Isovector and Gamow-Teller Strength from Small-Angle (n, p) Reactions at 60 MeV

The ($n, p$) reactions to the analog giant magnetic dipole states, the inverse of the transitions in allowed Gamow-Teller $\beta$ decay, have been measured for ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ for forward angles using 59.6-MeV neutrons. With use of a relation between $\sigma \left(0\mathrm{}°\right)$ and the $\beta$-decay matrix elements, there results ${v_{\sigma \tau }}^c\mathrm{}\left(0\right)=157\mathrm{}\pm 11$ MeV ${\mathrm{fm}}^3$ for the $l=0\mathrm{}$, isovector part of the effective spin-flip nucleon-nucleon interaction. Comparison with 120-MeV ($p, n$) reactions indicates that ${v_{\sigma \tau }}^c$ has a small energy dependence in the range 60 to 120 MeV.