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Kinematic simulation of simultaneous four-neutron emission at $\alpha$-cluster decay of $^{12}\text{Be}^{*}$ highly-exited states has been considered in $^{13}\text{C}(n,2p)^{12}\text{Be}^{*}$ reaction on RADEX cascade neutron. The cluster decay fragments should have specific energy and angular correlations reflecting strong spatial correlations of "valence" nucleons orbiting in the decay nucleus [1]. The study of characteristics of cluster decay channels is extremely important for studying the cluster properties of various nuclear states [2]. Calculations using the antisymmetric model of molecular dynamics revealed the α-cluster structure of the isotopes $\text{Be}$, $\text{B}$, and $\text{C}$ [3]. In $^{12}\text{Be}$ highly-exited states the possibility the formation of $^{8}\text{Be}$-cluster and a $4n$-correlated cluster with a radius of $\le$ 3 fm in a nuclear field $\ge$ 3 MeV or as a resonance with an energy of 2 MeV in the continuous spectrum [4]. Excitation of the highly-exited $\alpha$-cluster states in $^{12}\text{Be}$ is possible when a proton pair is quasi-elastically knocked out of $^{13}\text{C}$ at an angle of $\sim 15^{\circ}$ by a cascade neutron with an energy of $\ge$ 40 MeV or in an $n-p$ charge exchange reaction followed by rescattering by a proton at an energy $\le$ 100 MeV. In the work a two-stage kinematic simulation of the process of formation and escape of $4n$-correlated cluster in $^{13}\text{C}(n,2p2\alpha)4n$ reaction was carried out. At the first stage, the $^{13}\text{C}(n,2p)^{12}\text{Be}^{*}$ reaction was considered with excitation of double analog state of $^{12}\text{C}$ (Fig. 1a). At the second stage, subsequent $\alpha$-cluster decay of $^{12}\text{Be}^{*}$ on $4n$-correlated cluster and $^{8}\text{Be}$ or $\alpha$-particles was considered.
Estimated parameter of the pulsed source of cascade neutrons at an energy of 40-100 MeV is $10^{13}$ n/s. Calculations show that of two-proton registration from the formation of an excited state of $^{12}\text{Be}^{*}$ is possible in a narrow cone. The decay of the $\alpha$-cluster excited state of $^{8}\text{Be}+4n$ should be recorded at the widest solid angle. The registration of 4-particle coincidence must suppress the background (Fig. 1b).
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- D.Rodkin at al // Int. Conf. "Nucleus-2020", Book of Abstracts, Dubna, 51 (2020).
- Y.Kanada-En'yo, K.Ogata. // Phys.Rev.C.2019.V.100.p.064616.
- S.C.Pieper // Argonne, Illinois 60439, USA. 2018, arxiv: nucl-th/0302048v2.
