Neutron Shell Structure inSn125by (d,p) and (α,He3) Reactions

Differential cross sections for ${}_{}{}^{124}{}_{}{}^{}\mathrm{Sn}\mathrm{}(d,p)\mathrm{}$ at 33.3 MeV were measured in 5° increments from 12.5 to 47.5° lab. The resolution was about 30 MeV full width at half maximum. The ($\alpha ,{}_{}{}^3{}_{}{}^{}\mathrm{He}$) spectra with $\sim 55$-keV resolution were obtained at 15 and 20° lab with 65.7-MeV $\alpha$ particles. Distorted-wave calculations were made, allowing the assignment of $l$ values, some of which were not made in earlier neutron-transfer studies. Spin assignments and spectroscopic factors were obtained in accordance with the shell model. Consistent spectrocopic factors were obtained from the ($d,p$) and ($\alpha ,{}_{}{}^3{}_{}{}^{}\mathrm{He}$) reactions. Sums of spectroscopic factors and centers of gravity are presented for the levels observed and are compared with the results of pairing theory. Essentially all the neutron strength remaining in the neutron shell between $N=50\mathrm{}$ and $N=82\mathrm{}$ was located. Most of the strength in the $2f_{\frac{7}{2}}$, $3p_{\frac{3}{2}}$, and $1h_{\frac{9}{2}}$ levels of the next major shell was located.