Unitarity Corrections and a FourPole Fit to Peripheral pp Scattering below 350 MeV
Abstract
Protonproton partialwave amplitudes for l>=1 and for lab kinetic energies below 350 MeV are fitted with a collection of singleparticle exchanges taken in Born (fixedpole) approximation. Since the Born terms are real, and consequently nonunitary, a correction term is added which makes the full amplitude unitary, and which at the same time satisfies the appropriate dispersion relation and threshold condition. The nature of this correction term and of its association with a strip approximation to the Mandelstam representation are discussed. The particle parameters were fitted to a reduced matrix representation of the pp data, as described by Arndt and MacGregor in another publication. The Swave dependence was removed in a manner also discussed by these authors. The gross structure of the partialwave amplitudes is found to be approximately given by a sum of four mesonexchange poles, those corresponding to a π meson (J^{P}=0^{}, I=1, g_{π}^{2}=14, M_{π}=135 MeV), a σ meson (J^{P}=0^{+}, I=0, g_{σ}^{2}=2.9, M_{σ}=450 MeV), an ω meson (J^{P}=1^{}, I=0, g_{ω}^{2}=4, (fg)_{ω}=0, M_{ω}=783 MeV), and a ρ meson (J^{P}=1^{}, I=1, g_{ρ}^{2}=1.2, (fg)_{ρ}=4, M_{ρ}=763 MeV). The searched parameters were g_{π}^{2}, g_{σ}^{2}, g_{ω}^{2}, g_{ρ}^{2}, and M_{σ} the remaining parameters were fixed at their "physical" values. It is further found that the relatively small unitarizing corrections play an essential role in determining the goodness of fit, but they do not appreciably alter the pole parameters determined from the search. Studies were also undertaken to determine the manner in which this (obviously lowenergy) model becomes quantitatively worse as lowangularmomentum and highenergy contributions are added to the calculation.
 Publication:

Physical Review
 Pub Date:
 December 1966
 DOI:
 10.1103/PhysRev.152.1490
 Bibcode:
 1966PhRv..152.1490A