High-spin states in ${}^{136}\mathrm{La}$ and possible structure change in the $N=79$ region

High-spin states in the odd-odd nucleus ${}^{136}\mathrm{La}$, which is located close to the $\beta$-stability line, have been investigated in the radioactive-beam-induced fusion-evaporation reaction ${}^{124}\mathrm{Sn}({}^{17}\mathrm{N},5n)$. The use of the radioactive beam enabled a highly sensitive and successful search for a new isomer [${14}^{+},T_{1/2}=187\left(27\right)$ ns] in ${}^{136}\mathrm{La}$. In the $A=130$–140 mass region, no such long-lived isomer has been observed at high spin in odd-odd nuclei. The ${}^{136}\mathrm{La}$ level scheme was revised, incorporating the ${14}^{+}$ isomer and six new levels. The results were compared with pair-truncated shell model (PTSM) calculations which successfully explain the level structure of the $\pi h_{11/2}\otimes \nu h_{11/2}^{-1}$ bands in ${}^{132}\mathrm{La}$ and ${}^{134}\mathrm{La}$. The isomerism of the ${14}^{+}$ state was investigated also by a collective model, the cranked Nilsson-Strutinsky (CNS) model, which explains various high-spin structures in the medium-heavy mass region. It is suggested that a new type of collective structure is induced in the PTSM model by the increase of the number of $\pi g_{7/2}$ pairs, and/or in the CNS model by the configuration change associated with the shape change in ${}^{136}\mathrm{La}$.

Figure 1

Partial level schemes of ${}^{136}\mathrm{La}$ proposed by (a) Ref. [6], (b) Ref. [7], and (c) Ref. [8]. The levels above the $\pi h_{11/2}\otimes \nu h_{11/2}^{-1}$ band head are displayed.

Figure 2

Estimated relative population distributions in a spin vs. excitation-energy plane for (a) ${}^{130}\mathrm{Te}\left({}^{11}\mathrm{B},5n\right){}^{136}\mathrm{La}$ at $4.7\mathrm{MeV}$/u, as in the previous work [8], and (b) ${}^{124}\mathrm{Sn}({}^{17}{\mathrm{N},5n)}^{136}\mathrm{La}$ at $5.2\mathrm{MeV}$/u, as in the present work.

Figure 3

Schematic layout of the secondary beam-line at RCNP [13, 14]. The dipole, quadrupole, and sextupole magnets are denoted by D, Q, and SX, respectively. The beam swinger magnet (SW) makes the primary beam tilted at the production target F0. The reaction products are angular-focused at the dispersive focal plane F1 and achromatic-focused at F2, where the beam-particle detector (PPAC) and the Ge array are placed.

Figure 4

Total $\gamma \text{−}\gamma$ projection spectrum with the time window of $\pm 800$ ns. The peaks labeled with closed circles and asterisks are originated from the known $\gamma$ rays associated with ${}^{135}\mathrm{La}$ and ${}^{136}\mathrm{La}$, respectively. The numbers are the $\gamma$-ray energies in keV.

Figure 5

Schematic two dimensional matrix of (energy of prompt $\gamma$ ray) vs. (energy of delayed $\gamma$ ray), i.e., $E_{\mathrm{prompt}\text{−}\gamma }-E_{\mathrm{delayed}\text{−}\gamma }$ matrix, assuming an illustrative level scheme in the inset, and projection spectra. The time gates for the prompt and delayed coincidence are schematically shown in the inset.

Figure 6

Sum of coincidence spectra gated by the intense 156-, 281-, 407-, and 425-keV $\gamma$ rays with a time window of $\pm 800$ ns.

Figure 7

Time difference spectra between the beam (PPAC) and the $\gamma$ rays gated by (a) 281-keV and (b) 618-keV $\gamma$ rays.

Figure 8

Sum of coincidence spectra gated by the 156-, 281-, 407-, 425-, and 585-keV $\gamma$ rays (a) with coincidence between the delayed-$\gamma$ components and the delayed-$\gamma$ components, (b) with coincidence between the delayed-$\gamma$ and the prompt-$\gamma$ components. The $\gamma$-ray peaks labeled with asterisks are newly found in the present work.

Figure 9

Time spectrum of the newly found isomer at $\widetilde{E_x}$ = 2.261 MeV in ${}^{136}\mathrm{La}$. The solid line is the result of least-square fitting with an exponential function.

Figure 10

Partial level scheme of ${}^{136}\mathrm{La}$ established in the present work. The excitation energy is shown in the reduced form of $\widetilde{E_x}$, in which the excitation energy is scaled from that of the 114 ms isomer. The transitions and levels associated with asterisks were observed for the first time and are newly proposed, respectively. Tentative transitions and levels are displayed with dashed arrows and lines, respectively. The arrows denoting the $\gamma$ transitions schematically illustrate the intensities of the observed $\gamma$ transitions (black) and of the calculated internal conversion (white).

Figure 11

Comparison of the experimental level energies of the $\pi h_{11/2}\otimes \nu h_{11/2}^{-1}$ bands in La isotopes. The level energy is plotted relative to the $9^{+}$ band head.

Figure 12

Comparison of the experimental level energies of the $\pi h_{11/2}\otimes \nu h_{11/2}^{-1}$ bands in the $N=79$ isotones, ${}^{134}\mathrm{Cs},{}^{136}\mathrm{La},{}^{138}\mathrm{Pr}$, and ${}^{140}\mathrm{Pm}$. The level energy is plotted relative to the $9^{+}$ band head.

Figure 13

Comparison of the level energies in ${}^{136}\mathrm{La}$ between the experimental results and the PTSM predictions. The level energies are rescaled with respect to the $9^{+}$ state.

Figure 14

Comparison of the kinematic moment of inertia ${\mathcal{J}}^{\left(1\right)}$ in ${}^{136}\mathrm{La}$ between the experimental results (square) and the PTSM predictions (diamond), together with the experimental values of ${}^{134}\mathrm{La}$ (closed circle, data from Ref. [18]).