We investigate the possibility of lanthanum (La)-nucleus creation via the reaction Cs(2d, γ)La on the three-ion quasi-molecule CsD 2 in the CsD 2 Pd 12-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 CsD 2 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 CsD 2 quasi molecular modified states is calculated. It should be stressed that the WFO value is of critical importance for the existence of the electromagnetic transition in the Cs(2d, 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-type long range hadron potential, and gives a promising result for the reaction. The result is also followed by the three-body Faddeev calculation. This article belongs to the Topical Collection "Ludwig Faddeev Memorial Issue".

We present a two-body calculation method for a rigorous treatment of Coulomb interaction in momentum (p-)space. The method is based on a modified Coulomb potential which is equivalent to the genuine Coulomb potential in configuration (r-)space. We also use the two-potential theory with the auxiliary potential. The calculated proton-proton phase shifts are in very good agreement with the experimental data for the states 0 l 2. The phase shifts for the 3 l 5 states are also calculated. Practical applications of our method in a few hadron problems are discussed.

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