Isoscalar monopole and dipole excitations of cluster states and giant resonances in ${}^{12}$C

Abstract

The isoscalar monopole(ISM) and dipole(ISD) excitations in ${}^{12}$C are theoretically investigated 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 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 calculation describes the ISM and ISD excitations in a wide energy region covering cluster modes in the low-energy region and the giant resonances in the high-energy region, though 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 radial motion of $\alpha$ 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 EWSR, which is consistent with the experimental data for the ${}^{12}$C($0_2^{+}$;7.65 MeV) and ${}^{12}$C($0_3^{+}$;10.3 MeV) measured by $(e,e^{\prime })$, $(\alpha ,{\alpha }^{\prime })$, and (${}^6$Li,${}^6$Li${}^{\prime }$) scatterings. In the calculated low-energy ISD strengths, two $1^{-}$ states (the $1_1^{-}$ and $1_2^{-}$) with the significant strengths are obtained in $E=10-15$ MeV. It is indicated that the ISD excitations can be a good probe to experimentally search for new cluster states such as the ${}^{12}$C($1_2^{-}$) obtained in the present calculation.

Comments: 13 pages, 6 figures. arXiv admin note: text overlap with arXiv:1511.08530