States of spin ${\frac{7}{2}}^{-}$ in ${\mathrm{Ti}}^{47}$, ${\mathrm{Ti}}^{49}$, ${\mathrm{Cr}}^{51}$, ${\mathrm{Fe}}^{53}$, ${\mathrm{Fe}}^{55}$, ${\mathrm{Fe}}^{57}$, ${\mathrm{Ni}}^{57}$, ${\mathrm{Ni}}^{59}$, and ${\mathrm{Ni}}^{61}$ were observed by means of the ($p,d$) reaction with 28-MeV incident protons. In each case the highest ${\frac{7}{2}}^{-}$ state seen was found to be the isobaric analog of the lowest ${\frac{7}{2}}^{-}$ state of the isobar with one more neutron. Coulomb displacement energies were obtained which are in excellent agreement with known values in this mass region. The lower ${\frac{7}{2}}^{-}$ states were interpreted as "configuration states," that is, states associated with the same configuration as the analog, but with isospin lower by unity. The angular distributions in all cases were in good agreement with distorted-wave calculations. Comparison of the spectroscopic factors for the analog and configuration states with the predictions of $j-j$-coupling sum rules revealed that the normal procedures used in distorted-wave calculations predict too large a $Q$ dependence. However, by using radial wave functions for the picked-up neutron that are identical for all $1f_{\frac{7}{2}}$ states in a given nucleus, reasonable agreement with the sum rules was obtained. Reasonable agreement was also found with the strengths for various states computed from $1f_{\frac{7}{2}}$ shell-model calculations. The energy splitting between the analog state and the strength-weighted mean of the configuration states was also found to be in agreement with theoretical estimates.

• Received 8 April 1965

DOI:https://doi.org/10.1103/PhysRev.139.B1272