Coriolis-coupling model applied to odd-neutron nuclear spectra of the1g92shell

A Coriolis-coupling model extended to include a residual pairing type interaction is applied to investigate the energy levels of low lying states of the odd nuclei of the $1g_{\frac{9}{2}}$ shell $73<A<\mathrm{}87\mathrm{}$. This deformed rotational treatment includes spectra of both parities originating from overlapping states of the $N=4\mathrm{}$ and $N=3\mathrm{}$ positive and negative parity shells. Single particle energy levels and wave functions throughout a shell are computed using spin-orbit and well-flattening parameters $C=-0.26\mathrm{}\hslash {\omega }_0$ and $D_{N=4,3\mathrm{}}=-0.040\mathrm{}\hslash {\omega }_0$ $-0.053\mathrm{}\hslash {\omega }_0$, respectively, the latter values being consistent with $d_{\frac{5}{2}}$ parentage states of ${}_{}{}^{79}{}_{}{}^{}\mathrm{Se}$ (positive parity) and $f_{\frac{5}{2}}$ states of ${}_{}{}^{83}{}_{}{}^{}\mathrm{Kr}$ (negative parity). Inclusion of an extracore pairing interaction primarily introduces a multiplicative effective overlap which serves as a quenching factor to the strength of off-diagonal Coriolis coupling terms. All parameters in the analysis are taken from available experimental considerations. The rotational constant $A$ and deformation $\beta$, in particular, are derived from the location of the first excited $2^{+}$ state of the neighboring even-even nucleus and its observed $E2\mathrm{}$ transition rate to the ground state. For each set of parameters both a single particle and a Coriolis coupling diagonalization are performed over an entire shell of 10 or 15 Nilsson states to obtain final negative or positive parity spectra and wave functions. The results of this essentially fixed parameter model are presented and compared with experimental determinations with which they are in substantial agreement. In general, the model favors a prolate description for the nuclei in this region. Energy excitation spectra are all in general agreement, and in particular: (a) ground state spins and lowest lying opposite parity spins are always correctly predicted; (b) many otherwise anomalous low lying and often ground state ${7/2}^{+}$, ${5/2}^{+}$ spins are well predicted. The systematic reproduction of experimental spectra provided by the model points to the validity of a statically deformed interpretation of the odd neutron nuclei of the $1g_{\frac{9}{2}}$ shell, in contrast to the purely spherical and vibrational approaches to which the region has been restricted in the past.