Isospin and spin-isospin dipole oscillations in12C

Abstract

Recent measurements of the cross-sections for excitation of 12C by electron scattering provide us with values of the longitudinal form factor tZZ(q, Ex) and transverse form factor i~r(q, Ex) for values of the excitation energy Ex in the giant resonance region and large values of momentum transfer q(> 0.5 fm-1). The longitudinal form factor F z is due to the isospin dipole oscillation (T-mode oscillation), while the transverse form factor F r is due to the spin-isospin dipole oscillation (aT-mode oscillation) as well as the v-mode oscillation. Since the q dependence of the oscillator strength for the ~v-modc differs from that for the T-mode, _F~(q, Ex) for large q (> 0.5 fln -1) is mainly due to the ~v-mode oscillation and F for small q to the T-mode oscillation--_~(q, Ex) is related to Fz(q, Ex) through the Siegert theorem in the limit of q-* 0. Figure 1-1 and Fig. 1-2 show the experimental values (1) of F~(q, Ex) ~nd F~(q, Ex) as a function of Ex for a fixed value of q(~ 0.75 fm-1). Since q is large, i~(q, Ex) (Fig. 1-2) gives us information on the strength of the ~v-mode oscillations, while Fz (q, Ex) is related to the strength of the v-mode oscillation. In Fig. 1-1 there are three peaks of i~Z(q, Ex) at Ex : 22.0, 23.8 and 25.5 MeV, which are experimentally identified as the dipole resonance states (1-). If we compare these with the doubly-split giant resonance observed in the photo-excitation of ~2C, the two lower peaks (22.0 and 23.8 MeV) together should correspond to the lower peak (~-~ 23 MeV) and the 25.5 ~ e V peak to the higher peak of the photo-excitation. In Fig. 1-2 we also find the two small corresponding peaks of F~(q, Ex) at Ex ~ 23 MeV and 25.5 MeV. These two peaks are also seen more clearly in the Stanford data for q ~ 0.54 fm -1 (2). Therefore, some dipole states with large oscillator strength of the ~v-mode must exist in the region of the lower peak (~-~ 23 MeV) as well as the higher peak (~ 25.5 MeV) of the giant resonance. Likewise, there should be some dipole states with large oscillator strength of the v-mode in the both regions. Previous calculations of the form factors for photo-excitation of ~2C based on the conventional j-j coupling shell model (~) could not obtain the large second peak at