Two-Pion-Exchange Contribution to Nucleon-Nucleon Scattering on the Basis of Pion-Pion Dynamics

Abstract

the systematic studies of low energy strong interactions. The essential part of the present work is a quantitative evaluation of the two-pion-exchange contribution to nucleon-nucleon scattering, starting from the pion-pion scattering phase shifts in the I= L=O and I= L= 1 states. In this calculation, the parameters for the two-pion contribution with I= L= 1 state are predetermined from the iso-vector part of the nucleon electromagnetic form factors. For the I=L=O state, both cases of the up-down and the down-up solutions for S-vvavc pion-pion scattering are examined. The I =0 S-wave pion-pion phase shift o°C 0l in the former case shows a very broad enhancement below 1 GeV region, whereas o 0 2, pion-pion correlations are neglected. In addition to these two-pion contributions and the one-pion contribution, inclusion of the w- and the 'lj-meson contributions leads us to the results which agree well with the ex­ perimentally determined nucleon-nucleon scattering amplitudes, when we take the up-down solution for o°C 0l. However, the down-up solution for o°C0l makes the 1=--=-L=O part of the two­ pion contribution too large and we cannot obtain reasonable fit with the experiment on nu­ cleon-nucleon scattering for the latter case. From the present analysis we may conclude that the up-down solution for S-wave pion­ pion scattering is superior to the down-up solution. This gives another indication to the im­ portance of the non-resonant part of two-pion contribution as well as that given by the anal­ ysis of the nucleon electromagnetic fonn factors. It is also shown that in the present treat­ ment the 'lj-meson contribution becomes rather large. § l. :h:aLroductio:n. It is the purpose of this paper to investigate the structure of two-vion-ex­ change contribution for the nuclear force in the region II where the two-pion contribution plays an important role, starting from the dynamics of pion-pion in­ teraction. According to the extensive investigations which have been done so far/), 2 ) the two-pion contributions for nucleon-nucleon scattering can be qualita­ tively described in terms of the one-boson-exchange approximation by adjusting the mass and the coupling constant. Conversely, the results of the one-boson­ exchange model,a) which is very powerful for analysing the nucleon-nucleon in­ teraction, should be reinterpreted as a phenomenological iit. In view of the fact that the pion-pion scattering phase shifts are becoming