Low-energy band structures in light odd-A La isotopes using the quasiparticle-phonon coupling plus rotor approach

Quasiparticle-phonon coupling based on one quadrupole phonon is investigated to study the low-energy states of the $A\ensuremath{\approx}130$ mass transitional region. The coupling is constructed by using the deformed average field of Nilsson, monopole pairing interaction, and quadrupole-quadrupole forces. Microscopic structure of the quadrupole phonon is given from the Tamm-Dancoff approximation. The effects of the recoil and Coriolis forces are included with the assumption of axially symmetric rotational motion. Since theoretical treatment is performed for odd-$A$ nuclei, the configuration of intrinsic states contains both one-quasiparticle and quasiparticle-phonon components. This model is applied to describe the systematic structure of $^{121}\mathrm{Cs}, ^{125}\mathrm{Pr}$, and $^{123,125,127,129}\mathrm{La}$ nuclei, showing a reasonable agreement with the available experimental data at low excitation energies. From isotonic systematics, a strong Coriolis effect is revealed for negative-parity states and a strong pairing effect is shown for positive-parity ones. For the first time, the lowest (ground) $5/{2}^{+}$ state of $^{123,}\mathrm{La}$ is proposed to belong to the $1/{2}^{+}$[420] band from the isotopic systematic trend.