The He isoelectronic series and the Hooke's law model: Correlation measures and modifications of Collins' conjecture

The recently developed concept of a correlation entropy, S, as a quantitati ve measure of the correlation strength present in a correlated quantum many -body state is applied to the ground states of the He isoelectronic series He( Z) with varying nuclear charge Z and of the Hooke's law model HLM(omega ) with varying oscillator frequency omega. S is constructed from the natura l orbital occupation numbers. It vanishes for weak correlation (large coupl ing constants Z or omega), and increases monotonically with decreasing Z or omega (strengthening correlation). A reduced correlation energy per partic le Delta e(corr) and a dimensionless ratio epsilon = \E-corr/E\ are introdu ced which vanish asymptotically in the weak correlation limit in contrast t o E-corr and e(corr) = E-corr/N. These two intensive quantities, Delta e(co rr) and epsilon, are compared with s = S/N. For both model systems, d Delta e(corr)/ds greater than or equal to 0 and d epsilon/ds greater than or equ al to 0 (which modifies Collins' conjecture that \E-corr\similar to S). (C) 1999 American Institute of Physics. [S0021-9606(99)01212-X].