The one-pion and two-pion-exchange contributions to pion-nucleon scattering, nucleon-electron scattering (nucleon electromagnetic form factors), and nucleon-nucleon scattering are examined using as closely similar methods as possible. These contributions are compared to experimental phase shifts which do not depend on the exchange of more than two pions.

In 1956, the one-pion-exchange potential (OPEP) at large internucleon distances was established and this first success in substantial understanding of nuclear forces has become the keystone in studying nuclear forces since then. As was reported in the review article in 1956, this success was obtained by our Japanese group following the Taketani theory, which proposes to approach nuclear forces from the outside of the nucleon by combining meson-theoretical predictions at large distances with phenomenological descriptions at small distances. In this article we intend to report basic thoughts of approaches and main results recently obtained, in the theoretical works in Japan concerning nuclear forces at small distances.

Exchange of $\pi$, $\eta$, $\rho$, $\omega$, $\phi$ mesons and a pair of pions in the relative $s$ state can account for all the important features of the nucleon-nucleon interaction. The method of dispersion relation is employed to calculate nucleon-nucleon phase shifts starting from the relativistic single-particle-exchange Feynman diagrams. Validity of the method is tested in the nonrelativistic limit where the solution of the dispersion relation is compared to the solution of the Schrödinger equation for a superposition of Yukawa potentials. For potentials that contain a long-range attraction and a strong short-range repulsion there is little difference between the two solutions. In the meson model, the attraction comes primarily from the $\pi$ and the $s$-wave two-pion exchange. The exchange of $\omega$ and $\phi$ produces the required short-range repulsive force.

Two approaches to the nucleon-nucleon scattering problem were considered. (a) The meson model was taken to be the basis of a detailed fit to the scattering data. A total of 12 adjustable parameters were introduced and a fit to the $\mathrm{pp}$ and $\mathrm{np}$ data was obtained. The accuracy is comparable to that of pure phenomenological potentials with considerably more parameters. (b) The number of parameters in the meson model is minimized using approximate symmetry considerations to clarify the physical significance of the model. With only four adjustable parameters, all the important features of the phase shift are reproduced. These results lend support to the idea that the strongly correlated multimeson systems $\rho$, $\omega$, and $\phi$ play a dominant role in the inner part (≲0.3 F) of the nucleon-nucleon potential while the exchange of two pions in a relative $s$-state accounts for the gross feature of the medium-range attraction.

The nucleon-nucleon data are fitted by a boundary condition model interaction determined largely by theoretical forms. One-and two-pion, $\rho$, $\omega$, and $\eta$ meson exchange adiabatic local potentials determine the interaction outside ${\mathcal{r}}_0\approx \frac{1}{2}{\mu }^{-1\mathrm{}}$. Only the two-pion-exchange contribution contains a degree of ambiguity measured by the parameters $\xi$ and $\lambda$ for the pion ladder and nucleon pair diagrams, respectively. The interaction is determined at ${\mathcal{r}}_0$ by an energy-independent boundary condition for those partial waves sensitive to the short-range interaction. A very good fit to the $p-p$ data and a good fit to the $n-p$ data below 350-MeV nucleon laboratory energy, are obtained, comparable to the best phenomenological fits. The optimum or fixed values of exchange particle masses and coupling constants corresponds to their known physical values, and the $\lambda$ and $\xi$ parameters optimize in their theoretical range. The value attained by ${\mathcal{r}}_0$ corresponds to that predicted by the theory of the boundary condition model. There remain 19 boundary condition parameters, freely fitted, to which the data are sensitive. These may in principle be related to pion-nucleon amplitudes. Rescattering and $\phi$ meson exchange contributions to the potential remain to be investigated, as does the effect of coupling to inelastic channels.

One-boson-exchange interactions are derived for pseudoscalar ($P$), vector ($V$), scalar ($S$), axial vector ($A$), and antisymmetric tensor ($T$) mesons. The Schrödinger-Pauli-Breit limit is obtained for a combination of such Diracian OBE interactions. We calculate the phase shifts for purely relativistic $\pi -5\mathrm{}\omega$ model and find it possible to fit the $S$-wave phase shifts by adjusting one coupling constant and one regularization parameter. Then by breaking this model slightly we develop several accurate representations of the $N-N$ interaction for all waves with a moderate number of adjustable parameters, several of which are fixed by external considerations. We present a physical interpretation of the results particularly the velocity-dependent interactions. Finally we discuss the results in relationship to other $\mathrm{PVS}$ models.

Pion instability effects are inserted into the OPEP part of the Hamada-Johnston and Yale potentials to determine if any observables are affected by these corrections. A contribution of 0.030 F to the observed neutron-neutron and singlet state neutron-proton scattering length difference is found.

A summary of the knowledge of the low-energy interaction of two nucleons with one unit of isobaric spin is presented. The single energy analyses of accurate low-energy proton-proton scattering data are discussed with emphasis upon the electromagnetic effects which have been included and those which should be. The phase shifts which result are presented and discussed in terms of the effective range expansion and potentials. A brief discussion of charge symmetry and independence in terms of potentials and dispersion relations is given. The equality of the neutron-neutron and proton-proton nuclear interactions, which seems to be established, may not be sufficient for understanding the problem of mirror nuclei. The question of charge independence is much more difficult.

The present status of the problem of charge dependence is discussed. The information about the neutron-neutron interaction derived from the two-neutron system, three-nucleon systems, final-state interactions in multiparticle reactions, and peripheral processes is critically evaluated. The experimental data indicate the breakdown of charge independence by about 3-5%. Evidence concerning the violation of charge symmetry is inconclusive, but it seems that most of the data are consistent with the assumption that charge symmetry is satisfied within 0.5-1%. The most suitable studies which might improve the knowledge of the neutron-neutron forces are indicated.

The use of a polarized proton target (PPT) in experiments below 30 MeV opens new possibilities for investigating deviations from pure $S$ scattering, occurring at these energies. It seems highly probable, that a detailed investigation of $P$- and $D$-state nucleon interactions at 10-20 MeV, will make it possible to extend the region, in which the scattering amplitude is determined unambiguously to energies, at which the nucleons interact practically only in the $S$ state, so that the phase-shift analysis is considerably simpler. It is therefore important to perform a phase-shift analysis of the existing experimental data in order to obtain information necessary for the planning of future experiments. This has been done at 9.7, 14.5, and 18.2 MeV.

New $p-p$ and $n-p$ phase-parameter multiple energy fits (Y-IV) intended for the energy range from ∼8 MeV to ∼340 MeV employing 947 measurements for $p-p$ and 1023 for $n-p$ are discussed. Improvements over older work include: (a) more careful joining to low-energy data involving phase searches beginning at 1.397 MeV for $p-p$ and 3.205 MeV for $n-p$; (b) inclusion of triple scattering and polarization data at 430 MeV; (c) data lumping in smaller groups than previously; (d) increased accuracy of one-pion-exchange (OPE) phases; (e) graded introduction of OPE treatment. Related matters include: (1) effects of Coulomb field corrections and of corrections for the apparent violation of shortrange charge independence for the new fits and the older YRB1 (${\mathrm{K}}_0$) - YLAN4M; (2) effects of varying the difference between the $p-p$ and $n-p$ effective ranges within its uncertainty limits; (3) analyses of mockups of experiments designed to improve knowledge of the difference just mentioned; (4) comparisons of values of the pion-nucleon coupling constant ${g_0}^2$ derived from $p-p$ and $n-p$ data in relation to the long-range charge independence of $N-N$ interactions.

A phase-shift analysis of $p-p$ scattering data from 10 to 400 MeV is presented. Phase-shift energy-dependent forms having a plausible analytic structure are used, and matrix techniques are employed for the search procedure. An interation process was used to arrive at a self-consistent $p-p$ data set. This analysis is being extended to higher energies and to the $n-p$ system.

Results of recent analyses of proton-proton and neutron-proton data in the 140-MeV region and of proton-proton data at 50 MeV are reported. The existing neutron-proton data in the 25-MeV region are examined and suggestions for experiments are made. It is argued that in fact the available data in this region tell one very little about the interaction.

The $p-p$ differential cross section has been remeasured at 52.3 MeV within 1% accuracy by Sanada et al. We have made a phase-shift analysis by using these new data and those on $C_{\mathrm{nn}}$, $C_{\mathrm{kp}}$, $P$, $D$, $R$, and $A$. All of these data were normalized at 50.0 MeV. The solution is ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{} 39.00\pm 0.35$, ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{} 1.97\pm 0.15$, ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{} 12.57\pm 0.52$, ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{} -7.86\mathrm{}\pm 0.27$, ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{} 5.98\pm 0.13$, ${\epsilon }_2 -1.90\mathrm{}\pm 0.19$, ${}_{}{}^3{}_{}{}^{}F_2^{}{}_{}{}^{} 0.43\pm 0.18$ (in degrees). The present solution shows that the parameters ${\epsilon }_2$ and $\delta \left({}_{}{}^3{}_{}{}^{}F_2^{}{}_{}{}^{}\right)$ are given essentially by the OPE forces. Other features of the solution are similar to those of the previous one. The values of the $\delta \left({}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\right)$ and $\delta \left({}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}\right)$ of the present solution are larger by about three standard deviations than those given from the Hamada-Johnston potential.

We have measured the neutron-proton total cross section in hydrogen gas and the neutron-carbon total cross section in pyrolytic graphite between 0.3-and 400-eV laboratory energy. After subtracting the capture cross section and molecular binding effects, we find 20.37±0.02 b for the free neutron-proton scattering cross section and 4.7534±0.0045 b for the free neutron-carbon cross section. The effects of these measurements and those of L. Koester on the singlet and triplet $n-p$ scattering lengths and effective ranges are discussed.

The status of $N-P$ scattering and polarization experiments near 25 MeV is reviewed. Recent data on polarization and spin correlation observables are discussed in relation to phase-shift analyses, with some emphasis on the role of the $S-D$ coupling parameter.

A brief description of present work at Harwell is given. The final results of the $C_{\mathrm{NN}}$ measurements at 73.5, 98, and 142 MeV are given and the status of the precision measurements at 100 MeV is presented. The results of the measurement of the forward cross section for the reaction $d(p, n)2p$ at 95.7 and 143.9 MeV are given and mention is made of recent $p$, $n$ reaction results.

Finally a description is given of the recent 50-MeV $p$, $p$ differential cross-section measurement made at the proton linear accelerator of the Rutherford Laboratory.

The spin-spin correlation parameter $C_{\mathrm{NN}}$ for $p-p$ scattering has been measured at 5 energies between 305 and 415 MeV. Measurements were made over the angular range of 50° to 90° in the c.m. system. A polarized beam, produced by scattering of the internal proton beam of the Chicago cyclotron, and the Argonne polarized proton target were used for the experiment. Results obtained for $C_{\mathrm{NN}}\left(90\mathrm{}°\right)$ are: 0.52±0.08 at 305 MeV, 0.48±0.08 at 330 MeV, 0.50±0.05 at 358 MeV, 0.46±0.06 at 386 MeV, and 0.42±0.04 at 415 MeV. Comparisons with other experimental results and with theoretical and phenomenological models will be made.

We summarize experiments which have been done to measure spin-correlation parameters in nucleon-nucleon scattering and compare results with phase-shift models.