Algebraic Nilsson cranking model and its prediction for 20Ne

Abstract

Previously, Nilsson-Ragnarsson solved numerically the conventional cranking model (CCRM3) with deformed oscillator potential and spin-orbit interaction (refer to as Nilsson CCRM3) and predicted the 20Ne ground-state rotational-band yrast energies at the angular momenta I=2,4,6, and 8. However, CCRM3 is semi-classical and phenomenological and breaks a number of nuclear symmetries. Recently, we developed, starting from the nuclear Schrodinger equation, a microscopic, quantal, self-consistent cranking model (MSCRM3), where, among other features, the angular velocity is microscopic derived. We solved algebraically the MSCRM3 equations for the pure oscillator potential and used the model to predict energies and rotation types in 20Ne. Some interesting results were obtained, such as the quenching or the transition of planar rotation to a uniaxial rotation thereby reducing the excitation energy at I=8 in 20Ne. In this article, we use the algebraic method developed in our MSCRM3 analysis to solve iteratively the self-consistent Nilsson-CCRM3 Schrodinger equation. The application of this algebraic Nilsson-CCRM3 model to the 20Ne nucleus predicts ground-state rotational-band excitation energies at the angular momenta I=2,4,6, and 8 that are in a much better agreement with the measured energies than those predicted earlier by Nilsson-Ragnarsson using a numerical solution method. This agreement and the predicted excited-state energies at I =4 and 8 that vary periodically with the iteration steps (because of single-particle level crossings) provide a possible explanation for the measured lower yrast-state energies at I =4 and 8 relative to those at the I =2 and 6, somewhat resembling the quenching of planar rotation at I =8 mentioned above. This better agreement may also provide a further indication of the weakness of the pairing correlations in 20Ne.