Structure of ${}^{130}\mathrm{La}$ at low and medium spins

Low- and medium-spin states of the odd-odd nucleus ${}^{130}\mathrm{La}$ were studied by in-beam and pulsed-beam $\gamma$-ray spectroscopy using the ${}^{121}\mathrm{Sb}({}^{12}\mathrm{C},3n)$ and ${}^{116}\mathrm{Sn}({}^{16}\mathrm{O},pn)$ fusion-evaporation reactions. The decay out of the $\pi h_{11/2}\otimes \nu h_{11/2}$ and $\pi h_{11/2}\otimes \nu g_{7/2}$ rotational structures to the ground state has been elucidated. Spin and parity values have been assigned to most of the newly observed states, as well as to the bandheads of the rotational bands. Two isomeric states were identified and placed in the level scheme, with the characteristics $J^{\pi }=5^{+},E_x=214.0$ keV, $T_{1/2}=0.76\left(9\right)$ $\mu$s and $J^{\pi }=6^{+},E_x=319.1$ keV, $T_{1/2}=33\left(1\right)$ ns. The magnetic and quadrupole interactions of the $6^{+}$ isomeric state have been investigated by the time-differential perturbed $\gamma$-ray angular distribution method. The $g$ factor value, $g\left(6^{+}\right)=+0.48\left(3\right)$, and the quadrupole coupling constant in polycrystalline metallic Sn lattice, ${\nu }_Q\left(6^{+}\right)=37\left(4\right)$ MHz, have been derived. The experimental data are compared with the predictions of two-quasiparticles plus rotor model calculations.

Figure 1

Partial level scheme of ${}^{130}\mathrm{La}$ from the present work. Arrow widths are proportional to transition intensities, while unfilled regions show the extent of internal conversion. The arrows with energy labels in parentheses indicate unobserved tentative transitions.

Figure 2

Coincidence spectra from the symmetric $E_{\gamma }\text{−}{E}_{\gamma }$ matrix. The $\gamma$ rays in ${}^{130}\mathrm{La}$ are labeled by the energy. Peaks marked with full triangles and full circles belong to bands 1 and 2, respectively. The inset evidences the presence of the weak 116.9 keV transition in coincidence with the 118.0 keV $\gamma$ ray.

Figure 3

Spectra registered by the planar detectors, obtained from the $E_{\gamma }^{\mathrm{planar}}\text{−}{E}_{\gamma }^{\mathrm{total}}$ matrix, showing the coincidence relations between selected transitions in the decay-out of band 1 and the low-energy transitions of 42.3, 45.8, and 72.4 keV.

Figure 4

Spectra registered by the planar detectors showing prompt-delayed $\gamma \text{−}\gamma$ coincidences in ${}^{130}\mathrm{La}$. (a) Delayed $\gamma$ rays in coincidence with the prompt 113.7-keV transition. (b) Delayed $\gamma$ rays in coincidence with the prompt 72.4-keV transition. (c) Prompt $\gamma$ rays in coincidence with the delayed 103.6 keV transition.

Figure 5

Time spectra of the 105.1- and 82.5-keV $\gamma$ rays de-exciting the state at excitation energy of 319.1 keV, obtained by gating on the sum of 72, 118, and 137 keV transitions.

Figure 6

Delayed $\gamma$ spectra corresponding to two successive time intervals after the ${}^{16}\mathrm{O}$ beam pulse, obtained using the thick tin target. The delayed transitions in ${}^{130}\mathrm{La}$ are marked by energies. Transitions deexciting other short lived isomers are indicated by the corresponding nuclei. The $\gamma$ lines coming from long-lived activities are marked with a star.

Figure 7

Experimental time spectra for the 105.1- and 103.6-keV $\gamma$ rays and least-squares fits.

Figure 8

Experimental modulation ratio for the 105.1-keV $\gamma$ ray deexciting the $6^{+}$ isomer in ${}^{130}\mathrm{La}$ in external magnetic field and the least-squares fit.

Figure 9

Experimental TDPAD spectrum showing the quadrupole interaction of the $6^{+}$ isomer in polycrystalline metallic Sn lattice and least-squares fit.

Figure 10

Experimental partial level scheme of ${}^{130}\mathrm{La}$ (from Ref. [19] and present work) compared to two-quasiparticles plus rotor model calculations performed at deformation parameters ${\epsilon }_2=0.20$ and ${\epsilon }_4=0.02.$ The valence proton and neutron configurations used in the calculations are shown in the figure. The proton and neutron located in the positive-parity orbitals of the $N=4$ shell are denoted with $\pi +$ and $\nu +$, respectively. Calculations were performed for $\xi =1$ and without $p\text{−}n$ residual interaction.

Figure 11

Experimental yrast positive-parity band of ${}^{130}\mathrm{La}$ (from Ref. [19] and present work) compared to two-quasiparticles plus rotor model calculations performed without (a) and with (b) $p\text{−}n$ residual interaction. The excitation energies are relative to that of the $9^{+}$ bandhead. Calculations were performed for $\xi =1$.

Figure 12

Experimental low-lying positive-parity states of ${}^{130}\mathrm{La}$ (from Ref. [19] and present work) compared to two-quasiparticles plus rotor model calculations performed without [(a) and (b)] and with (c) $p\text{−}n$ residual interaction. The values of the attenuation of the Coriolis matrix elements $\xi$ used in the calculations are shown in the figure.