Compton scattering from the deuteron below pion-production threshold

Differential cross sections for elastic scattering of photons from the deuteron have recently been measured at the Tagged-Photon Facility at the MAX IV Laboratory in Lund, Sweden. These first new measurements in more than a decade further constrain the isoscalar electromagnetic polarizabilities of the nucleon and provide the first-ever results above 100 MeV, where the sensitivity to the polarizabilities is increased. We add 23 points between 70 and 112 MeV, at angles ${60}^{\circ }$, ${120}^{\circ }$, and ${150}^{\circ }$. Analysis of these data using a chiral effective field theory indicates that the cross sections are both self-consistent and consistent with previous measurements. Extracted values of ${\alpha }_s=[12.1\pm 0.8(\mathrm{stat})\pm 0.2(\mathrm{BSR})\pm 0.8\left(\mathrm{th}\right)]\times {10}^{-4}{\mathrm{fm}}^3$ and ${\beta }_s=[2.4\pm 0.8(\mathrm{stat})\pm 0.2(\mathrm{BSR})\pm 0.8\left(\mathrm{th}\right)]\times {10}^{-4}{\mathrm{fm}}^3$ are obtained from a fit to these 23 new data points. This paper presents in detail the experimental conditions and the data analysis used to extract the cross sections.

Figure 1

The layout of the experimental area showing the location of the tagging spectrometer, focal-plane hodoscope, deuterium target, and NaI(Tl) detectors labeled DIANA, BUNI, and CATS.

Figure 2

Enlarged diagram of the tagger magnet and FP hodoscope portion of the experimental layout (not to scale).

Figure 3

A plot of the predicted photon energy for each FP channel versus the peak position of the ADC spectrum ($P_{\mathrm{ADC}}$) for the same channel. The plot is fit with a linear function to determine the calibration of the NaI(Tl) detector. (Inset) A typical tagged-photon ADC spectrum for BUNI showing the location of the ADC channel corresponding to the peak ($P_{\mathrm{ADC}}$).

Figure 4

In-beam detector response as a function of missing energy for the BUNI detector. The data points are the result of summing the energy deposition in both the NaI(Tl) core and annulus. The solid red curve is the simulated geant4 detector response fitted to the data. The dashed line is the ME spectrum obtained by analyzing only the core crystal. The addition of the annulus energy improves the FWHM by almost 50%.

Figure 5

The FP TDC spectrum for the scattering data. The prompt (red) and the accidental (shaded) windows are indicated.

Figure 6

Top panel: The result of fitting the sum (solid) of the accidental spectrum (dashed) and the fitted detector response to the prompt spectrum. Bottom panel: The true elastic peak (prompts minus accidentals) together with the fitted detector response (solid). The vertical, dashed lines indicate the region of integration over which the yield extraction occurs, $-2.0\mathrm{MeV}\le \mathrm{ME}\le 2.0\mathrm{MeV}$.

Figure 7

Time evolution of the tagging efficiency measured using the compact lead-glass detector for the $E_{\gamma }=93.4$ MeV bin from RP1. The shaded region indicates the uncertainty due to daily variations in ${\varepsilon }_{\mathrm{tag}}$.

Figure 8

Measurements of the deuteron Compton-scattering cross section from the current experiment (RP1 $[•]$ and RP2 $\left[\blacksquare \right]$) are shown. Previous measurements from References [15] ($\circ$), [16] ($\square$), and [17] ($\diamond$) are included for comparison. Statistical uncertainties only are shown. The solid and dashed lines represent the free and BSR-constrained fits to the present data only. The shaded region is obtained by varying the BSR-constrained fit for ${\alpha }_s$ and ${\beta }_s$ by its statistical uncertainty.