Macroscopic and microscopic description of low-energy collective states in ${}^{86,88}\mathrm{Se}$

Algebraic collective model (ACM) calculations for the even-even selenium isotopes ${}^{86,88}\mathrm{Se}$ have been performed to describe collective properties of these two transitional nuclei with only two and four valence neutrons, respectively. From the perspective of the ACM the nuclei turn out to be only weakly deformed, described by a very $\gamma$-soft potential. This is confirmed by Skyrme and Gogny energy density functional calculations. Additionally, the fully microscopic symmetry conserving configuration mixing method with the Gogny interaction has been applied to the study of these isotopes. The results show the transitional character of ${}^{86}\mathrm{Se}$ and the relevant role of the triaxial degree of freedom in the structure of these nuclei.

Figure 1

Analytical benchmarks in the Casten triangle.

Figure 2

Experimental energies of the $2_1^{+}$ states and the energy ratios $E\left(4_1^{+}\right)/E\left(2_1^{+}\right)$, $E\left(2_2^{+}\right)/E\left(2_1^{+}\right)$ for Ge, Se, Kr, and Sr isotopes.

Figure 3

Experimental spectra of ${}^{84}\mathrm{Ge}$, ${}^{86,88}\mathrm{Se}$, and ${}^{90,92}\mathrm{Kr}$.

Figure 4

E(5) spectrum and its ACM counterpart. The $\mathrm{B}\left(E2\right)$ transition rates are shown as percentages of that for the $2_1^{+}\to 0_1^{+}$ transition.

Figure 5

Experimental spectrum of ${}^{86}\mathrm{Se}$ (Grachev 2017 [5]) and its ACM counterpart. The $B\left(E2\right)$ transition rates are shown as percentages of that for the $2_1^{+}\to 0_1^{+}$ transition.

Figure 6

Experimental spectrum of ${}^{88}\mathrm{Se}$ (Grachev 2017 [5]) as compared with different ACM spectra obtained with the parameters $\alpha =0.55$, 0.60, 0.65, and 0.70. The $B\left(E2\right)$ transition rates are shown as percentages of that for the $2_1^{+}\to 0_1^{+}$ transition.

Figure 7

ACM energies of the $2_2^{+}$ ($4_1^{+}$) and $3_1^{+}$ ($4_2^{+}$) states as a function of the parameter $\alpha$

Figure 8

PEC as a function of ${\beta }_2$ for ${}^{86}\mathrm{Se}$. The calculated SHF potential energies $E$ and energy differences $\mathrm{\Delta }E$ between the oblate and prolate minima and the barrier heights are listed in the frame.

Figure 9

PEC as a function of ${\beta }_2$ for ${}^{88}\mathrm{Se}$. $E$ and $\mathrm{\Delta }E$ are the same quantities as in Fig. 8.

Figure 10

PECs as functions of ${\beta }_2$ for the chain of isotopes ${}^{84–92}\mathrm{Se}$ for two SHF parametrizations, SVbas (a) and sym34 (b).

Figure 11

Triaxiality, oblate and prolate PEC minima, and corresponding deformations ${\beta }_2$ for two SHF parametrizations for isotopes of Se.

Figure 12

Calculated energies of the first $2^{+}$ states for two SHF parametrizations for isotopes of Se.

Figure 13

Particle-number projected energy surfaces obtained with the Gogny D1S interaction in the $({\beta }_2,\gamma )$ plane for (a) ${}^{86}\mathrm{Se}$ and (b) ${}^{88}\mathrm{Se}$ isotopes.

Figure 14

Excitation energies computed with the SCCM method with the Gogny D1S interaction for (a) ${}^{86}\mathrm{Se}$ and (b) ${}^{88}\mathrm{Se}$ isotopes. Experimental values are also shown.

Figure 15

Collective wave functions calculated for ${}^{86}\mathrm{Se}$. The colors of the boxes correspond to the colors of the bands shown in Fig. 14.

Figure 16

Same as Fig. 15 but for ${}^{88}\mathrm{Se}$.