Comparison of Experiment and Theory for Nuclear Excitation inIn115by Threshold-Energy Electrons

The Duke inelastic-electron-scattering program provides a major step in obtaining spin-parity assignments and mixing ratios for nuclear energy levels from threshold-energy electron scattering which populates an isomer. A detailed account of the Duke distorted-wave Born-approximation calculation for threshold-energy electrons is given, and the contribution and Coulomb distortion of the partial waves for $M1\mathrm{}$ and $E2\mathrm{}$ transitions is quantitatively presented. The finite tip observed in threshold electroexcitation is quantitatively accounted for by Coulomb distortion of $s$- and $d$-electron waves in the $M1\mathrm{}$ and $E2\mathrm{}$ transitions, respectively. A detailed comparison is made between experiment and theory for the 1.078- and 1.450-MeV states of ${}_{49}{}^{115}{}_{}{}^{}\mathrm{In}_{66}^{}{}_{}{}^{}$, replacing earlier semiquantitative comparisons which used plane-wave Born-approximation calculations that resulted in factors of 2-5 disagreement for 1-2-MeV electrons. The agreement between the electron excitation functions for isomer population for the 1.078- and 1.450-MeV states and the Duke calculation is well within the ±35% experimental errors. $\frac{M1\mathrm{}}{E2\mathrm{}}$ mixing ratios are extracted from the comparison. The 1.078- and 1.450-MeV states of ${}_{}{}^{115}{}_{}{}^{}\mathrm{In}$ are both ${\frac{7}{2}}^{+}$ with $\frac{M1\mathrm{}}{E2\mathrm{}}$ mixing ratios, $a=\frac{{\Gamma }_{0E2}}{{\Gamma }_{0M1}}$, given by $a=0.7\mathrm{}\pm 0.3 \mathrm{and} \le 0.3$, respectively. The mixing ratios are from photon self-absorption and Coulomb-excitation measurements of the same transitions, and corroborate the electron-scattering results. In this regard a search for the 1.078-MeV $\gamma$ ray following ${\beta }^{-}$ decay of ${}_{}{}^{115m}{}_{}{}^{}\mathrm{Cd}$ using a Ge(Li) Duode spectrometer yielded a null result, $log\mathrm{ft}>\mathrm{}11.5\mathrm{}$ for the ${\beta }^{-}$ transition. With the ${\frac{7}{2}}^{+}$ assignments made in this work, the coexistence of spherical and rotational bands in ${}_{}{}^{115}{}_{}{}^{}\mathrm{In}$ is discussed.