A Semi-Classical Treatment of Non-Local Potentials

Abstract

Since the exchange kernels of RGM or GCM are now calculable in completely analytical forms, the analysis of these non-local kernels (without solving the RGM or GCM equation of motion) is expected to enable us to make general discussions (not restricted to individual cases) on the characteristic features of the inter­ nucleus force. An important contribution in this direction was clone by Brussels group 5 ' on the basis of the analysis of the parity-projected diagonal kernels of GCM, namely, the parity-projected energy curves. In their study they assume that the parity­ projected energy curve is directly related with the inter-nucleus force as seen in regarding the parity-range of the energy curve as equivalent with that of the inter-nucleus force. This assumption is, however, somewhat doubtful, and we dis­ cuss this point in more detail in another paper. Another important contribution was given by LeMere and Tang 6J who analysed the equivalent local potentials obtained from the RGM norm kernels by the prescription of Greenlees and Tang.7l Their argument is based on the assumption that the essential features of the exchange kernels of RGM are ctlready contained in the exchange norm kernel of RGM. This assumption was justified by the analysis of the RGM interaction kernels clone by LeMere, Stubeda, Tang and the present author. 8' The prescrip­ tion of Greenlees and Tang which transforms the non-local kernel to the equivalent