Quasiparticle random phase approximation based on the relativistic Hartree-Bogoliubov model. II. Nuclear spin and isospin excitations

The proton-neutron relativistic quasiparticle random-phase approximation (PN-RQRPA) is formulated in the canonical single-nucleon basis of the relativistic Hartree-Bogoliubov model, for an effective Lagrangian characterized by density-dependent meson-nucleon couplings. The model includes both the $T=1$ and $T=0$ pairing channels. Pair configurations formed from the fully or partially occupied states of positive energy in the Fermi sea, and the empty negative-energy states from the Dirac sea, are included in PN-RQRPA configuration space. The model is applied to the analysis of charge-exchange modes: isobaric analog resonances and Gamow-Teller resonances.

Figure 1

PN-RQRPA $J^{\pi }=0^{+}$ strength distributions. The excitations of the isobaric analog resonances are compared with experimental data (thick arrows) for ${}^{48}\mathrm{Ca}$ [37], ${}^{90}\mathrm{Zr}$ [12, 38], and ${}^{208}\mathrm{Pb}$ [39].

Figure 2

RHB plus proton-neutron RQRPA results for the isobaric analog resonances of the sequence of even-even Sn target nuclei. The experimental data are from Ref. 40.

Figure 3

PN-RQRPA $J^{\pi }=0^{+}$ strength distributions for even-even Sn target nuclei with $A=108–118$. For description see text.

Figure 4

Same as in Fig. 3, for even-even Sn target nuclei with $A=120–130$.

Figure 5

PN-RQRPA $J^{\pi }=0^{+}$ discrete spectra for ${}^{108}\mathrm{Sn}$, ${}^{114}\mathrm{Sn}$, and ${}^{120}\mathrm{Sn}$. The panels on the left correspond to calculations performed without including pairing correlations. $T=1$ Gogny pairing is included in the RHB calculations of ground states in the middle panels. The panels on the right-hand side display the results obtained by fully-consistent PN-RQRPA calculations, including the $T=1$ proton-neutron pairing channel.

Figure 6

Gamow-Teller strength distributions for ${}^{48}\mathrm{Ca}$, ${}^{90}\mathrm{Zr}$, and ${}^{208}\mathrm{Pb}$. PN-RQRPA results are shown in comparison with experimental data (thick arrows) for the GTR excitation energies in ${}^{48}\mathrm{Ca}$ [37], ${}^{90}\mathrm{Zr}$ [12, 38], and ${}^{208}\mathrm{Pb}$ [39, 41, 42].

Figure 7

The running sum of the GTR strength for ${}^{208}\mathrm{Pb}$. The dashed line corresponds to a PN-RRPA calculation with only positive-energy ph configurations. For the calculation denoted by the solid line the RRPA space contains configurations formed from occupied states in the Fermi sea and empty negative-energy states in the Dirac sea. The total sum of the GT strength is compared to the model independent Ikeda sum rule (dotted line).

Figure 8

The PN-RQRPA strength distribution of discrete $J^{\pi }=1^{+}$ ${\text{GT}}^{-}$ states. The panel on the right-hand side contains the positive energy $\pi p-\nu h$ strength. The left panel displays the negative energy spectrum built from $\pi \alpha -\nu h$ transitions.

Figure 9

The Gamow-Teller strength distribution in ${}^{118}\mathrm{Sn}$, calculated for different values of the strength parameter of the $T=0$ pairing interaction (14). The insert displays the corresponding calculated centroids of the direct spin-flip GT strength.

Figure 10

RHB plus proton-neutron RQRPA results for the energy spacings between the Gamow-Teller resonances and the respective isobaric analog resonances for the sequence of even-even ${}^{112–124}\mathrm{Sn}$ target nuclei. The experimental data are from Ref. 40.

Figure 11

The proton-neutron RQRPA and experimental [40] differences between the excitation energies of the GTR and IAR, as a function of the calculated differences between the rms radii of the neutron and proton density distributions of even-even Sn isotopes (upper panel). In the lower panel the calculated differences $r_n-r_p$ are compared with experimental data [48].