A 2-D Algebraic Model for First 0+ Excited States in Light Nuclei
P. Gulshani 1*, P. Gulshani 1*
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There has been a limited theoretical study of the first excited 0+ states in the light nuclei (A less than121), and such studies were concerned with only 12C and 16O. This article presents a microscopic algebraic approach for describing these states as monopole-oscillation states. The previously-derived microscopic, unified, uni-axial rotational-model Schroedinger equation is transformed using the rigid-flow-moment-of-inertia or the multi-nucleon radius as a variable. The resulting Schroedinger equation describes nuclear monopole oscillations and its coupling to the intrinsic nucleon motion. For a harmonic oscillator mean-field potential and a frozen intrinsic motion, the monopole part of the transformed equation is shown to possess an su(1,1) dynamical algebra. This su(1,1) connection is used to solve the monopole Schroedinger equation in a closed form, and obtain the well-known formula E=82A-1/3 for the excitation energy of the first 0+ excited nuclear states. This formula predicts an energy that is significantly higher than the experimentally observed excitation energy. This discrepancy is attributed to assigning all of the A-oscillator restoring-force strength to the monopole degree of freedom. For an unfrozen intrinsic configuration and ignoring the coupling between the intrinsic and monopole motions, the resulting Schroedinger equation is solved using an appropriate sharing of the oscillator restoring-force strength between the intrinsic and monopole motions. The resulting E is found to be significantly lower than, but has the same trend with the mass number as, the observed energies in all the light nuclei but the lightest three. To reduce this discrepancy the transformed Schroedinger equation including the coupling term is solved by expanding the nuclear wavefunction in terms of the product of the su(1,1) basis states and oscillator particle-hole excited states, and retaining the significant zeroth-order expansion coefficients. The resulting E is found to be significantly higher than that obtained for zero coupling, but it is still lower than the experimental excitation energy except for the three lightest nuclei. In a separate article, this discrepancy will be investigated for the effects of: the third dimension, l2 and spin-orbit coupling in the Nilsson oscillator model, and monopole-monopole effective two-body interaction.