Enhanced $B\left(E3\right)$ strength observed in ${}^{137}\mathrm{La}$

The ${}^{137}\mathrm{La}$ nucleus was populated by the reaction ${}^{130}\mathrm{Te}({}^{11}\mathrm{B}, 4n$) at 40-MeV beam energy and the lifetime of the $11/2^{-}$ state at $1004.6\mathrm{keV}$ was measured using a hybrid array of HPGe clover and ${\mathrm{LaBr}}_3$(Ce) detectors by electronic fast-timing technique, providing the value $T_{1/2}=263\pm 12\mathrm{ps}$. The reduced transition probability $B\left(E3\right)=23.3\pm 2.4\mathrm{W}.\mathrm{u}.$ is found to be significantly larger compared to the values observed in lighter odd-$A$ La isotopes. The experimentally determined $B\left(E3\right)$ value is compared with theoretical calculations of random-phase approximation which explains the enhanced transition probability to be arising from higher contribution of the $g_{9/2}$ orbital to the proton transition density.

Figure 1

Partial level scheme of ${}^{137}\mathrm{La}$ relevant for this work. Numbers on the left of each level show the excitation energy in keV. Numbers in each arrow are the transition energy in keV and the thickness of the arrows are proportional to intensities. The transition energies shown in the level scheme have been rounded to the nearest whole numbers. Red line 87.2-, $169.4$-, 993.7-, and $1004.6\text{−}\mathrm{keV}\gamma$ rays have been used for evaluating branching ratio of 993.7-keV transition.

Figure 2

${\mathrm{LaBr}}_3$(Ce) energy spectrum obtained by gating on the 825-keV transition in the HPGe clover detectors.

Figure 3

Time difference spectrum (fitted with exponential convoluted by Gaussian function as represented by red color solid line) was depicted between ${\mathrm{LaBr}}_3$(Ce) detectors with $\gamma$ gated on HPGe, while $169.4\mathrm{keV}$ at start, and $782\mathrm{keV}$ at stop in ${\mathrm{LaBr}}_3$(Ce), showing $T_{1/2}=263\pm 12\mathrm{ps}$ for 1004.6-keV energy level. The prompt curve (fitted with Gaussian function as represented by blue color dashed line) having $\mathrm{FWHM}=985\pm 23\mathrm{ps}$ was generated with start at $94\mathrm{keV}$ and stop at $455\mathrm{keV}$ (not shown in Fig. 1) from ${}^{137}\mathrm{La}$ nucleus.

Figure 4

Variation of experimental $B\left(E3\right)$ strengths in Ba and La isotopes. The RPA results have been compared with the experimental data. The experimental $B(E3;11/2^{-}\to 5/2^{+})$ of ${}^{129,133}\mathrm{La}$ isotopes from Ref. [15] and $B(E3;3^{-}\to 0^{+})$ of ${}^{132,134,136,138}\mathrm{Ba}$ isotopes have been adopted from Ref. [11]. The $B(E3;11/2^{-}\to 5/2^{+})$ of ${}^{137}\mathrm{La}$ is from present work. The experimental and theoretical values are overlapping for the ${}^{133}\mathrm{La}$ isotope.

Figure 5

Proton and neutron transition densities ($r^2\delta {\rho }_{L=3}$) decomposed to hole states. The gray solid line, cyan dashed double-dotted line, amber long-dashed line, red dashed line, green dotted line, and blue solid line are for $h_{11/2}, d_{3/2}, s_{1/2}, d_{5/2}, g_{7/2}$, and $g_{9/2}$, respectively.