(Received April 25, 1955)
The nonstatic corrections to the second plus fourth order potentials are studied in the symmetrical Ps(ps) moson theory. The potentials are constructed by means of canonical transformation, and the nonstatic corrections are obtained by the use of the expansion in powers of (p/2M)∼(k/2M)∼(µ/2M), the validity of which is examined for the special case of the no-pair contributions.
The nonstatic correction are negligible for the large separation r>1/µ between two nucleons, and are large in the interior region but would not alter the main features of the static potentials except for the central force in triple odd state and the one-pair contributions. The results for the small separation should be accepted only qualitatively because of the inadequacy of the pwer series expansion in this region.
It is shown that the separation of the no-pair contributions from the one- and the two-pair contributions leads to the unreasonable results for the velocity dependent potentials, and that the more careful treatment is needed for the inclusion of the effects of the pair suppression. The spin-orbit coupling in the two-pair contributions obtained by Klein is found to be cancelled by the inclusion of the one-pair contributions.
Finally, it is remarked that the potentials determined by this canonical transformation give the correct results for the scattering problem up to g4.
URL : http://ptp.ipap.jp/link?PTP/14/16/
DOI : 10.1143/PTP.14.16