Speaker
Prof.
Pieter Van Isacker
Description
The shell model has become one of the standard tools for the interpretation of nuclear properties. It exists in a variety of guises ranging from the ab initio version where all nucleons interact with each other, to more phenomenological versions with schematic interactions between nucleons in the valence shell. Shell-model calculations frequently are computationally intensive, requiring the diagonalization of large matrices, the dimension of which nowadays can reach several billion. In such situations it is always desirable to obtain qualitative insight into numerical results by alternative means.
In this talk a geometry of the shell model is derived by taking the limit of large angular momentum of shell-model matrix elements. The procedure relies on the classical expressions for 3nj symbols as proposed by Wigner [1] and is reminiscent of the interpretation of nuclear matrix elements in terms of the angle between the vectors of the single-particle angular momenta, as proposed by Schiffer [2] and developed in more detail by Molinari et al. [3]. An application is presented which consists of the derivation of the shears mechanism [4] from the nuclear shell model.
References:
[1] E. P. Wigner, Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra (Academic, New York, 1959).
[2] J. P. Schiffer, Ann. Phys. (NY) 66 (1971) 798.
[3] A. Molinari, M. B. Johnson, H. A. Bethe and W. M. Alberico, Nucl. Phys. A 239 (1975) 45.
[4] S. Frauendorf, Nucl. Phys. A 557 (1993) 259c.
