Antisymmetric distorted wave impulse approximation calculations of spin transfer cross sections for(3He→,t→)reactions to the continuum

Abstract

A formalism is presented for the calculation of spin transfer cross section for intermediate energy charge exchange ${(}^{3}\mathrm{He}\ensuremath{\rightarrow},\stackrel{\ensuremath{\rightarrow}}{t})$ [and $(\stackrel{\ensuremath{\rightarrow}}{p},\stackrel{\ensuremath{\rightarrow}}{n})]$ reactions to the continuum. The nuclear structure part of the formalism is based on the continuum Tamm-Dancoff method and the nuclear reaction part is treated within the distorted wave impulse approximation. In the nuclear structure part, we thus include particle-hole correlations and continuum effects on the excited particle. The knockon-exchange effect and the damping of the particle through an imaginary potential added to the single particle real potential are also taken into account. Results of numerical calculations are presented for the inclusive cross sections $\ensuremath{\sigma}(0\ifmmode^\circ\else\textdegree\fi{})$ and the spin transfer coefficients ${D}_{\mathrm{nn}}(0\ifmmode^\circ\else\textdegree\fi{})$ for forward scattering, for the intermediate energy ${(}^{3}\mathrm{He}\ensuremath{\rightarrow},\stackrel{\ensuremath{\rightarrow}}{t})$ and $(\stackrel{\ensuremath{\rightarrow}}{p},\stackrel{\ensuremath{\rightarrow}}{n})$ reactions on ${}^{12}\mathrm{C}$ and ${}^{90}\mathrm{Zr}$ targets leading to Gamow-Teller resonances in the continuum. It is shown that ${D}_{\mathrm{nn}}(0\ifmmode^\circ\else\textdegree\fi{})$ for this case takes a value of $\ensuremath{-}1/3,$ regardless of the details of nuclear structure and reaction mechanisms, if the reaction is assumed to proceed as an orbital angular momentum transfer ${l}_{t}=0$ process, and that deviations from $\ensuremath{-}1/3$ come from admixture of ${l}_{t}=2$ components. A simple closed form of the expression is derived which can be used to understand a subtle dependence of the ${D}_{\mathrm{nn}}$ values on nuclear structure and effective interaction.