Compton Scattering on the Deuteron in Baryon Chiral Perturbation Theory

Compton scattering on the deuteron is studied in the framework of baryon chiral perturbation theory to third order in small momenta, for photon energies of order the pion mass. The scattering amplitude is a sum of one- and two-nucleon mechanisms with no undetermined parameters. Our results are in good agreement with existing experimental data, and a prediction is made for higher-energy data being analyzed at SAL.Comment: 39 pages LaTeX, 19 figures (uses epsf

Explicit Delta(1232) Degrees of Freedom in Compton Scattering off the Deuteron

We examine elastic Compton scattering off the deuteron for photon energies between 50 MeV and 100 MeV in the framework of chiral effective field theories to next-to-leading order. We compare one theoretical scheme with only pions and nucleons as explicit degrees of freedom to another in which the Delta(1232) resonance is treated as an explicit degree of freedom. Whereas pion degrees of freedom suffice to describe the experimental data measured at about 70 MeV, the explicit Delta(1232) gives important contributions that help to reproduce the angular dependence at higher energies. The static isoscalar dipole polarizabilities alpha_E^s and beta_M^s are fitted to the available data, giving results for the neutron polarizabilities alpha_E^n=(14.2+-2.0(stat)+-1.9(syst))*10^(-4)fm^3, beta_M^n=(1.8+-2.2(stat)+-0.3(syst))*10^(-4)fm^3. These values are in good agreement with previous experimental analyses. Comparing them to the well-known proton values we conclude that there is currently no evidence for significant differences between the proton and neutron electromagnetic dipole polarizabilities.Comment: 24 pages, 11 figure

Deuteron Compton Scattering in Effective Field Theory And Spin-Independent Nucleon Polarizabilities

Deuteron Compton scattering is calculated to $\mathcal{O}(Q^2)$ in pionless effective field theory using a dibaryon approach. The vector amplitude, which was not included in the previous pionless calculations, contributes to the cross section at $\mathcal{O}(Q^2)$ and influences significantly the extracted values of nucleon electric polarizability at incident photon energy 49 MeV. We recommend future high precision deuteron compton scattering experiments being performed at 25-35 MeV photon energy where the nucleon polarizability effects are appreciable and the pionless effective field theory is most reliable. For example, a measurement at 30 MeV with a 3% error will constrain the isoscalar nucleon electric polarizability $$ with a $\sim 30$ error.Comment: 11 pages, 5 figures include

Compton scattering on the proton, neutron, and deuteron in chiral perturbation theory to O(Q^4)

We study Compton scattering in systems with A=1 and 2 using chiral perturbation theory up to fourth order. For the proton we fit the two undetermined parameters in the O(Q^4) $\gamma$p amplitude of McGovern to experimental data in the region $\omega,\sqrt{|t|} \leq 180$ MeV, obtaining a chi^2/d.o.f. of 133/113. This yields a model-independent extraction of proton polarizabilities based solely on low-energy data: alpha_p=12.1 +/- 1.1 (stat.) +/- 0.5 (theory) and beta_p=3.4 +/- 1.1 (stat.) +/- 0.1 (theory), both in units of 10^{-4} fm^3. We also compute Compton scattering on deuterium to O(Q^4). The $\gamma$d amplitude is a sum of one- and two-nucleon mechanisms, and contains two undetermined parameters, which are related to the isoscalar nucleon polarizabilities. We fit data points from three recent $\gamma$d scattering experiments with a chi^2/d.o.f.=26.6/20, and find alpha_N=13.0 +/- 1.9 (stat.) +3.9/-1.5 (theory) and a beta_N that is consistent with zero within sizeable error bars.Comment: 57 pages, 16 figures. Substantial changes. Correction of errors in deuteron calculation results in different values for isoscalar polarizabilities. Results for the proton are unaffected. Text modified to reflect this change, and also to clarify various point

Analyzing the Effects of Neutron Polarizabilities in Elastic Compton Scattering off 3{}^3He

Motivated by the fact that a polarized ${}^3$He nucleus behaves as an `effective' neutron target, we examine manifestations of neutron electromagnetic polarizabilities in elastic Compton scattering from the Helium-3 nucleus. We calculate both unpolarized and double-polarization observables using chiral perturbation theory to next-to-leading order (${\mathcal O}(e^2 Q)$) at energies, $\omega \leq m_{\pi}$, where $m_{\pi}$ is the pion mass. Our results show that the unpolarized differential cross section can be used to measure neutron electric and magnetic polarizabilities, while two double-polarization observables are sensitive to different linear combinations of the four neutron spin polarizabilities. [Note added in 2018] The qualitative conclusions and analytic formulae presented in this paper are correct, but several of the numerical results are wrong: see the erratum posted as arXiv:1804.01206 for further details. A full suite of corrected numerical results for cross sections and asymmetries can be found in Margaryan et al., arXiv:1804.00956. They can also be obtained as an interactive Mathematica notebook by emailing [email protected]: 40 pages, 16 figure

Nucleon Polarizabilities from Deuteron Compton Scattering within a Green's-Function Hybrid Approach

We examine elastic Compton scattering from the deuteron for photon energies ranging from zero to 100 MeV, using state-of-the-art deuteron wave functions and NN-potentials. Nucleon-nucleon rescattering between emission and absorption of the two photons is treated by Green's functions in order to ensure gauge invariance and the correct Thomson limit. With this Green's-function hybrid approach, we fulfill the low-energy theorem of deuteron Compton scattering and there is no significant dependence on the deuteron wave function used. Concerning the nucleon structure, we use Chiral Effective Field Theory with explicit \Delta(1232) degrees of freedom within the Small Scale Expansion up to leading-one-loop order. Agreement with available data is good at all energies. Our 2-parameter fit to all elastic $\gamma d$ data leads to values for the static isoscalar dipole polarizabilities which are in excellent agreement with the isoscalar Baldin sum rule. Taking this value as additional input, we find \alpha_E^s= (11.3+-0.7(stat)+-0.6(Baldin)) x 10^{-4} fm^3 and \beta_M^s = (3.2-+0.7(stat)+-0.6(Baldin)) x 10^{-4} fm^3 and conclude by comparison to the proton numbers that neutron and proton polarizabilities are essentially the same.Comment: 47 pages LaTeX2e with 20 figures in 59 .eps files, using graphicx. Minor modifications; extended discussion of theoretical uncertainties of polarisabilities extraction. Version accepted for publication in EPJ

Nucleon Spin-Polarisabilities from Polarisation Observables in Low-Energy Deuteron Compton Scattering

We investigate the dependence of polarisation observables in elastic deuteron Compton scattering below the pion production threshold on the spin-independent and spin-dependent iso-scalar dipole polarisabilities of the nucleon. The calculation uses Chiral Effective Field Theory with dynamical Delta(1232) degrees of freedom in the Small Scale Expansion at next-to-leading order. Resummation of the NN intermediate rescattering states and including the Delta induces sizeable effects. The analysis considers cross-sections and the analysing power of linearly polarised photons on an unpolarised target, and cross-section differences and asymmetries of linearly and circularly polarised beams on a vector-polarised deuteron. An intuitive argument helps one to identify kinematics in which one or several polarisabilities do not contribute. Some double-polarised observables are only sensitive to linear combinations of two of the spin-polarisabilities, simplifying a multipole-analysis of the data. Spin-polarisabilities can be extracted at photon energies \gtrsim 100 MeV, after measurements at lower energies of \lesssim 70 MeV provide high-accuracy determinations of the spin-independent ones. An interactive Mathematica 7.0 notebook of our findings is available from [email protected]: 30 pages LaTeX2e, including 22 figures as 66 .eps file embedded with includegraphicx; three errors in initial submission corrected. This submission includes ot the erratum to be published in EPJA (2012) and the corrections in the tex

Building light nuclei from neutrons, protons, and pions

In these lectures I first explain, in a rather basic fashion, the construction of effective field theories. I then discuss some recent developments in the application of such theories to two- and three-nucleon systems.Comment: 54 pages, uses czjphys.cls. Lectures given at 14th Summer School "Understanding the Structure of Hadrons", Prague, July 2001. To appear in Czechoslovak Journal of Physic

Tensor Polarized Gamma-Deuteron Compton Scattering in Effective Field Theory

The differential cross section for gamma-deuteron Compton scattering from a tensor polarized deuteron is computed in an effective field theory. The first non-vanishing contributions to this differential cross section are the interference terms between the leading electric coupling diagrams and the subleading single potential pion exchange diagrams or the subleading magnetic moment coupling diagrams. At 90 degree photon scattering angle, only the pion term contributes at this order to the tensor polarized differential cross section. This provides a clean way to study the photon pion dynamics in the two nucleon sector. The effect is measurable for photon energies between 40 and 80 MeV provided the uncertainty in the measured cross sections are less than 7%.Comment: references and one figure adde