Excitation of $0^{+}$, $2^{+}$, $0^{+\prime }$, $2^{+\prime }$, $4^{+}$ analog states in the even selenium isotopes with 19—25 MeV protons; coupled-channel analysis

Analogs of the ground state and the $2^{+}$ one-phonon state have been populated in ${}_{}{}^{76,80,82}{}_{}{}^{}\mathrm{Se}(p, n)$ by 19, 20, 22, and 25 MeV protons. The two-phonon triplet in ${}_{}{}^{76}{}_{}{}^{}\mathrm{Se}(p, n)$, the $4^{+}$ analog state and the $0^{+\prime }$, $2^{+\prime }$ doublet in ${}_{}{}^{80}{}_{}{}^{}\mathrm{Se}(p, n)$, and the $0^{+\prime }$ analog state and the $2^{+\prime }$, $4^{+}$ doublet in ${}_{}{}^{82}{}_{}{}^{}\mathrm{Se}(p, n)$, have also been observed. The integrated cross sections for the ground and $2^{+}$ one-phonon states display a smooth energy dependence over this bombarding energy region. $\frac{\sigma \left(0^{+}\right)}{\mathrm{}(N-Z)\mathrm{}}$ and $\frac{\sigma \left(2^{+}\right)}{\left[{\beta }^2\mathrm{}\right(N-Z\left)\right]}$ show an upward trend as a function of $A$, which is a downward trend with increasing collectivity. A coupled-channel analysis has been made using primarily a generalized optical potential deduced from the Ohio University global optical potential for neutrons. The $0^{+}$, $2^{+}$, $0^{+\prime }$, $2^{+\prime }$, and $4^{+}$ states and their analogs in Br are coupled in the harmonic-vibrator model but using experimentally determined deformation parameters ($\beta \text{'}\mathrm{s}$). Optical parameters deduced from fitting $\mathrm{Se}(n, n)$ and ($n, n^{\prime }$) data yield excellent fits to the ${}_{}{}^{76,80,82}{}_{}{}^{}\mathrm{Se}(p, n)$ ground state analog transitions. If allowance is made for the fractionation of the two-phonon strength, good agreement is also obtained for the one-phonon $2^{+}(p, n)$ transitions. Evidence for one-phonon mixing in the $2^{+\prime }$ state is seen from the weakness of the $0^{+\prime }$, $2^{+\prime }$ doublet in ${}_{}{}^{80}{}_{}{}^{}\mathrm{Se}(p, n)$ and of the $2^{+\prime }$, $4^{+}$ doublet in ${}_{}{}^{82}{}_{}{}^{}\mathrm{Se}(p, n)$ as calculated with the harmonic model. Inclusion of a one-phonon component into the $2^{+\prime }$ state through the use of the measured $\beta$ values brings the calculated cross sections into reasonable agreement with experiment.