Evolution of Spectroscopic Factors in Neutron-deficient $p$-shell Nuclei in connection with Short-Range Correlations

Abstract

We report an uncertainty-controlled determination of neutron-removal spectroscopic factors in the neutron-deficient $p$-shell nuclei $^{12}\mathrm{C}$, $^{10}\mathrm{C}$, $^{9}\mathrm{C}$, and $^{8}\mathrm{B}$, all measured under uniform conditions through exclusive ground-state-to-ground-state $(p,d)$ reactions at about 50 MeV/nucleon in a liquid hydrogen target at the GANIL/LISE facility. The deuterons were detected in the highly-segmented MUST2 detector placed at forward angles and the excitation energy was reconstructed by the missing mass method. Several transitions, including a new state in $^7\mathrm{B}$, were observed. Differential cross sections, which display an $L=1$ pattern for all nuclei, were fitted with 416 sets of uncertainty-quantified optical-model potential parameters and considering various single-particle bound-state wavefunctions to derive $C^2S$ values. The ratio between experimental and shell-model calculated values, $R_S$, is found to be slightly decreasing as a function of increasing proton to neutron separation energy asymmetry $\Delta S$, with a slope of $-0.0049(36)_{\rm stat}(13)_{\rm omp}(8)_{\rm s.p.}$. The observed trend is compatible with the phenomenological expectation that the short-range correlation effect on $C^2S$ increases with the degree of nucleon minority. The present data set delivers a high-precision benchmark that will tightly constrain future microscopic descriptions of short-range correlations in asymmetric nuclei.