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Register a new userErratum: Investigating Neutron Polarizabilities through Compton Scattering on ${}^3$He
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We provide updated predictions for elastic gamma ${}^3$He cross sections and asymmetries that correct erroneous results we published in Phys. Rev. Lett. 98, 232303 (2007) and Nucl. Phys. A 819, 98 (2009).
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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].
Differential cross sections for quasi-free Compton scattering from the proton and neutron bound in the deuteron have been measured using the Glasgow/Mainz tagging spectrometer at the Mainz MAMI accelerator together with the Mainz 48 cm $oslash$ $times$ 64 cm NaI(Tl) photon detector and the Gottingen SENECA recoil detector. The data cover photon energies ranging from 200 MeV to 400 MeV at $theta^{LAB}_gamma=136.2^circ$. Liquid deuterium and hydrogen targets allowed direct comparison of free and quasi-free scattering from the proton. The neutron detection efficiency of the SENECA detector was measured via the reaction $p(gamma,pi^+ n)$. The free proton Compton scattering cross sections extracted from the bound proton data are in reasonable agreement with those for the free proton which gives confidence in the method to extract the differential cross section for free scattering from quasi-free data. Differential cross sections on the free neutron have been extracted and the difference of the electromagnetic polarizabilities of the neutron have been obtained to be $alpha-beta= 9.8pm 3.6(stat){}^{2.1}_1.1(syst)pm 2.2(model)$ in units $10^{-4}fm^3$. In combination with the polarizability sum $alpha +beta=15.2pm 0.5$ deduced from photoabsorption data, the neutron electric and magnetic polarizabilities, $alpha_n=12.5pm 1.8(stat){}^{+1.1}_{-0.6}pm 1.1(model)$ and $beta_n=2.7mp 1.8(stat){}^{+0.6}_{-1.1}(syst)mp 1.1(model)$ are obtained. The backward spin polarizability of the neutron was determined to be $gamma^{(n)}_pi=(58.6pm 4.0)times 10^{-4}fm^4$.
Microscopic calculations of four-body collisions become very challenging in the energy regime above the threshold for four free particles. The neutron-${}^3$He scattering is an example of such process with elastic, rearrangement, and breakup channels. We aim to calculate observables for elastic and inelastic neutron-${}^3$He reactions up to 30 MeV neutron energy using realistic nuclear force models. We solve the Alt, Grassberger, and Sandhas (AGS) equations for the four-nucleon transition operators in the momentum-space framework. The complex-energy method with special integration weights is applied to deal with the complicated singularities in the kernel of AGS equations. We obtain fully converged results for the differential cross section and neutron analyzing power in the neutron-${}^3$He elastic scattering as well as the total cross sections for inelastic reactions. Several realistic potentials are used, including the one with an explicit $Delta$ isobar excitation. There is reasonable agreement between the theoretical predictions and experimental data for the neutron-${}^3$He scattering in the considered energy regime. The most remarkable disagreements are seen around the minimum of the differential cross section and the extrema of the neutron analyzing power. The breakup cross section increases with energy exceeding rearrangement channels above 23 MeV.
This review gives an update on virtual Compton scattering (VCS) off the nucleon, $gamma^* N to N gamma$, in the low-energy regime. We recall the theoretical formalism related to the generalized polarizabilities (GPs) and model predictions for these observables. We present the GP extraction methods that are used in the experiments: the approach based on the low-energy theorem for VCS and the formalism of Dispersion Relations. We then review the experimental results, with a focus on the progress brought by recent experimental data on proton generalized polarizabilities, and we conclude by some perspectives in the field of VCS at low energy.
We propose a practical folding model to describe $^{3}$He elastic scattering. In the model, $^{3}$He optical potentials are constructed by making the folding procedure twice. First the nucleon-target potential is evaluated by folding the Melbourne $g$-matrix with the target density and localizing the nonlocal folding potential with the Brieva--Rook method, and second the resulting local nucleon-target potential is folded with the $^{3}$He density. This double single-folding model well describes $^{3}$He elastic scattering from $^{58}$Ni and $^{208}$Pb targets in a wide incident-energy range from 30 MeV/nucleon to 150 MeV/nucleon with no adjustable parameter. Spin-orbit force effects on differential cross sections are found to be appreciable only at higher incident energies such as 150 MeV/nucleon. Three-nucleon breakup effects of $^{3}$He are investigated with the continuum discretized coupled-channels method and are found to be appreciable only at lower incident energies around 40 MeV/nucleon. Effects of knock-on exchange processes are also analyzed.
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