Stabilization of octupole deformation with angular-momentum increase in the alternating-parity bands

Background: Low-lying octupole collective excitations play an important role in describing the structure of nuclei in different regions of the nuclide chart. Ground state alternating-parity rotational bands combining both positive- and negative-parity states are known in several nuclei. The experimental data indicate that octupole deformation becomes stable with increase of the angular momentum.

Purpose: We introduce a nondimensional characteristic of the spectra of the ground state alternating-parity bands and apply it to investigation of a stabilization of the octupole deformation with increase of the angular momentum.

Method: We analyze the experimental data on the energies of the states belonging to the alternating-parity bands based on the ratio of the interpolated and the experimental energies of the negative-parity states. Interpolated energies are determined by the experimental energies of the neighboring positive-parity states assuming smooth dependence on the angular momentum.

Results: The values of the ratio of the interpolated and the experimental energies of the negative-parity states belonging to the ground state alternating-parity bands of ${}^{144,146}\text{Ba}$ and some rare-earth and actinide nuclei are evaluated.

Conclusion: It is shown that the angular-momentum dependence of the ratio of the interpolated and the experimental energies of the negative-parity states belonging to the ground state alternating-parity bands of ${}^{144,146}\text{Ba}$ and some rare-earth and actinide nuclei indicates stabilization of the octupole deformation with angular-momentum increase.

Figure 1

The values of $R_{\mathrm{oct}}$ as a function of the angular momentum $I$ derived from experimental data by means of Eqs. (1), (3), and (8). The solid line corresponds to ${}^{144}\text{Ba}(R_{4/2}=2.66)$. The dashed line corresponds to ${}^{146}\text{Ba}(R_{4/2}=2.84)$.

Figure 2

The values of $R_{\mathrm{oct}}$ as a function of the angular momentum $I$ derived from experimental data by means of Eqs. (1), (3), and (8). The solid line corresponds to ${}^{150}\text{Sm}(R_{4/2}=2.32)$. The dotted line corresponds to ${}^{152}\text{Sm}(R_{4/2}=3.01)$. The dashed line corresponds to ${}^{152}\text{Gd}(R_{4/2}=2.19)$. The dash-dotted line corresponds to ${}^{156}\text{Gd}(R_{4/2}=3.24)$.

Figure 3

The values of $R_{\mathrm{oct}}$ as a function of the angular momentum $I$ derived from experimental data by means of Eqs. (1), (3), and (8). The solid line corresponds to ${}^{218}\text{Ra}(R_{4/2}=1.91)$. The dashed line corresponds to ${}^{220}\text{Ra}(R_{4/2}=2.30)$. The dash-dot-dot line corresponds to ${}^{222}\text{Ra}(R_{4/2}=3.13)$. The dash-dotted line corresponds to ${}^{224}\text{Ra}(R_{4/2}=2.97)$. The dotted line corresponds to ${}^{226}\text{Ra}(R_{4/2}=2.71)$.

Figure 4

The values of $R_{\mathrm{oct}}$ as a function of the angular momentum $I$ derived from experimental data by means of Eqs. (1), (3), and (8). The solid line corresponds to ${}^{224}\text{Th}(R_{4/2}=2.90)$. The dashed line corresponds to ${}^{226}\text{Th}(R_{4/2}=3.14)$. The dotted line corresponds to ${}^{228}\text{Th}(R_{4/2}=3.23)$. The dash-dotted line corresponds to ${}^{230}\text{Th}(R_{4/2}=3.27)$. The dash-dot-dot line corresponds to ${}^{232}\text{Th}(R_{4/2}=3.28)$.

Figure 5

The values of $R_{\mathrm{oct}}$ as a function of the angular momentum $I$ derived from experimental data by means of Eqs. (1), (3), and (8). The dashed line corresponds to ${}^{144}\text{Ba}(R_{4/2}=2.66)$. The dotted line corresponds to ${}^{152}\text{Gd}(R_{4/2}=2.19)$. The solid line corresponds to ${}^{220}\text{Ra}(R_{4/2}=2.30)$. The dash-dotted line corresponds to ${}^{232}\text{Th}(R_{4/2}=3.28)$. The dash-dot-dot line corresponds to ${}^{238}\text{U}(R_{4/2}=3.30)$. The short-dashed line corresponds to ${}^{240}\mathrm{Pu}(R_{4/2}=3.31)$.

Figure 6

The values of $R_{\mathrm{oct}}$ for ${}^{222}\text{Ra}$ as a function of the angular momentum $I$ derived from experimental data by means of Eqs. (1), (3), and (8) (solid line). The dashed line corresponds to the vibrational limit for ${}^{222}\text{Ra}(R_{4/2}=2.71)$ determined according to (13). The dash-dotted line corresponds to the limit of the rigid octupole deformation with the parity splitting equal to zero.

Figure 7

The values of $R_{\mathrm{oct}}$ for ${}^{156}\text{Gd}$ as a function of the angular momentum $I$ derived from experimental data by means of Eqs. (1), (3), and (8) (solid line). The dashed line corresponds to the vibrational limit for ${}^{156}\text{Gd}(R_{4/2}=3.24)$ determined according to (13). The dash-dotted line corresponds to the limit of the rigid octupole deformation with the parity splitting equal to zero.