Abstract
In this paper it is shown that the eigenvalues of the intermediate Hamiltonians of Bazley and Fox, and of Gay, appear as crossing points of the ε1=ε line in the branches of the corresponding multivalued bracketing function ε1. It is further shown that it is possible, from the properties of ε1, to resolve the problem of determining to which level of H a value, obtained using the procedure due to Gay, is a lower bound. It is then shown that the crossing points of ε1 are independent of the size of the reference manifold φa0. These relationships are illustrated by a calculation of lower bounds to some of the low-lying 3S levels of helium and Li+.
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