\documentclass[12pt,a4paper]{article}

\usepackage[utf8]{inputenc} % размер
\usepackage[final]{pdfpages}
\usepackage[T2A]{fontenc} % указывает внутреннюю кодировку TeX

\usepackage[ngerman,english]{babel}

\usepackage{epsfig}
\usepackage{xcolor}

\usepackage[labelformat=simple]{subcaption}
\usepackage{array,graphicx,caption}
\usepackage{xcolor,color}		

\begin{document}	
	
\section{Introduction}

The search for the the multineutron systems is one of the most attractive fields of modern nuclear physics.
The first suggestion about the stability of such systems was made in works \cite{Zeldovich:1960,Goldansky:1960}, but multiple experimental attempts of search for bound states of the neutron clusters (e.g. 2n in Ref.\ \cite{WILLARD1964339}, 3n in Ref.\ \cite{belozyorov:1988}, 4n in Ref.\ \cite{Marques_PhysRev:2002,Kisamori:2016}) were unsuccessful.
Never the less, the issue of bound neutron nuclei existence is still addressed in the modern theoretical works, see Ref.\ \cite{Pieper:2003,Timofeyuk:2003b,Higgins:2021}.
The recently published work \cite{Duer:2022} reported the observation of the resonance at 2.37\,MeV  with $\Gamma=1.75$\,MeV, which was interpreted as a tetraneutron state produced in a high-energy knockout reaction of alpha core from the $^8$He beam.
The ensuing theoretical work \cite{Lazauskas:2023} provides the possible realistic explanation of observed phenomenon using the model based on a transition between initial and final state of four studied neutrons.
The published in Ref.\ \cite{Duer:2022} results are undoubtedly convincing but the used reaction of knockout of the alpha core from the $^8$He was studied only at very backward angles.
Moreover, authors summarized that the obtained results are limited by the single approach of four-neutron system production and do not describe the correlation of the component neutrons.
This work is dedicated to the results on the $^2$H($^8$He,$^6$Li) reaction studied at forward angles at ACCULINNA-2 fragment separator. 


\section{Experiment}


ACCULINNA-2 facility, FLNR, JINR, produced the 26\,AMeV $^{8}$He beam with intensity $\approx10^{5}$\,pps.
This beam was focused on the cryogenic gaseous deuterium 27\,K target with a temperature of 27\,K equipped with stainless steel and mylar windows. 
Initially, the experiment was dedicated to $^{7}$H studies, see Ref.\ \cite{Muzalevskii:2021}, but the detection system allowed to measure the product of the $^2$H($^8$He,$^6$Li)4n reaction and further neutron decay.
The employed detector system is widely described in Ref.\ \cite{Muzalevskii:2021}.

The beam particles were identified by two plastic scintillators, which allowed to measure the energy of the projectile from its time-of-flight (ToF). 
%The particle identification (PID) of the beam was performed by the dE-ToF 
%For the beam particle identification and its energy determination two plastic scintillators were used. 
The motion vector of were reconstructed by two pairs of multi-wire proportional chambers. 
The special run with the empty target cell was conducted to estimate the background conditions, which had $\approx$16\% of the total $^8$He beam time.

Detection of the charged reaction products was realized by $\Delta E$-$E$ telescopes.
The latter allowed to identify $^6$Li with clear separation from other registered lithium isotopes.
%The side assembly of three (20\,$\mu$m, 1\,mm and 1\,mm thick) silicon strip detector (SSD) telescope, and the front telescope made of the 1.5\,mm double side SSD coupled to the CsI(Tl) scintillator array.
%The thin, 20\,$\mu$m detectors in the side telescopes allowed one to reliably identify and reconstruct low-energy particles (the recoil $^4$He nuclei with energy $\ge$5\,MeV), see Ref.\ \cite{Muzalevskii:2020}, emitted from the target in the laboratory angular range between $8^{\circ}$ and $26^{\circ}$.
%The first one covered the laboratory angular range between $8^{\circ}$ and $26^{\circ}$ and allowed to identify and reconstruct low-energy particles, see Ref.\ \cite{Muzalevskii:2020}.
%The front telescope covered angles $\leq9^{\circ}$ and was used to measure the high-energy particles (tritons with energy up to 160\,MeV), stopping them in the CsI(Tl) crystal.
Neutron were detected by the ToF stilbene modules \cite{Bezbakh:2018}, which provides clear neutron-gamma separation and allow to calculate the particle energy from its ToF.

%The neutron identification was realized 

\section{Results}

The most important part of the $^2$H($^8$He,$^6$Li)4n reaction analysis was neutron identification and reconstruction.
The dE-TAC correlation presented Fig.\,\ref{fig:ND_id} (a) shows that the signals produced by gamma and neutron interaction with detector material are well separated. 
However, the selection each of them on the ToF distribution, see Fig.\,\ref{fig:ND_id} (b) leads to the suggestion that some gamma-type signals correspond to neutron-like ToF.
We make a suggestion that these gammas are produced by the interaction of the neutrons with the stilbene housing and that is why can be considered as neutron events.

%-------------------------------------------------------------------------------
\begin{figure}
	\centering
	\begin{tabular}{cc}			
		\includegraphics[width=0.52\linewidth]{figures/gamma-n} 
		&
		\includegraphics[width=0.48\linewidth]{figures/tof} \\
		(a) & (b)
	\end{tabular}
	\caption{
		(a) The dE-TAC correlation providing clear separation of gammas from neutrons.
		(b) The ToF distribution. 
		The set of three peaks on the left corresponds to the gammas produced in the diaphragm installed 20 cm upstream the target plane, target frame, and CsI(Tl) array.
		Green ad red-line histograms formed by the events, identified as gamma/neutron by the dE-TAC method.
	}
	\label{fig:ND_id}
\end{figure}
%-------------------------------------------------------------------------------

Tetranuetron was reconstructed from the recoil $^6$Li as a missing component in $^2$H($^8$He,$^6$Li) reaction.
The total number of $^6$Li-neutron coincidences found in the recorded data was 136.
But, due to the kinematic selection, only 108 of these events were identified as the population of 4n.
The correlation we used for this selection is shown in Fig.\ \ref{fig:mm_4n} (b).
This is the correlation of the neutron kinetic energy in the 4n center-of-mass frame with the reconstructed energy $E_T$.
The fact that the most events are located below the kinematic border proves the good channel identification of the studied reaction.
Another evidence for the 4n population is that the data collected with the empty target has zero events satisfying the used selections.
The missing mass (MM) spectrum of 4n reconstructed after kinematic selection is shown in Fig.\ \ref{fig:mm_4n} b).

%-------------------------------------------------------------------------------
\begin{figure}
	\centering
	\begin{tabular}{cc}			
		\includegraphics[width=0.518\linewidth]{figures/triangle} 
		&
		\includegraphics[width=0.482\linewidth]{figures/mm_spec} \\
		(a) & (b)
	\end{tabular}
	\caption{
		(a) Correlation between the neutron energy in the 4n frame and the 4n decay energy.
		The kinematical border showing the $E_{n} < 3/4 E_T (4$n) relation is shown with the red line.	
		(b) The 4n MM spectrum projected from red events in (a) by using the kinematical condition.	
		The orange dotted curve illustrates the 4-body phase volume $\sim E_T^{7/2}$.
	}
	\label{fig:mm_4n}
\end{figure}
%-------------------------------------------------------------------------------

Obviously, this spectrum shape can not be described just as a contribution of the 4-body phase space volume, see the orange dotted curve in Fig.\ \ref{fig:mm_4n} (b), indicating the presence of some resonance states of 4n lying at 3-4\,MeV above the 4n decay threshold.
Its important to notice that the observed peak is consistent with the reported in Ref.\ \cite{Duer:2022} and previous Ref.\ \cite{Kisamori:2016} results.
Its important evidence for the tetraneutron resonance at low energies above the 4n decay threshold obtained at forward angles in the reaction of alpha core knockout from the $^8$He beam.


\section{Conclusion}

The $^2$H($^8$He,$^6$Li)4n reaction was studied at forward angles.
The observed peak at 3-4 MeV above the 4n threshold is in agreement with Ref.\ \cite{Duer:2022,Kisamori:2016}.
The obtained results are pushing the investigation of the neutron clusters.
The configuration of the detector setup specifically for such reaction and improved neutron detection efficiency is demanded in the future experiments.
The latter will not also increase statistics but also will allow to study neutron cluster decays in full kinematics reconstructed by the invariant mass methods. 


\section{Acknowledgement}

%Institute of Physics of Silesian University in Opava 
We acknowledge the principal support of this work by the Russian Science
Foundation grant No.\ 22-12-00054. The authors are grateful to
Profs.\ Yu.Ts.\ Oganessian and S.N.\ Dmitriev for the long-term support and
development of this activity. We acknowledge important contribution of Prof.\
M.S.\ Golovkov to the development of the experimental methods and useful
discussions. Also, authors express their gratitude to the
acceleration team for the stable work of U-400M cyclotron during all runs.

\bibliographystyle{unsrt}
\clearpage
\bibliography{all1} 

\includepdf[pages=-]{add.pdf}

	
\end{document}