One-neutron transfer from ${}^{16}\mathrm{O}$ to ${}^{27}\mathrm{Al}$ and ${}^{28}\mathrm{Si}$ targets at $E_{\text{lab}}=240\mathrm{MeV}$

Background: Transfer reactions induced by heavy ions have been explored to study the role of pairing in the two-nucleon transfers. However, many reaction channels are often open and couplings between them must be considered. Some of these couplings are effectively taken by suitable optical potentials whereas other channels are explicitly considered into the coupling scheme. The interplay between optical potentials and coupling schemes may lead to ambiguities in the interpretation of transfer mechanisms.

Purpose: Relevant parameters in the calculations can be constrained by several reactions measured under the same experimental conditions. This may lead to a unified theoretical reaction scheme that can be applied to properly judge the role of sequential and simultaneous processes in the two-nucleon transfers.

Methods: In this work we analyze the one-neutron transfer reactions to ${}^{27}\mathrm{Al}$ and ${}^{28}\mathrm{Si}$ induced by (${}^{16}\mathrm{O},{}^{15}\mathrm{O}$) at $E_{\mathrm{lab}}=240$ MeV. The choice of targets is of particular interest: within the weak coupling model, the ${}^{27}\mathrm{Al}$ can be interpreted as a proton hole coupled to the ${}^{28}\mathrm{Si}$ core. The parameters of the optical potentials to describe the elastic and inelastic scattering in these reactions have been studied in a previous publication. Here, we focus on the reaction and nuclear structure models to describe the experimental cross sections. We performed coupled channel Born approximation (CCBA) and coupled reaction channels (CRC) using spectroscopic amplitudes obtained from shell model with three different interactions and single-particle model spaces.

Results: The optical potentials and coupling schemes provide a good description of the angular distributions of the cross sections, in which the CRC calculations give a slightly better agreement with experimental than the CCBA one. We compare CRC calculations using spectroscopic amplitudes from three different shell-model interactions. They all give a reasonable description of the experimental data except for the transfer that populates the $7/2_1^{-}$ state in ${}^{29}\mathrm{Si}$. This requires a $1f_{7/2}$ single-particle state, present only in the model space for one of the considered interactions.

Conclusions: Within the same theoretical methodology, we are able to achieve an overall good description of the experimental data for one-neutron transfer in the ${}^{27}\mathrm{Al}({}^{16}\mathrm{O},{}^{15}\mathrm{O}){}^{28}\mathrm{Al}$ and ${}^{28}\mathrm{Si}({}^{16}\mathrm{O},{}^{15}\mathrm{O}){}^{29}\mathrm{Si}$ at 240 MeV. This methodology will be adopted to study the proton transfer channels in these systems in a future work.

Figure 1

Energy differential cross-section spectra obtained for (${}^{16}\mathrm{O}, {}^{15}\mathrm{O}$) one-neutron stripping reaction at 240 MeV in ${}^{27}\mathrm{Al}$ target, that populates states in ${}^{28}\mathrm{Al}$ nucleus (a) and in ${}^{28}\mathrm{Si}$ target, that populates states in ${}^{29}\mathrm{Si}$ nucleus (b).

Figure 2

Detailed view of the excitation energy spectra at low-lying states for ${}^{28}\mathrm{Al}$ (a) and ${}^{29}\mathrm{Si}$ (b). Continuous red curves correspond to a multi-gaussian fittings to the experimental data points whereas the colored gaussian curves under the fit represent the individual contributions. The experimental cross sections are determined for the region of interest (ROI) indicated in each spectrum.

Figure 3

Coupling schemes adopted in the calculations of the one-neutron transfer in the ${}^{27}\mathrm{Al}({}^{16}\mathrm{O},{}^{15}\mathrm{O}){}^{28}\mathrm{Al}$ (a) and ${}^{28}\mathrm{Si}({}^{16}\mathrm{O},{}^{15}\mathrm{O}){}^{29}\mathrm{Si}$ (b) reactions. Red arrows indicate the couplings considered in the initial mass partition, while the blue arrows indicate the couplings introduced within the CCBA reaction scheme. In the CRC framework, all arrows have to be considered bidirectional (see text).

Figure 4

Comparison between CRC and experimental data for the elastic scatterings in the ${}^{27}\mathrm{Al}+{}^{16}\mathrm{O}$ (a) and ${}^{28}\mathrm{Si}+{}^{16}\mathrm{O}$ (b) systems. Experimental data from Ref. [18].

Figure 5

Comparisons between experimental and theoretical cross sections for one-neutron transfer in the ${}^{27}\mathrm{Al}({}^{16}\mathrm{O},{}^{15}\mathrm{O}){}^{28}\mathrm{Al}$ reaction (a) and (b) and the ${}^{28}\mathrm{Si}({}^{16}\mathrm{O},{}^{15}\mathrm{O}){}^{29}\mathrm{Si}$ reaction [(c)–(e)]. Theoretical curves obtained within the CCBA and CRC approaches using spectroscopic amplitudes obtained from the PSDMOD interaction.

Figure 6

Angular distribution of the experimental cross sections for one-neutron stripping in the ${}^{27}\mathrm{Al}({}^{16}\mathrm{O},{}^{15}\mathrm{O}){}^{28}\mathrm{Al}$ system for the ROI-1 (a), ROI-2 (b), and ROI-3 (c) considered. The curves are CRC calculations using SFs from the PSDMOD (solid red), PSDMWKPN (dashed blue), and SDPF-U (dot-dashed orange) interactions.

Figure 7

Comparisons between theoretical and experimental differential cross sections for the low-lying states for ${}^{28}\mathrm{Al}$ (a) and ${}^{29}\mathrm{Si}$ (b). Continuous red, dashed blue, and dot-dashed orange curves correspond the theoretical spectra generated from the cross sections given by the CRC calculations with PSDMOD, PSDMWKPN, and SDPF-U interactions, respectively. Dotted green curves correspond to a scaled SPDF-U spectra. Further details in the text.