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Collective rotational bands were observed for the first time in neutron-rich odd–odd [Formula: see text]La by means of [Formula: see text]-[Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text]-[Formula: see text]-[Formula: see text] coincidence measurements of prompt fission [Formula: see text] rays from [Formula: see text]Cf using multi-detector array Gammasphere. Similarity between the yrast band of [Formula: see text]La and those of neighboring [Formula: see text]La, [Formula: see text]Ce was found and interpreted as quasiparticle excitations. PES calculations suggested triaxial deformation for the ground state of 142La. Considerable triaxial and near zero octupole deformations were deduced for the yrast band of [Formula: see text]La by the TRS model calculations. The band-crossing observed in the yrast band of [Formula: see text]La was interpreted to be caused by alignment of the (h[Formula: see text])2 proton pair, and the crossing frequency was best reproduced by the TRS calculations taking into account triaxial deformations. In contrast to the interpretations for the band crossing of [Formula: see text]La, alignments of the (i[Formula: see text])2 neutron pair were found to be responsible for the band-crossing of the yrast band in the neighboring even-N [Formula: see text]La, and triaxial degree of freedom was found to play a more significant role than octupole deformations in the nucleus, although its [Formula: see text] values deduced are large.

We present a generator-coordinate method for realistic shell-model Hamiltonians that closely approximates the full shell model calculations of the matrix elements for the neutrinoless double-$\ensuremath{\beta}$ decay of $^{124}\mathrm{Sn}$, $^{130}\mathrm{Te}$, and $^{136}\mathrm{Xe}$. We treat not only quadrupole deformations but also the proton-neutron pairing amplitudes as generator coordinates. We validate this method by calculating and comparing spectroscopic quantities with the exact shell model results and experimental data. Our Hamiltonian-based generator-coordinate method produces $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ matrix elements much closer to the shell model ones, compared to the existing energy-density-functional-based generator-coordinate approaches. The remaining overestimation of $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ nuclear matrix element suggests that additional correlations may be needed to be taken into account for $^{124}\mathrm{Sn}$, $^{130}\mathrm{Te}$, and $^{136}\mathrm{Xe}$ when calculating with the Hamiltonian-based generator-coordinate method. The validation of this method may open the possibility of calculating $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ matrix element of $^{150}\mathrm{Nd}$ in a large shell-model space.

The spectroscopy of $^{73}\text{Ge}$ has been investigated via the $^{70}\text{Zn}(^{7}\text{Li},3np)^{73}\text{Ge}$ fusion-evaporation reaction. A previously known band built on the $\ensuremath{\nu}({f}_{5/2})$ orbital is extended up to higher-spin states and a new rotational band built on the $\ensuremath{\nu}({g}_{9/2})$ orbital is established. The observed band crossing and shape evolution induced by the alignment in $^{73}\text{Ge}$ are studied in comparison with the similar structures in the neighboring $N=41$ isotones and the cranked Woods--Saxon--Strutinsky calculations by means of total-Routhian-surface (TRS) methods. The inversion of the order of the ${g}_{9/2}$ neutron and the ${g}_{9/2}$ proton crossing frequency observed in the negative-parity $\ensuremath{\nu}({f}_{5/2})$ bands between $^{73}\text{Ge}$ and $^{75}\text{Se}$, $^{77}\text{Kr}$ can be ascribed to their different triaxial deformations. At higher spins, both the $\ensuremath{\nu}({f}_{5/2})$ and $\ensuremath{\nu}({g}_{9/2})$ bands in $^{73}\text{Ge}$ undergo a shape evolution with sizable alignments occurring. The characters of large signature splitting in $\ensuremath{\nu}({g}_{9/2})$ band of $^{73}\text{Ge}$ are discussed.