Charge-exchange excitations with finite-range interactions including tensor terms

We study charge-exchange excitations in doubly magic nuclei by using a self-consistent Hartree-Fock plus random phase approximation model. We use four Gogny-like finite-range interactions, two of them containing tensor forces. We investigate the effects of the various parts of the tensor forces in the two computational steps of our model, and we find that their presence is not negligible and improves the agreement with the experimental data.

Figure 1

Pure tensor (a) and tensor-isospin (b) terms of the D1ST2c and D1MT2c parametrizations used in this work as a function of the relative momentum of the interacting nucleon pair, compared with the analogous terms of the realistic interaction AV18 [28].

Figure 2

Energy distributions of the ${\Gamma }_{1^{+}}^{\mathrm{GT}-}\left(\omega \right)$ (left panels) and ${\Gamma }_{1^{+}}^{\mathrm{SQ}-}\left(\omega \right)$ (right panels) strengths, as given by Eq. (12). The red solid curves have been obtained with the D1M interaction while the blue dashed curves with the D1MT2c force. The arrows indicate the experimental energies of the main peaks [44, 45, 46, 47, 48, 49]. The black squares show the ${}^{48}\mathrm{Ca},{}^{90}\mathrm{Zr}$, and ${}^{208}\mathrm{Pb}$ experimental data, taken, respectively, from Refs. [39, 47, 49].

Figure 3

Energy distributions of the ${\Gamma }_{J^{\pi }}^{\mathrm{SD}-}\left(\omega \right)$ and ${\Gamma }^{\mathrm{SD}-}\left(\omega \right)$ strengths for ${}^{48}\mathrm{Ca}$ (left panels), ${}^{90}\mathrm{Zr}$ (central panels), and ${}^{208}\mathrm{Pb}$ (right panels) nuclei. The red solid curves have been obtained with the D1M interaction while the blue dashed curves with the D1MT2c force. The squares indicate the experimental data of Ref. [38], for ${}^{90}\mathrm{Zr}$, and of Refs. [48, 49], for ${}^{208}\mathrm{Pb}$.

Figure 4

Energy distributions of the ${\mathrm{T}}_{-}$ responses of ${}^{90}\mathrm{Zr}$ calculated with the D1MT2c interaction. We show in panels (a)–(c) the strengths ${\Gamma }_{0^{+}}^{\mathrm{F}-}\left(\omega \right),{\Gamma }_{1^{+}}^{\mathrm{GT}-}\left(\omega \right),$ and ${\Gamma }^{\mathrm{SD}-}\left(\omega \right)$, respectively. The SD strengths for the $0{}^{-},1{}^{-}$, and $2{}^{-}$ multipoles are shown in the right panels. The red solid lines labeled [$0,0$] indicate the results obtained without tensor terms in both HF and RPA calculations, those labeled [$1,0$] (black dotted curves) indicate the results obtained by considering the tensor force only in the HF calculations, and, finally, those identified with [$1,1$] (blue dashed) have been obtained by considering the tensor force in both HF and RPA calculations. The arrows indicate the experimental energies of the main peaks for the SD [43] and GT [45, 47] excitations. Experimental data (black solid squares) are from Ref. [47] for GT strength and from Ref. [38] for SD strength.

Figure 5

The same as in Fig. 4. In this case, all the calculations have been carried out by including tensor force in the HF calculations. The [$1,0$] black dotted and [$1,1$] blue dashed lines are the same as those of Fig. 4 and have been included here to facilitate the comparison with the other results. The [$1,\mathrm{t}$] red dashed-dotted curves have been obtained by including only the pure tensor force in RPA calculations, while those obtained by including only the tensor-isospin force are named [$1,\mathrm{ti}$] (green solid curves).