The role of the overlap function in describing angular distributions of single-nucleon transfer reactions

TL;DR

This study shows that overlap functions derived from the Gamow shell model, which include inter-nucleon correlations and continuum coupling, provide a more accurate input for single-nucleon transfer reactions than traditional single-particle overlaps. Using CCBA with GSM overlaps for the $^6\mathrm{He}(d,n)^7\mathrm{Li}$ and $^{208}\mathrm{Pb}(^7\mathrm{Li},^6\mathrm{He})^{209}\mathrm{Bi}$ systems, the authors demonstrate improved reproduction of both the shape and magnitude of angular distributions, and they extract spectroscopic factors and ANCs that reflect realistic interior structure and asymptotics. In contrast, overlaps from NCSM without continuum fail to capture asymptotics, and standard s.p. overlaps underpredict the data when combined with GSM SFs, underscoring the necessity of continuum-aware structure inputs. The results support a framework where reaction calculations are fed with state-of-the-art GSM overlaps, possibly complemented by quenching factors, to achieve consistent SF and ANC extractions and more reliable insights into nuclear structure at the limits of stability.

Abstract

Single-nucleon transfer reactions offer a valuable way to probe nuclear structure. We explore the effect of directly introducing overlap functions computed using the Gamow shell model (GSM) into reaction calculations, taking the $\left< ^7\mathrm{Li} \mid \protect{^6\mathrm{He}} + p \right>$ single proton overlap as a case study. By incorporating both inter-nucleon correlations and continuum coupling, the GSM provides accurate overlap functions in both interior and asymptotic regions, together with the corresponding spectroscopic factors (SFs). These theoretical SFs and overlap functions were included in a coupled channels Born approximation analysis of the \(^{6}{\rm He}(d,n)^7{\rm Li}\) transfer reaction. Overlap functions derived from \textit{ab initio} no-core shell model (NCSM) calculations as well as standard single-particle (s.p.) wave functions were also considered for comparison. Our results reveal significant differences between the calculated angular distributions when employing theoretical SFs with standard s.p.\ wave functions compared to the full theoretical overlap functions. Discrepancies were also observed between angular distributions calculated with GSM and NCSM overlap functions, highlighting the importance of internal structure and correct asymptotic behavior in reliable reaction calculations. The GSM overlap functions also provided a good description of the $^{208}$Pb($^7$Li,$^6$He)$^{209}$Bi reaction when included in a coupled reaction channels calculation.

Figures (6)

• Figure 1: Comparison of the $\rm \langle ^7Li|^6He+p \rangle$ overlap functions calculated with s.p. wave functions and those from GSM, NCSM, VMC, and GFMC calculations. $\sqrt{C^2S} \psi_{\ell j}^{sp}(r)$ denotes the s.p. wave function normalized by the GSM SF.
• Figure 2: Comparison of angular distributions for the $^6$He($d,n$)$^7$Li transfer reaction calculated with different nuclear structure inputs for the $\rm \langle ^7Li|^6He+p \rangle$ overlap functions: (a) CCBA calculations using GSM SFs and s.p. wave functions, (b) CCBA calculations using overlap functions derived from the GSM, and (c) CCBA calculations using overlap functions derived from the NCSM.
• Figure 3: Angular distributions of the $^6$He($d,n$)$^7$Li reaction leading to the 0.0-MeV $3/2^-$ and 0.478-MeV $1/2^-$ states of $^7$Li, plus their sum, calculated using the D4 deuteron optical potential and GSM overlap functions (O.F.) and s.p. wave functions normalized by GSM SFs (SF), compared with the data of Ref. Li2010.
• Figure 4: The 52-MeV $^{208}$Pb($^7$Li,$^6$He)$^{209}$Bi data of Zeller et al.Zel79 (filled circles) compared with the results of CRC calculations employing the GSM $\left< ^7\mathrm{Li} \mid {^6\mathrm{He}} + p \right>$ overlaps (solid curves).
• Figure 5: Comparison of SFs (a) and ANCs (b) for the ground state of $^7 \mathrm{Li}$ extracted from the $^{6}\text{He}(d,n)^7\text{Li}$ data by the present CCBA analyses using s.p. wave functions (s.p.) and GSM overlap functions (GSM O.F.) with SFs from other work: Li10 Li2010, Clarke92 Clarke_1992, Lapikas99 PhysRevLett.82.4404 and Bekbaev91 Bek91 (solid blue symbols), and theoretical values (open symbols) calculated using the GSM, conventional SM PhysRevC.88.044315COHEN19671, and VMC PhysRevC.83.041001.