Pion-Nucleon Scattering in the Tamm-Dancoff Approximation

Abstract

The pion-nucleon scattering is treated in the Tamm·Dancoff approximation wiing the symmetrical ps-ps theory, with emphasis particularly on the renormalization procedure. The number of mesons and nucleon-pairs is restricted up to two and one, respectively, in every intermediate state. In order to perform the renormalization consistently, it is required to adopt the five-box approximation of Bethe and Dyson. But even in this case, the meson self-energy term is n.ot treated consistently and should be ·discarded. A method is proposed to remove the overlapping divergences and it is shown that the Salam's procedure can be carried out in a closed form. The scattering phase shifts are evaluated and compared with experiments. §I. IntroductionThe experimental and theoretical analysis of the pion-nucleon (rr-N) scattering has attracted our attention for the past few years, in expectation that it would give an essential knowledge about the elementary interaction between the pion and the nucleon. Recent results of the experi· ments up to 210 Mev by Fermi and co·workers 1 > together with those of the low energy scattering at Rochester and Columbia 21 have come . to a fairly reliable stage. Furthermore, the ex· perimental data for the high energy rr-N scattering are going to be arranged at Brookhaven, 3 > and we shall gain much more knowledge about the n--N interaction in the near future.At present, however, it should be noted that the measurements of the angular distribution, in particular those of forward and backward scattering are somewhat inaccurate and consequently the phase shift analysis has many ambiguities. It is not always certain that we may believe the strong dependence of the S-wave phase shifts on energy and isotopic spin. Further, the D-wave contribution may not be neglected even in the low energy region. But it would be certain that the (3/2, 3/2) state (the first number 3/2 represents the isotopic spin state of the 7r-N system and the second the spacial spin state) has a resonance-like phenomenon and that the S-wave contribution is consiqerably large.* Now, we would like to give an outline of the theoretical analysis of the rr-N interaction performed so far. First, while the type of the pion is definitely pseudoscalar, the type of the coupling between pion and nucleon has two possibilities; pseudoscalar (p.s.) and pseudovector (p.v.). It is possible that both types of coupling mix together, but it is convenient, for the sake of simplicity, to treat either of the two. (An assumption that a greater part * Recent analysis by Glicksman ~ to ~ mo~e favorable frQ!n the theoretical point of view, (priva~ c~qnicadon) at University of Hawaii, PBRC, Kewalo Marine Lab. on June 6, 2015 http://ptp.oxfordjournals.org/ Downloaded from * The strong coupling theory cannot giw the anomalous magnetic moment con:ectly as well, though it has succeeded in explaining the resonance pbenomena in the x--N scattering. ** The. Dyson transformation used by Drell and HeDley (Phys. Rev. 88 (19~2), 1053.) is not sufficient to eliminate ...

Searching for new physics through atomic, molecular and optical precision measurements

“…Changes in these ratios change the relative energies of atomic and nuclear states, reviewed in Ref. [8]; here we will highlight only a few AMO-based searches.…”