Pseudo-spin structure and large N expansion for a class of generalized helium Hamiltonians
Abstract
A pseudo-spin formulation of the 1/N expansion is employed to study the helium Hamiltonian and some of its generalizations. A Holstein-Primakoff representation is derived for the Sp(4, R) pseudo-spin algebra associated with such Hamiltonians. The semiclassical nature of the large N limit is discussed, and an algorithm for calculating higher-order corrections is presented. The first three terms for the low-lying eigenvalues are explicitly calculated. The calculated terms for the helium ground state exhibit the same behavior as the corresponding terms in the convergent hydrogen series. The same level of approximation yields better than 1% accuracy for crude quark-like Hamiltonians.
- Publication:
-
Annals of Physics
- Pub Date:
- January 1981
- DOI:
- 10.1016/0003-4916(81)90181-0
- Bibcode:
- 1981AnPhy.131....1M