Recoil-corrected continuum shell model calculations for ${}^{11}$B${(p,n)}^{11}$C, ${}^{11}$B${(p,{p}^{\ensuremath{'}})}^{11}$B${}^{*}$, ${}^{12}$C$(e,{e}^{\ensuremath{'}}x)$

Recoil-corrected continuum shell model calculations for $^{11}$ B ${(p, n)}^{11}$ C, $^{11}$ B ${(p, p^{'})}^{11}$ B $^{*}$ , $^{12}$ C $(e, e^{'} x)$

Dean Halderson

Phys. Rev. C 88, 014610 – Published 19 July 2013

Abstract

Background: The recoil-corrected continuum shell model provides coupled-channels solutions for bound and unbound wave functions from realistic effective interactions. The wave functions are antisymmetric and contain no spurious components because the calculations are performed in the center-of-mass system.

Purpose: This model has now been extended to include 1 $ℏ ω$ excitations in the structure of $p$ -shell target (residual) nuclei, hence allowing 0 $s$ -shell knockout processes. Several reactions involving the $^{12}$ C compound system are investigated to demonstrate the utility of the model.

Methods: The states of $^{11}$ B and $^{11}$ C are constructed in the nonspurious 0 $ℏ ω$ plus 1 $ℏ ω$ model space. An interaction, fitted to Cohen and Kurath (8-16) plus Reid soft core $g$ -matrix elements, is employed. One nucleon is coupled to these states to create a basis for the bound and scattering states for $^{12}$ C.

Results: Calculated elastic and inelastic cross sections agree well with available data. The calculated transverse response at high momentum transfer is lower than that extracted from data. Although significant, meson exchange currents are not sufficient to give agreement with data. Likewise inclusion of 0 $s$ -shell knockout is not sufficient to provide agreement. The high-energy octupole resonance appears at low momentum transfer and an energy of 106/ $A^{1 / 3}$ .

Conclusions: The model should provide meaningful predictions for states near the proton drip line via the ( $p$ , $n$ ) reaction. Coupled-channels solutions are necessary for describing $^{12}$ C( $e$ , $e^{'} x$ ) at low momentum transfer. Lack of strength at low energy and momentum transfer in optical model calculations of $^{12}$ C( $e$ , $e^{'} x$ ) is at least partly attributable to the omission of giant resonances. Data for ( $π^{+}$ , $π^{+'} p$ )/( $π^{-}$ , $π^{-'} p$ ) could verify this conclusion. Lack of strength in the transverse response may be attributable to recoil terms which are omitted in most calculations.