Gamow-Teller response and its spreading mechanism in doubly magic nuclei

The scope of the paper is to apply a state-of-the-art beyond mean-field model to the description of the Gamow-Teller response in atomic nuclei. This topic recently attracted considerable renewed interest, due, in particular, to the possibility of performing experiments in unstable nuclei. We study the cases of ${}^{48}\mathrm{Ca},{}^{78}\mathrm{Ni},{}^{132}\mathrm{Sn}$, and ${}^{208}\mathrm{Pb}$. Our model is based on a fully self-consistent Skyrme Hartree-Fock plus random phase approximation. The same Skyrme interaction is used to calculate the coupling between particles and vibrations, which leads to the mixing of the Gamow-Teller resonance with a set of doorway states and to its fragmentation. We compare our results with available experimental data. The microscopic coupling mechanism is also discussed in some detail.

Figure 1

Diagrammatic representation of the four terms whose sum gives the matrix element $W_{ph,p^{\prime }{h}^{\prime }}^{\downarrow }$. The analytic expressions are shown in Eq. (8).

Figure 2

Gamow-Teller resonance peak energy [panel (a)] and FWHM [panel (b)] in ${}^{208}\mathrm{Pb}$, calculated within HF (squares), RPA (triangles), and RPA+PVC (circles) approaches with the Skyrme interactions SkI3, SkM*, SAMi, and SGII. For convenience, they are shown as a function of the Landau parameter $g_0^{\prime }$ associated with each force. The unperturbed HF energy $E_{\mathrm{unper}}$ is the weighted average of the two main configurations $\nu i_{13/2}\to \pi i_{11/2}$ and $\nu h_{11/2}\to \pi h_{9/2}$. The experimental peak energy and width are shown by the black straight lines.

Figure 3

Gamow-Teller strength distributions [panels (a), (d), and (g)], their cumulative sums [panels (b), (e), and (h)] and scaled cumulative sums [panels (c), (f), and (i)], calculated with the Skyrme interactions SAMi (first column) and SGII (second and third columns) for the nucleus ${}^{208}\mathrm{Pb}$. The red-dotted lines and blue-dashed lines denote the results of RPA and RPA+PVC model, respectively. The smearing parameter $\Delta$ in the calculations is assumed either of the order of the experimental energy resolution ($\Delta =1.0$ MeV, first and second columns), or smaller ($\Delta =0.2$ MeV, third column). The experimental data [39] are displayed by black dots and black solid lines.

Figure 4

The same as Fig. 3, in the case of the nucleus ${}^{48}\mathrm{Ca}$ and the interaction SGII. The experimental data are taken from Ref. [44].

Figure 5

Gamow-Teller strength distributions [panels (a) and (c)] with their cumulative sums [panels (b) and (d)] calculated with the Skyrme interaction SGII for the nucleus ${}^{132}\mathrm{Sn}$. The red dotted lines and black solid lines denote the results of the RPA and RPA+PVC models, respectively. The smearing parameter $\Delta$ in the calculations takes either a small value $\Delta =0.2$ MeV (first column) or a large one $\Delta =1.0$ MeV (second column).

Figure 6

The same as Fig. 5 in the case of the nucleus ${}^{78}\mathrm{Ni}$.

Figure 7

The imaginary part multiplied by $-2$ [panel (a)] and the real part [panel (b)] of the self-energy of the main RPA state for the nucleus ${}^{48}\mathrm{Ca}$, calculated by the interaction SGII with a smearing parameter $\Delta =0.2$ MeV. In addition to the total results, the contributions from phonons with different multipolarities are shown separately. The vertical short-dotted olive line represents the energy position $E_{\mathrm{RPA}}$ of the GTR peak calculated in the RPA approach, while the dashed line in panel (b) represents the function $y=E-E_{\mathrm{RPA}}$.

Figure 8

Proton and neutron single-particle spectrum in ${}^{48}\mathrm{Ca}$ obtained from the HF calculation with SGII interaction.

Figure 9

The same as Fig. 7 in the case of the nucleus ${}^{208}\mathrm{Pb}$.

Figure 10

Proton and neutron single-particle spectrum in ${}^{208}\mathrm{Pb}$ obtained from the HF calculation with the SGII interaction.