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SD pair shell model and Interacting boson model

SD pair shell model and Interacting boson model. Y.A. Luo 1,2,3 , F. Pan 2,3 and J. P. Draayer 2 1 Nankai University, Tianjin 300071 P. R. China 2 Louisiana State University, LA 70803 USA 3 Liaoning Normal University, Dalian 116029 P. R. China.

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SD pair shell model and Interacting boson model

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  1. SD pair shell model and Interacting boson model Y.A. Luo1,2,3, F. Pan2,3 and J. P. Draayer2 1 Nankai University, Tianjin 300071 P. R. China 2 Louisiana State University, LA 70803 USA 3 Liaoning Normal University, Dalian 116029 P. R. China

  2. Introduction • How to describe collective motion in terms of shell model is an interesting and challenging problem • Modern computing tool is still out of reach for direct large space shell model calculation, one has to use some truncation • Through the success of the IBM, it was known that SD pairs play a dominant role

  3. Over a decade, much effort has been devoted to the study of the microscopic foundation of the IBM • By using Generalized Wick Theory, Nucleon-pair shell model (NPSM) has been proposed

  4. # The advantage of the NPSM The single-particle term was included Some other model like FDSM is its special case It allows a truncation from S-pair model space to full shell model space The pairs are not symmetry dictated, they are “realistic” pairs # Disadvantage Computing time increase dramatically, so we have to truncated to SD subspace (SDPM)

  5. The Hamiltonian and E2 transition operator we used here are

  6. In this report, the degenerate single particle levels were used. The SD pairs are determined as

  7. Results for identical system For identical system, N=4 pairs is used The Hamiltonian reduced to

  8. Vibration spectrum

  9. The main components of the wavefunction for vibration

  10. Rotational spectrum

  11. The main components of eigenstates for rotational limit

  12. -soft spectrum

  13. The main components of the wavefunction for -soft spectrum

  14. Results for proton-neutron coupling system Vibrational spectrum • The Hamiltonian and parameters are as follows

  15. -soft spectrum

  16. Rotational spectrum The Hamiltonian and parameter used here are

  17. Conclusion • The limiting cases in IBM can all be reproduced within SDPM • Our study confirm that IBM has a sound shell model foundation which encourage us further explore the SDPM

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