Structure of the low-lying positive-parity states in ${}^{154}\mathrm{Sm}$

The proton-neutron symplectic model with Sp(12,$R$) dynamical algebra is applied to the simultaneous description of the microscopic structure of the low-lying states of the lowest ground, $\beta$, and $\gamma$ bands in ${}^{154}\mathrm{Sm}$. For this purpose, the model Hamiltonian is diagonalized in a U(6)-coupled basis, restricted to the state space spanned by the fully symmetric U(6) irreps. A good description of the energy levels of the three bands under consideration as well as the intraband $B\left(E2\right)$ transition strengths between the states of the ground band is obtained without the use of an effective charge. The microscopic structure of low-lying collective states in ${}^{154}\mathrm{Sm}$ shows that there are no admixtures from the higher shells and hence shows the presence of a very good U(6) dynamical symmetry. It is also shown that, in contrast to the Sp(6,$R$) case, the lowest excited bands, e.g., the $\beta$ and $\gamma$ bands, naturally appear together with the ground band within a single Sp(12,$R$) irreducible representation. The obtained results is given a simple geometrical multiphonon interpretation, based on the algebraic realization of the coupled two-rotor picture, which in turn suggests an interpretation of the low-lying excited bands as relative proton-neutron excitations of the two-component nuclear system, governed by the $Q_p·Q_n$ interaction.

Figure 1

Comparison of the theoretical [within the space of stretched SU(3) states] and experimental energy levels for the ground, $\beta$, and $\gamma$ bands in ${}^{154}\mathrm{Sm}$.

Figure 2

Calculated [within the space of stretched SU(3) states] and experimental intraband $B\left(E2\right)$ values between the states of the ground band in ${}^{154}\mathrm{Sm}$. No effective charge is used.

Figure 3

Calculated [within the space of stretched SU(3) states] probability distributions for the SU(3) wave function components $(\lambda +2n,\mu )$ from each $n\hslash \omega$ shell for the $0^{+}$ states of the ground and $\beta$ bands and for the $2^{+}$ state of the $\gamma$ band, as a function of $n$. The starting SU(3) configurations for the ground and $\beta ,\gamma$ bands are (30,0) and (26,0), respectively.

Figure 4

Calculated $B(E2;2_1^{+}\to 0_1^{+})$ transition strength in ${}^{154}\mathrm{Sm}$ as a function of the model parameter $\chi$. No effective charge is used.

Figure 5

Comparison of the theoretical and experimental energy levels for the ground, $\beta$, and $\gamma$ bands in ${}^{154}\mathrm{Sm}$. The values for the model parameters are as follows (in MeV): $\chi =0.0032$, $\xi =0.0053$, and $a=0.013$.

Figure 6

Calculated and experimental intraband $B\left(E2\right)$ values between the states of the ground band in ${}^{154}\mathrm{Sm}$. No effective charge is used. The values for the model parameters are as follows (in MeV): $\chi =0.0032$, $\xi =0.0053$, and $a=0.013$.

Figure 7

Calculated SU(3) probability distributions for the wave functions for the $0^{+}$ states of the ground and $\beta$ bands, and for the $2^{+}$ state of the $\gamma$ band. The values for the model parameters are as follows (in MeV): $\chi =0.0032$, $\xi =0.0053$, and $a=0.013$.