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Numerical solution of the time-dependent Schrodinger equation (TDSE) 1 is used for studying neutron transfer processes at near-barrier energies. The evolution of the wave functions for outer neutron is determined for reactions $^{181}$Ta($^{18}$O,$^{19}$O). TDSE allows us to visualize the dynamics of taking place processes [1-3]. The probabilities are calculated for neutrons transfer from outer shells of the target $^{181}$Ta. The results of calculations of transfer cross sections are in satisfactory agreement with experimental data [4] for reaction $^{181}$Ta($^{18}$O,$^{19}$O). High probability of neutron transfer from the $^{181}$Ta nucleus to the 2$s$ orbital of $^{18}$O nucleus at near-barrier energies has been yielded (see Figure 1).
In our previous work [4], differential cross sections for the formation of oxygen isotopes in the reaction $^{18}$O+$^{181}$Ta have been measured at projectile nucleus energy 10$A$ MeV on the high-resolution magnetic spectrometer MAVR. Theoretical analysis has been performed in the DWBA formalism using the FRESCO code under the assumption of sequential neutron transfer mechanism.
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 65 (2020) 292.
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, Yu.G. Sobolev, V.V. Samarin, M.A. Naumenko, Peculiarities in total cross sections of reactions with weakly bound nuclei $^{6}$He, $^{9}$Li // Physics of Atomic Nuclei 80 (2017) 928.
4 A.K. Azhibekov, V.A. Zernyshkin, V.A. Maslov, Yu.E. Penionzhkevich et al., Differential Production Cross Sections for Isotopes of Light Nuclei in the $^{18}$O+$^{181}$Ta Reaction // Physics of Atomic Nuclei 83 (2020) 94.
