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Compton Scattering from Deuterium and Nucleon Polarizabilities (Feldman) The electromagnetic polarizabilities of the nucleon have been of considerable interest for over two decades. These are fundamental structure constants that characterize the response of the nucleon (a composite object) to external electric or magnetic fields. In the past ten years, great progress has been made in studies of the proton polarizabilities through Compton scattering [Mac95, Olm01], largely facilitated by the advent of high duty-cycle tagged photon facilities. Investigations of the neutron polarizabilities, however, have lagged behind, primarily due to the lack of free neutron targets. Typically these measurements are performed on deuterium, using either the quasi-free D(g,g¢ n)p reaction or the elastic scattering D(g,g)D reaction. In the case of the proton, the electric (ap) and magnetic (bp) polarizabilities enter at order w2 (where w is the photon energy) in the Compton cross section, due to an interference with the leading Thomson amplitude. For a "free" neutron (as in the quasi-free reaction), there is no Thomson term (the neutron is uncharged), so the polarizabilities enter at order w4 and are much harder to determine. Moreover, strong model dependences in the analysis can hinder the extraction of an and bn. In elastic Compton scattering on deuterium, the Thomson term is recovered, so the polarizability extraction is similar (in principle) to the proton case, except for the fact that only the sum of the proton and neutron polarizabilities (ap+an and bp+bn) can be unambiguously deduced from the data. But with the improved knowledge of the proton values available today, extracting the values of an and bn is mostly limited by the quality of the deuteron Compton scattering data. Only three measurements of the D(g,g)D reaction have been performed to date. Four angles at 49 MeV and two angles at 69 MeV were measured at Illinois [Luc94], only a limited range of forward and backward angles at 55 and 66 MeV were covered at Lund [Lun03], and the energy range was extended up to 95 MeV for a five-point angular distribution at SAL [Hor00]. Statistical uncertainties were ~7% for the 95-MeV data and ~10% at the lower energies. The sensitivity to aN and bN (where we now refer to the "isospin averaged" nucleon polarizabilities) increases with photon energy, but this poses a daunting experimental problem. The loosely bound deuteron has a two-body breakup threshold only 2.23 MeV below the elastic peak, so a detector (usually NaI) must have sufficiently good resolution to separate the elastic and inelastic contributions in the scattered photon spectrum. The largest existing NaI detectors have about 2% energy resolution, so Eg = 100 MeV is effectively a practical upper limit for performing these experiments by detecting the scattered photon. More common 10"´ 10" NaI detectors with ~3% resolution are adequate for energies Eg £ 70 MeV. Thus, the lower-energy experiments are easier to do, but at the cost of sacrificing some sensitivity to the polarizabilities. On the theoretical side, a new "industry" of effective field theory (EFT) has arisen in the past ten years (starting with the development of chiral perturbation theory) and great attention has been focused on Compton scattering calculations for the proton and deuteron. Using this formalism, it is possible to make predictions for the D(g,g)D cross section which are in fair agreement with the data at 49-55 MeV. At 66-69 MeV, the data are more sparse and somewhat scattered, so it is difficult to make a meaningful statement about the comparison. However, at 95 MeV, the agreement between data and theory is not very good, especially at the backward angles [Bea02]. A fit to these data [Hor00], in which the polarizabilities are free parameters, yields a result in which bN actually equals or exceeds aN, which is in striking contrast with the proton polarizability values (ap » 12 and bp » 2 in units of 10-4 fm3). Thus far, the back-angle points in the 95 MeV data set have eluded a theoretical explanation, and so it will be particularly important to reproduce these experimental points in an independent measurement. Clearly, improved data are required in order to make better comparisons with the increasingly precise results coming from modern EFT calculations being carried out by various theoretical groups. We propose to conduct a systematic study of elastic Compton scattering on deuterium at HIGS using polarized photons, which will constitute the first polarization observables measured in this reaction. A new model-independent calculation has been developed [Gri02] in a low-energy EFT without dynamical pions and shows considerable promise for comparisons with data below 60 MeV. Aside from the Illinois and Lund data sets at 49 and 55 MeV, respectively, there are no other data below that energy. Precise data will not only provide information on the isospin-averaged nucleon polarizabilities (aN and bN) but will also serve as a benchmark to test the EFT results at low energy. The cross-section results of [Gri02] are presented at next-to-next-to-leading order (NNLO) in the expansion parameter and are expected to be accurate to ~3%. The HIGS facility offers two unique features that will be exploited in these studies. First, the projected photon beam intensity at HIGS will be 109 Hz and the beam will be monoenergetic to within a few percent (depending on the beam collimation). Thus, HIGS will provide an increase of a factor of 1000 in photon flux for a narrow energy bin as compared with current tagged-photon facilities (which have ~106 Hz per tagging channel). Second, the photon beam is 100% linearly polarized which will enable the first-ever polarization measurements to be made on the D(g,g)D reaction. Calculations [Rup03] of the differential cross section s(q) and polarized photon beam asymmetry S(q) below 50 MeV are shown in Fig. 2. Using a model-independent sum rule to constrain aN+bN essentially fixes the forward-angle cross section. The back-angle cross section is sensitive to aN- bN, and clearly there is sensitivity to three different combinations of this difference. Even so, the data from [Luc94] shown in the figure are not sufficiently precise to determine the polarizabilities. There is also some sensitivity to the beam asymmetry forward and backward of q = 90° , although it is not very pronounced. This is surprising at first glance, but it is possible that other polarization observables yet to be calculated in the EFT (for example, double-polarization observables with a polarized target) will show more sensitivity to the nucleon polarizabilities. Precise measurements of s and S that can be made at HIGS will not only serve as stringent tests of the EFT calculations but also provide significant new constraints on aN and bN. 
Figure 2. Differential cross section (top panel) and photon-beam asymmetry (bottom panel) for elastic Compton scattering from deuterium at 50 MeV. The calculation is from [Rup03] and the data are from [Luc94]. Three curves are shown, corresponding to three different values of the polarizability difference aN- bN (where the sum is held fixed). To perform these experiments, elastically scattered photons will be detected simultaneously in four NaI detectors mounted at azimuthal angles f = 0° , 90° , 180° , 270° (left, up, right, down). A frame to hold the NaI detectors has been constructed at HIGS and has aptly been dubbed the "eggbeater" due to its appearance. The eggbeater has already been utilized in a Compton-scattering commissioning run on oxygen (see Section 2 below). The eggbeater frame can be rotated in the azimuthal angle f so that detector locations (horizontal and vertical) can be interchanged in order to reduce systematic errors. The "arms" of the eggbeater allow variation of the polar angle q between 90° and 150° in the backward hemisphere (or between 90° and 30° in the forward hemisphere). Thus, a complete set of q and f angles can be investigated in a manner such as to reduce systematic effects in the polarized-photon asymmetry as much as possible. The very low cross section (~10-15 nb/sr) for this reaction below 100 MeV has been the principal hindrance in all of the previous experiments. With a HIGS photon flux of 109 Hz, counting rates of ~1000 counts/hour can be achieved. Thus, even with some background subtraction, a measurement with ~3% accuracy (at one angle) can be made in a day, and a full angular distribution can be measured inside of a week. The unprecedented capabilities of the HIGS facility running at such a photon flux begin to be appreciated when put into this context. Initial measurements will be made at Eg = 30 MeV, in order to "calibrate" the EFT results compared with the data in a region where polarizabilities do not play a significant role. This will test the inputs and assumptions of the effective field theory. Moving up to 50 or 60 MeV will bring in more sensitivity to the polarizabilities, which will allow the extraction of more precise values than currently exist. Ultimately, it will be desirable to obtain data at 90-100 MeV in order to confirm the validity of the SAL data [Hor00] at 95 MeV, especially at the back angles. Moreover, new EFT calculations that include explicit D-resonance degrees of freedom are being developed at 95 MeV [Phi03]. |
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