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#

Residual Interaction in Finite Nuclei

Equation (14) gives the most general form of the
residual interaction in finite nuclei. Only a few terms contribute to
the 1^{+} isovector excitations of the even-even nuclei we are interested
in. First of all, only the isovector densities contribute. Next, the
conditions
and
between
ground state and excited states imply that the only terms in the
energy functional that can contribute are quadratic in local tensor
or vector parity-even densities/currents. As can be seen from
Table 2 in [20], all possible contributions are time-odd.
One finally obtains

where
and
are defined in
Appendix 8. Since the coupling constants depend only
on the scalar isoscalar density ,
there are no rearrangement
terms in the spin-isospin channel of the residual interaction.
Unsymmetrized proton-neutron matrix elements of this interaction are
to be inserted into the QRPA equations as outlined in Ref. [11].

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*Jacek Dobaczewski*

*2002-03-15*