Two-Nucleon Problem with Pion Theoretical Potential, II

Abstract

Low energy parameters in the singlet even state· are analysed from the point of view of the pion theory. It is shown that the properties which are required for the potential in the singlet even state are as follows: The one-pion-exchange potential in the outer region, a s~rong attractive force in the region from the pion range to one half of it, which is cons:s:ent with the prediction by the •wo-pionexchange potential, and a strong repulsion at small distances at least up to x=0.20. The value of the effective (oupling constant of the one-pion-exchange potential is limited as g8 2/4rr>0.07 by the present analysis. This result, together with that of the article I, gives an allowed region for the coupling constant as o.o7<g. 2 /4n<o.o9.

Two-Nucleon Potential with Full Recoil. III: Detailed Discussions on Its Characteristic Features

“…21 > Even in the presence of the HM potential the same conclusion as in the case of OPEP is obtained with slight changes in numerical values concerned. That is, a strong attractive force in the two-pion-exchange region is to be added to the HM potential.…”

Chapter 7. On Repulsive Core of Nuclear Forces

“…12 showed that the splitting among the .triplet P phase shifts is of the spin·orbit coupling (LS) type. 5 ),s) In 1960, Breit 13 ) and SakuraP 4 ) dealt with the isoscalar-vector-meson exchange as the simplest possibility of a common {)rigin of the repulsive core and the LS force and estimated the meson mass as well as the coupling constant. No serious attempts at examining consequences of the isoscalar-vector-meson exchange were made, however, until the so-called one-boson-exchange model was developed as will be explained 'later.…”

“…4 ) The points of their argument are as follows': Let us .assume a potential consisting of a hard core with the radius rc and a surrounding attractive well and discuss what such a potential implies for the scattering length a and the effective range re giving the low energy phase shift behaviour:…”

“…that current potential mo::lels with large hard core radius (rc--..0.5 X 10-13 cm) -such as Hamada and Johnston's 65 ) or the Yale potentiaF 4 ) give only a bind- When the offenergy-shell effect is fully taken into account, the discrepancy becomes 76 ) although the three-body correlation is known to tend to cancel the binding energy lost by the off-energy-shell €ffect. 77 ) At any rate, the potentials with a large hard core radius seem to be unable to give the binding energy larger than one half of the reasonable -one, and also unable to explain the reasonable equilibrium density.…”

Two-Pion Exchange Potential

“…Some examples of features which are much improved by the present potential are (i) the P-wave phase shift analysis 6 of the p-p scattering below 4.2 Mev when one considers the effect due to the vacuum polarization, 7 and (ii), the interpretation of the scattering length and the effective range in the singlet even state. 8 A more detailed account will be published presently in Progress of Theoretical Physics.…”