Investigation of one-neutron transfer in ${}^{13}\mathrm{C}+{}^{27}\mathrm{Al}$ at $E_{\text{lab}}=32\mathrm{MeV}$

The ${}^{13}\mathrm{C}+{}^{27}\mathrm{Al}$ reaction ($E_{\text{lab}}=32$ MeV) has been measured, and the elastic scattering, target excitation, and one-neutron transfer channels have been investigated. A comparison of the data with the results of different theoretical frameworks indicates the necessity of including the effect of the spin-orbit interaction of the target to properly reproduce the data. The inclusion of the one-neutron transfer did not significantly affected the elastic angular distribution. The one-neutron transfer reaction could be well reproduced when the psdmod interaction was used to describe the ${}^{27,28}\mathrm{Al}$ nuclei and their associated features. The results reported here are consistent with those previously reported for the ${}^{13}\mathrm{C}+{}^{28}\mathrm{Si}$ reaction measured at similar bombarding energies, providing further evidence of the similarities between these nuclei.

Figure 1

Calibrated spectrum for the scattering of ${}^{13}\mathrm{C}$ in ${}^{27}\mathrm{Al}$ for a bombarding energy of 32 MeV.

Figure 2

$Q$-value spectrum at ${\theta }_{\text{lab}}={35}^{\circ }$. The elastic, inelastic, and transfer peaks are indicated in the figure. Some contaminants are present in the target: ${}^{39}\mathrm{K}$ (peak 1), ${}^{32}\mathrm{S}$ (peak 2), and an unidentified element (peak 3). Data obtained with the ${}^{27}\mathrm{Al}$ target foil. See text for further details.

Figure 3

Schematic view of the excited levels of ${}^{27,28}\mathrm{Al}$ nuclei considered in the calculations of the present work. For the carbon isotopes, only the g.s. were considered. The dashed blue lines show the adopted couplings between each inelastic state and the g.s. The nuclear transitions $M\left(E2\right)(e{\mathrm{fm}}^2$) intensities adopted may be visualized in Table 1. The dotted red lines show the couplings considered in the one-neutron transfer reaction between ${}^{27,28}\mathrm{Al}$ nuclei. The respective spectroscopic amplitudes and the quantum numbers adopted for each transition may be visualized in Table 2.

Figure 4

Elastic scattering angular distribution for ${}^{13}\mathrm{C}+{}^{27}\mathrm{Al}$ at $E_{lab}=32$ MeV. The dashed-dotted blue line represents the CC calculation with an internal WS optical potential and no spin-orbit potential. The solid black line is the result of a similar calculation but including the target spin-orbit potential. The dashed green line brings the same coupling scheme and potentials previously mentioned but changing the WS shape of the imaginary potential to a SPP shape with normalization of $N_I=0.1$. The red dashed-dotted line is similar to the green, but with an imaginary normalization of $N_I=0.3$.

Figure 5

(Top) Angular distribution of the inelastic scattering cross section for the first excited states of the ${}^{27}\mathrm{Al}$ ($0.84+1.01$). (Bottom) Angular distribution of the inelastic scattering cross section third excited state ${}^{27}\mathrm{Al}$ (2.21). The calculations performed are the same as Fig. 4.

Figure 6

Angular distribution of the elastic scattering cross section for the ${}^{12}\mathrm{C}+{}^{27}\mathrm{Al}$ reaction at $E_{\mathrm{lab}}=21$ MeV. The dashed dotted blue line represents a CC calculation with an internal WS optical potential and no spin-orbit effect. The solid black line is the same of the red one but including the target spin-orbit.

Figure 7

One neutron transfer angular distribution for ${}^{13}\mathrm{C}+{}^{27}\mathrm{Al}\to {}^{12}\mathrm{C}+{}^{28}\mathrm{Al}$ at the bombarding energy of 32 MeV. The solid magenta line is a CRC calculation using the $\mathcal{S}$ values obtained with psdmwkpn interaction. The solid black line brings the $\mathcal{S}$ values obtained with the psdmod interaction. The dashed black line shows the individual contribution of the transfer to the g.s. of ${}^{28}\mathrm{Al}$, while the dotted black line shows the contribution for its first excited state. The individual contributions displayed is made solely for the psdmod interaction.