7Nihs15ZBPwP/RYtzQ==
"]]},
Annotation[#, "Charting`Private`Tag$426866#1"]& ]}, {}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{None, None},
AxesOrigin->{225.0000000000005, 0},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
ImagePadding->All,
Method->{
"DefaultBoundaryStyle" -> Automatic,
"DefaultGraphicsInteraction" -> {
"Version" -> 1.2, "TrackMousePosition" -> {True, False},
"Effects" -> {
"Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2},
"Droplines" -> {
"freeformCursorMode" -> True,
"placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None,
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& )}},
PlotRange->{{225, 230}, {-0.053789888713922096`, 0.12440886406701779`}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Output",
CellChangeTimes->{3.868594718906636*^9, 3.8685948636051292`*^9,
3.868595801986965*^9, 3.868599678253955*^9, 3.86859979678286*^9,
3.8685999656321163`*^9, 3.869628052988927*^9},
CellLabel->"Out[54]=",ExpressionUUID->"01ca38e8-4fdc-4873-bac0-259fd0f0d105"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"FindRoot", "[",
RowBox[{
RowBox[{
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{
SuperscriptBox[
RowBox[{"PsiD", "[",
RowBox[{
FractionBox["kProton", "197.327"], ",",
FractionBox["q", "197.327"], ",", "r"}], "]"}], "2"], "*",
SuperscriptBox["r", "2"]}], ",",
RowBox[{"{",
RowBox[{"r", ",", "0", ",", "Infinity"}], "}"}], ",",
RowBox[{"Assumptions", "\[Rule]",
RowBox[{
RowBox[{"Re", "[", "q", "]"}], ">", "0"}]}]}], "]"}], "\[Equal]",
SuperscriptBox["4.04", "2"]}], ",",
RowBox[{"{",
RowBox[{"q", ",", "228", ",", "229"}], "}"}]}], "]"}]], "Input",
CellChangeTimes->{
3.8685948815172367`*^9, {3.86859588791683*^9, 3.8685958896563807`*^9}, {
3.86859605938684*^9, 3.8685960772373877`*^9}},
CellLabel->"In[55]:=",ExpressionUUID->"cab76d12-2dad-42c6-94b6-db201a8c18ec"],
Cell[BoxData[
RowBox[{"{",
RowBox[{"q", "\[Rule]", "228.46513877063487`"}], "}"}]], "Output",
CellChangeTimes->{
3.868594890181797*^9, {3.868595866815669*^9, 3.868595896125098*^9},
3.868596082875332*^9, 3.869565537017137*^9, 3.86962805962097*^9},
CellLabel->"Out[55]=",ExpressionUUID->"50db03d0-7166-4dd1-b1ad-8af23d2f754f"]
}, Open ]],
Cell[BoxData[
RowBox[{"(*",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"PsiD", "[",
RowBox[{
FractionBox["kProton", "197.327"], ",",
FractionBox["228.465", "197.327"], ",", "rad"}], "]"}], ",",
RowBox[{"{",
RowBox[{"rad", ",", "0", ",", "20"}], "}"}]}], "]"}], "*)"}]], "Input",
CellChangeTimes->{
3.866791446129416*^9, 3.866791571950573*^9, {3.867204290835143*^9,
3.867204291028899*^9}, {3.867204355843154*^9, 3.867204356378105*^9},
3.867388638320077*^9, {3.868366587067737*^9, 3.8683665895065203`*^9}, {
3.8684236246644173`*^9, 3.8684236247974253`*^9}, {3.8685917891913433`*^9,
3.868591790296854*^9}, {3.868591869164423*^9, 3.868591875614442*^9},
3.868592070839036*^9, 3.868592298847458*^9, {3.868592922751924*^9,
3.868592930081027*^9}, {3.868596211643444*^9, 3.868596220693158*^9}, {
3.868597808816976*^9, 3.8685978218062897`*^9}, 3.8685978683675537`*^9, {
3.868597913253585*^9, 3.868597915875341*^9}, 3.868597990681909*^9, {
3.868598789768701*^9,
3.8685987918538237`*^9}},ExpressionUUID->"363c9fee-04cf-4e5c-90ea-\
4a0da118130e"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"Plot", "[",
RowBox[{
RowBox[{
RowBox[{
FractionBox[
RowBox[{
SqrtBox["2"], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["\[ExponentialE]",
RowBox[{
RowBox[{"-", "k"}], " ", "r"}]], "-",
SuperscriptBox["\[ExponentialE]",
RowBox[{
RowBox[{"-", "q"}], " ", "r"}]]}], ")"}]}],
SqrtBox[
RowBox[{
FractionBox["1", "k"], "+",
FractionBox["1", "q"], "-",
FractionBox["4",
RowBox[{"k", "+", "q"}]]}]]], "/.",
RowBox[{"k", "->", " ",
FractionBox["kProton", "197.327"]}]}], " ", "/.",
RowBox[{"q", "->",
FractionBox["228.465", "197.327"]}]}], " ", ",",
RowBox[{"{",
RowBox[{"r", ",", "0", ",", "30"}], "}"}]}], "]"}],
"\[IndentingNewLine]"}]], "Input",
CellChangeTimes->{{3.868598005232416*^9, 3.86859802860509*^9}, {
3.868598079627*^9, 3.868598114995576*^9}, {3.868598206253788*^9,
3.868598214091436*^9}, 3.86859833210946*^9, {3.868598489203175*^9,
3.868598593828712*^9}, {3.868598640088954*^9, 3.868598643934705*^9},
3.868598773730584*^9},
CellLabel->"In[56]:=",ExpressionUUID->"ec406fd6-54f4-4e5f-8e73-4494b58edd50"],
Cell[BoxData[
GraphicsBox[{{{}, {},
TagBox[
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwVlnk01esXxg+iUroNR9wkkSQzZSrH8yoNlKmuqUHmyjUkDTdlOmUoQ6SQ
XGVo4pqFJEkkJdXJPJyvQkXm4Zj5nd8f79rrs96117v3s553ry1p73HIiZdG
o73nnv9HDru6Qjo0VbfUWz1xeUmSbl2i6CW9JiZWREctWSfnDyL8yV606RbM
lF3eJP8RiQumaY18Tcn45NxnPlVwH6sGRG5NNeYiIVVs77rfmaBKjD3GGstR
pRmrxHZ8iXhhEUcv/gr0CwXZ8C99hb/cKasRtUo8YDJV6w6X4b3EmV1D4VXg
3ODjmPS+RgEzSrhvdw1SbhoO+E5UYK90b/twIwvBZ+Amdvc9Uk2NrXLcv6Ip
YZtD4K4P4PHJZZ3hrwNxU5F60PMBJfXeVYNq9Xjb6yTCq/oRqsHLcvrDG1GY
4v1G7uEnrO9VuNazuw12lb8ENekseK+Nmn/S0gZF9fNrflmy0Lhr/J9Tnu2o
PJ/YnhTPwq17L91+JrKRezwtf4f4V1yTeZw+cqUDTMWUkoMidZhq1Lwz1Pgd
sqcWzW7/Vo8itSW2j7d2Qpcmmisl1oAL4U1yNpc7ob3s8k/xvxowsutS2YcN
XRj85XFn/5sG9GYU/37k1I0PaZt9XsU04smS0ILjhd0ICov6fbq6Ec4ORwPo
S3/gDL9+oNZMIzpFZ9cy//uBq96fRw4ea0LbVcau46M/wTkgLJBAb0Y8W0iI
vucXSgsDLHNIM6y02Y3vY34hOpHHe+HvZtQP+Lpp7eiB5gPXcZOyZtRal8Wt
CejFc428kEW2LShT3j1YvaIfAhdPur7waYXvjTXF/rb96AhOkz+X2Aqd7s5r
mrn9IPwuT66XtuJ5/LV1D80HEDzgPsKabUUu/9s9/gmD2E8KJdeebYOnbcxK
zYFBxLFszPrC2xB3PK+fIzGEhsV89UpP22BRdLUow3MIG5+la9DYbWC5SRuL
CQ+DLKt6K6DXDtV7YXkcxjBmH26UPGvVjsh3Y6Is52G8n9tNs/Joh/Gmys6Q
omEU6Ivxxt9rx/smp0ucoyOQTeoclh5ox1aBWvaXayNwn3c+d4uHjZBtGvoZ
GSNYbnLJOZjOxt4IgT8cF0ZgML0rX0ibjTe7H6d+SR7FeyWTZ8+usKESkdUz
8W4U4UW0a36hbCQ2FSptGBxF340k2967bPzj9q7IZecY6Fs1Pzx+xoZSbE8N
X90YRAJWunT8YiPh2/Aquekx5Dtbv/kyxsZShWkL043j0NtT+cuVRqGrTPBb
gus4GiRLXqaupRDfKz+uzs9BcPoFjgYoLFHfvuOYPAcTR/kUovdTOO+n48c0
48DjxqxSkhkFU7rR0k//cvD+t9bpBnsKL23MjcffcDC0pd5vwYWC3NPj0WK9
3PyURCn2WQr8uu7ipzQmcF+8OPNVAIWzIRfsI45NQOd2un1FCIUOlu/jfOYE
NhmJaDFvUig+eVOV59MEWoulXiskUJDNjb2wZXwCT09elxdLpnBn9v4LI7FJ
cEr5N799TOFMVPae+JOT2LzUV9Q8lwK7tehGWfgkri+gYEchhQMyrz/9yJsE
T0S2XMcLCkVnqulCLdz7wxy9vWUUZF58sd5GmwJtdKLSrYJCNH9LorXMFLQM
7H0t31GgmX7v9Ds4hfaoTJVFNRRau0bcauKmcER+LPwpi8J+5ZnckdIpQJn+
PKWeQsElvknR7ikI2HmwHZoobKpYxsCyaVgWNRT1tlCIXEFnOqlO40+hZTza
7RTmrdZXhVpOo6+63M2EovB3ivTyXB8uR2TlKX2j0NSvYNaUMg165dXAxu8U
9mqpx8xXT0NOajLasItCPpPRKj00jSTxL+Eh3RQkP+7ZeGDtDOwtuiRu/aAQ
IWLs5Kkzg+Ye8fGTPynM2lmkxdrPQLkksEDwF4XT/9kMvgyZgWSu/rLLXG7g
OG/vypyBe9vTuOdc1tfzuCRYPwOBO8q8VVzOCb1YqjLDzY/w70nh8oYGPz5L
yVnUfL0yYMrlsI0h+332cblUN6uW+96US2R4itssRFol3olz2flZHKs6ehbf
Xr38qsutr27hgcjQ81nUt8y7qHHr1zN8emxtxyz6FUU2T3VSyLydk6QjMAdz
WnhsNLf/9dTzH/YKc3BkMix4ufrQRj3jqs3mcJtXnf5//boE5AxVLs7hRH9d
91muvu/WfZ+JSZhDZVa3mXsrhQyl+Iy513OYvlHYrtdM4dauQyccf85BPVJG
aKCBwgULwVUfls9D4FaivVcdBV1f73NxlvOIntRlLvtEQeqWmszClXkoZakY
SnD9IPCot9EpeR4r71duW1FNofbjkZ3b+ufh983Uyq+cwgnxnby1zAXo5Lut
Kcnj6qk6mrf9yQJmDRI3FGRx/b0n3enexwV4bV3LezOdwj8F4Y7bl9NIwgcW
neL6nbDnqngsaWQ+O/bSokgKar+aNz47TSOHTMdP8IRSkB55dunUFRoJshUM
7Ajk/l8Bd/lPSTQiG6Quu+8yhS+K7IiEPhpJ++DbXuZIoUKz+KfJAo2YaDyp
abHh+lUvhvCt5iGqbw6LtFhx54G58chpTR7y9oKQ9o2DFOx9Ss01mTxkXFCx
uliNwkhN4nqWCC8RmPyckTbNRleD9/lAOV5yxoYK0h9lo6HDolaLwUtmhbKV
q3+zUTy2wv++PS9RmWYp3G5j4+p6v07XDF5STvUbaL9kg+56Im3xbj5iU+U5
QrvMhtzilLemlnyk7vNDgWxPNkjyj+93/+Yjgg3jkQdOseHa5CamcJuPKErm
WBmYs1GhfyXMtJuPVP3UzTmlxMY58bvud4MXkShXKc3L7e34WstSk6/hJ+En
eky6VdpxS3XvC2PzJWQgJ1Go83krmuNUyoZXCpF9y+/v7mM1ITTV7xPvn6uI
sHCzTv7Leojc7rwe/e8aMmFgvWVslLsX/GWgy+IIkwrjK1fEEz/DSzvpRDVT
lNjdFD439boG+oPT3u6d68jAljQpD9FqBOiY2a3TEidbBypsx4YrsSPzbr7v
KwlyOyRw7+aJcrhODvu/E5IkZ2zv6KuHlWFKfiVb0VyKTLU0DuuFlkAn/b8H
MTGbyOcVQwGjmUUYXm1oa1EuTfyDfiztDH+GrjBbi7OLZYhqRN7FQ/dyYTB4
0aBbYwu5GrPzsK1WNvoclnjl+8kSSq5yenQsnbvfiPAGl28lunfkyn1kn2D1
R5mI7EE5In2zIfst/SHWh2SZamgoEHpUOtKUkxEnr71yzUlFIotUyVdZ9/F+
nZ76aJQSWeR1xImdcQ871pdHKjcoE3mxO+oSP2Oxgi/5nB1ThejQqyyMm25j
Q4CEjrWMKhGZ2B8XNhmFpZuPFRyqUiU+Zvahs6tuQonxZ9bF42pENWg851+J
UJxlr35jSNtGBP1lj3ieCsbgaJi5Qdw24uRh3e/jfA37lN/GGyhuJ7WMyD2f
vwagdHTnzETtdiLifFrA/aMv3BXUWr44qZPcNzKyNpQ3GAOOddZLNUjN43Mu
2xQvYo+0qJFQsga5vVI7MEL5HGT9b/xTrqlJBEV/ZP5+4Ak5J+1Xm1s0SXXN
4OarZ9zhVHrqWr6nFqld+eXV+HUXvHpQ5zgsrE0c/otx/kA5Y+zJwoRyoTb5
vu7yYHuFAxw2py+NN9pB7hru6P9N7DAsF62RO7SD2K/Im6Iqj6ModebbeMhO
wpz+t39oyBpH9DeRnRt0iNdstPLIUwuIuQU/VyrTIdf3VN2ViD4MYUHXHCNL
BomN3H6gYLUZUnf7eA9ZM0h0nu3YwSVmUPOJ2B19jEEK/+jj9MyZwngou77J
jkEM1j6a1OgxRVDD+JSDK4MoPWcx15eZYjLZb5d3AINUfKQfXe1hipad0V8f
pTPIosLiIvEUE5w6n5pgkMkg/u6zL1g3TcDJfObUl80gj45tvBp9xQSrpZom
VAsYZJeHLdGyMMGBJeLrX5YxiFvLUKaQoAlK6h45fq1nEJ3qRQrfvYxhuKJI
8UITg+wTGv/T1M4YTfuqOaKtDHIwjO9otbExxop/h9h0MIhvPlXcvtUYikkq
GT29DLJEH6rhHUYoadG7ENbPIJpWmRN/1RrBkH4YykMMYnXds2VLiRGcg89/
OTfO1eMgu3kg1ghjZUHxIpMMkqW+uOd7oBGY07EOxdMMktjFnPrmZYSV258q
HJ9jEIcD9xb12Rkh0a14fGGBQXK9Evl4TI3wP8cUPHo=
"]]},
Annotation[#, "Charting`Private`Tag$517545#1"]& ]}, {}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{None, None},
AxesOrigin->{0, 0},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
ImagePadding->All,
Method->{
"DefaultBoundaryStyle" -> Automatic,
"DefaultGraphicsInteraction" -> {
"Version" -> 1.2, "TrackMousePosition" -> {True, False},
"Effects" -> {
"Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2},
"Droplines" -> {
"freeformCursorMode" -> True,
"placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None,
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& )}},
PlotRange->{{0, 30}, {0., 0.4985826035829891}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Output",
CellChangeTimes->{{3.8685985735871162`*^9, 3.868598595359455*^9}, {
3.8685987585892277`*^9, 3.8685987934634542`*^9}, 3.869628071502441*^9},
CellLabel->"Out[56]=",ExpressionUUID->"2bd6fbb1-9564-433a-b163-c5529f0a682d"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"(*",
RowBox[{
"\:0424\:0443\:0440\:044c\:0435", "-",
"\:043f\:0440\:0435\:043e\:0431\:0440\:0430\:0437\:043e\:0432\:0430\:043d\
\:0438\:0435"}], "*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{
RowBox[{"PsiP", "[",
RowBox[{"k_", ",", "q_", ",", "p_"}], "]"}], ":=",
RowBox[{"Simplify", "[",
RowBox[{
RowBox[{
FractionBox[
SqrtBox[
RowBox[{"4", " ", "\[Pi]"}]], "p"],
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{
FractionBox[
RowBox[{
SqrtBox["2"], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["\[ExponentialE]",
RowBox[{
RowBox[{"-", "k"}], " ", "r"}]], "-",
SuperscriptBox["\[ExponentialE]",
RowBox[{
RowBox[{"-", "q"}], " ", "r"}]]}], ")"}]}],
SqrtBox[
RowBox[{
FractionBox["1", "k"], "+",
FractionBox["1", "q"], "-",
FractionBox["4",
RowBox[{"k", "+", "q"}]]}]]], "*",
RowBox[{"Sin", "[",
RowBox[{"p", " ", "r"}], "]"}]}], ",",
RowBox[{"{",
RowBox[{"r", ",", "0", ",", "Infinity"}], "}"}]}], "]"}]}], ",",
RowBox[{"Assumptions", "\[Rule]",
RowBox[{
RowBox[{"k", ">", "0"}], " ", "&&", " ",
RowBox[{"q", ">", "0"}]}]}]}], "]"}]}], "*)"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"PsiP", "[",
RowBox[{"k_", ",", "q_", ",", "p_"}], "]"}], ":=",
RowBox[{"Simplify", "[",
RowBox[{
RowBox[{
SqrtBox[
FractionBox["2", "\[Pi]"]],
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{
FractionBox[
RowBox[{
SqrtBox["2"], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["\[ExponentialE]",
RowBox[{
RowBox[{"-", "k"}], " ", "r"}]], "-",
SuperscriptBox["\[ExponentialE]",
RowBox[{
RowBox[{"-", "q"}], " ", "r"}]]}], ")"}]}],
SqrtBox[
RowBox[{
FractionBox["1", "k"], "+",
FractionBox["1", "q"], "-",
FractionBox["4",
RowBox[{"k", "+", "q"}]]}]]], "*",
RowBox[{"Sin", "[",
RowBox[{"p", " ", "r"}], "]"}]}], ",",
RowBox[{"{",
RowBox[{"r", ",", "0", ",", "Infinity"}], "}"}]}], "]"}]}], ",",
RowBox[{"Assumptions", "\[Rule]",
RowBox[{
RowBox[{"k", ">", "0"}], " ", "&&", " ",
RowBox[{"q", ">", "0"}]}]}]}], "]"}]}], "\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{"PsiP", "[",
RowBox[{"k", ",", "q", ",", "p"}], "]"}], "]"}]}]}]], "Input",
CellChangeTimes->{{3.842429619361777*^9, 3.842429677633604*^9}, {
3.842429720856079*^9, 3.842429753812727*^9}, {3.842430187216261*^9,
3.842430258057073*^9}, {3.842430358025407*^9, 3.842430363366953*^9}, {
3.842431304234517*^9, 3.8424313168119774`*^9}, 3.8424313659165783`*^9, {
3.84243142345732*^9, 3.8424314893812175`*^9}, {3.842432125684045*^9,
3.842432157645306*^9}, {3.8424321906882353`*^9, 3.8424322290137844`*^9}, {
3.842433503697682*^9, 3.8424335156930647`*^9}, {3.842433964243157*^9,
3.8424339654450226`*^9}, {3.842441765367482*^9, 3.842441789073285*^9}, {
3.8424418280029216`*^9, 3.8424418302671328`*^9}, {3.842441902445393*^9,
3.842441904619342*^9}, {3.842442407989282*^9, 3.8424424240173473`*^9}, {
3.8424446932159224`*^9, 3.84244470052919*^9}, {3.8424483586356497`*^9,
3.842448371032787*^9}, 3.8424486628033075`*^9, {3.8424492882931213`*^9,
3.842449296532782*^9}, {3.842458930056344*^9, 3.842458959414255*^9}, {
3.8429757852823305`*^9, 3.842975785602333*^9}, {3.8429758182078094`*^9,
3.8429758427135096`*^9}, {3.84297588039443*^9, 3.8429758824232917`*^9}, {
3.8429759476812525`*^9, 3.8429759822454915`*^9}, {3.8429761768185596`*^9,
3.8429761802928667`*^9}, {3.868592046564624*^9, 3.868592100595749*^9}, {
3.868592455157613*^9, 3.868592462999556*^9}, {3.8685926812186604`*^9,
3.868592681493209*^9}, {3.8685953160084543`*^9, 3.8685953222658443`*^9}, {
3.8685994009874973`*^9, 3.8685994014156713`*^9}, {3.868612439195859*^9,
3.8686124712931223`*^9}, {3.868612700424255*^9, 3.868612713038343*^9}},
CellLabel->"In[57]:=",ExpressionUUID->"589fa93e-41d0-46c0-b8d3-ab8df683f53d"],
Cell[BoxData[
TemplateBox[{
FractionBox[
RowBox[{"2", " ", "p", " ",
RowBox[{"(",
RowBox[{
FractionBox["1",
RowBox[{
SuperscriptBox["k", "2"], "+",
SuperscriptBox["p", "2"]}]], "-",
FractionBox["1",
RowBox[{
SuperscriptBox["p", "2"], "+",
SuperscriptBox["q", "2"]}]]}], ")"}]}],
RowBox[{
SqrtBox["\[Pi]"], " ",
SqrtBox[
RowBox[{
FractionBox["1", "k"], "+",
FractionBox["1", "q"], "-",
FractionBox["4",
RowBox[{"k", "+", "q"}]]}]]}]],
RowBox[{
RowBox[{
RowBox[{"Im", "[", "p", "]"}], "<", "k"}], "&&",
RowBox[{
RowBox[{"Im", "[", "p", "]"}], "<", "q"}]}]},
"ConditionalExpression"]], "Print",
CellChangeTimes->{3.868604232135943*^9, 3.868612603799876*^9,
3.868612825817466*^9, 3.869565741857703*^9, 3.869626276514852*^9,
3.869628183693252*^9},
CellLabel->
"During evaluation of \
In[57]:=",ExpressionUUID->"2946d86e-f35b-4b75-b95e-a5caa077a51c"]
}, Open ]],
Cell[BoxData[
RowBox[{"\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{
"\:041f\:0440\:043e\:0432\:0435\:0440\:0438\:043c", " ",
"\:043d\:043e\:0440\:043c\:0438\:0440\:043e\:0432\:043a\:0443"}],
"*)"}]}]], "Input",
CellChangeTimes->{{3.868595166146923*^9,
3.8685951681358547`*^9}},ExpressionUUID->"58e80c3d-daed-4f30-890a-\
2e8e52e60c0c"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"(*",
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{"4", " ", "\[Pi]", " ",
SuperscriptBox["p", "2"], " ",
SuperscriptBox[
RowBox[{"PsiP", "[",
RowBox[{"k", ",", "q", ",", "p"}], "]"}], "2"], " ",
FractionBox["1",
SuperscriptBox[
RowBox[{"(",
RowBox[{"2", " ", "\[Pi]"}], ")"}], "3"]]}], ",",
RowBox[{"{",
RowBox[{"p", ",", "0", ",", "Infinity"}], "}"}], ",",
RowBox[{"Assumptions", "\[Rule]",
RowBox[{
RowBox[{"k", ">", "0"}], " ", "&&", " ",
RowBox[{"q", ">", "0"}]}]}]}], "]"}], "*)"}], "\[IndentingNewLine]",
RowBox[{"Integrate", "[",
RowBox[{
SuperscriptBox[
RowBox[{"(",
FractionBox[
RowBox[{"2", " ", "p", " ",
RowBox[{"(",
RowBox[{
FractionBox["1",
RowBox[{
SuperscriptBox["k", "2"], "+",
SuperscriptBox["p", "2"]}]], "-",
FractionBox["1",
RowBox[{
SuperscriptBox["p", "2"], "+",
SuperscriptBox["q", "2"]}]]}], ")"}]}],
RowBox[{
SqrtBox["\[Pi]"], " ",
SqrtBox[
RowBox[{
FractionBox["1", "k"], "+",
FractionBox["1", "q"], "-",
FractionBox["4",
RowBox[{"k", "+", "q"}]]}]]}]], ")"}], "2"], ",",
RowBox[{"{",
RowBox[{"p", ",", "0", ",", "Infinity"}], "}"}], ",",
RowBox[{"Assumptions", "\[Rule]",
RowBox[{
RowBox[{"k", ">", "0"}], " ", "&&", " ",
RowBox[{"q", ">", "0"}]}]}]}], "]"}]}]], "Input",
CellChangeTimes->{{3.8424297759514723`*^9, 3.8424298904774303`*^9}, {
3.8424302132641673`*^9, 3.842430221226556*^9}, 3.8424308283157177`*^9, {
3.842431023031686*^9, 3.842431045030918*^9}, {3.842441926294345*^9,
3.8424419379889317`*^9}, 3.8424421645252914`*^9, {3.8424447346828985`*^9,
3.8424447531082444`*^9}, {3.8424451876234922`*^9, 3.842445210127918*^9}, {
3.842445241924023*^9, 3.842445249688614*^9}, {3.8424483961307383`*^9,
3.8424484004242554`*^9}, {3.8424589935407553`*^9,
3.8424590247120314`*^9}, {3.8429767149416723`*^9, 3.842976731081705*^9}, {
3.842977308206172*^9, 3.842977317290962*^9}, {3.842977460771119*^9,
3.842977479967112*^9}, {3.8429776043458705`*^9, 3.842977607769457*^9}, {
3.868595004463093*^9, 3.8685950206623774`*^9}, {3.868595172460483*^9,
3.868595185484193*^9}, {3.8685952966840687`*^9, 3.868595300860848*^9}, {
3.868595532269759*^9, 3.8685955362275753`*^9}, {3.8686126439376163`*^9,
3.8686126745347157`*^9}, 3.868612839045279*^9, {3.869628388967555*^9,
3.8696283893478117`*^9}},
CellLabel->"In[65]:=",ExpressionUUID->"c95e48ba-da31-4186-9fab-e23d54171786"],
Cell[BoxData["1"], "Output",
CellChangeTimes->{3.868595287863023*^9, 3.86859563951444*^9,
3.868596926165069*^9, 3.8685971501862993`*^9, 3.868612678323316*^9,
3.8686128422832127`*^9, 3.869565750199133*^9, 3.869626296911549*^9,
3.869628191962613*^9, 3.869628395777919*^9, 3.869628872721054*^9},
CellLabel->"Out[65]=",ExpressionUUID->"605d794b-f8c9-4677-b077-aada9b92bbd5"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"(*", " ",
RowBox[{
RowBox[{
"\:0421\:0442\:0440\:043e\:0438\:043c", " ",
"\:0424\:0443\:0440\:044c\:0435", " ",
RowBox[{
"\:043e\:0431\:0440\:0430\:0437", ".", " ",
"\:041a\:043e\:044d\:0444\:0444\:0438\:0446\:0438\:0435\:043d\:0442"}],
" ", "197.327", " ", "\:043d\:0435", " ",
"\:043d\:0443\:0436\:0435\:043d"}], ",", " ",
RowBox[{
"\:043f\:043e\:0442\:043e\:043c\:0443", " ", "\:0447\:0442\:043e", " ",
"\:043c\:044b", " ", "\:043d\:0435", " ",
"\:043f\:0435\:0440\:0435\:0432\:043e\:0434\:0438\:043c", " ", "\:0432",
" ", "\:0424\:0435\:0440\:043c\:0438"}], ",", " ",
RowBox[{
"\:0430", " ", "\:0440\:0430\:0431\:043e\:0442\:0430\:0435\:043c", " ",
"\:0432", " ",
"\:0438\:043c\:043f\:0443\:043b\:044c\:0441\:043d\:043e\:043c", " ",
"\:043f\:0440\:0435\:0434\:0441\:0442\:0430\:0432\:043b\:0435\:043d\:0438\
\:0438"}]}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"(",
FractionBox[
RowBox[{"2", " ", "p", " ",
RowBox[{"(",
RowBox[{
FractionBox["1",
RowBox[{
SuperscriptBox["k", "2"], "+",
SuperscriptBox["p", "2"]}]], "-",
FractionBox["1",
RowBox[{
SuperscriptBox["p", "2"], "+",
SuperscriptBox["q", "2"]}]]}], ")"}]}],
RowBox[{
SqrtBox["\[Pi]"], " ",
SqrtBox[
RowBox[{
FractionBox["1", "k"], "+",
FractionBox["1", "q"], "-",
FractionBox["4",
RowBox[{"k", "+", "q"}]]}]]}]], ")"}], "/.",
RowBox[{"k", "->", " ", "kProton"}]}], " ", "/.",
RowBox[{"q", "->", "228.465"}]}], ",",
RowBox[{"{",
RowBox[{"p", ",", "0", ",", "300"}], "}"}]}], "]"}]}]], "Input",
CellChangeTimes->{{3.868604821326149*^9, 3.86860483549179*^9}, {
3.8686048918037643`*^9, 3.8686049478840723`*^9}, {3.868610320523445*^9,
3.8686103884198303`*^9}, 3.86861285794902*^9, {3.869628970187204*^9,
3.869628984962192*^9}},
CellLabel->"In[67]:=",ExpressionUUID->"af705252-b6bb-4c46-94eb-0f4dbbf1db66"],
Cell[BoxData[
GraphicsBox[{{{}, {},
TagBox[
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwV1Xk4Vev3AHCJQpKGqxRdKkPpIqJjyFrOKKTomlOEyhROKI0yxDFmiBQy
VErm2T6mJIX4RoNriJQhEpIMZfjt3x/72c/n2Wvv533Xu9ba0qfcTRx5eXh4
xsjr/+9FZgu/vud06px6a7JrLvKkDqfhRIdxZBnsvKVe1DelDbe6/C9vj3wJ
XYmZd0KmDCFuIK6FL7ID0ssCxQWnjkP8SPLMbMQwfK0czfKddIXNrjvCfkTM
QiYLsr1Gr4B5joPpeMRqrFtKkYprD4fZliBiLGIzCp675RjvlQQOIERZP70Z
OQvdJ/O+JUF7fmSJmtUW/P12RCnmVDLkxibkX5MVxzexAdKFR1LAwfLJI9Ga
rdgVWZmWvjEV2gdex+yflET2mSajm4Np0LHIUdPZvQNtZz+I83s8hKJNbWtv
hsmjq0nGGVGRbKj03DagxpVH5R8yOf9pZ0N9qyMxOCqPo3MszYsu2fAh5Pdp
hv5uXNR9H6D9KhvmFnbW8gnuQRmLcfv313NAZ9CHHXBTAcOuZS/LDudCU4lE
h98NRcw9Zxyf35QP7RvO5CgXKCI1qPP16b586HYvCPj0SRHnzVc8XjWdD2O7
mcqISljfnSe9UrIA1qW4c5aXlPB1tr7QuFsB7KH1S0K1Mg4cNR0PWFMIHgr7
31RpqeDqjt5rN9SKoPcAa1nymApGV+d+XckqgsN0K8VrzipI8UgX97Aogj02
fuE6iSqYPJnUzH+5CAYjX+vVzKig2OAPc9maIrCacnhWW6CKUn6FW7RpxUCr
uF34XE4N196JpTVolkDhi8f9O0ENS7W8/w04VAJS7VzRQDM1/Li+1X2PRQks
jfafowepYcS5fT3q3iVQLqGo8OKzGp7/SlE5lFsCe/0aMhqS1XGN+r4US4lS
EGPNxjVupOD5KJ7Htl9LYeqVwdyufyhYECAQ7/mrFFr0U639mBS8W87qd+It
g0CjQzsO+FJwZnT+hahEGUyZ3st70EtBtuDiEQ2jMmhxgKbrTzSQZTylwptb
Bo+HYv/prtNApf3FRVEV5Ptnv95S79HA3kTj6/wvykDTNdr8u4gm3idGD2R1
k/HnvwxYeWkiNeftn87V5RDoH7ysBlrocnTmQb91Odjy9ZyKttBC286m/D+O
5aB1U7lhzFMLHcOuiC+7l8MUpzM844EW7ovj0a8LIOOjFbauF9JG/2398tpZ
5aCd+r/9Y++0kSWcqi7ysxx+Vm12TnfWwQ5z1+BCrwqYM1ZONPTXwRsJap9T
LlfAwqDeq5lEHew14k319a8APpFLsgaNOqjr9u7m76gKEDvR8/mnHGDAywPt
ClkVQFlKtWYMAuZgxh+r7grQjqkInVgA7PfONFXrrwCpjSM9hkKIp41Uti8P
VYBM5grhWWlErSMndOymKkDxfyrOBsaIB6c14uwECIC/b8tO5yG+eJ/uaLeP
AKqTtE4jF1H5RvVtTXUC6EU5pikvEXdfo9D4tAjQYzUE6vUhZs+vtXKiE3DU
ffZzkogu/lJxN75iRsCpGsv7DDdd/EovUnl3gQAHwaHSrb66eFYsVbbqMgGn
j7FbJwJ1ceS+/KOE6wS4DIcuJibpYsGwaph0MAFe6yqtx5t10fGwaV3obQKC
Tm7fkrCHioHv/lx9lkeAjkNzo9MBKh6qq72ypoiAmbMXL2vTqRimtraSUUrA
WXZ7b78NFRkwdySskgD9oJsP90ZT8VShzF82rwjgDVU1X06mYmPoeVuFZgK4
kZ8E2rOo6Fz+PGa0hYC9dzRdL9RT0a51cEnrLQEiT8dV6mapWJwgvf+fjwQ0
5N0biOOjYYlx5UxgHwHXi/Xiz6ynYYPVHnprPwGTVenzwgo03Lsv9I3aEAFv
35jVmp+goZzw8BercQLC369k73GhYen04j7dSTK/Xfk7Fy/QsDqn+Kn4FAGl
X4SC06Np6CTu6Zn2i4A7M9WHv9fTcCRI011kgcz3H5flmjYapvfX0kIWCRDk
ES+I6aXhe3O7/uklAi4Jnt9EmaOhcmT6i0cruKAqItUgxE/H2xvnVMZ4uTC2
oeXCx/V0vMPXVrqLjws2EnLd/gp0TP/5zsh9FRfEpN+Fm1Lo+ISjw7mxmgut
Mjd05Bl0PBb8WDZYgAuo1J3WcoKO3vf//eAqxIU51ZBjqS50/DZgLXJ4DRcK
KGr85y/SUaLi+7SUMBd2UKPObomhoxtP9JYHa7nQxdTe+i2FjtK0b5eOiXAh
1mCkueopHQmO3YcZ0oZH46/eKqdjdbHHwch1XOAzpSnZv6CjSkFQnbgoF6os
Jz+ptZPPHRcvJJL2OZEcI9BHR9nUXR5r13NB0V6f3v2NjlErKVXepIfPzP7K
maPjjll7z3bSqa4PMv34Gehwuz5l5wYuWHgaWx7bwMCpe47mTqTX+ywJyf7N
wDFrak4G6aZLTyvnFBjYlMUobCftf93iXDOFgXVvD12cIa0VyC+VwmBgEWfL
+nUbuTAdUtjmYcLAxE7nSAnS2REnA2gnGegiObLib9JWN1aad7kwMOPOfJUY
aQHvzD2eFxmo+u/n2ZWkS88aLK0OYqBAwu7aIfL79scn2lKiGfhyjiFXQ1r0
aOxDtRQy3iLlYATpatoB39dZDHzdxtloTNr1QLehfRm5n9IjFUKktypcl/r9
nIG2QXJAkPt/tX3n9K03DPy7j1JykrTPhpcv5T4y8Ln/PYU/ZD53rXK5Vz3C
QC26eWE46bZ5EXfTGQa28ztYbiJ97XshdYyXiU8LnijHkOezt99MLGAdE9NV
efRWkQ55lVKVL8/EgCMT3m3keatXUqNZaky8lDD8VJ70QN6QQ68uE7+szrf1
IesDEhSFha2ZqN1VE/iLrKex0Pa+9DNMrFIa2iBH+u41nyINLyY2Rty1OSLI
hRnHaqszEUwcfV7hGEjW5wPLU4pLiUx0dvTXjSbr1+TwKt7bj5i4nBwndpuf
Czn7jZ7U1TCR7+L9rzdWcsFhZe+s5BQT9bNXt/wg+2XD7I3m4iUm5uxmbSon
+6l2VOa+wRoWdoXoNHuT/bat3Y3pu4uFg6ct6jrmCWhPXYx7Z8bCsPqGMwem
CfCLSzvrYs/C6931NQTZv4ohDG1eDxa263ycV/tBAMc94osSh4XZB6wNN5H9
jzqSKmFcFq5emB/3HCZgfN8z/h2vWKgR8aSnZJCAJBnHzvJ3LKxNa9k69YWA
WeEcv6HvLPS74l597BMBud3a/9OV0sMUFz/xqv/I9fked50L1MNKk85kVXK+
9Xp/flh6Sw+vdFFz5RsISGWf7fNK0sN67t3nm+sJ2OXqZfKjSA/Ds0tlBmrI
eXcynDL6WQ8FJc/3q5eR85VRydeDh3A4ZW/f6wcE2K2XSK5ZOITfRUU/LJLz
e5dI+oerAvooGHfLjOlLwJCQvKj2JtLfFoVCfQhw5tsfUK6gjxyzMJWVngSw
Zw2cCqz00epwwLkqRwICP15WyyjXR90Ts6ssjQjIfNLdctPLAH1SBqcdJQiQ
svNPo94wwNM/nmf0biHn35bd3ksRBtiXvvaTyV8EhAb7SPhkGuBbFldWUYQA
V8f1Lo5dBtjYe24qf7kClKVZAnQ0RCGH5JsT5P+QuFNIXSF8GMvmPdZGZlRA
azCn7HKGEcq6uu3YKFkBoe97hGVaj+J/H9ueXRUshzcv2q+I0kywOGX/TdZo
KQwIf1LO6ziGZjbJRX3ZJRDso5imaWyKPFdoW32Ci2FWPc7Ud9QMtwwNTBww
KYI1Hzr0tK9YYHlsVp2AUiHkJhyf+zZliVFOcqPMvQWwPX/umxHHGisuzVAv
7MgHyW/v76Xw2WB+U3jIskcujF5pikq7fwI/dlqp2cRlQ46PkV2cuC1ejP/j
q96bBf/gfxat723x0rOXLZMnnsDGErep/jQ7pGz4rF/fmQm63J2jLrancDdH
07ol6BE8y9dbQdlmjy+LbCd3HX4Imca+xMdBe8wfWzGRuu4BvA9oaptPd8C1
3xeHTv5OB2c7ubAJd0dM+XaaoPangbHiT3s5jdMoUc1fGNmXCtfD++6+nz6N
P43ndF4v3IdN8R3nbWrP4KkPgsWWqikwqTyZZX3tLDbPbkmwy0iC7dwLK5Io
ThjWbOT+XeUeFE0K/S7hdUZPXe/kVm4iRJVVH2XWOGNkFNq5nb8D7buvHcoP
c0EdgcsLdjIJcPyfE6m39F3RzMom6SlPPFCkcsSK+N1Q2U+07epUHFyuXq2U
98YNNb3W1831xgL/uP9D6chz+Dt9/z3V7zEw80qw2s3aHTdneNe3zURDUuPy
76sbPNAmvr718cZosJsVYvp5eKDTM+d3qw1vQefvbafcP3hgi/EqYgdPFPxi
HsxJVPNEG0sxysHECCCExAQGYzxxuCtsW4ZhOKg8mFaVnPNE+rGPQVOzoWB0
80vkLTM2Zt21aKxv5gBLP9JQ3YKN9rcD7+Y0cABFNIR6LNm4rqorK+EZB/bF
RwbJ2bBRj34v2L2MA5seaVyptmfjxYNhcooZHOh+EeU05sHGh1/PFw5d4sBZ
fm26Xhgbr36JCqQqcMCucWjFeDgbW57ER5jIcsAqIromNpKNmbezmuylOWD4
17BmXzQbg3yT+zibOaAkE7PP5w4bV2Qqugys5MAM/ev2Bw/Z+EXJuKq9JwQm
BGJ7DmWyMa84svdXRwh8fX3w7sRjNuZs8FLc+jYEOv+N/Usrm42BxZ8sTjeG
QKWDjnB7IRsjuydahUtDoER+pPFCMRvfEuLHNQpCIHcsNliylI1EN/WvM9kh
kOo1wutUwcZ7kSjUkB4CiZS4WhEuG4sorozZ5BCIWdC5VlzJxtB/GU93J4ZA
aO2IllU1GwXyL2jZxIVAQGDc/HING4+p5v2KjgqB/wPx8vnf
"]]},
Annotation[#, "Charting`Private`Tag$584362#1"]& ]}, {}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{None, None},
AxesOrigin->{0, 0},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
ImagePadding->All,
Method->{
"DefaultBoundaryStyle" -> Automatic,
"DefaultGraphicsInteraction" -> {
"Version" -> 1.2, "TrackMousePosition" -> {True, False},
"Effects" -> {
"Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2},
"Droplines" -> {
"freeformCursorMode" -> True,
"placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None,
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& )}},
PlotRange->{{0, 300}, {0., 0.10576051518102296`}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Output",
CellChangeTimes->{{3.8686048309051447`*^9, 3.868604837191936*^9}, {
3.8686103236765223`*^9, 3.868610390025558*^9}, 3.8686128611831083`*^9,
3.869565753444449*^9, 3.8696263002800617`*^9, 3.869628196004326*^9,
3.869628399732347*^9, 3.869628986502192*^9},
CellLabel->"Out[67]=",ExpressionUUID->"e98c5906-814e-490d-b5ad-0e56295f99ab"]
}, Open ]],
Cell[BoxData[
RowBox[{"Clear", "[", "x", "]"}]], "Input",
CellChangeTimes->{{3.869629313118025*^9, 3.869629319664421*^9}},
CellLabel->"In[68]:=",ExpressionUUID->"1e43fbb6-0494-4504-bdc4-df71c6e9d5e3"],
Cell[BoxData[
RowBox[{"Clear", "[", "y", "]"}]], "Input",
CellChangeTimes->{{3.869629323185244*^9, 3.869629326216897*^9}},
CellLabel->"In[69]:=",ExpressionUUID->"b34abcdd-b1ba-4557-8728-df3df5b28b02"],
Cell[BoxData[
RowBox[{
RowBox[{"PsiP1", "[",
RowBox[{"k_", ",", "q_", ",", "px_", ",", "py_"}], "]"}], ":=",
FractionBox[
RowBox[{"2", " ",
RowBox[{"(",
RowBox[{
FractionBox["1",
RowBox[{
SuperscriptBox["k", "2"], "+",
SuperscriptBox[
RowBox[{"(",
RowBox[{"px", "+", "py"}], ")"}], "2"]}]], "-",
FractionBox["1",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"px", "+", "py"}], ")"}], "2"], "+",
SuperscriptBox["q", "2"]}]]}], ")"}]}],
RowBox[{
SqrtBox["\[Pi]"], " ",
SqrtBox[
RowBox[{
FractionBox["1", "k"], "+",
FractionBox["1", "q"], "-",
FractionBox["4",
RowBox[{"k", "+", "q"}]]}]]}]]}]], "Input",
CellChangeTimes->{
3.869629300173646*^9, {3.869629377151785*^9, 3.869629475904372*^9}},
CellLabel->"In[72]:=",ExpressionUUID->"e24edc1d-a3ff-4c8b-bb21-62fa5fe16f06"],
Cell[BoxData[
RowBox[{"Clear", "[", "k", "]"}]], "Input",
CellChangeTimes->{{3.869630365766315*^9, 3.8696303681353207`*^9}},
CellLabel->"In[78]:=",ExpressionUUID->"dfd70dbc-5fed-4e5c-a039-a3b3f88789e3"],
Cell[BoxData[
RowBox[{
RowBox[{"PsiP2", "[",
RowBox[{"k_", ",", "q_", ",", "px_", ",", "py_"}], "]"}], ":=",
RowBox[{"Simplify", "[",
SuperscriptBox[
RowBox[{"(",
FractionBox[
RowBox[{"2", " ",
RowBox[{"(",
RowBox[{"px", "+", "py"}], ")"}],
RowBox[{"(",
RowBox[{
FractionBox["1",
RowBox[{
SuperscriptBox["k", "2"], "+",
SuperscriptBox[
RowBox[{"(",
RowBox[{"px", "+", "py"}], ")"}], "2"]}]], "-",
FractionBox["1",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"px", "+", "py"}], ")"}], "2"], "+",
SuperscriptBox["q", "2"]}]]}], ")"}]}],
RowBox[{
SqrtBox["\[Pi]"], " ",
SqrtBox[
RowBox[{
FractionBox["1", "k"], "+",
FractionBox["1", "q"], "-",
FractionBox["4",
RowBox[{"k", "+", "q"}]]}]]}]], ")"}], "2"], "]"}]}]], "Input",
CellChangeTimes->{{3.8696303068554907`*^9, 3.869630331365758*^9}, {
3.869630391073823*^9, 3.869630393423407*^9}, {3.869630598960945*^9,
3.869630604762298*^9}},
CellLabel->"In[84]:=",ExpressionUUID->"f53dd42a-ae11-462a-bf9f-c07d88f298c5"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Print", "[",
RowBox[{"PsiP2", "[",
RowBox[{"k", ",", "q", ",", "px", ",", "py"}], "]"}], "]"}]], "Input",
CellChangeTimes->{{3.8696304109161053`*^9, 3.869630430062149*^9}},
CellLabel->"In[85]:=",ExpressionUUID->"417870a7-4839-4f81-8586-d217e9ba44f9"],
Cell[BoxData[
FractionBox[
RowBox[{"4", " ", "k", " ",
SuperscriptBox[
RowBox[{"(",
RowBox[{"px", "+", "py"}], ")"}], "2"], " ", "q", " ",
SuperscriptBox[
RowBox[{"(",
RowBox[{"k", "+", "q"}], ")"}], "3"]}],
RowBox[{"\[Pi]", " ",
SuperscriptBox[
RowBox[{"(",
RowBox[{
SuperscriptBox["k", "2"], "+",
SuperscriptBox[
RowBox[{"(",
RowBox[{"px", "+", "py"}], ")"}], "2"]}], ")"}], "2"], " ",
SuperscriptBox[
RowBox[{"(",
RowBox[{
SuperscriptBox["px", "2"], "+",
RowBox[{"2", " ", "px", " ", "py"}], "+",
SuperscriptBox["py", "2"], "+",
SuperscriptBox["q", "2"]}], ")"}], "2"]}]]], "Print",
CellChangeTimes->{3.869630432023151*^9, 3.869630611331956*^9},
CellLabel->
"During evaluation of \
In[85]:=",ExpressionUUID->"bf7a1e53-2a8c-4713-ad3f-6433be47849b"]
}, Open ]],
Cell[BoxData[
RowBox[{"\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{
RowBox[{
"\:041f\:0430\:0440\:0430\:043b\:043b\:0435\:043b\:044c\:043d\:044b\:0439\
", " ", "\:0438\:043c\:043f\:0443\:043b\:044c\:0441"}], " ", "-", " ",
RowBox[{
"\:0438\:043d\:0442\:0435\:0433\:0440\:0438\:0440\:043e\:0432\:0430\:043d\
\:0438\:0435", " ", "\:043f\:043e", " ",
SuperscriptBox["PsiP", "2"], "*", "py", "*", "d",
RowBox[{"(", "py", ")"}]}]}], " ", "*)"}]}]], "Input",
CellChangeTimes->{
3.868613231554058*^9, {3.868613430567326*^9, 3.868613521155683*^9}, {
3.868613778472742*^9, 3.8686137787214823`*^9}, {3.869566081566175*^9,
3.869566081836238*^9}},ExpressionUUID->"dffe0abc-3dc5-4360-a36a-\
ddf70a8a91e3"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"PsiPar", "[",
RowBox[{"k_", ",", "q_", ",", "px_"}], "]"}], "=",
RowBox[{"Simplify", "[",
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{
FractionBox[
RowBox[{"4", " ", "k", " ",
SuperscriptBox[
RowBox[{"(",
RowBox[{"px", "+", "py"}], ")"}], "2"], " ", "q", " ",
SuperscriptBox[
RowBox[{"(",
RowBox[{"k", "+", "q"}], ")"}], "3"]}],
RowBox[{"\[Pi]", " ",
SuperscriptBox[
RowBox[{"(",
RowBox[{
SuperscriptBox["k", "2"], "+",
SuperscriptBox[
RowBox[{"(",
RowBox[{"px", "+", "py"}], ")"}], "2"]}], ")"}], "2"], " ",
SuperscriptBox[
RowBox[{"(",
RowBox[{
SuperscriptBox["px", "2"], "+",
RowBox[{"2", " ", "px", " ", "py"}], "+",
SuperscriptBox["py", "2"], "+",
SuperscriptBox["q", "2"]}], ")"}], "2"]}]], "*", "py"}], ",",
RowBox[{"{",
RowBox[{"py", ",", "0", ",", "Infinity"}], "}"}], ",",
RowBox[{"Assumptions", "\[Rule]",
RowBox[{
RowBox[{"k", ">", "0"}], " ", "&&", " ",
RowBox[{"q", ">", "0"}]}]}]}], "]"}], "]"}]}]], "Input",
CellChangeTimes->{{3.869567112352491*^9, 3.8695671238156633`*^9},
3.869626815028455*^9, {3.869627933495741*^9, 3.8696279413023233`*^9}, {
3.8696284459881773`*^9, 3.869628460102339*^9}, {3.86962952577512*^9,
3.869629595424942*^9}, 3.869629948310508*^9, {3.869630088217606*^9,
3.86963009471539*^9}, {3.869630131374378*^9, 3.869630131770316*^9},
3.86963019598332*^9, 3.869630440713748*^9, {3.8696304731362457`*^9,
3.8696304770559893`*^9}, 3.8696306183960943`*^9, {3.869630881142564*^9,
3.8696308850055428`*^9}},
CellLabel->"In[91]:=",ExpressionUUID->"a4ef5eb4-7778-43b2-8376-e6e4431de66f"],
Cell[BoxData[
TemplateBox[{
FractionBox[
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"k", "+", "q"}], ")"}], "3"], " ",
RowBox[{"(",
RowBox[{
RowBox[{"-",
RowBox[{"(",
RowBox[{
RowBox[{"(",
RowBox[{"k", "-", "q"}], ")"}], " ",
RowBox[{"(",
RowBox[{
RowBox[{
SuperscriptBox["k", "2"], " ", "\[Pi]", " ", "px"}], "+",
RowBox[{"2", " ", "k", " ",
RowBox[{"(",
RowBox[{
RowBox[{"2", " ", "k"}], "-",
RowBox[{"\[Pi]", " ", "px"}]}], ")"}], " ", "q"}], "+",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"4", " ", "k"}], "+",
RowBox[{"\[Pi]", " ", "px"}]}], ")"}], " ",
SuperscriptBox["q", "2"]}]}], ")"}]}], ")"}]}], "-",
RowBox[{"2", " ", "px", " ", "q", " ",
RowBox[{"(",
RowBox[{
RowBox[{"3", " ",
SuperscriptBox["k", "2"]}], "+",
SuperscriptBox["q", "2"]}], ")"}], " ",
RowBox[{"ArcTan", "[",
FractionBox["px", "k"], "]"}]}], "+",
RowBox[{"2", " ", "k", " ", "px", " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["k", "2"], "+",
RowBox[{"3", " ",
SuperscriptBox["q", "2"]}]}], ")"}], " ",
RowBox[{"ArcTan", "[",
FractionBox["px", "q"], "]"}]}], "+",
RowBox[{"2", " ", "k", " ", "q", " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["k", "2"], "+",
SuperscriptBox["q", "2"]}], ")"}], " ",
RowBox[{"(",
RowBox[{
RowBox[{"Log", "[",
RowBox[{
SuperscriptBox["k", "2"], "+",
SuperscriptBox["px", "2"]}], "]"}], "-",
RowBox[{"Log", "[",
RowBox[{
SuperscriptBox["px", "2"], "+",
SuperscriptBox["q", "2"]}], "]"}]}], ")"}]}]}], ")"}]}],
RowBox[{"\[Pi]", " ",
SuperscriptBox[
RowBox[{"(",
RowBox[{
SuperscriptBox["k", "2"], "-",
SuperscriptBox["q", "2"]}], ")"}], "3"]}]],
InterpretationBox[
DynamicModuleBox[{Typeset`open = False},
TemplateBox[{"Expression",
StyleBox[
TagBox[
TooltipBox["\"condition\"",
TagBox[
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"k", "\[NotEqual]",
RowBox[{"Im", "[", "px", "]"}]}], "&&",
RowBox[{"(",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{
SuperscriptBox["k", "2"], "\[GreaterEqual]",
SuperscriptBox[
RowBox[{"Im", "[", "px", "]"}], "2"]}], "&&",
RowBox[{
SuperscriptBox["q", "2"], "\[GreaterEqual]",
SuperscriptBox[
RowBox[{"Im", "[", "px", "]"}], "2"]}]}], ")"}], "||",
RowBox[{
RowBox[{"Re", "[", "px", "]"}], "\[GreaterEqual]",
"0"}]}], ")"}], "&&",
RowBox[{"q", "\[NotEqual]",
RowBox[{"Im", "[", "px", "]"}]}], "&&",
RowBox[{
RowBox[{"k", "+",
RowBox[{"Im", "[", "px", "]"}]}], "\[NotEqual]", "0"}],
"&&",
RowBox[{
RowBox[{"q", "+",
RowBox[{"Im", "[", "px", "]"}]}], "\[NotEqual]", "0"}]}],
")"}], "||",
RowBox[{
RowBox[{"Re", "[", "px", "]"}], ">", "0"}]}], ")"}]}],
")"}], "||",
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"k", "+",
RowBox[{"Im", "[", "px", "]"}]}], "\[NotEqual]", "0"}],
"&&",
RowBox[{
RowBox[{"Re", "[", "px", "]"}], ">", "0"}]}], ")"}]}],
Short[#, 7]& ]], Annotation[#,
Short[
Or[
And[$CellContext`k != Im[$CellContext`px],
Or[
And[
Or[
And[$CellContext`k^2 >=
Im[$CellContext`px]^2, $CellContext`q^2 >=
Im[$CellContext`px]^2], Re[$CellContext`px] >=
0], $CellContext`q !=
Im[$CellContext`px], $CellContext`k + Im[$CellContext`px] !=
0, $CellContext`q + Im[$CellContext`px] != 0],
Re[$CellContext`px] > 0]],
And[$CellContext`k + Im[$CellContext`px] != 0,
Re[$CellContext`px] > 0]], 7], "Tooltip"]& ],
"IconizedCustomName", StripOnInput -> False],
GridBox[{{
RowBox[{
TagBox["\"Head: \"", "IconizedLabel"], "\[InvisibleSpace]",
TagBox["Or", "IconizedItem"]}]}, {
RowBox[{
TagBox["\"Byte count: \"", "IconizedLabel"], "\[InvisibleSpace]",
TagBox["2000", "IconizedItem"]}]}},
GridBoxAlignment -> {"Columns" -> {{Left}}}, DefaultBaseStyle ->
"Column",
GridBoxItemSize -> {
"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}],
Dynamic[Typeset`open]}, "IconizedObject"]],
Or[
And[$CellContext`k != Im[$CellContext`px],
Or[
And[
Or[
And[$CellContext`k^2 >= Im[$CellContext`px]^2, $CellContext`q^2 >=
Im[$CellContext`px]^2], Re[$CellContext`px] >= 0], $CellContext`q !=
Im[$CellContext`px], $CellContext`k + Im[$CellContext`px] !=
0, $CellContext`q + Im[$CellContext`px] != 0], Re[$CellContext`px] >
0]],
And[$CellContext`k + Im[$CellContext`px] != 0, Re[$CellContext`px] > 0]],
SelectWithContents -> True, Selectable -> False]},
"ConditionalExpression"]], "Output",
CellChangeTimes->{
3.869567239297608*^9, 3.869626935103006*^9, 3.869629942396744*^9,
3.869630078096586*^9, 3.869630189648635*^9, 3.869630294281685*^9, {
3.869630480764154*^9, 3.869630505310848*^9}, 3.8696306349033403`*^9,
3.869630903121903*^9},
CellLabel->"Out[91]=",ExpressionUUID->"63a40424-d528-4ecd-bf57-728421a50da7"]
}, Open ]],
Cell[BoxData[
RowBox[{
RowBox[{"paral", "[", "px_", "]"}], ":=",
RowBox[{"Simplify", "[",
RowBox[{"PsiPar", "[",
RowBox[{"kProton", ",", "228.465", ",", "px"}], "]"}], "]"}]}]], "Input",
CellChangeTimes->{{3.8696279016627913`*^9, 3.869627911089171*^9}, {
3.869630713019814*^9, 3.8696307684281597`*^9},
3.869630947432231*^9},ExpressionUUID->"d6114d76-496a-4526-9235-\
2e2b26389c18"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Print", "[",
RowBox[{"paral", "[", "px", "]"}], "]"}]], "Input",
CellChangeTimes->{{3.8696307762609797`*^9, 3.8696307859832897`*^9}},
CellLabel->"In[88]:=",ExpressionUUID->"ea14538f-b536-4fe7-a74f-f5e25d13093b"],
Cell[BoxData[
TemplateBox[{
RowBox[{
RowBox[{"-", "109.13809733550005`"}], "-",
RowBox[{"1.0000000000000004`", " ", "px"}], "-",
RowBox[{"0.7563855522068201`", " ", "px", " ",
RowBox[{"ArcTan", "[",
RowBox[{"0.004377038058345917`", " ", "px"}], "]"}]}], "+",
RowBox[{"1.3930053245744016`", " ", "px", " ",
RowBox[{"ArcTan", "[",
RowBox[{"0.02187868155499205`", " ", "px"}], "]"}]}], "-",
RowBox[{"59.119288258590586`", " ",
RowBox[{"Log", "[",
RowBox[{"2089.0926720349003`", "\[VeryThinSpace]", "+",
SuperscriptBox["px", "2"]}], "]"}]}], "+",
RowBox[{"59.119288258590586`", " ",
RowBox[{"Log", "[",
RowBox[{"52196.256225000005`", "\[VeryThinSpace]", "+",
SuperscriptBox["px", "2"]}], "]"}]}]}],
InterpretationBox[
DynamicModuleBox[{Typeset`open = False},
TemplateBox[{"Expression",
StyleBox[
TagBox[
TooltipBox["\"condition\"",
TagBox[
RowBox[{
RowBox[{
RowBox[{"-", "45.70659331031903`"}], "<",
RowBox[{"Im", "[", "px", "]"}], "<", "45.70659331031903`"}],
"||",
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"228.465`", "\[VeryThinSpace]"}], "+",
RowBox[{"Im", "[", "px", "]"}]}], "\[NotEqual]", "0"}],
"&&",
RowBox[{
RowBox[{
RowBox[{"45.70659331031903`", "\[VeryThinSpace]"}], "+",
RowBox[{"Im", "[", "px", "]"}]}], "\[NotEqual]", "0"}],
"&&",
RowBox[{
RowBox[{"Im", "[", "px", "]"}], "\[NotEqual]",
"45.70659331031903`"}], "&&",
RowBox[{
RowBox[{"Im", "[", "px", "]"}], "\[NotEqual]",
"228.465`"}], "&&",
RowBox[{
RowBox[{"Re", "[", "px", "]"}], "\[GreaterEqual]", "0"}]}],
")"}], "||",
RowBox[{
RowBox[{"Re", "[", "px", "]"}], ">", "0"}]}], Short[#, 7]& ]],
Annotation[#,
Short[
Or[
Inequality[-45.70659331031903, Less,
Im[$CellContext`px], Less, 45.70659331031903],
And[
228.465 + Im[$CellContext`px] != 0,
45.70659331031903 + Im[$CellContext`px] != 0,
Im[$CellContext`px] != 45.70659331031903, Im[$CellContext`px] !=
228.465, Re[$CellContext`px] >= 0], Re[$CellContext`px] > 0], 7],
"Tooltip"]& ], "IconizedCustomName", StripOnInput -> False],
GridBox[{{
RowBox[{
TagBox["\"Head: \"", "IconizedLabel"], "\[InvisibleSpace]",
TagBox["Or", "IconizedItem"]}]}, {
RowBox[{
TagBox["\"Byte count: \"", "IconizedLabel"], "\[InvisibleSpace]",
TagBox["1168", "IconizedItem"]}]}},
GridBoxAlignment -> {"Columns" -> {{Left}}}, DefaultBaseStyle ->
"Column",
GridBoxItemSize -> {
"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}],
Dynamic[Typeset`open]}, "IconizedObject"]],
Or[
Inequality[-45.70659331031903, Less,
Im[$CellContext`px], Less, 45.70659331031903],
And[228.465 + Im[$CellContext`px] != 0,
45.70659331031903 + Im[$CellContext`px] != 0, Im[$CellContext`px] !=
45.70659331031903, Im[$CellContext`px] != 228.465, Re[$CellContext`px] >=
0], Re[$CellContext`px] > 0], SelectWithContents -> True, Selectable ->
False]},
"ConditionalExpression"]], "Print",
CellChangeTimes->{3.869630787819367*^9},
CellLabel->
"During evaluation of \
In[88]:=",ExpressionUUID->"5d9c5e6a-5231-4a6e-a4f7-21f99a3e5607"]
}, Open ]],
Cell[BoxData[
RowBox[{"Plot", "[",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"PsiPar", "[",
RowBox[{"k", ",", "q", ",", "px_"}], "]"}], "/.",
RowBox[{"k", "->", " ", "kProton"}]}], " ", "/.",
RowBox[{"q", "->", "228.465"}]}], ",",
RowBox[{"{",
RowBox[{"px", ",", "0", ",", "50"}], "}"}]}], "]"}]], "Input",
CellChangeTimes->{{3.868614314625906*^9, 3.868614370031674*^9},
3.868615202683779*^9, {3.868673640124902*^9, 3.868673659152135*^9},
3.868675910704361*^9, {3.868676129813981*^9, 3.86867615006883*^9},
3.868677386578944*^9, {3.869567104276265*^9, 3.869567107186659*^9}, {
3.869630793399475*^9, 3.869630807789693*^9}, {3.869630838289406*^9,
3.869630873887835*^9}},
CellLabel->"In[92]:=",ExpressionUUID->"9f6413c0-e44e-4126-b089-740d915bb48d"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"paral", "[", "px", "]"}], ",",
RowBox[{"{",
RowBox[{"px", ",", "0", ",", "200"}], "}"}]}], "]"}]], "Input",
CellChangeTimes->{{3.8696309646911507`*^9, 3.869631022431979*^9}},
CellLabel->"In[97]:=",ExpressionUUID->"37c239c3-4ac2-401f-963b-6c070eeb2f73"],
Cell[BoxData[
GraphicsBox[{{{}, {},
TagBox[
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwVzGk4FHgAx/GhwzEzj8hRUjRRyMpEQjQ/nhmGxrgmt3YYzB8ppKQsSqtx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"]]},
Annotation[#, "Charting`Private`Tag$685471#1"]& ]}, {}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{None, None},
AxesOrigin->{0, 0},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
ImagePadding->All,
Method->{
"DefaultBoundaryStyle" -> Automatic,
"DefaultGraphicsInteraction" -> {
"Version" -> 1.2, "TrackMousePosition" -> {True, False},
"Effects" -> {
"Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2},
"Droplines" -> {
"freeformCursorMode" -> True,
"placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None,
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& )}},
PlotRange->{{0, 200}, {0., 81.12437652072705}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Output",
CellChangeTimes->{
3.868614371860661*^9, 3.868615484963463*^9, {3.868673641721901*^9,
3.8686736607060003`*^9}, 3.868675912288126*^9, {3.86867613698822*^9,
3.868676151839303*^9}, 3.8686773890716133`*^9, 3.869630809858492*^9,
3.8696308592115803`*^9, 3.8696309557226753`*^9, {3.8696309956820498`*^9,
3.869631024177164*^9}},
CellLabel->"Out[97]=",ExpressionUUID->"030448a6-0fbd-4cf2-a9d9-83eed4c20ddd"]
}, Open ]],
Cell[BoxData[
RowBox[{"(*", " ",
RowBox[{
RowBox[{
"\:041f\:043e\:043f\:0435\:0440\:0435\:0447\:043d\:044b\:0439", " ",
"\:0438\:043c\:043f\:0443\:043b\:044c\:0441"}], " ", "-", " ",
RowBox[{
"\:0438\:043d\:0442\:0435\:0433\:0440\:0438\:0440\:043e\:0432\:0430\:043d\
\:0438\:0435", " ", "\:043f\:043e", " ",
SuperscriptBox["PsiP", "2"], "*", "d",
RowBox[{"(", "px", ")"}]}]}], " ", "*)"}]], "Input",
CellChangeTimes->{{3.868677479644743*^9,
3.868677489346261*^9}},ExpressionUUID->"cc447812-1c6e-4129-943e-\
0459fce59f1e"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"PsiPerp", "[",
RowBox[{"k_", ",", "q_", ",", "py_"}], "]"}], "=",
RowBox[{"Simplify", "[",
RowBox[{"Integrate", "[",
RowBox[{
FractionBox[
RowBox[{"4", " ", "k", " ",
SuperscriptBox[
RowBox[{"(",
RowBox[{"px", "+", "py"}], ")"}], "2"], " ", "q", " ",
SuperscriptBox[
RowBox[{"(",
RowBox[{"k", "+", "q"}], ")"}], "3"]}],
RowBox[{"\[Pi]", " ",
SuperscriptBox[
RowBox[{"(",
RowBox[{
SuperscriptBox["k", "2"], "+",
SuperscriptBox[
RowBox[{"(",
RowBox[{"px", "+", "py"}], ")"}], "2"]}], ")"}], "2"], " ",
SuperscriptBox[
RowBox[{"(",
RowBox[{
SuperscriptBox["px", "2"], "+",
RowBox[{"2", " ", "px", " ", "py"}], "+",
SuperscriptBox["py", "2"], "+",
SuperscriptBox["q", "2"]}], ")"}], "2"]}]], ",",
RowBox[{"{",
RowBox[{"px", ",", "0", ",", "Infinity"}], "}"}], ",",
RowBox[{"Assumptions", "\[Rule]",
RowBox[{
RowBox[{"k", ">", "0"}], " ", "&&", " ",
RowBox[{"q", ">", "0"}]}]}]}], "]"}], "]"}]}]], "Input",
CellChangeTimes->{{3.8696310639392776`*^9, 3.8696310748684053`*^9},
3.86963113563931*^9},
CellLabel->"In[99]:=",ExpressionUUID->"b86a339e-b949-4516-8eb5-8294678723fc"],
Cell[BoxData[
TemplateBox[{
FractionBox[
RowBox[{
FractionBox[
RowBox[{
RowBox[{"(",
RowBox[{"k", "-", "q"}], ")"}], " ",
RowBox[{"(",
RowBox[{
RowBox[{"\[Pi]", " ",
SuperscriptBox["py", "2"], " ",
SuperscriptBox["q", "2"], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["py", "2"], "+",
SuperscriptBox["q", "2"]}], ")"}]}], "-",
RowBox[{"2", " ",
SuperscriptBox["k", "3"], " ", "q", " ",
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"-", "py"}], " ", "q"}], "+",
RowBox[{"\[Pi]", " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["py", "2"], "+",
SuperscriptBox["q", "2"]}], ")"}]}]}], ")"}]}], "+",
RowBox[{
SuperscriptBox["k", "4"], " ",
RowBox[{"(",
RowBox[{
RowBox[{"2", " ", "py", " ", "q"}], "+",
RowBox[{"\[Pi]", " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["py", "2"], "+",
SuperscriptBox["q", "2"]}], ")"}]}]}], ")"}]}], "-",
RowBox[{"2", " ", "k", " ", "py", " ", "q", " ",
RowBox[{"(",
RowBox[{
RowBox[{"\[Pi]", " ", "py", " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["py", "2"], "+",
SuperscriptBox["q", "2"]}], ")"}]}], "-",
RowBox[{"q", " ",
RowBox[{"(",
RowBox[{
RowBox[{"2", " ",
SuperscriptBox["py", "2"]}], "+",
SuperscriptBox["q", "2"]}], ")"}]}]}], ")"}]}], "+",
RowBox[{
SuperscriptBox["k", "2"], " ",
RowBox[{"(",
RowBox[{
RowBox[{"\[Pi]", " ",
SuperscriptBox[
RowBox[{"(",
RowBox[{
SuperscriptBox["py", "2"], "+",
SuperscriptBox["q", "2"]}], ")"}], "2"]}], "+",
RowBox[{"2", " ", "py", " ", "q", " ",
RowBox[{"(",
RowBox[{
RowBox[{"2", " ",
SuperscriptBox["py", "2"]}], "+",
SuperscriptBox["q", "2"]}], ")"}]}]}], ")"}]}]}], ")"}]}],
RowBox[{
RowBox[{"(",
RowBox[{
SuperscriptBox["k", "2"], "+",
SuperscriptBox["py", "2"]}], ")"}], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["py", "2"], "+",
SuperscriptBox["q", "2"]}], ")"}]}]], "+",
RowBox[{"2", " ", "q", " ",
RowBox[{"(",
RowBox[{
RowBox[{"3", " ",
SuperscriptBox["k", "2"]}], "+",
SuperscriptBox["q", "2"]}], ")"}], " ",
RowBox[{"ArcTan", "[",
FractionBox["py", "k"], "]"}]}], "-",
RowBox[{"2", " ", "k", " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["k", "2"], "+",
RowBox[{"3", " ",
SuperscriptBox["q", "2"]}]}], ")"}], " ",
RowBox[{"ArcTan", "[",
FractionBox["py", "q"], "]"}]}]}],
RowBox[{"\[Pi]", " ",
SuperscriptBox[
RowBox[{"(",
RowBox[{"k", "-", "q"}], ")"}], "3"]}]],
InterpretationBox[
DynamicModuleBox[{Typeset`open = False},
TemplateBox[{"Expression",
StyleBox[
TagBox[
TooltipBox["\"condition\"",
TagBox[
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"k", "\[NotEqual]",
RowBox[{"Im", "[", "py", "]"}]}], "&&",
RowBox[{"(",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{
SuperscriptBox["k", "2"], "\[GreaterEqual]",
SuperscriptBox[
RowBox[{"Im", "[", "py", "]"}], "2"]}], "&&",
RowBox[{
SuperscriptBox["q", "2"], "\[GreaterEqual]",
SuperscriptBox[
RowBox[{"Im", "[", "py", "]"}], "2"]}]}], ")"}], "||",
RowBox[{
RowBox[{"Re", "[", "py", "]"}], "\[GreaterEqual]",
"0"}]}], ")"}], "&&",
RowBox[{"q", "\[NotEqual]",
RowBox[{"Im", "[", "py", "]"}]}], "&&",
RowBox[{
RowBox[{"k", "+",
RowBox[{"Im", "[", "py", "]"}]}], "\[NotEqual]", "0"}],
"&&",
RowBox[{
RowBox[{"q", "+",
RowBox[{"Im", "[", "py", "]"}]}], "\[NotEqual]", "0"}]}],
")"}], "||",
RowBox[{
RowBox[{"Re", "[", "py", "]"}], ">", "0"}]}], ")"}]}],
")"}], "||",
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"k", "+",
RowBox[{"Im", "[", "py", "]"}]}], "\[NotEqual]", "0"}],
"&&",
RowBox[{
RowBox[{"Re", "[", "py", "]"}], ">", "0"}]}], ")"}]}],
Short[#, 7]& ]], Annotation[#,
Short[
Or[
And[$CellContext`k != Im[$CellContext`py],
Or[
And[
Or[
And[$CellContext`k^2 >=
Im[$CellContext`py]^2, $CellContext`q^2 >=
Im[$CellContext`py]^2], Re[$CellContext`py] >=
0], $CellContext`q !=
Im[$CellContext`py], $CellContext`k + Im[$CellContext`py] !=
0, $CellContext`q + Im[$CellContext`py] != 0],
Re[$CellContext`py] > 0]],
And[$CellContext`k + Im[$CellContext`py] != 0,
Re[$CellContext`py] > 0]], 7], "Tooltip"]& ],
"IconizedCustomName", StripOnInput -> False],
GridBox[{{
RowBox[{
TagBox["\"Head: \"", "IconizedLabel"], "\[InvisibleSpace]",
TagBox["Or", "IconizedItem"]}]}, {
RowBox[{
TagBox["\"Byte count: \"", "IconizedLabel"], "\[InvisibleSpace]",
TagBox["2000", "IconizedItem"]}]}},
GridBoxAlignment -> {"Columns" -> {{Left}}}, DefaultBaseStyle ->
"Column",
GridBoxItemSize -> {
"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}],
Dynamic[Typeset`open]}, "IconizedObject"]],
Or[
And[$CellContext`k != Im[$CellContext`py],
Or[
And[
Or[
And[$CellContext`k^2 >= Im[$CellContext`py]^2, $CellContext`q^2 >=
Im[$CellContext`py]^2], Re[$CellContext`py] >= 0], $CellContext`q !=
Im[$CellContext`py], $CellContext`k + Im[$CellContext`py] !=
0, $CellContext`q + Im[$CellContext`py] != 0], Re[$CellContext`py] >
0]],
And[$CellContext`k + Im[$CellContext`py] != 0, Re[$CellContext`py] > 0]],
SelectWithContents -> True, Selectable -> False]},
"ConditionalExpression"]], "Output",
CellChangeTimes->{3.869631098566168*^9, 3.8696311495711813`*^9},
CellLabel->"Out[99]=",ExpressionUUID->"e2a7570f-7b25-4460-9f7b-a0b86b653c41"]
}, Open ]],
Cell[BoxData[
RowBox[{
RowBox[{"perp", "[", "py_", "]"}], ":=",
RowBox[{"Simplify", "[",
RowBox[{"PsiPerp", "[",
RowBox[{"kProton", ",", "228.465", ",", "py"}], "]"}], "]"}]}]], "Input",
CellChangeTimes->{{3.869631129704208*^9, 3.869631132293288*^9}, {
3.869631164376565*^9, 3.8696311890788593`*^9}},
CellLabel->
"In[101]:=",ExpressionUUID->"804a318d-428e-46d0-af1d-4cf0f2a8856f"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Print", "[",
RowBox[{"perp", "[", "py", "]"}], "]"}]], "Input",
CellChangeTimes->{{3.869631185940134*^9, 3.869631194927557*^9}},
CellLabel->
"In[102]:=",ExpressionUUID->"3c17de4c-76db-4de9-9355-68bece89103c"],
Cell[BoxData[
TemplateBox[{
RowBox[{
FractionBox["1",
RowBox[{"1.0904281638730356`*^8", "+",
RowBox[{"54285.348897034906`", " ",
SuperscriptBox["py", "2"]}], "+",
SuperscriptBox["py", "4"]}]],
RowBox[{"(",
RowBox[{"1.090428163873036`*^8", "+",
RowBox[{"2.962299845908087`*^6", " ", "py"}], "+",
RowBox[{"54285.34889703492`", " ",
SuperscriptBox["py", "2"]}], "+",
RowBox[{"109.13809733550004`", " ",
SuperscriptBox["py", "3"]}], "+",
RowBox[{"1.0000000000000002`", " ",
SuperscriptBox["py", "4"]}], "+",
RowBox[{
RowBox[{"(",
RowBox[{"8.247841088729748`*^7", "+",
RowBox[{"41060.65360222363`", " ",
SuperscriptBox["py", "2"]}], "+",
RowBox[{"0.75638555220682`", " ",
SuperscriptBox["py", "4"]}]}], ")"}], " ",
RowBox[{"ArcTan", "[",
RowBox[{"0.004377038058345917`", " ", "py"}], "]"}]}], "+",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"-", "1.5189722383410266`*^8"}], "-",
RowBox[{"75619.78005994874`", " ",
SuperscriptBox["py", "2"]}], "-",
RowBox[{"1.3930053245744014`", " ",
SuperscriptBox["py", "4"]}]}], ")"}], " ",
RowBox[{"ArcTan", "[",
RowBox[{"0.02187868155499205`", " ", "py"}], "]"}]}]}], ")"}]}],
InterpretationBox[
DynamicModuleBox[{Typeset`open = False},
TemplateBox[{"Expression",
StyleBox[
TagBox[
TooltipBox["\"condition\"",
TagBox[
RowBox[{
RowBox[{
RowBox[{"-", "45.70659331031903`"}], "<",
RowBox[{"Im", "[", "py", "]"}], "<", "45.70659331031903`"}],
"||",
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"228.465`", "\[VeryThinSpace]"}], "+",
RowBox[{"Im", "[", "py", "]"}]}], "\[NotEqual]", "0"}],
"&&",
RowBox[{
RowBox[{
RowBox[{"45.70659331031903`", "\[VeryThinSpace]"}], "+",
RowBox[{"Im", "[", "py", "]"}]}], "\[NotEqual]", "0"}],
"&&",
RowBox[{
RowBox[{"Im", "[", "py", "]"}], "\[NotEqual]",
"45.70659331031903`"}], "&&",
RowBox[{
RowBox[{"Im", "[", "py", "]"}], "\[NotEqual]",
"228.465`"}], "&&",
RowBox[{
RowBox[{"Re", "[", "py", "]"}], "\[GreaterEqual]", "0"}]}],
")"}], "||",
RowBox[{
RowBox[{"Re", "[", "py", "]"}], ">", "0"}]}], Short[#, 7]& ]],
Annotation[#,
Short[
Or[
Inequality[-45.70659331031903, Less,
Im[$CellContext`py], Less, 45.70659331031903],
And[
228.465 + Im[$CellContext`py] != 0,
45.70659331031903 + Im[$CellContext`py] != 0,
Im[$CellContext`py] != 45.70659331031903, Im[$CellContext`py] !=
228.465, Re[$CellContext`py] >= 0], Re[$CellContext`py] > 0], 7],
"Tooltip"]& ], "IconizedCustomName", StripOnInput -> False],
GridBox[{{
RowBox[{
TagBox["\"Head: \"", "IconizedLabel"], "\[InvisibleSpace]",
TagBox["Or", "IconizedItem"]}]}, {
RowBox[{
TagBox["\"Byte count: \"", "IconizedLabel"], "\[InvisibleSpace]",
TagBox["1168", "IconizedItem"]}]}},
GridBoxAlignment -> {"Columns" -> {{Left}}}, DefaultBaseStyle ->
"Column",
GridBoxItemSize -> {
"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}],
Dynamic[Typeset`open]}, "IconizedObject"]],
Or[
Inequality[-45.70659331031903, Less,
Im[$CellContext`py], Less, 45.70659331031903],
And[228.465 + Im[$CellContext`py] != 0,
45.70659331031903 + Im[$CellContext`py] != 0, Im[$CellContext`py] !=
45.70659331031903, Im[$CellContext`py] != 228.465, Re[$CellContext`py] >=
0], Re[$CellContext`py] > 0], SelectWithContents -> True, Selectable ->
False]},
"ConditionalExpression"]], "Print",
CellChangeTimes->{3.869631197009533*^9},
CellLabel->
"During evaluation of \
In[102]:=",ExpressionUUID->"a7a3cfc5-6831-43bc-a688-44c0eec53d7e"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"perp", "[", "py", "]"}], ",",
RowBox[{"{",
RowBox[{"py", ",", "0", ",", "300"}], "}"}]}], "]"}]], "Input",
CellChangeTimes->{{3.869631214201191*^9, 3.869631226589404*^9}},
CellLabel->
"In[104]:=",ExpressionUUID->"57f1c25e-794f-4adf-bd78-75639085813a"],
Cell[BoxData[
GraphicsBox[{{{}, {},
TagBox[
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwd1AkwVf0bwHGREpIlecuS7EuuLUXkeZKs5SVRlhYlStYbKkWL5RJu4aZE
kSRkS0lRJBGSVK8oSxSV7R77Fvn/+p+ZM2c+M9+Z35x5znPWHfLZdYSTg4Oj
hNx/nw/t5yaG8j4bcvz/Goaomv0tNswS8DxdN7ewQMGVLxfPSDFfw2jMjh9/
zVa6z30p5z3EZG3L/mtWD+vtYmYLFOl5aP315rSQq+f8OmBifbD3H+JhtUe0
4Jxu+OylbzFPXMWXHb85pQdWu7kV/SZO7Ls5ORX7E7YEv0yYIT72Ot6x+Fw/
FF8Ta5skNrjLKKf7DYFKombAGHHkVkOh65rDoPRflxVF7FeoWxWYMwJjmbO7
+4kd12oH2MmOAX+7g38PsTFTTXFDyjgYbPqa1EFMm1f8LCw6CcnDfkXNxGKe
MtEjsVOgqcVxv4GYo01iS9OSGVC8es73JXG/uRiVf24WOm4NUY+JPz4Ruh07
/Rvst1ivyiF+pshv6+k3D4HbHjclE2cmLuG27P8DjT2b+GOIay+eb2NpcuBb
janioL/vUxq8YTGbA5/HSpe5Ez8YCYo9kbMIp7UGeGyJFZRP/fjmxolD6Ukx
BsQ3DgbALlkutJYL0pYjXnGdfr3yKxfOb/7Zv4w47J3PiEbKYuSXNksb+kPB
zBIvi7S93BijJ7T1HbG3ocedFaJLMDTuVWk+8Z48Vzt27FLMldSj3Igbelzy
91nw4O4Kk3AgRokDS98uWYZph1tzRIlVoh2e3j/Hiz/jGpxK5ym49dJeWNyA
D48Ozr6MJBaZtT1+aZoPeRq3++0mnjtqJXnMbznuOx7p9H2OzCfNMrBVTQCF
4j6fyCT+0WL2zrRfAIfZs9FuxEfv3MYETUG07NQO6PhNgQxID9VfFsSwrSjL
Im7/ciuJky2IivZLo02JbYRTRv1yhNDMnWWUMUsBf/6a1GweYbw4M+Wzk7jG
PMmy200YhzfuEh6bId/jhcQMa1kRXN4tQdcmHpcQtYm8IIKOUV3LG6cpKHiS
MF/xVQRbVxu1uRLLDV+xV09ZifkxsbURUxR0Rq/gcp9diZwFMa+FiJMUmQW3
9opi0+Tux9cnKRA4EM0jILoKI3+HytyYoGDqbXjpYKwYLnTOBBwbo8AVeHWF
xsVwrc6y7dWjFHwoZBbrOP6DwpuXlYgT5ydcKwxRWI2fa5p0ngyT3iE7U7Bi
DY4ucIfnDZG+Xk1OR14cF1kL27QPkvkYFN12iBbHd3rSStzE4mvLUtL3SKCn
ytF8437S9zTEbxiWRCywVjz9g/T2NoIO9lL4PP2nXWAvOe91c2zwMymU8tzJ
6dVDQVROZ2RN5FqctTKLM/lGgbTuKci9Io3fBiPLsjooaPHdHFJeJY3nSr/z
+rZTwMyee9Y0KY0hYs72Gm1k3msubJ5wXoeRlFNGcivp56N0DJVlMKB0d5D4
R9Jv3OFv7SyDXTxLlma/J/voI/Dw0GUZ3NNoska9iYKirngNxoQMZlFuN+Xe
kr4qWbWpUhbv27SmPqyhYPvcPo9v47JYaerUx1VNztsgnT2uKIdsk/PWO6oo
8MjMUFjNlENVUwHT6grSR+WtO+Qoj2dVNsXYPyF9pc9B/1h5zNR0PuX2mJw3
q5ka8UIeVR+pK3g/Iu/r+VjivoICBj96l+JaSHqrCrHxUQW0m1rcNniPgocr
3y+PiFbC54de+R26SvbdT7xHp0wJ+RKfKa5MoOBV45HS3n4ljH13QqP8CgWf
Imfdtlso47QlS+Z3NAXTc7IvFi9TQasm1pDYRQoMewPpoRGqeDaAVtnqSYGp
UaWZ9mNVjBjw117uQYF1Kt/a772qSMtyyNVzp8DFIe2N0fb1uGRyT0aQC9n3
t3VynIvVcEe/sH2KHQX1xRIt5y/Q0GyTdbizAZm/sHuexgMaXtt1WExQj4I2
nwehXV00fLTq1aUyHQoGlU00ENUxe2CD0CyN/E9u+UQt/FHHcZoKQ3Qd2fdt
3ZJQroHfr73rrOaiwFd1Q9NzfS3kfih+QaiKDZ2bTBckbbXw30suIS3lbNhp
7EgL8dDC3gCuhqulbFDZdz7GMEkL1VKow78fsKGX2WBWMamFp9JtOjzS2OA4
6lr54oE2Vp0c5Ow8w4ZtT68WVSnq4J+iBIaWGhuKqrO6ZUEHj5iILuNVYoP0
hzLBMHsddO6gu32RYcOf/m5v43AdZGeOvjnyDxueSNBUq7/p4Eq/kF+KXGxY
f77mTs3NjRgfpt6yv2UIVplOsepEdFG8gu5TEzQEo7WW03Jquhg8ue74Nv8h
eGuR5nTeRBerTVU5nnoNQZiVucym07pYOv5EknmQ9HbJBRmdusjcIG7YvZ30
rlB/LlsPy+6Mz2uvIP1FxoIO6OPYnLl1c8ogjD0X80j3MMSttql1fpkDEH5A
6p9rKkY4IqRfwMztg9zYA6HbDmzHWflPyoFuP0H8tLPndJgZUuZnG+eVe+Fe
dtvbCH9LTF2r3pOp+B0aGVElZ+5YofuXnTz1Et1wqbmdX77RGs3i9ta6lXRC
U/WHs4LbdiFXc/tHGqsNevi7NApabPFKg5vyvxdbgRFIu73Zxg5jCrdvjRpp
hqmNLLvT/fY41ffJ8FfgR+D71GJmcHYvUr94OaT+fQ/515ynB0YdMCGmyzuR
7x1IFU4PWEU5YV2OCss8+Q1IDjQn31q8D2+IWVPSVbXQf7b+8u3U/fhSReyY
GU8N5AVaubBWH8QBacZkaU4VqGHr3sbmg3jcP6zatLgSRIq9Rrtvu+CI/ITP
1rsVsLVMtv/4wUN4wGXou374M6gsNFukK34Yu9dZtNbUPoV7NqdLO3oP4xO7
ups9siXQHFr/fibdFUe/hVaojDwCDxfFaMrnCGYt8Q2MfV8ENrSxw4p6bqid
sbVdcKoQzsV8vdE87oaXpXz7vD/lw8rElhP7XrhjrnemNt+n+zCsMZzjFHIU
d+0AgT7bbJAqO7koRfcYcrCbTnFI3oOHw7yzxZweqO+eNqwzngGXS8qtTSo8
cH5Y1DxR7g58UA4xL4w+ji1hNh8vHLwNzmr7065YeGKpv802m7pU0JXOW/WQ
2wtL5U+MmSrehDPlS9ULmrzwspXD0/H4G8DNvnh3HdMbR/LHAxXcrsNk7bJy
LycfbGd2SN4xToSUuoXZYGFftFzT8uC4CwtcpnhNzvv64voTc2ahtfHweVb8
kM8nXzzBmqvk3xgHEyZb8pJ0/ND4Q1l9SeVlKOVdxdMb74ePjSbG+Q/EglbG
uLbktB+K7tW84sQVDVYR35lX7OlIO3Wk7/uiKDC1YO7YuJeOeXEya+xmIgEF
9HjbHehosl76ft1wJGgmMsMV99ExK7H357OvkbAyU+9s+WE6yqT/SX/zPBLa
qi8fG/Slo3cu+7/IoEg4ym1gbBZNx4HfkjMnJxngUvdjETuGjqw/15x2sRng
GBtXkcCkY/LgCKX+gwE7RH9u/hpHxxdf72WNNzNAXT5eM/A6HXlrRrUyihkw
afxLKuMuHbulhk7cCGAAxZPQbn6PjheqbHbe82LAr4YtN6gsOhrlehmVHGHA
590Jovq5dDxweG9Qlx0Dnrka8n8ooqPPpZnZPRsZUKzUV3fyER0tB0VigmkM
yB9MYEg+puNokSAtU4EBaf59nMee0tHVyTaVQ4wBSbqsFwJldLzaMHBcawUD
4ucMQx49o6NINZ+x+1IGXHrRp+9YTsf/lPYrpC5EQGgYa2ahgo72IUyhL1MR
8D8X86yZ
"]]},
Annotation[#, "Charting`Private`Tag$708369#1"]& ]}, {}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{None, None},
AxesOrigin->{0, 0},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
ImagePadding->All,
Method->{
"DefaultBoundaryStyle" -> Automatic,
"DefaultGraphicsInteraction" -> {
"Version" -> 1.2, "TrackMousePosition" -> {True, False},
"Effects" -> {
"Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2},
"Droplines" -> {
"freeformCursorMode" -> True,
"placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None,
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& )}},
PlotRange->{{0, 300}, {0., 1.}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Output",
CellChangeTimes->{{3.869631219529129*^9, 3.869631228317721*^9}},
CellLabel->
"Out[104]=",ExpressionUUID->"6204eb92-3b0b-4108-b9ed-f12beecf3760"]
}, Open ]]
},
WindowSize->{1389.75, 768.75},
WindowMargins->{{0, Automatic}, {0, Automatic}},
Magnification:>1.1 Inherited,
FrontEndVersion->"13.0 for Linux x86 (64-bit) (December 2, 2021)",
StyleDefinitions->"Default.nb",
ExpressionUUID->"d3eb6006-436a-464a-aded-6b72f7177dd4"
]
(* End of Notebook Content *)
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[558, 20, 1512, 28, 109, "Input",ExpressionUUID->"15f55500-85b0-49bd-b8c0-7ea00f0e2245"],
Cell[CellGroupData[{
Cell[2095, 52, 812, 21, 59, "Input",ExpressionUUID->"f1c72a75-7ee7-46f9-a8f7-4cd49fd00c7a"],
Cell[2910, 75, 548, 10, 37, "Output",ExpressionUUID->"787a36b5-5ebb-450b-97f8-6a66d36d74d3"]
}, Open ]],
Cell[3473, 88, 1048, 24, 57, "Input",ExpressionUUID->"40ae1148-daf9-4e15-8762-688f07195dad"],
Cell[4524, 114, 1122, 27, 57, "Input",ExpressionUUID->"7a2bcc4d-5447-48d1-ac24-841589704be5"],
Cell[CellGroupData[{
Cell[5671, 145, 261, 5, 33, "Input",ExpressionUUID->"b71993bf-44b9-4b50-90b9-025a29b6f35d"],
Cell[5935, 152, 440, 11, 54, "Output",ExpressionUUID->"36448c3c-ed58-4b87-bca0-c6f7044cd75e"]
}, Open ]],
Cell[6390, 166, 943, 18, 59, "Input",ExpressionUUID->"ed029352-16a6-45e1-b42a-177020211247"],
Cell[CellGroupData[{
Cell[7358, 188, 274, 5, 57, "Input",ExpressionUUID->"1508f981-ab16-4888-9c9d-70043439577a"],
Cell[7635, 195, 672, 20, 74, "Output",ExpressionUUID->"d7839f75-9aed-4efb-95bf-f0aa05801eb8"]
}, Open ]],
Cell[CellGroupData[{
Cell[8344, 220, 2347, 58, 114, "Input",ExpressionUUID->"cd919aeb-3101-4893-8360-ca90a34b5f8a"],
Cell[10694, 280, 729, 11, 37, "Output",ExpressionUUID->"b0e60b84-1f1f-4268-863d-06c8900b3b0b"]
}, Open ]],
Cell[CellGroupData[{
Cell[11460, 296, 2475, 66, 155, "Input",ExpressionUUID->"d1262ffb-87ed-4322-8f05-1b89384f8939"],
Cell[13938, 364, 3450, 75, 249, "Output",ExpressionUUID->"01ca38e8-4fdc-4873-bac0-259fd0f0d105"]
}, Open ]],
Cell[CellGroupData[{
Cell[17425, 444, 921, 24, 50, "Input",ExpressionUUID->"cab76d12-2dad-42c6-94b6-db201a8c18ec"],
Cell[18349, 470, 336, 6, 37, "Output",ExpressionUUID->"50db03d0-7166-4dd1-b1ad-8af23d2f754f"]
}, Open ]],
Cell[18700, 479, 1109, 22, 37, "Input",ExpressionUUID->"363c9fee-04cf-4e5c-90ea-4a0da118130e"],
Cell[CellGroupData[{
Cell[19834, 505, 1277, 35, 105, "Input",ExpressionUUID->"ec406fd6-54f4-4e5f-8e73-4494b58edd50"],
Cell[21114, 542, 6098, 118, 260, "Output",ExpressionUUID->"2bd6fbb1-9564-433a-b163-c5529f0a682d"]
}, Open ]],
Cell[CellGroupData[{
Cell[27249, 665, 4519, 106, 187, "Input",ExpressionUUID->"589fa93e-41d0-46c0-b8d3-ab8df683f53d"],
Cell[31771, 773, 1073, 33, 82, "Print",ExpressionUUID->"2946d86e-f35b-4b75-b95e-a5caa077a51c"]
}, Open ]],
Cell[32859, 809, 363, 9, 57, "Input",ExpressionUUID->"58e80c3d-daed-4f30-890a-2e8e52e60c0c"],
Cell[CellGroupData[{
Cell[33247, 822, 2744, 65, 124, "Input",ExpressionUUID->"c95e48ba-da31-4186-9fab-e23d54171786"],
Cell[35994, 889, 381, 5, 37, "Output",ExpressionUUID->"605d794b-f8c9-4677-b077-aada9b92bbd5"]
}, Open ]],
Cell[CellGroupData[{
Cell[36412, 899, 2238, 56, 113, "Input",ExpressionUUID->"af705252-b6bb-4c46-94eb-0f4dbbf1db66"],
Cell[38653, 957, 6896, 131, 256, "Output",ExpressionUUID->"e98c5906-814e-490d-b5ad-0e56295f99ab"]
}, Open ]],
Cell[45564, 1091, 203, 3, 33, "Input",ExpressionUUID->"1e43fbb6-0494-4504-bdc4-df71c6e9d5e3"],
Cell[45770, 1096, 203, 3, 33, "Input",ExpressionUUID->"b34abcdd-b1ba-4557-8728-df3df5b28b02"],
Cell[45976, 1101, 945, 30, 82, "Input",ExpressionUUID->"e24edc1d-a3ff-4c8b-bb21-62fa5fe16f06"],
Cell[46924, 1133, 205, 3, 33, "Input",ExpressionUUID->"dfd70dbc-5fed-4e5c-a039-a3b3f88789e3"],
Cell[47132, 1138, 1241, 36, 86, "Input",ExpressionUUID->"f53dd42a-ae11-462a-bf9f-c07d88f298c5"],
Cell[CellGroupData[{
Cell[48398, 1178, 283, 5, 33, "Input",ExpressionUUID->"417870a7-4839-4f81-8586-d217e9ba44f9"],
Cell[48684, 1185, 872, 27, 50, "Print",ExpressionUUID->"bf7a1e53-2a8c-4713-ad3f-6433be47849b"]
}, Open ]],
Cell[49571, 1215, 744, 16, 57, "Input",ExpressionUUID->"dffe0abc-3dc5-4360-a36a-ddf70a8a91e3"],
Cell[CellGroupData[{
Cell[50340, 1235, 1868, 45, 60, "Input",ExpressionUUID->"a4ef5eb4-7778-43b2-8376-e6e4431de66f"],
Cell[52211, 1282, 6867, 169, 83, "Output",ExpressionUUID->"63a40424-d528-4ecd-bf57-728421a50da7"]
}, Open ]],
Cell[59093, 1454, 404, 9, 33, "Input",ExpressionUUID->"d6114d76-496a-4526-9235-2e2b26389c18"],
Cell[CellGroupData[{
Cell[59522, 1467, 240, 4, 33, "Input",ExpressionUUID->"ea14538f-b536-4fe7-a74f-f5e25d13093b"],
Cell[59765, 1473, 3901, 90, 43, "Print",ExpressionUUID->"5d9c5e6a-5231-4a6e-a4f7-21f99a3e5607"]
}, Open ]],
Cell[63681, 1566, 802, 17, 33, "Input",ExpressionUUID->"9f6413c0-e44e-4126-b089-740d915bb48d"],
Cell[CellGroupData[{
Cell[64508, 1587, 323, 7, 33, "Input",ExpressionUUID->"37c239c3-4ac2-401f-963b-6c070eeb2f73"],
Cell[64834, 1596, 3712, 80, 284, "Output",ExpressionUUID->"030448a6-0fbd-4cf2-a9d9-83eed4c20ddd"]
}, Open ]],
Cell[68561, 1679, 557, 13, 33, "Input",ExpressionUUID->"cc447812-1c6e-4129-943e-0459fce59f1e"],
Cell[CellGroupData[{
Cell[69143, 1696, 1377, 38, 60, "Input",ExpressionUUID->"b86a339e-b949-4516-8eb5-8294678723fc"],
Cell[70523, 1736, 7831, 195, 122, "Output",ExpressionUUID->"e2a7570f-7b25-4460-9f7b-a0b86b653c41"]
}, Open ]],
Cell[78369, 1934, 401, 9, 33, "Input",ExpressionUUID->"804a318d-428e-46d0-af1d-4cf0f2a8856f"],
Cell[CellGroupData[{
Cell[78795, 1947, 239, 5, 33, "Input",ExpressionUUID->"3c17de4c-76db-4de9-9355-68bece89103c"],
Cell[79037, 1954, 4590, 108, 82, "Print",ExpressionUUID->"a7a3cfc5-6831-43bc-a688-44c0eec53d7e"]
}, Open ]],
Cell[CellGroupData[{
Cell[83664, 2067, 324, 8, 33, "Input",ExpressionUUID->"57f1c25e-794f-4adf-bd78-75639085813a"],
Cell[83991, 2077, 5546, 111, 282, "Output",ExpressionUUID->"6204eb92-3b0b-4108-b9ed-f12beecf3760"]
}, Open ]]
}
]
*)
duetron1.nb 0 → 100644
View file @ ffa3296f
(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 13.0' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
NotebookDataLength[ 32406, 751]
NotebookOptionsPosition[ 29673, 698]
NotebookOutlinePosition[ 30101, 715]
CellTagsIndexPosition[ 30058, 712]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
RowBox[{
RowBox[{"(*",
RowBox[{
RowBox[{
"\:0417\:0430\:0434\:0430\:043d\:0438\:0435", " ",
"\:0425\:044e\:043b\:044c\:0442\:0435\:043d\:043e\:0432\:0441\:043a\:043e\
\:0433\:043e", " ", "\:0430\:043d\:0437\:0430\:0446\:0430"}], ",", " ",
RowBox[{
"\:044d\:043d\:0435\:0440\:0433\:0438\:0439", " ",
"\:0441\:0432\:044f\:0437\:0438", " ", "\:0438", " ",
"\:043c\:0430\:0441\:0441", " ",
"\:0447\:0430\:0441\:0442\:0438\:0446"}]}], "*)"}], " ",
"\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"m1", "=", "938.2723"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"m2", "=", "939.5656"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"eeD", "=", "2.225"}], ";"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{
RowBox[{"Eb2", "=", "1.296"}], ";", "\[IndentingNewLine]",
RowBox[{"Eb3", "=", "7.77"}], ";"}], "*)"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"kProton", "=",
SqrtBox[
RowBox[{"2", "*", "eeD", "*",
FractionBox[
RowBox[{"m2", "*", "m1"}],
RowBox[{"m2", "+", "m1"}]]}]]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"j", "=", "197.327"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"radCh", " ", "=", " ", "2.1421"}], ";"}]}]}]], "Input",
CellChangeTimes->{{3.8418280761221857`*^9, 3.8418280761422033`*^9},
3.841862171517088*^9, {3.8419262080807543`*^9, 3.841926219260518*^9}, {
3.841928038092181*^9, 3.8419280541030884`*^9}, {3.841928487899782*^9,
3.841928488076267*^9}, {3.8420066140269156`*^9, 3.8420066793455715`*^9}, {
3.8420171976184487`*^9, 3.8420172488882537`*^9}, {3.8424381617095547`*^9,
3.842438201338784*^9}, {3.8424382660884786`*^9, 3.8424382663017025`*^9}, {
3.842439900950303*^9, 3.842439905584711*^9}, {3.842440130144476*^9,
3.8424401408080816`*^9}, {3.8431287176062517`*^9, 3.8431287369491*^9}, {
3.868506577438991*^9, 3.868506607725766*^9}, {3.8685082343880377`*^9,
3.868508264626708*^9}, 3.868508295057948*^9, {3.8685088480586357`*^9,
3.8685088658482113`*^9}, 3.868510178130962*^9, {3.868511111974544*^9,
3.868511122212982*^9}},
CellLabel->"In[37]:=",ExpressionUUID->"2526f2fe-15aa-4579-b9ea-decc3aa58e9d"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Solve", "[",
RowBox[{
RowBox[{
RowBox[{
RowBox[{
SuperscriptBox["radii", "2"], "/", "4"}], " ", "+", " ", "0.64", " ",
"-", "0.125"}], "==",
SuperscriptBox["radCh", "2"]}], ",", "radii", ",",
RowBox[{"Assumptions", "\[Rule]",
RowBox[{"{",
RowBox[{"radii", ">", "0"}], "}"}]}]}], "]"}]], "Input",
CellChangeTimes->{3.868508853568275*^9},
CellLabel->"In[43]:=",ExpressionUUID->"220ec690-b6e8-4041-b6db-85117c0aebe8"],
Cell[BoxData[
RowBox[{"{",
RowBox[{"{",
RowBox[{"radii", "\[Rule]", "4.036628499131423`"}], "}"}], "}"}]], "Output",\
CellChangeTimes->{3.86850888104244*^9, 3.868510185941433*^9,
3.868510993241634*^9, 3.8685111274856873`*^9, 3.868512725087854*^9,
3.86859260104237*^9},
CellLabel->"Out[43]=",ExpressionUUID->"813107a7-fdc0-40c0-9f52-d9967b7b2e97"]
}, Open ]],
Cell[BoxData[
RowBox[{
RowBox[{"Psi", "[",
RowBox[{"r_", ",", " ", "q_", ",", " ", "k_"}], "]"}], ":=",
RowBox[{"(",
RowBox[{
SuperscriptBox["\[ExponentialE]",
RowBox[{
RowBox[{"-", "k"}], " ", "r"}]], "-",
SuperscriptBox["\[ExponentialE]",
RowBox[{
RowBox[{"-", "q"}], " ", "r"}]]}], ")"}]}]], "Input",
CellChangeTimes->{{3.841500617220299*^9, 3.8415006194000273`*^9}, {
3.8415006763469276`*^9, 3.841500710264333*^9}, {3.8415121934261312`*^9,
3.8415122060456753`*^9}, {3.841926409979779*^9, 3.8419264177339487`*^9}, {
3.8419276456625643`*^9, 3.8419276518377705`*^9}, {3.841928494442438*^9,
3.841928503957432*^9}, {3.841928615751482*^9, 3.841928632201804*^9}, {
3.842033422958788*^9, 3.842033423943757*^9}, {3.842437713760228*^9,
3.842437735679245*^9}, {3.842438434224802*^9, 3.8424384347359476`*^9}, {
3.868510987173293*^9, 3.868510987328767*^9}},
CellLabel->"In[44]:=",ExpressionUUID->"86929842-b770-4ba7-b6e9-2ee5c585020a"],
Cell[BoxData[
RowBox[{"(*", "\:041d\:043e\:0440\:043c\:0438\:0440\:043e\:0432\:043a\:0430",
"*)"}]], "Input",
CellChangeTimes->{{3.86850598593543*^9, 3.868506006899047*^9}, {
3.86850635238809*^9, 3.8685063560504923`*^9}, 3.868506790939067*^9, {
3.868506872690419*^9, 3.868506873123567*^9}, {3.868507564336475*^9,
3.868507564837818*^9}, {3.868507601149354*^9,
3.8685076023106337`*^9}},ExpressionUUID->"3cba0c7d-b74d-44b7-be23-\
de4c6f445cac"],
Cell[BoxData[
RowBox[{
RowBox[{"Norm1", "[",
RowBox[{"q_", ",", "k_"}], "]"}], " ", ":=", " ",
RowBox[{"Integrate", "[",
RowBox[{
SuperscriptBox[
RowBox[{"Psi", "[",
RowBox[{"r", ",", "q", ",", "k"}], "]"}], "2"], ",",
RowBox[{"{",
RowBox[{"r", ",", "0", ",", "Infinity"}], "}"}], ",",
RowBox[{"Assumptions", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"k", ">", "0"}], ",",
RowBox[{"q", ">", "0"}]}], "}"}]}]}], "]"}]}]], "Input",
CellChangeTimes->{{3.8685067964058933`*^9, 3.868506817218575*^9}, {
3.868506878481089*^9, 3.868506881688241*^9}, {3.868506953305505*^9,
3.8685069547697687`*^9}, 3.868507608707961*^9, {3.8685096633820333`*^9,
3.868509668624763*^9}},
CellLabel->"In[45]:=",ExpressionUUID->"4f4d5d61-fdf8-4144-922d-24a1a9bcf65e"],
Cell[BoxData[
RowBox[{
RowBox[{"PsiNorm", "[",
RowBox[{"r_", ",", "q_", ",", "k_"}], "]"}], " ", ":=", " ",
FractionBox[
RowBox[{"Psi", "[",
RowBox[{"r", ",", "q", ",", "k"}], "]"}],
SqrtBox[
RowBox[{"Norm1", "[",
RowBox[{"q", ",", "k"}], "]"}]]]}]], "Input",
CellChangeTimes->{{3.868506842713272*^9, 3.868506890403079*^9}, {
3.8685096583025627`*^9, 3.86850965965059*^9}},
CellLabel->"In[46]:=",ExpressionUUID->"cfe62748-465f-49a4-8692-622aef7132ec"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Integrate", "[",
RowBox[{
SuperscriptBox[
RowBox[{"PsiNorm", "[",
RowBox[{"r", ",", "q", ",", "k"}], "]"}], "2"], ",",
RowBox[{"{",
RowBox[{"r", ",", "0", ",", "Infinity"}], "}"}], ",",
RowBox[{"Assumptions", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"k", ">", "0"}], ",",
RowBox[{"q", ">", "0"}]}], "}"}]}]}], "]"}]], "Input",
CellChangeTimes->{{3.86850691051902*^9, 3.868506919730239*^9}, {
3.868510573098914*^9, 3.868510576657299*^9}},
CellLabel->"In[47]:=",ExpressionUUID->"dcf5ac81-7b56-4e36-9ec0-4771a2422a75"],
Cell[BoxData["1"], "Output",
CellChangeTimes->{3.868509676339554*^9, 3.868510199738626*^9,
3.8685110058216476`*^9, 3.8685111481268797`*^9, 3.868512732307797*^9,
3.868592609613551*^9},
CellLabel->"Out[47]=",ExpressionUUID->"16cf9198-eff9-447b-9532-0738cceb8c19"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"(*",
RowBox[{
RowBox[{
RowBox[{
"\:0417\:0430\:0434\:0430\:043d\:0438\:0435", " ",
"\:0447\:0438\:0441\:043b\:0435\:043d\:043d\:043e\:0433\:043e", " ",
"\:0437\:043d\:0430\:0447\:0435\:043d\:0438\:044f", " ",
"\:043f\:0430\:0440\:0430\:043c\:0435\:0442\:0440\:0430", " ", "q", " ",
"\:0434\:043b\:044f", " ", "Eb"}], "=",
RowBox[{"2.224", " ",
RowBox[{
"\:041c\:044d\:0412", ".", " ", "\:041f\:043e\:0438\:0441\:043a"}], " ",
"\:0442\:043e\:0447\:043a\:0438"}]}], ",", " ",
RowBox[{
"\:0432", " ",
"\:043e\:043a\:0440\:0435\:0441\:0442\:043d\:043e\:0441\:0442\:0438",
" ", "\:043a\:043e\:0442\:043e\:0440\:043e\:0439", " ",
"\:0431\:0443\:0434\:0435\:043c", " ",
"\:0438\:0441\:043a\:0430\:0442\:044c", " ",
"\:0440\:0435\:0448\:0435\:043d\:0438\:0435", " ",
"\:0443\:0440\:0430\:0432\:043d\:0435\:043d\:0438\:044f", " ",
"\:043e\:0442\:043d\:043e\:0441\:0438\:0442\:0435\:043b\:044c\:043d\:043e\
", " ", "q"}]}], "*)"}], "\[IndentingNewLine]",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{
SuperscriptBox[
RowBox[{"PsiNorm", "[",
RowBox[{"r", ",",
FractionBox["q", "j"], ",",
FractionBox["kProton", "j"]}], "]"}], "2"], "*",
SuperscriptBox["r", "2"]}], ",",
RowBox[{"{",
RowBox[{"r", ",", "0", ",", "Infinity"}], "}"}]}], "]"}], "-",
SuperscriptBox["4.04", "2"]}], ",",
RowBox[{"{",
RowBox[{"q", ",", "225", ",", "230"}], "}"}]}], "]"}]}]], "Input",
CellChangeTimes->{{3.8685069805632257`*^9, 3.8685069818154287`*^9}, {
3.868507500761157*^9, 3.8685075067124577`*^9}, {3.868508302006258*^9,
3.868508321256205*^9}, {3.868508565660277*^9, 3.868508568900975*^9}, {
3.868508628382997*^9, 3.8685086311346188`*^9}, {3.868508909149338*^9,
3.868508951272414*^9}, {3.868509027462365*^9, 3.8685090293204203`*^9}, {
3.868509127679667*^9, 3.86850912963724*^9}},
CellLabel->
"In[185]:=",ExpressionUUID->"eb7f236f-52d0-4b04-a063-b8cb0b97aab5"],
Cell[BoxData[
GraphicsBox[{{{}, {},
TagBox[
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwV0ns022cYB/Cstm5unXFGrS5xP0spEUutzJtx5rBGOW3IKFamrRbR4qCl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"]]},
Annotation[#, "Charting`Private`Tag$3359577#1"]& ]}, {}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{None, None},
AxesOrigin->{225.0000000000005, 0},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
ImagePadding->All,
Method->{
"DefaultBoundaryStyle" -> Automatic,
"DefaultGraphicsInteraction" -> {
"Version" -> 1.2, "TrackMousePosition" -> {True, False},
"Effects" -> {
"Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2},
"Droplines" -> {
"freeformCursorMode" -> True,
"placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None,
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& )}},
PlotRange->{{225, 230}, {-0.05379576535584718, 0.12440295325961159`}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Output",
CellChangeTimes->{3.8685075058507223`*^9, 3.868507544875833*^9,
3.8685083720129213`*^9, 3.8685086160246487`*^9, 3.868508678634019*^9,
3.868508950160479*^9, 3.868509001639771*^9, 3.868509076619823*^9,
3.868509178998495*^9, 3.868510237029114*^9, 3.8685110516609907`*^9,
3.868511192825335*^9},
CellLabel->
"Out[185]=",ExpressionUUID->"55793edb-d5b8-4858-95ca-e7c9b007d219"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"FindRoot", "[",
RowBox[{
RowBox[{
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{
SuperscriptBox[
RowBox[{"PsiNorm", "[",
RowBox[{"r", ",",
FractionBox["q", "j"], ",",
FractionBox["kProton", "j"]}], "]"}], "2"], "*",
SuperscriptBox["r", "2"]}], ",",
RowBox[{"{",
RowBox[{"r", ",", "0", ",", "Infinity"}], "}"}], ",",
RowBox[{"Assumptions", "\[Rule]",
RowBox[{
RowBox[{"Re", "[", "q", "]"}], ">", "0"}]}]}], "]"}], "\[Equal]",
SuperscriptBox["4.04", "2"]}], ",",
RowBox[{"{",
RowBox[{"q", ",", "228", ",", "229"}], "}"}]}], "]"}]], "Input",
CellChangeTimes->{{3.8424411355629845`*^9, 3.842441156587248*^9}, {
3.842441619365672*^9, 3.842441624049182*^9}, {3.868509077312571*^9,
3.8685090989579687`*^9}, {3.868509241184043*^9, 3.868509246764495*^9},
3.868509283474368*^9},
CellLabel->"In[48]:=",ExpressionUUID->"d3c2ecc0-a8e6-4792-81ca-5b40050838c2"],
Cell[BoxData[
RowBox[{"{",
RowBox[{"q", "\[Rule]", "228.4649720223125`"}], "}"}]], "Output",
CellChangeTimes->{3.868510327526165*^9, 3.868511062385458*^9,
3.868512738222055*^9, 3.868592614917831*^9},
CellLabel->"Out[48]=",ExpressionUUID->"1a6fdb34-67f5-4729-a6c5-ec30d105838b"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"PsiNorm", "[",
RowBox[{"r", ",",
FractionBox["228.4649720223125`", "j"], ",",
FractionBox["kProton", "j"]}], "]"}]], "Input",
CellChangeTimes->{{3.868511613342454*^9, 3.8685116202709827`*^9}},
CellLabel->"In[49]:=",ExpressionUUID->"e7ab3299-968d-4d29-b2cd-447d8d1ff1e6"],
Cell[BoxData[
RowBox[{"0.9320838334751147`", " ",
RowBox[{"(",
RowBox[{
RowBox[{"-",
SuperscriptBox["\[ExponentialE]",
RowBox[{
RowBox[{"-", "1.1577988416299467`"}], " ", "r"}]]}], "+",
SuperscriptBox["\[ExponentialE]",
RowBox[{
RowBox[{"-", "0.23162873939354178`"}], " ", "r"}]]}], ")"}]}]], "Output",\
CellChangeTimes->{3.868511621518509*^9, 3.8685127401428013`*^9,
3.868592617205583*^9},
CellLabel->"Out[49]=",ExpressionUUID->"528622d6-520d-4dfb-95cb-02eedf8f9d0f"]
}, Open ]],
Cell[BoxData[
RowBox[{
RowBox[{"PsiD", "[", "r_", "]"}], ":=",
RowBox[{"PsiNorm", "[",
RowBox[{"r", ",",
FractionBox["228.4649720223125`", "j"], ",",
FractionBox["kProton", "j"]}], "]"}]}]], "Input",
CellChangeTimes->{{3.868509307138521*^9, 3.868509435603945*^9},
3.868509486682172*^9, {3.8685095247898083`*^9, 3.868509546146194*^9},
3.8685098213255653`*^9, {3.868510083158072*^9, 3.868510085697418*^9},
3.8685103325546827`*^9, {3.868510647018784*^9, 3.8685106476883497`*^9},
3.8685110704035378`*^9, {3.868511671930978*^9, 3.86851168516597*^9}, {
3.8685118943199244`*^9, 3.8685118972365713`*^9}, {3.868512143956333*^9,
3.8685121468388042`*^9}, {3.868512197211124*^9, 3.868512199341248*^9}},
CellLabel->"In[50]:=",ExpressionUUID->"baaeb7e8-47ee-48ec-a1d3-3cd762829736"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"PsiD", "[", "rad", "]"}], ",",
RowBox[{"{",
RowBox[{"rad", ",", "0", ",", "20"}], "}"}]}], "]"}]], "Input",
CellChangeTimes->{{3.86851220377577*^9, 3.868512215990354*^9}, {
3.868592491966135*^9, 3.868592493035427*^9}},
CellLabel->"In[51]:=",ExpressionUUID->"e5d127d6-d370-4347-8f24-faa40e61a8b6"],
Cell[BoxData[
GraphicsBox[{{{}, {},
TagBox[
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwVlXk81Nv/xzGukiVL9aVFdIsIYVLavE4JKakst5IoZcl6uVGRFoQUUcoS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"]]},
Annotation[#, "Charting`Private`Tag$1732599#1"]& ]}, {}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{None, None},
AxesOrigin->{0, 0},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
ImagePadding->All,
Method->{
"DefaultBoundaryStyle" -> Automatic,
"DefaultGraphicsInteraction" -> {
"Version" -> 1.2, "TrackMousePosition" -> {True, False},
"Effects" -> {
"Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2},
"Droplines" -> {
"freeformCursorMode" -> True,
"placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None,
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& )}},
PlotRange->{{0, 20}, {0., 0.49858292440373153`}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Output",
CellChangeTimes->{3.868512420171845*^9, 3.868512754293762*^9,
3.868592575576458*^9, 3.868592693087129*^9},
CellLabel->"Out[51]=",ExpressionUUID->"63f8f5c6-4182-4b3d-b68c-44d53c19d555"]
}, Open ]],
Cell[BoxData[
RowBox[{
RowBox[{"Psi2P", "[", "p_", "]"}], ":=",
RowBox[{"Simplify", "[",
RowBox[{
RowBox[{
FractionBox[
SqrtBox[
RowBox[{"4", " ", "\[Pi]"}]], "p"],
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{
RowBox[{"PsiD", "[", "r", "]"}], " ",
RowBox[{"Sin", "[",
RowBox[{"p", " ", "r"}], "]"}]}], ",",
RowBox[{"{",
RowBox[{"r", ",", "0", ",", "Infinity"}], "}"}]}], "]"}]}], ",",
RowBox[{"Assumptions", "\[Rule]",
RowBox[{"p", ">", "0"}]}]}], "]"}]}]], "Input",
CellChangeTimes->{{3.842429619361777*^9, 3.842429677633604*^9}, {
3.842429720856079*^9, 3.842429753812727*^9}, {3.842430187216261*^9,
3.842430258057073*^9}, {3.842430358025407*^9, 3.842430363366953*^9}, {
3.842431304234517*^9, 3.8424313168119774`*^9}, 3.8424313659165783`*^9, {
3.84243142345732*^9, 3.8424314893812175`*^9}, {3.842432125684045*^9,
3.842432157645306*^9}, {3.8424321906882353`*^9, 3.8424322290137844`*^9}, {
3.842433503697682*^9, 3.8424335156930647`*^9}, {3.842433964243157*^9,
3.8424339654450226`*^9}, {3.842441765367482*^9, 3.842441789073285*^9}, {
3.8424418280029216`*^9, 3.8424418302671328`*^9}, {3.842441902445393*^9,
3.842441904619342*^9}, {3.842442407989282*^9, 3.8424424240173473`*^9}, {
3.8424446932159224`*^9, 3.84244470052919*^9}, {3.8424483586356497`*^9,
3.842448371032787*^9}, 3.8424486628033075`*^9, {3.8424492882931213`*^9,
3.842449296532782*^9}, {3.842458930056344*^9, 3.842458959414255*^9}, {
3.8429757852823305`*^9, 3.842975785602333*^9}, {3.8429758182078094`*^9,
3.8429758427135096`*^9}, {3.84297588039443*^9, 3.8429758824232917`*^9}, {
3.8429759476812525`*^9, 3.8429759822454915`*^9}, {3.8429761768185596`*^9,
3.8429761802928667`*^9}, {3.868512449403376*^9, 3.86851247419938*^9}, {
3.868512560862237*^9, 3.868512586709832*^9}},
CellLabel->"In[27]:=",ExpressionUUID->"a3525874-ec58-484d-b703-72e51a5213c4"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Print", "[",
RowBox[{"Psi2P", "[", "p", "]"}], "]"}]], "Input",
CellChangeTimes->{{3.842429619361777*^9, 3.842429677633604*^9}, {
3.842429720856079*^9, 3.842429753812727*^9}, {3.842430187216261*^9,
3.842430258057073*^9}, {3.842430358025407*^9, 3.842430363366953*^9}, {
3.842431304234517*^9, 3.8424313168119774`*^9}, 3.8424313659165783`*^9, {
3.84243142345732*^9, 3.8424314893812175`*^9}, {3.842432125684045*^9,
3.842432157645306*^9}, {3.8424321906882353`*^9, 3.8424322290137844`*^9}, {
3.842433503697682*^9, 3.8424335156930647`*^9}, {3.842433964243157*^9,
3.8424339654450226`*^9}, {3.842441765367482*^9, 3.842441789073285*^9}, {
3.8424418280029216`*^9, 3.8424418302671328`*^9}, {3.842441902445393*^9,
3.842441904619342*^9}, {3.842442407989282*^9, 3.8424424240173473`*^9}, {
3.8424446932159224`*^9, 3.84244470052919*^9}, {3.8424483586356497`*^9,
3.842448371032787*^9}, 3.8424486628033075`*^9, {3.8424492882931213`*^9,
3.842449296532782*^9}, {3.842458930056344*^9, 3.842458959414255*^9}, {
3.8429757852823305`*^9, 3.842975785602333*^9}, {3.8429758182078094`*^9,
3.8429758427135096`*^9}, {3.84297588039443*^9, 3.8429758824232917`*^9}, {
3.8429759476812525`*^9, 3.8429759822454915`*^9}, {3.8429761768185596`*^9,
3.8429761802928667`*^9}, {3.868512492672875*^9, 3.868512495395587*^9},
3.8685125460867157`*^9},
CellLabel->"In[28]:=",ExpressionUUID->"cc59ea2d-418c-4b8c-ac8e-a4ae6081cd77"],
Cell[BoxData[
TemplateBox[{
FractionBox[
RowBox[{"3.5449077018110318`", " ",
SuperscriptBox["\[ExponentialE]",
RowBox[{"0``15.954589770191003", " ", "\[ImaginaryI]", " ", "p"}]],
" ",
RowBox[{"(",
RowBox[{
RowBox[{"(",
RowBox[{"0.`", "\[VeryThinSpace]", "+",
RowBox[{"3.469446951953614`*^-18", " ", "\[ImaginaryI]"}]}],
")"}], "+",
RowBox[{"1.1832672`", " ", "p"}], "-",
RowBox[{
RowBox[{"(",
RowBox[{"0.`", "\[VeryThinSpace]", "+",
RowBox[{"1.1102230246251565`*^-16", " ", "\[ImaginaryI]"}]}],
")"}], " ",
SuperscriptBox["p", "2"]}]}], ")"}]}],
RowBox[{"p", " ",
RowBox[{"(",
RowBox[{"0.06996024999999997`", "\[VeryThinSpace]", "+",
RowBox[{"1.3753999999999997`", " ",
SuperscriptBox["p", "2"]}], "+",
SuperscriptBox["p", "4"]}], ")"}]}]],
RowBox[{
RowBox[{"-", "0.23`"}], "<",
RowBox[{"Im", "[", "p", "]"}], "<", "0.23`"}]},
"ConditionalExpression"]], "Print",
CellChangeTimes->{{3.868512542207122*^9, 3.868512616831279*^9},
3.868512815778482*^9},
CellLabel->
"During evaluation of \
In[28]:=",ExpressionUUID->"9a4bd1ce-ec2f-4298-a2b7-7b0fe899b662"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"(*",
RowBox[{
"\:041f\:0440\:043e\:0432\:0435\:0440\:043a\:0430", " ",
"\:043d\:043e\:0440\:043c\:0438\:0440\:043e\:0432\:043a\:0438", " ",
"\:043f\:043e\:043b\:0443\:0447\:0438\:0432\:0448\:0435\:0439\:0441\:044f\
", " ", "\:0412\:0424"}], "*)"}], "\[IndentingNewLine]",
RowBox[{"Simplify", "[",
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{"4", " ", "\[Pi]", " ",
SuperscriptBox["p", "2"], " ",
SuperscriptBox[
RowBox[{"Psi2P", "[", "p", "]"}], "2"], " ",
FractionBox["1",
SuperscriptBox[
RowBox[{"(",
RowBox[{"2", " ", "\[Pi]"}], ")"}], "3"]]}], ",",
RowBox[{"{",
RowBox[{"p", ",", "0", ",", "Infinity"}], "}"}]}], "]"}],
"]"}]}]], "Input",
CellChangeTimes->{{3.843130807463869*^9, 3.8431308540633965`*^9}, {
3.868512639539876*^9, 3.868512664514215*^9}},
CellLabel->"In[10]:=",ExpressionUUID->"6673e5ab-f6af-4ce5-8409-31c716b83d8a"],
Cell[BoxData[
RowBox[{
SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"],
RowBox[{
FractionBox[
RowBox[{"2", " ",
SuperscriptBox[
RowBox[{"(",
RowBox[{
SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"],
RowBox[{
RowBox[{
RowBox[{"PsiD", "[", "r", "]"}], " ",
RowBox[{"Sin", "[",
RowBox[{"p", " ", "r"}], "]"}]}],
RowBox[{"\[DifferentialD]", "r"}]}]}], ")"}], "2"]}], "\[Pi]"],
RowBox[{"\[DifferentialD]", "p"}]}]}]], "Output",
CellChangeTimes->{3.868512666516981*^9},
CellLabel->"Out[10]=",ExpressionUUID->"b0e48659-f42d-4f96-84a1-34f3c8bb4a45"]
}, Open ]]
},
WindowSize->{1389.75, 768.75},
WindowMargins->{{0, Automatic}, {0, Automatic}},
Magnification:>1.1 Inherited,
FrontEndVersion->"13.0 for Linux x86 (64-bit) (December 2, 2021)",
StyleDefinitions->"Default.nb",
ExpressionUUID->"fbe802a9-0dee-4109-84a1-e1844fd98e1b"
]
(* End of Notebook Content *)
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[558, 20, 2258, 48, 248, "Input",ExpressionUUID->"2526f2fe-15aa-4579-b9ea-decc3aa58e9d"],
Cell[CellGroupData[{
Cell[2841, 72, 487, 13, 35, "Input",ExpressionUUID->"220ec690-b6e8-4041-b6db-85117c0aebe8"],
Cell[3331, 87, 363, 8, 37, "Output",ExpressionUUID->"813107a7-fdc0-40c0-9f52-d9967b7b2e97"]
}, Open ]],
Cell[3709, 98, 992, 20, 35, "Input",ExpressionUUID->"86929842-b770-4ba7-b6e9-2ee5c585020a"],
Cell[4704, 120, 460, 8, 33, "Input",ExpressionUUID->"3cba0c7d-b74d-44b7-be23-de4c6f445cac"],
Cell[5167, 130, 825, 20, 35, "Input",ExpressionUUID->"4f4d5d61-fdf8-4144-922d-24a1a9bcf65e"],
Cell[5995, 152, 486, 12, 59, "Input",ExpressionUUID->"cfe62748-465f-49a4-8692-622aef7132ec"],
Cell[CellGroupData[{
Cell[6506, 168, 596, 15, 35, "Input",ExpressionUUID->"dcf5ac81-7b56-4e36-9ec0-4771a2422a75"],
Cell[7105, 185, 269, 4, 37, "Output",ExpressionUUID->"16cf9198-eff9-447b-9532-0738cceb8c19"]
}, Open ]],
Cell[CellGroupData[{
Cell[7411, 194, 2165, 49, 77, "Input",ExpressionUUID->"eb7f236f-52d0-4b04-a063-b8cb0b97aab5"],
Cell[9579, 245, 3574, 78, 249, "Output",ExpressionUUID->"55793edb-d5b8-4858-95ca-e7c9b007d219"]
}, Open ]],
Cell[CellGroupData[{
Cell[13190, 328, 1009, 25, 52, "Input",ExpressionUUID->"d3c2ecc0-a8e6-4792-81ca-5b40050838c2"],
Cell[14202, 355, 286, 5, 37, "Output",ExpressionUUID->"1a6fdb34-67f5-4729-a6c5-ec30d105838b"]
}, Open ]],
Cell[CellGroupData[{
Cell[14525, 365, 307, 6, 53, "Input",ExpressionUUID->"e7ab3299-968d-4d29-b2cd-447d8d1ff1e6"],
Cell[14835, 373, 523, 14, 39, "Output",ExpressionUUID->"528622d6-520d-4dfb-95cb-02eedf8f9d0f"]
}, Open ]],
Cell[15373, 390, 813, 14, 53, "Input",ExpressionUUID->"baaeb7e8-47ee-48ec-a1d3-3cd762829736"],
Cell[CellGroupData[{
Cell[16211, 408, 369, 8, 33, "Input",ExpressionUUID->"e5d127d6-d370-4347-8f24-faa40e61a8b6"],
Cell[16583, 418, 6589, 127, 260, "Output",ExpressionUUID->"63f8f5c6-4182-4b3d-b68c-44d53c19d555"]
}, Open ]],
Cell[23187, 548, 1973, 37, 57, "Input",ExpressionUUID->"a3525874-ec58-484d-b703-72e51a5213c4"],
Cell[CellGroupData[{
Cell[25185, 589, 1470, 21, 33, "Input",ExpressionUUID->"cc59ea2d-418c-4b8c-ac8e-a4ae6081cd77"],
Cell[26658, 612, 1323, 34, 66, "Print",ExpressionUUID->"9a4bd1ce-ec2f-4298-a2b7-7b0fe899b662"]
}, Open ]],
Cell[CellGroupData[{
Cell[28018, 651, 977, 24, 77, "Input",ExpressionUUID->"6673e5ab-f6af-4ce5-8409-31c716b83d8a"],
Cell[28998, 677, 659, 18, 59, "Output",ExpressionUUID->"b0e48659-f42d-4f96-84a1-34f3c8bb4a45"]
}, Open ]]
}
]
*)
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment