Structure of krypton isotopes within the interacting boson model derived from the Gogny energy density functional

The evolution and coexistence of the nuclear shapes as well as the corresponding low-lying collective states and electromagnetic transition rates are investigated along the krypton isotopic chain within the framework of the interacting boson model (IBM). The IBM Hamiltonian is determined through mean-field calculations based on the several parametrizations of the Gogny energy density functional and the relativistic mean-field Lagrangian. The mean-field energy surfaces, as functions of the axial $\beta$ and triaxial $\gamma$ quadrupole deformations, are mapped onto the expectation value of the interacting-boson Hamiltonian that explicitly includes the particle-hole excitations. The resulting boson Hamiltonian is then used to compute low-energy excitation spectra as well as $E2$ and $E0$ transition probabilities for ${}^{70–100}\mathrm{Kr}$. Our results point to a number of examples of prolate-oblate shape transitions and coexistence both on the neutron-deficient and neutron-rich sides. A reasonable agreement with the available experimental data is obtained for the considered nuclear properties.

Figure 1

SCMF $(\beta ,\gamma )$-deformation energy surfaces for the ${}^{70–100}\mathrm{Kr}$ nuclei, obtained with the Gogny-D1M EDF. The energy difference between neighboring contours is 100 keV.

Figure 2

The same as in Fig. 1, but for ${}^{74}\mathrm{Kr}, {}^{76}\mathrm{Kr}, {}^{96}\mathrm{Kr}$, and ${}^{98}\mathrm{Kr}$, computed with the DD-PC1 EDF.

Figure 3

The same as in Fig. 1, but for the mapped IBM energy surfaces.

Figure 4

Derived IBM parameters for the $\left[n_b\right], [n_b+2]$, and $[n_b+4]$ configurations as functions of the neutron number.

Figure 5

Experimental [12, 13, 14, 15, 53] and computed excitation spectra for the $2_1^{+}, 4_1^{+}, 0_2^{+}$, and $2_2^{+}$ states in ${}^{70–100}\mathrm{Kr}$ as functions of $N$. The theoretical results are obtained with the Gogny-D1M and relativistic DD-PC1 EDFs.

Figure 6

The experimental [4, 53, 55] and theoretical $B(E2;2_1^{+}\to 0_1^{+})$ (a), $B(E2;4_1^{+}\to 2_1^{+})$ (b), $B(E2;0_2^{+}\to 2_1^{+})$ (c), and $B(E2;2_2^{+}\to 2_1^{+})$ (d) transition strengths (in Weisskopf units), and ${\rho }^2(E0;0_2^{+}\to 0_1^{+})$ values for the ${}^{70–100}\mathrm{Kr}$ nuclei depicted as functions of the neutron number. The theoretical calculations were performed based on the Gogny-D1M and relativistic DD-PC1 EDFs.

Figure 7

The theoretical low-energy excitation spectra and $B\left(E2\right)$ transition strengths (in W.u., indicated by along arrows) of the ${}^{74}\mathrm{Kr}$ and ${}^{76}\mathrm{Kr}$ isotopes obtained from the Gogny-D1M EDF, in comparison to the available experimental data [4, 53].

Figure 8

The same as in Fig. 7, but for ${}^{96}\mathrm{Kr}$ and ${}^{98}\mathrm{Kr}$. The experimental data were taken from Refs. [12, 14, 15].

Figure 9

Comparison of the low-energy excitation spectra obtained for ${}^{76}\mathrm{Kr}$ and ${}^{98}\mathrm{Kr}$ with the Gogny D1S, D1M, and D1N EDFs as well as with the relativistic DD-ME2 and DD-PC1 EDFs. The corresponding experimental spectra are also included in the plot.