Shell model space and the collectivity of low-lying states in SD- pair shell model Yanan Luo 1, Feng Pan 2, Yu Zhang 2 and Jerry P Draayer 3 1. School of Physics, Nankai University, Tianjin P. R. China 2. Department of Physics, Liaoning Normal University, Dalian, P. R. China 3. Department of physics & astronomy, Louisiana state university, Baton Rouge, USA 湖州

Introduction  The low-lying spectroscopy of the medium and heavy nuclei exhibit striking regularities that are characteristic of the collective states  How to describe these collective states in terms of the shell model is a challenging problems in nuclear structure theory.

 In relatively simple cases of the medium weight and heavy nuclei, shell model configurations are around Modern computers fail for all these cases.  Through the success of the interacting boson model (IBM), it was recognized that the S and D pairs play a dominant role in the low-lying nuclear spectroscopy. But the collective S and D-fermion pairs are approximated as s and d bosons in the IBM.

 The tremendous success of the IBM has suggested a possible truncation, the truncation to the SD subspace with S-D collective nucleon-pairs as the building blocks.  Based on the generalized Wick theorem for fermion clusters a nucleon-pair shell model (NPSM) has been proposed for nuclear collective motion.

 Considering the success of the IBM, we truncated the full shell model space to SD- pair space, which is called SDPSM  But because of our collective SD-pair are constructed from non-collective pairs, the model space that we used to construct the collective SD-pair becomes very important.

we want to know: 1. The effect of the abnormal parity states 1. The effect of the size of the model space

A brief review of the SD-pair shell model

The effect of the abnormal parity states

 The lower the intruder level, the greater the contribution from the intruder level to the low-lying states, but the smaller the deformation.  The relative position of the intruder level is crucial in producing the rotational spectrum in the SDPSM.

 The nucleons in the intruder level may couple with those in its unique-parity partner level in upper oscillator shell to form coherent pairs.  (50-82)shell +( )shell consider together. The position of the other levels in upper oscillator shell we used is 4.0MeV, and all of them are degenerate.

The case for the full shell model calculation Full shell model calculation for 24 Mg was studied. J=4J=6J=8 Intruder level close to those normal parity levels f7/2 far above the normal parity levels Rotational limit SDPSM

The effect of the size of the model space  It is known that the Pauli-blocking effect in the fermion system plays an important role.  The number of nucleon pairs is fixed as N=4 for identical nucleon system.  The vibrational and rotational spectra in fp shell, gds shell, hfp shell and a toy case with j=1/2, 3/2, 5/2,7/2,9/2,11/2,13/2,15/2,17/2,19/2 are studied.

Vibrational spetrum in the toy case

Rotational spetrum in the proton- neutron coupled system

Summary  The vibrational character of the spectrum is found to depend upon the size of the active model space and not on the parity of the populated levels;  The intruder level has a tendency to reduce the deformation for nuclei in lower and middle shell, play an important role in determining the onset of rotational behavior

 The Pauli-blocking effect in the fermion system plays an important role.  With fixed number of nucleons, this effect becomes less important with the increase of degeneracy  If the degeneracy tends to infinity, the role of a nucleon pair will be similar to that of the boson.

Thanks!