Abstract
The two pion exchange potentials are evaluated by carrying out the numerical integrations of three Feynman parameters in the corresponding Feynman diagrams. The two pion exchange potentials give rise to the attractive force which is quite similar to the effective scalar meson with its mass of mss4.7mπ and its strength of at T = 0 channel. However, there is a strong isospin dependence of (t1·t2)2 which should be different from the phenomenological σ-meson exchange calculations. Therefore, the medium range attraction of the T = 0 nuclear interaction should be due to the two pion exchange processes, but the T = 1 channel is still an open problem.
Highlights
The nuclear potential is first described by Yukawa [1] who introduces one meson exchange process, and this is reasonable since pion is the lightest meson in nature
The evaluation of the two boson exchange potential should be carefully made due to the double counting problem. This is clear since the solution of the Schrödinger equation with the one boson exchange potential should contain the repeat of the one boson exchange process in some way or the other, and the inclusion of the two pion exchange diagrams in the field theory evaluation should be examined to what extent it should be considered for the nucleon-nucleon interaction
It is quite possible that the six order calculation of three pion exchange process may not necessarily be smaller than one pion exchange potential, and we should take this effect into account
Summary
The nuclear potential is first described by Yukawa [1] who introduces one meson (pion) exchange process, and this is reasonable since pion is the lightest meson in nature. There are already sufficiently large numbers of works available for the determination of the shape of nucleon-nucleon potential with one boson exchange processes. There is one important problem which is not solved yet completely This is related to the medium range attraction of the nucleon-nucleon potential, and this is normally simulated by the effective scalar meson exchange process. Which should be compared with the phenomenological values of the σ meson mass and coupling constant as determined by fitting to the nucleon-nucleon scattering data for the T = 0 channel [8] [9]. The two pion exchange diagrams have no such suppression and they can give rise to the largest contribution to the nucleon-nucleon potential Since it is the fourth order process, it turns out to be an effective scalar interaction which is always attractive.
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