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 $A\approx 130$ 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.

Figure 1

Experimental vibrational excitation energy $E\left(2^{+}\right)$ for the isotonic chain $N=64–76$ in the region of $42\le Z\le 64$ [63]. The surrounded points indicate the energy of the even-even core considered by TDA calculations. The excitation energy of ${}^{124}\mathrm{Ce}$ is obtained by extrapolation from the value of experimental $E\left(2^{+}\right)$.

Figure 2

Nilsson diagram for protons of the closest shells of $50\le Z\le 82$. The different color lines localize, as a function of deformation parameter, the expected core orbitals: light blue for ${}^{120}\mathrm{Xe}$ (${\varepsilon }_2=0.225$), green for ${}^{124}\mathrm{Ce}$ (${\varepsilon }_2=0.275$), red for ${}^{122,124}\mathrm{Ba}$ (${\varepsilon }_2=0.25$), blue for ${}^{126}\mathrm{Ba}$ (${\varepsilon }_2=0.233$), and pink for ${}^{128}\mathrm{Ba}$ (${\varepsilon }_2=0.2$).

Figure 3

Intrinsic states of ${}^{123}\mathrm{La}$ showing the contribution of successive addition of different terms of quadrupole (with index $Q$), recoil ($J$), and residual pairing ($P$) forces to the initial pairing interaction. For orientation, the dashed lines connect the states characterized by the same asymptotic quantum numbers ${\mathrm{\Omega }}_{\pi }[N,n_z,\mathrm{\Lambda }]$, as commented in Table 2.

Figure 4

Low-energy spectroscopic schemes for isotonic nuclei of ${}^{121}\mathrm{Cs}$ (left), ${}^{123}\mathrm{La}$ (middle), and ${}^{125}\mathrm{Pr}$ (right). The calculated levels using the QPRM approach are compared to the available experimental data from [71, 74, 75].

Figure 5

Low-energy spectroscopic schemes for isotopic nuclei of ${}^{125}\mathrm{La}$ (left), ${}^{127}\mathrm{La}$ (middle), and ${}^{129}\mathrm{La}$ (right) compared to the available experimental data from [75, 78, 79]. In red, the first excited state of the $1/2^{+}\left[420\right]$ band is connected to the isotopic chain.