New techniques for evaluating parity-conserving and parity-violating contact interactions

The accurate evaluation of expectation values such as I1=ψ|δ(r→1)|ψ and I12=ψ|δ(r→1-r→2)|ψ, where ψ=ψ(r→1,r→2,...r→N) is an eigenfunction of a Hamiltonian H is of interest for a variety of problems in atomic physics. Transformations are found to new forms I1′ and I12′, which are likely to give considerably more accurate values when, as is usually the case, only approximate wave functions are available. A successful test of the method is presented for the case of electron-electron and electron-nucleus contact interactions in helium. We give some identities which may be similarly useful in the evaluation of off-diagonal matrix elements of relativistic operators such as γ5δ(r→1), which arise from the parity-violating part of the neutral-current interaction and are important in the calculation of parity mixing in atoms.