LAUSR

We investigate the possibility of lanthanum (La)-nucleus creation via the reaction Cs(2d, $$\gamma $$γ)La on the three-ion quasi-molecule $$\hbox {CsD}_2$$CsD2 in the $$\hbox {CsD}_2\hbox {Pd}_{{12}}$$CsD2Pd12-cluster. In order to calculate d–Cs–d (or D–Cs–D) three-body bound states and wave functions, we adopt a very accurate three-body variational method with more than 80 figures. The $$\hbox {CsD}_2$$CsD2 and La binding energies and wave functions are obtained with an S-wave trial functions. The wave function overlap (WFO) value between the La nuclear excited state and the several $$\hbox {CsD}_2$$CsD2 quasi molecular modified states is calculated. It should be stressed that the WFO value is of critical importance for the existence of the electro-magnetic transition in the Cs(2d, $$\gamma $$γ)La reaction. We found that the WFO value is very sensitive to the nuclear potential tail with a two- or three-body $$1/r^2$$1/r2-type long range hadron potential, and gives a promising result for the reaction. The result is also followed by the three-body Faddeev calculation.