Isoscalar monopole and dipole excitations of cluster states and giant resonances in 12C

The isoscalar monopole (ISM) and dipole (ISD) excitations in C-12 are investigated theoretically with the shifted antisymmetrized molecular dynamics (AMD) plus 3 alpha-cluster generator coordinate method (GCM). The small-amplitude vibration modes are described by coherent one-particle one-hole excitations expressed by a small shift of single-nucleon Gaussian wave functions within the AMD framework, whereas the large-amplitude cluster modes are incorporated by superposing 3 alpha-cluster wave functions in the GCM. The coupling of the excitations in the intrinsic frame with the rotation and parity transformation is taken into account microscopically by the angular-momentum and parity projections. The present a calculation that describes the ISM and ISD excitations over a wide energy region covering cluster modes in the low-energy region and the giant resonances in the high-energy region, although the quantitative description of the high-energy part is not satisfactory. The low-energy ISM and ISD strengths of the cluster modes are enhanced by the distance motion between alpha clusters, and they split into a couple of states because of the angular motion of alpha clusters. The low-energy ISM strengths exhaust 26% of the energy-weighted sum rule, which is consistent with the experimental data for the 12C(0(2)(+); 7.65 MeV) and C-12(0(3)(+); 10.3 MeV) measured by (e, e'), (alpha, alpha'), and (Li-6, Li-6') scatterings. In the calculated low-energy ISD strengths, two 1(-) states (the 1(1)(-) and 1(2)(-) states) with the significant strengths are obtained over E = 10-15 MeV. The results indicate that the ISD excitations can be a good probe to experimentally search for new cluster states such as the C-12(1(2)(-)) obtained in the present calculation.