---
abstract: 'We present first calculations for Compton scattering on $^3$He. The objective of the calculation is an extraction of the neutron polarizabilities.'
address:
- |
    Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA\
    E-mail: $^*$choudhur@phy.ohiou.edu; $^\dagger$phillips@phy.ohiou.edu
- |
    Institut f$\ddot{u}$r Kernphysik, Forschungszentrum J$\ddot{u}$lich, J$\ddot{u}$lich, Germany\
    E-mail: a.nogga@fz-juelich.de
author:
- 'D. CHOUDHURY$^*$ and D. R. PHILLIPS$^\dagger$'
- 'A. NOGGA'
title: 'COMPTON SCATTERING ON HE-3'
---

Introduction {#intro}
============

Our goal is to devise ways to extract the neutron polarizabilities. Direct experiments on the neutron are not possible due to the lack of free neutron targets and this encouraged physicists to look at other avenues to extract information about the neutron polarizabilities. Elastic Compton scattering on $^3$He is one such avenue and here we report on the first calculations of this process. Our results indicate that $\gamma \,^3$He scattering is indeed a promising way to extract the neutron polarizabilities.

The Calculation and Results
===========================

The irreducible amplitudes for the elastic scattering of real photons from the $NNN$ system are first ordered and calculated in Heavy Baryon Chiral Perturbation Theory (HB$\chi$PT) to ${\mathcal
O}(Q^3)$– they are the same as those computed in Ref. . These amplitudes are then sandwiched between the nuclear wavefunctions to finally obtain the scattering amplitude– $${\mathcal M}=\bra \Psi_f|{\hat O}|\Psi_i \ket. \label{eq1}$$ Using these amplitudes we calculate the differential cross-section (dcs) or the double polarization observables, $\Delta_z$ or $\Delta_x$ [@us].

In Fig. \[fig1\] shows the differential cross-section in the center of mass (c.m.) frame at 80 MeV. The left panel corresponds to calculations at different orders– ${\mathcal O}(Q^3)$, impulse approximation (IA) which is actually ${\mathcal O}(Q^3)$ but does not include two-body currents, and ${\mathcal O}(Q^3)$; and the right panel to varying the value of $\beta_n$ around its ${\mathcal
O}(Q^3)$ predicted value.

Fig. \[fig2\] shows the variation in $\Delta_z$ (at 120 MeV in the c.m. frame) when $\Delta \gamma_{1n}$($\times 10^{-4}$fm$^4$) is varied and that in $\Delta_x$ when $\Delta \gamma_{4n}$($\times
10^{-4}$fm$^4$) is varied.

Both Figs. \[fig1\] and \[fig2\] suggest sizeable sensitivity to the neutron polarizabilities in the $\gamma \,^3$He dcs and the double polarization observables. For a more detailed description of the calculation and results please refer to Ref. .

[9]{}

S. R. Beane, M. Malheiro, D. R. Phillips, and U. van Kolck, Nucl. Phys. [**A656**]{}, 367 (1999).

D. Choudhury, D. R. Phillips, and A. Nogga, (in preparation).
