Multiphonon $\gamma$-vibrational bands in the $\gamma$-soft nucleus ${}^{138}$Nd

The low spin states of ${}^{138}$Nd have been reinvestigated via the ${}^{124}$Te(${}^{19}$F,$4n1p$) reaction at a beam energy of 103 MeV. The quasi-one-phonon $\gamma$-vibrational band based on the 1013.7 keV level has been expanded and the quasi-two-phonon $\gamma$-vibrational band built on the 1842.7 keV level has been proposed. A systematic comparison supports our assignments for multiphonon $\gamma$-vibrational bands in ${}^{138}$Nd. The characteristics of $\gamma$ softness in ${}^{138}$Nd have been discussed. Triaxial projected shell model calculations can well describe the rotational feature of the bands, but they fail to reproduce simultaneously the bandhead energies of the two $\gamma$-vibrational bands if a fixed triaxial deformation is assumed.

Figure 1

Partial level scheme of ${}^{138}$Nd deduced from the present work. The $*$ denotes $\gamma$ transitions reported for the first time here by an in-beam experiment (compare, e.g., to Refs. [14, 15]).

Figure 2

Portion of $\gamma$-ray spectrum obtained by gating on 520.7 keV $\gamma$ transition in ${}^{138}$Nd. The energy intervals of $\gamma$ peaks are (a) from 430 to 895 keV and (b) from 920 to 1720 keV. (The peaks marked with $*$ are the transitions at high spins that have been reported in Ref. [14]).

Figure 3

Portion of $\gamma$-ray spectra obtained by (a) summing gating on 493.0, 930.2, and 437.2 keV $\gamma$ transitions, (b) summing gating on 278.6 and 440.1 keV $\gamma$ transitions, and (c) gating on 1278.9 keV $\gamma$ transition in ${}^{138}$Nd.

Figure 4

Empirical values of the $E_S/E\left(2_1^{+}\right)$ in some even-even isotopes of Ba, Ce, and Nd.

Figure 5

Comparison of experimental and the calculated band structures for ${}^{138}$Nd.

Figure 6

Calculated bandhead energies of the ground, 1$\gamma$, and 2$\gamma$ bands as functions of triaxiality ${\varepsilon }^{\prime }$.