How Threshold Effects in Spectroscopic Factors Influence Heavy-Ion Knockout Reactions

Abstract

A two-decade-old puzzle in heavy-ion one-nucleon knockout reactions is the strong correlation between the reduction factor $R_s=σ_{\rm exp}/σ_{\rm th}$ and the Fermi surface asymmetry $ΔS$. Theoretical cross sections typically rely on spectroscopic factors (SFs) from shell model (SM) calculations, which neglect continuum coupling effects. Here, we employ the Gamow shell model (GSM), which explicitly incorporates continuum coupling, to compute SFs for $p$-shell nuclei and predict corresponding theoretical cross sections. Systematic calculations demonstrate that using GSM-derived SFs substantially reduces discrepancies between theoretical and experimental results. This improvement is particularly significant for deeply bound nucleon knockout in nuclei near the dripline, where traditional SM-based calculations fall short. As a result, using GSM SFs, the ratio $R_s$ exhibits no pronounced dependence on $ΔS$. Furthermore, both the ratio of GSM SFs to SM SFs and their corresponding reaction cross sections ratios exhibit a strong $ΔS$ dependence. We have also compared GSM SFs and cross sections with those from the no-core shell model calculations, giving a similar pronounced sensitivity to $ΔS$. Detailed analysis attributes these correlations to threshold effects for SFs in weakly bound systems. Overall, incorporating continuum coupling via GSM enhances the reliability of SF predictions for exotic, weakly bound nuclei and provides key insights toward resolving the enduring puzzle in heavy-ion knockout reactions from a nuclear structure perspective.

Figures (4)

• Figure 1: The reduction factor $R_s$ as a function of the asymmetry parameter $\Delta S$. Experimental inclusive nucleon removal cross sections, $\sigma_{\text{exp}}$, are taken from Refs. PhysRevLett.106.162502PhysRevLett.102.232501PhysRevC.86.024315PhysRevC.102.044614MARKENROTH2001462AKSYUTINA200919110.1063/1.4909557. The theoretical cross sections, $\sigma_{\text{th}}$, are computed by combining reaction model calculations with nuclear structure inputs derived from both GSM and SM SFs.
• Figure 2: Panels (a) and (b) show the ratios $\mathrm{SF}_{\mathrm{GSM}}/\mathrm{SF}_{\mathrm{SM}}$ and $\sigma_{\mathrm{GSM}}/\sigma_{\mathrm{SM}}$ plotted as functions of the asymmetry parameter $\Delta S$, respectively. The shaded region indicates the $1\sigma$ uncertainty from the linear fit.
• Figure 3: Similar to Fig. \ref{['RS_th']}, but with $\rm SF_{NCSM}$ and $\rm \sigma_{NCSM}$ rather than $\rm SF_{SM}$ and $\rm \sigma_{SM}$.
• Figure 4: SFs as functions of separation energy. (a) Proton SF of the ground state of ${}^{7}\mathrm{Li}$ and neutron SF of its mirror nucleus ${}^{7}\mathrm{Be}$, plotted against the two-nucleon separation energy $S_{2n/2p}$. (b) Proton SF of the ground state of ${}^{8}\mathrm{Li}$ and neutron SF of its mirror nucleus ${}^{8}\mathrm{B}$ with $p_{3/2}$ partial waves and (c) corresponding results with $p_{1/2}$ partial waves, shown as functions of the single-nucleon separation energy $S_{1n/1p}$.