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

Abstract

A complete set of linearly independent observables in Compton scattering with arbitrarily polarised real photons off an arbitrarily polarised spin-1 target is introduced, for the case that the final-state polarisations are not measured. Adopted from the one widely used e.g. in deuteron photo-dissociation, it consists of 18 terms: the unpolarised cross section, the beam asymmetry, 4 target asymmetries and 12 asymmetries in which both beam and target are polarised. They are expressed by the helicity amplitudes and -where available -related to observables discussed by other authors. As application to deuteron Compton scattering, their dependence on the (isoscalar) scalar and spin dipole polarisabilities of the nucleon is explored in Chiral Effective Field Theory with dynamical ∆(1232) degrees of freedom at order e 2 δ 3 . Some asymmetries are sensitive to only one or two dipole polarisabilities, making them particularly attractive for experimental studies. At a photon energy of 100 MeV, a set of 5 observables is identified from which one may be able to extract the spin polarisabilities of the nucleon. These are experimentally realistic but challenging and mostly involve tensor-polarised deuterons. Relative to Compton scattering from a nucleon, sensitivity to the "mixed" spin polarisabilities γ E1M 2 and γ M 1E2 is increased because of interference with the D wave component of the deuteron and with its pion-exchange current. An interactive Mathematica 9.0 notebook with results for all observables at photon energies up to 120 MeV is available from hgrie@gwu.edu.Note May This arXiv version presents the article corrected for these errors.

News on Compton ScatteringγX→γXin Chiral EFT

“…But a theoretical description of their energy levels with adequate accuracy is involved. For the proton, amplitudes on the 2%-level are available; for deuteron and 3 He, we now extend descriptions with similar accuracies into the Delta resonance region. Around 3 He-4 He- 6 Li may well be the "sweetspot" between needs and wants of theorists and experimentalists.…”

“…6.1]. Recently, the deuteron cross section and asymmetry with arbitrary photon and target polarisations has for example been parametrised via 18 independent observables [3]. Particularly attractive are some asymmetries which are sensitive to only 1 or 2 polarisabilities.…”

“…We review theoretical progress and prospects to understand the nucleon's static dipole polarisabilities from Compton scattering on few-nucleon targets, including new values; see Refs. [1][2][3][4][5] for details and a more thorough bibliography.Why Compton Scattering? Since the electromagnetic field of a real photon induces radiation multipoles by displacing charged constituents and currents, the energy-and angle-dependence of the emitted radiation elucidates the distribution, symmetries and dynamics of the charges and currents which constitute the low-energy degrees of freedom inside the nucleon and nucleus; see e.g.…”

“…We review theoretical progress and prospects to understand the nucleon's static dipole polarisabilities from Compton scattering on few-nucleon targets, including new values; see Refs. [1][2][3][4][5] for details and a more thorough bibliography.…”

“…(2) shows that this is mostly an issue of better data. Therefore, MAMI, MAXlab and HIγS aim for deuteron data with statistical and systematic uncertainties of better than 5%, and plan extensions to 3 He. In general, heavier nuclei are experimentally better to handle and provide count rates which scale at least linearly with the target charge when photons scatter incoherently from the protons, i.e.…”