From the standpoint of the meson theory of nuclear force, results of current analysis on phenomenological nuclear potentials are reexamined. A new method of the theory of nuclear forces is proposed. We employed meson potentials for the outside region, and phenomenological parameters for the inside region of the nuclear forces.

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From static to non-staticIn our report of 1956,1) entitled 'Meson Theory III' (Nuclear Force '1956 report (Suppl.)') we presented our study on the nuclear potential as far as we could do by meson theory within the scope of its static version. There, we were able to confirm the statements described in our earlier paper~ Taketani, Nakamura and Sasaki 2 ) (T. N. S.) of 1951 by the results of various investigations which had been made along the line given by T. N. S. In other words, the theory of nuclear forces was established as far as in the region I of our version. On this basis we then proceeded to study the non-static potential by meson theory. Just since that time the experimental informations about the scattering of protons with energy over 100 1\1e V on proton have been increasingly accumulated, which enabled us to explore the problem in fu11-scale. Consistent perspecive for the dynamical regionThe non-static theory of nuclear force is investigated in following various ways, and all of the works were systematically organized under the common strategy. They are investigations on; i) the nuclear potential expressed by the mom.entum space variables with full recoil, ii) the semi-phenomenological non-static potential in the coordinate space, iii) the two-pion exchange potential calculated by the dispersion theory, iv) the nuclear force by the one-boson exchange model, v) phase shift analysis on the elastic scattering of nucleon-nucleon collision by taking into account the contributions from the inelastic processes (such considerations being necessary because we enter into the high energy region), vi) hard cores in the region III, vii) effects of the hard core and absorption on the nucleon-nucleon scattering with energy over several Ge V.By the combined results of these attacks we are now able to reach a unified view point satisfactorily. This means that the internal relationship between various .ways of attacks is made clear so that we arrive at a unified at UPVA on June 3, 2015 http://ptps.oxfordjournals.org/ Downloaded from 2 M. Taketani understanding for the nuclear force3 in the region II. Thus the present report, we expect, contains contributions comparable to that of the earlier report of 1956 in providing systematic understanding on the problem. Our way of researchHere we shall briefly review history of research activities on the nuclear force in Japan which were based on tradition of 'the Yukawa theory. Our traditional way of research on elementary particle physics is different from that of the foreign countries in many respects. In foreign countries, main concern of publice.tions and discussions is on works which are already accomplished. In Japan we do the same thing at the occasion of the formal meeting. However, we have organized several inter-university groups attacking the specific subjects on elementary particles in collaboration. Our group of "nuclear force" is one of the leading grcu ps. We often hold small meeting of the group where we discuss freely on the strategical problems of the research,...

The general formal construction of potential in the field theory is given. It is constructed so as to conserve the normalization of the wave function, irrespective of the switch-off or -on of the potential. The potential is anaiyzed into its normal part and probability operator. The probability operator is shown to be related to the probability of the system staying in the same state as it does when the interaction is switched off.From the probability character of the probability operator, we can get a measure of the applicable region of the power series expansion of potential in the coupling constant. The intense meson cloud around the nucleon gives rise to strong singularities in the normal part of the potential, but, on the other hand, the probability of the nucleon to be bare becomes much smalier, and thus it turns out that the actual potential has a lesser singularity. Both potentials derived previously by Taketani-Machida-Onuma1l (T.M.O.) and its corrected form by Brueckner-Watson2l (B.W.) are shown to be two extreme cases in handling this probability operator, but the latter one is more appropriate qualitatively in many cases. The reasonable way of constructing the potential is given in the following paragraphs and the justification of this argument will be illustrated in a separate paper for the pseudo-scalar meson theory~l § 1. General remark There are various ways to get the field theoretical potential, most of which give the same results in the so-called static approximation. The method of using the canonical transformation was first applied to this probelm by M¢ller and Rosenfeld in a general form and developed by many authors 4l • This leads necessarily to the Taketani-Machida-6numa 1 ) potential, as shown by Nishijima 4l • Several authors have also attempted to derive the potential from the scattering matrix; usually, however, this method has some very ambiguous points.Especially, the derivation of the potential needs the off-energy-shell matrix elements of the scattering matrix; But usually only the diagonal-energy-shell matrix elements are used expecting that the off-and diagonal-elements are not so different in the adiabatic limittt. The third one is due to Tamm and Dancoff6) and formulated in a com'

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