Multi-neutron emission of Cd isotopes

An influence of the phonon-phonon coupling (PPC) on the $\beta$-decay half-lives and multi-neutron emission probabilities is analyzed within the microscopic model based on the Skyrme interaction with tensor components included. The finite-rank separable approximation is used in order to handle large two-quasiparticle spaces. The even-even nuclei near the $r$-process paths at $N=82$ are studied. The characteristics of ground states, $2^{+}$ excitations, and $\beta$-decay strength of the neutron-rich Cd isotopes are treated in detail. It is shown that a strong redistribution of the Gamow-Teller strength due to the PPC is mostly sensitive to the multi-neutron emission probability of the Cd isotopes.

Figure 1

Deformation energy curve as a function of the mass quadrupole deformation. The curves of ${}^{128}\mathrm{Cd}_{}, {}^{130}\mathrm{Cd}_{}$, and ${}^{132}\mathrm{Cd}_{}$ are denoted by the dashed, solid, and dotted lines, respectively.

Figure 2

Calculated $\beta$-decay windows $Q_{\beta }$ of the parent nuclei (squares) and one- (triangles) and two-neutron (circles) separation energies for the daughter nuclei. The upper and lower panels correspond to the even $N=82$ isotones and the even Cd isotopes, respectively. Results of the HF-BCS calculations are denoted by the open symbols. Experimental data (solid symbols) are taken from Ref. [58].

Figure 3

GT strength distributions of ${}^{126–134}\mathrm{Cd}_{}$ as functions of the excitation energy of the daughter nuclei. The QRPA calculations with the tensor interaction and without the tensor interaction are shown as dashed lines and dotted lines, respectively. The solid lines correspond to the quadrupole-phonon coupling effect on the QRPA results obtained with the tensor interaction.

Figure 4

Energies and $B\left(E2\right)$ values for up-transitions to the ${\left[2_1^{+}\right]}_{\text{QRPA}}$ states in the neutron-rich Cd isotopes. Results of the QRPA calculations are denoted by the triangles. Experimental data (diamonds) are taken from Refs. [59, 60, 61].

Figure 5

Same as Fig. 2, but for the neutron-rich $N=82$ isotones. Experimental data (diamonds) are taken from Refs. [59, 62, 63, 64].

Figure 6

The phonon-phonon coupling effect on the $\beta$-transition rates in ${}^{130}\mathrm{Cd}_{}$ (top) and ${}^{132}\mathrm{Cd}_{}$ (bottom). The left and right panels correspond to the calculations within the QRPA and taking into account the ${[1_i^{+}\otimes 2_{i^{\prime }}^{+}]}_{\text{QRPA}}$ configurations, respectively. The calculated $Q_{\beta 1n}$ and $Q_{\beta 2n}$ energies are denoted by the solid and dashed arrows, respectively.

Figure 7

The phonon-phonon coupling effect on $\beta$-decay half-lives of the neutron-rich $N=82$ isotones. The circles correspond to the half-lives calculated with inclusion of the ${[1_i^{+}\otimes 2_{i^{\prime }}^{+}]}_{\text{QRPA}}$ configurations; the triangles are the QRPA calculations. Experimental data (diamonds) are from Refs. [28, 67].

Figure 8

The phonon-phonon coupling effect on $\beta$-delayed neutron-emission probabilities of the neutron-rich Cd isotopes. The circles correspond to the probabilities calculated with inclusion of the ${[1_i^{+}\otimes 2_{i^{\prime }}^{+}]}_{\text{QRPA}}$ configurations; the triangles are the QRPA calculations.