Neutron polarizabilities from Compton scattering on the deuteron?

Abstract

A calculation of deuteron Compton scattering using non-relativistic perturbation theory is presented, with the primary motivation of investigating the feasibility of determining the neutron polarizabilities from this type of experiment. This calculation is expected to be valid for energies below 100 MeV. Pion-exchange, relativistic, and recoil corrections are also included. The lowenergy theorem for gauge invariance is shown to be satisfied. The relative effects of the different terms and their effects on the determinations of the polarizabilities are discussed at energies of 49, 69, and 95 MeV. The cross-section is dominated by the seagull, polarizability, and electromagnetic multipole interactions. Relativistic and pion-exchange terms are also important, while recoil corrections and multipoles of L=2 and greater are negligible. The calculation provides a reasonable description of the experimental data points at 49 and 69 MeV. The polarizabilities are difficult to determine at these energies. A more accurate determination of the polarizabilities may be possible at 95 MeV.

Dissecting deuteron Compton scattering I: The observables with polarised initial states

“…Karakowski and Miller used an approach similar to that which will be outlined in Sec. 3.1, but without a dynamical ∆(1232) and without some pion-exchange diagrams dictated by chiral symmetry [12,13]. Their results at 49 and 69 MeV agree up to about 30% in shape and magnitude with the ones presented below.…”

“…Often, observables are expressed not in terms of the degrees of deuteron vector and tensor polarisations, but via the occupation numbers p ±,0 of a state quantised along d. From Eq. (2.2), the density matrix of a pure deuteron state |M d is: The first tensor observable was constructed by Chen [11], and also used by Karakowski and Miller [12,13]. His definition of a cross section combination for an unpolarised beam on a deuteron which is tensor polarised along the z axis translates into the observables of Eq.…”

“…While several single and double polarisation observables have been constructed and their sensitivity to the nucleon polarisabilities explored [6][7][8][9][10], no systematic study of vector and tensor polarisation observables exists. Only one tensor observable has been considered explicitly, namely for an unpolarised beam [11][12][13]. What is more, some deuteron "vector" observables which were defined analogous to the spin- 1 2 case will be shown to actually receive contributions from both vector and tensor polarisations.…”

From Hadrons to Nuclei: Crossing the Border

“…199 , higher by several nb/sr at back angles than Ref. 200 , and several nb/sr lower than the calculation with no polarizabilities of Ref.…”

“…Hence, extraction of nucleon polarizabilities requires a theoretical calculation of Compton scattering on the deuteron that is under control in the sense that it accounts for all mechanisms to a given order in χP T . There exist a few calculations of this reaction in the framework of conventional potential models 198,199,200 . These calculations yield similar results if similar input is supplied, but typically mechanisms for nucleon polarizabilities and two-nucleon contributions are not treated consistently.…”