Microscopic description of hexadecapole collectivity in even-even rare-earth nuclei near $N=90$

We present an extensive study of hexadecapole correlations in the rare-earth region near $N=90$ and the effects these correlations have on various nuclear properties, such as the low-energy spectra, as well as quadrupole, hexadecapole, and monopole transition strengths. In order to examine hexadecapole correlations, we employ a mapped $sdg$ interacting boson model, with parameters derived from a self-consistent mean-field calculations with a relativistic energy density functional. We apply this model to even-even isotopes of Nd, Sm, Gd, Dy, and Er ($Z=60–68$) with neutron numbers $N=84–96$. The obtained results show a good agreement with the experiment. By comparing the results with the ones obtained from a simpler mapped $sd$ interacting boson model, we show that the inclusion of the hexadecapole degree of freedom via the $g$ boson is necessary to improve the results of the $J^{\pi }\ge 6^{+}$ yrast energies in the nuclei with $N=84$ and 86, being near the neutron shell closure. The $sdg$ interacting boson model increases the quadrupole transition strengths between yrast states in the $N=90$ and 92 well deformed nuclei, which is in good agreement with the experiment for most of those isotopes. The presence of $g$ bosons does have an important effect on hexadecapole transition strengths, although experimental data for such transitions are limited. The obtained monopole transition strengths do not differ significantly from the ones obtained from the simpler $sd$ model.

Figure 1

Axially symmetric quadrupole (${\beta }_{20}$) and hexadecapole (${\beta }_{40}$) constrained energy surfaces for the ${}^{144–154}\mathrm{Nd}$ isotopes calculated within the relativistic Hartree-Bogoliubov method using the DD-PC1 energy density functional and the pairing force of finite range. Energy difference between neighboring contours is 0.3 MeV, and the absolute minimum is indicated by an open triangle.

Figure 2

Same as the caption for Fig. 1, but for ${}^{146–156}\mathrm{Sm}$.

Figure 3

Same as the caption for Fig. 1, but for ${}^{148–158}\mathrm{Gd}$.

Figure 4

Same as the caption for Fig. 1, but for ${}^{150–160}\mathrm{Dy}$.

Figure 5

Same as the caption for Fig. 1, but for ${}^{152–162}\mathrm{Er}$.

Figure 6

Same as the caption for Fig. 1, but for the mapped $sdg$-IBM energy surfaces of ${}^{144–154}\mathrm{Nd}$.

Figure 7

Same as the caption for Fig. 1, but for the mapped $sdg$-IBM energy surfaces of ${}^{146–156}\mathrm{Sm}$.

Figure 8

Same as the caption for Fig. 1, but for the mapped $sdg$-IBM energy surfaces of ${}^{148–158}\mathrm{Gd}$.

Figure 9

Same as the caption for Fig. 1, but for the mapped $sdg$-IBM energy surfaces of ${}^{150–160}\mathrm{Dy}$.

Figure 10

Same as the caption for Fig. 1, but for the mapped $sdg$-IBM energy surfaces of ${}^{152–162}\mathrm{Er}$.

Figure 11

Parameters of the $sdg$-IBM Hamiltonian (5) as functions of the boson number $N_B$.

Figure 12

Parameters of the $sd$-IBM Hamiltonian (10) as functions of the boson number $N_B$.

Figure 13

Calculated excitation energies of the yrast band states up to spin $J^{\pi }={14}^{+}$ as functions of the neutron number $N$ within the mapped $sdg$-IBM (left column) and $sd$-IBM (right column), represented by solid symbols connected by solid lines. Experimental data are taken from Ref. [38], and are depicted as open symbols connected by dotted lines.

Figure 14

Same as Fig. 13, but for the $0_2^{+}, 2_3^{+}$, and $4_3^{+}$ states.

Figure 15

Same as Fig. 13, but for the $2_2^{+}, 3_1^{+}$, and $4_2^{+}$ states.

Figure 16

$B\left(E2\right)$ transition strengths in the ground state band of the well-deformed $N=90$ (left) and $N=92$ (right) nuclei as functions of spin $J$, calculated with the mapped $sdg$-IBM (solid curves) and $sd$-IBM (dotted curves). The experimental data, represented by solid circles, are adopted from Ref. [38].

Figure 17

$B\left(E4\right)$ strengths in W.u. for the transitions of the first [panels (a) and (b)], second [panels (c) and (d)], third [panels (e) and (f)], and fourth [panels (g) and (h)] $4^{+}$ states to the $0_1^{+}$ ground state as functions of the mass number $A$, calculated with the mapped $sdg$-IBM (left column) and $sd$-IBM (right column). Experimental data are taken from Refs. [25, 26, 27, 38], and are indicated by solid circles in the plots.

Figure 18

${\rho }^2(E0;0_i^{+}\to 0_j^{+})$ values as functions of the neutron number $N$ for Sm and Gd isotopes, calculated with the mapped $sdg$-IBM (left column) and $sd$-IBM (right column). Experimental values are adopted from Refs. [38, 44], and are plotted as solid circles.