su(1,1) model of first 0+ excited monopole states in light nuclei: 2D case

The previously-derived microscopic, unified, uni-axial rotational-model Schroedinger equation is transformed into a form suitable for describing nuclear breathing or isoscalar monopole oscillations coupled to intrinsic motion. For isotropic harmonic oscillator mean-field potential uo, the transformed equation and its underlying su(1,1) dynamical Lie algebra are used to compute the excitation energy ΔE of the first 0+ excited monopole states in the light nuclei. For a frozen intrinsic degrees of freedom, ΔE is shown to be given by the well-known formula ΔE=82A−1/3, with values between 17-52 MeV. These values are much higher than the observed values of ΔE (less than 21 MeV) in the light nuclei. For unfrozen intrinsic motion, with an appropriate split of uo between the intrinsic and monopole motions and ignoring the coupling between these motions, ΔE is predicted to be significantly lower than, but having the same trend with the mass number as, the experimental values for all the light nuclei but the lightest three. With the coupling term and the resulting one-particle-one-hole intrinsic core excitations approximately accounted for, higher values of ΔE are predicted, but these values are still lower than the observed values for all the light nuclei but the lightest three. This discrepancy is attributed to the neglect of higher order terms and a realistic shell structure, and the restriction to two dimensions.