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The angular distributions of $^7$Li$_{g.s.}$, and $^6$He$_{g.s.}$, $^6$Li$_{g.s.}$, $^6$Li$_{3.56}$ reaction products of one-nucleon transfer in $^7$Li+$^{10}$B interaction were measured at $E_{7Li}$=58 MeV of U-400 @ FLNR JINR, Dubna. One of the aim of our studies was to compare the spatial dimension parameters of A=6 isobar triplet nuclei obtained in the direct one-step n , p-transfer reactions. The $^6$Li$^*_{3.56}$ is the IAS of $^6$He$_{g.s.}$. The angular distributions of $^{10}$B($^7$Li,$^6$He)$^{11}$C, $^{10}$B($^7$Li,$^6$Li)$^{11}$B and $^{10}$B($^7$Li,$^6$Li$^*_{3.56}$)$^{11}$B were measured under the same experiment for the first time. The analysis to derive the angular distributions was performed by using the finite-range coupled reaction channel approach. To microscopically derive the angular distributions concerning the 1$n$- and 1$p$- transfer processes some ingredients were needed, such as optical potential and spectroscopic amplitudes. For the optical potential in each partition the double- folding São Paulo potential [1,2] was used in both real and imaginary parts. Couplings with the first excited states of the projectile and target nuclei were explicitly included in the coupled equations scheme. The 1$n$- and 1$p$- spectroscopic amplitudes used in the single particle states were determined by shell model calculations, using the NuSHellX code [3].
Fig.1 shows the coupled scheme used in the one-nucleon transfer reactions calculation. A good agreement between theory and experiment was obtained for the elastic scattering and the transfer to the $^6$Li$_{g.s.}$(1$^+$) + $^{11}$B$_{g.s.}$(3/2$^-$) channel. On the other hand, the theory overestimates the data of one-neutron transfer populating the $^6$Li$^*_{3.56}$ (0$^+$) + $^{11}$B$_{g.s.}$(3/2$^-$). The same thing occurring with one-proton transfer populating the $^6$He$_{g.s.}$(0$^+$) + $^{11}$C$_{g.s.}$(3/2$^-$) channel. The reason is that the CRC calculations did not account for the breakup process of the $^6$Li and when it is left in its 0$^+$ excited state or the breakup effect on the ground state of the $^6$He nucleus. To show the relevance of the breakup process on the $^6$Li$_{3.56}$(0$^+$) excited state, we include the coupling between the g.s. and the 0$^+$ (3.56 MeV) from the single particle excitation approach as used in the CDCC calculation. So, a bin-state was set to describe the scattering between the $^4$He$_{g.s.}$ and the $p$-$n$ system inside the $^6$Li. To properly include this configuration, the $p$-$n$ valence particles were considered with spin $j$=0. The theoretical analysis when the breakup process of the $^6$Li$_{3.56}$(0$^+$) excited state is included in the CRC calculation gives a good description of the measured $^6$Li$_{3.56}$(0$^+$) + $^{11}$B$_{g.s.}$(3/2$^-$) channel. This research was funded by the Russian Science Foundation, project No. 24-22-00117. Brazilian authors were supported by CNP, FAPERJ, CAPES, and INCT-FNA (research project No. 464898/2014-5).
[1] L.C. Chamon, D. Pereira, M.S. Hussein, M.A. Cândido Ribeiro, D. Galetti, Phys. Rev. Lett. 79, 5218 (1997).
[2] L. C. Chamon, B. V. Carlson, L. R. Gasques, D. Pereira, C. De Conti, M. A. G. Alvarez, M. S. Hussein, M. A. Cândido Ribeiro, E. S. Rossi, and C. P. Silva, Phys. Rev. C 66, 014610 (2002).
[3] NuShellX. www.garsington.eclipse.co.uk
