Substate Excitation of2+States Produced by Inelastic Scattering of Protons onC12,Fe54, andNi58

Abstract

A combined analysis of absolute in-plane and $z$-axis (spin-flip) $p\ensuremath{-}\ensuremath{\gamma}$ angular correlation measurements for ${0}^{+}$-${2}^{+}$-${0}^{+}$ transitions leads to various combinations of substate cross sections, populations, and phase angles. These quantities are compared with predictions based on reaction-mechanism theories. The test is very stringent. Measurements and analyses have been carried out for $^{12}\mathrm{C}(p,{p}^{\ensuremath{'}}\ensuremath{\gamma})^{12}\mathrm{C}^{*}$(4.44 MeV) and $^{58}\mathrm{Ni}(p,{p}^{\ensuremath{'}}\ensuremath{\gamma})^{58}\mathrm{Ni}^{*}$(1.45 MeV) at ${E}_{p}=20$ MeV, and for $^{54}\mathrm{Fe}(p,{p}^{\ensuremath{'}}\ensuremath{\gamma})^{54}\mathrm{Fe}^{*}$(1.41 MeV) at ${E}_{p}=19.6$ MeV.Each of the three nuclei studied exhibits the following qualitative features: (1) The total inelastic cross sections have a less pronounced structure than do the individual substate cross sections. (2) The $M=0$ cross section is the most diffractionlike; the oscillations are out of phase with respect to the oscillations of the elastic cross section. (3) The sum of the $M=+2$ and $M=\ensuremath{-}2$ cross sections also are diffractionlike, but are not in phase with the $M=0$.Detailed comparisons with collective-model distorted-wave Born-approximation predictions are, on the whole, quite good for $^{58}\mathrm{Ni}$ and $^{54}\mathrm{Fe}$, especially when the full Thomas form for the spin-dependent perturbation potential is used. The isotropic term in the in-plane angular-correlation function is particularly sensitive to the form and strength of the spinorbit coupling potential. For $^{54}\mathrm{Fe}$ the predictions are further improved when the strength of the spin-dependent perturbation potential is increased by setting the spin-dependent deformation equal to twice the central-potential deformation.