Particle-hole operators as state generators defects in the random phase approximation (as evidenced by calculations on the frozen-K-shell model of the B+ Ion)

The state-generating properties of particle-hole operators are analyzed for the 2-fermion case, and applied to the analysis of approximation procedures of the random phase approximation (RPA) type. Calculations were performed on the frozen-K-shell model of the B$sup +$ ion (a quasi 2-electron system). These calculations are used to analyze the validity of the assumptions and approximations made by the RPA. It is found that the ''(ls$sup 2$2s2p)'' $sup 1$P/sub odd/ and $sup 3$P/sub odd/ states and the (1s$sup 2$2s3s) $sup 3$S state could be moderately well described by the standard PRA. The (1s$sup 2$2s3d) $sup 1$D and $sup 3$D states require the use of a correlated ground state and ''killer- condition''-satisfying particle-hole operators not of the standard RPA type, if they are to be adequately described by a method of the RPA family. The (1s$sup 2$2s3d) $sup 1$S state requires, in addition, the use of non-''killer-condition''- satisfying particle-hole operators (''number'' operators) in order to be adequately described by a particle-hole method. Such number operators are not supported by methods of the RPA family, as they cannot be sustained by the particle-hole inner projection of the Fourier-transformed polarization more » propagator (causal Green's function). The analysis of the particle-hole operators also leads to the definition of particle-hole wave functions that represent their associated states in forming scalar products. The form of these wave functions is also presented here. (auth) « less