Energy dependence of the ratio of isovector effective interaction strengths $\left|\frac{J_{\sigma \tau }}{J_{\tau }}\right|$ from 0° ($p$,$n$) cross sections

Information concerning the ratio of the isovector effective interaction strengths $\left|\frac{J_{\sigma \tau }}{J_{\tau }}\right|$ may be obtained from the ratio of ($p$,$n$) Gamow-Teller and isobaric analog state 0° differential cross sections. We have examined 0° ($p$,$n$) data for the energy range 5-200 MeV and find that for energies larger than 50 MeV and for targets with $A=7-42\mathrm{}$ the product of the interaction-strength and distortion-factor ratios $\left|\frac{J_{\sigma \tau }}{J_{\tau }}\right|{\left(\frac{N_{\sigma \tau }}{N_{\tau }}\right)}^{\frac{1}{2}}$ appears to be mass independent and linear as a function of bombarding energy.