Phase variation of hadronic amplitudes

Abstract

The phase variation with angle of hadronic amplitudes is studied with a view to understanding the underlying physical quantities that control it and how well it can be determined in free space. We find that unitarity forces a moderately accurate determination of the phase in standard amplitude analyses but that the nucleon-nucleon analyses done to date do not give the phase variation needed to achieve a good representation of the data in multiple scattering calculations. Models are examined that suggest its behavior near forward angles is related to the radii of the real and absorptive parts of the interaction. The dependence of this phase on model parameters is such that if these radii are modified in the nuclear medium (in combination with the change due to the shift in energy of the effective amplitude in the medium) then the larger magnitudes of the phase needed to fit the data might be attainable but only for negative values of the phase variation parameter.

Connection between angle-dependent phase ambiguities and the uniqueness of the partial-wave decomposition

“…On the basis of Eqs. (9) and (10) applied to the toy model, we observe several important features of the angledependent phase rotations:…”

“…This effect has been extensively discussed in refs. [9,17] for elastic scattering in near-threshold inelastic region, and it was shown that inelastic unitarity practically eliminates all solutions obtained by the angle dependent phase rotation of the initial one found in a unitarity constrained fit. However, for inelastic processes the situation changes significantly.…”

“…The discussion of angle dependent phase rotation was always scarce, and to our knowledge, mentioned only "in passing" in old ref. [8], and very recently, but in different context, also in [9]. Some other related studies on phase ambiguities were performed [10,11], but concentrated on cases without a complete set of experimental data.…”

Study of Different Forms of Density Distributions in Proton–Nucleus Total Reaction Cross Section and the Effect of Phase in NN Amplitude

“…Studies show that by treating γ nn as a free parameter, good agreement between theoretical and experimental cross sections could be achieved [31][32][33]. Recently, considering three different models for the interaction potential, Dedonder et al [34] have shown that the phase of the scattering amplitude is a sensitive function of the relative size of the radii of the real and imaginary parts of potential. Their study showed that unitarity forces a moderately accurate determination of the phase in standard amplitude analyses, but the NN analyses to date do not give the phase variation needed to achieve a good representation of the data in multiple scattering calculations.…”

Role of angle-dependent phase rotations of reaction amplitudes in η photoproduction on protons

“…However, almost no attention has been paid to the situation when the arbitrary phase function is angle dependent. This possibility was mentioned in [14][15][16][17] where the effect was established, but the discussion was not followed through. The whole deduction chain for understanding the full role of angle dependent phase rotations in continuum ambiguity was finally presented in [1].…”