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The results of theoretical calculation of the neutron transfer and nuclear breakup for the $^{11}$Li+$^{28}$Si reaction at energy range 1–55 MeV/nucleon are presented. The total cross sections for the $^{11}$Li+$^{28}$Si reaction are calculated based on a numerical solving of the time-dependent Schrödinger equation for the external weakly bound neutrons of the projectile nucleus $^{11}$Li. Based on probabilities of neutron transfer and nuclear breakup obtained from an exact solving of time-dependent Schrodinger equation, we calculated two-neutron removal cross sections $\sigma_{-2n}$. In the low-energy region for the nuclear reaction with weakly bound nucleus $^{11}$Li, the neutron transfer process gives a large contribution to the two-neutron removal cross sections $\sigma_{-2n}$ [1]. Contributions of reaction channels to the total cross sections were defined.

The shell model of spherical nuclei without spin-orbit interaction was used for description of outer neutrons in the $^{11}$Li nucleus and states of transferred neutron in the target nucleus $^{28}$Si. To confirm the applicability of this principle for calculating reaction cross sections with weakly bound nuclei, we compare calculations taking into account the spin-orbit interaction [2] and without it. The approach without taking into account the spin-orbit interaction does not lead to significant differences in the results.

Enhancement of the total cross section for reactions with light weakly bound lithium nuclei $^{8,9,11}$Li nuclei as compared to with reactions with $^{6,7}$Li arouse great interest. Mechanisms leading to increase in the total cross section at low energies for $^{11}$Li+$^{28}$Si reaction will enable us to explain important problems of nucleosynthesis (nuclear astrophysics) [2-6]. This effect is especially strongly manifested for light nuclei with a neutron halo [7].

References

[1] A.K.Azhibekov, V.V.Samarin, K.A.Kuterbekov, Time-dependent calculations for neutron transfer and nuclear breakup processes in $^{11}$Li+$^{9}$Be and $^{11}$Li+$^{12}$C reactions at low energy, Chinese Journal of Physics (2020) doi:10.1016/j.cjph.2020.01.009

[2] Yu.E. Penionzhkevich, Yu.G. Sobolev, V.V. Samarin et al., Energy dependence of the total cross section for the $^{11}$Li+$^{28}$Si reaction, Phys. Rev. C 99 (2019) 014609.

[3] Yu.E.Penionzhkevich, Nuclear Astrophysics, Phys. Atom. Nuclei 73 (2010) 1460.

[4] V.I.Zagrebaev, V.V.Samarin, W.Greiner, Sub-barrier fusion of neutron-rich nuclei and its astrophysical consequences, Phys. Rev. C 75 (2007) 035809.

[5] K.A.Kuterbekov, A.M.Kabyshev, A.K.Azhibekov, Peculiarities of interaction of weakly bound lithium nuclei (A=6–11) at low energies: Elastic scattering and total reaction cross sections, Chinese Journal of Physics 55 (2017) 2523.

[6] A.M.Kabyshev, K.A.Kuterbekov et al., Some peculiarities of interactions of weakly bound lithium nuclei at near-barrier energies, J. Phys. G Nucl. Part. Phys. 45 (2018) 025103.

[7] A.Lemasson et al., Modern Rutherford Experiment: Tunneling of the Most Neutron-Rich Nucleus, Phys. Rev. Lett. 103 (2009) 232701.