If one attempts to express the isospin splittings of two particletwo hole states in terms of the energies of one particle-one hole states, then very bad answers come out if one limits oneself to very simple configurations for the lp-lh states and chooses an interaction which will fit their energies. This may be viewed as a failure of the simple effective interaction method. In this work a formalism, which takes account of the complexity of the one particle-one hole states either in T.D.A. or R.P.A., is used. This may be regarded as extending the use of the R.P.A. to two pa&Is-two hole states.
In this work we address ourselves to a very conspicuous failure of the simple effective interaction method to correlate the energies of two particle-two hole states in a nucleus with the one particle-one hole states. We shall use 40Ca as an example.
It is natural to try to explain the low-lying negative parity states of 40Ca as one particle-one hole states relative either to uncorrelated (T.D.A.) or correlated (R.P.A.) ground states.
Referring to Fig. 1, we see that the low-lying negative parity states break up into two multiplets, the lower having T = 0, the upper T = 1. To be realistic we must note that in the midst of the T = 0, mainly Ip-lh states, there is a 3p-3h rotational band, the lowest member of which is the l-at 5.91 MeV [2]. The other known members are the 2-, 3-at 6.03 E 6.29 MeV. The identification of the one particle-one hole configuration to the second 2-state at 6.74 MeV is on the basis of its stronger population in (3He, d) on 3gK. Admixtures of 3p-3h into the basic lp-lh states will shift around the energies.
Suppose that we adopt a simple-minded approach and assign the configuration