Measurement of the Reaction ${}^2\mathrm{H}(e,e^{\prime })$ at 180° Close to the Deuteron Breakup Threshold

Inclusive inelastic electron scattering off the deuteron under 180° has been studied at the S-DALINAC close to the breakup threshold at momentum transfers $q=0.27{\mathrm{fm}}^{-1}$ and $0.74{\mathrm{fm}}^{-1}$ with good energy resolution sufficient to map in detail the spin flip $M1$ response, which governs the starting reaction $pn\to d\gamma$ of big-bang nucleosynthesis over most of the relevant temperature region. Results from potential model calculations and (for $q=0.27{\mathrm{fm}}^{-1}$) from pionless nuclear effective field theory are in excellent agreement with the data.

Figure 1

Spectra of the ($e$, $e^{\prime }$) reaction on deuterated polyethylene at $E_0=27.8$ and 74.0 MeV and $\Theta =180°$ and their decomposition into elastic scattering from ${}^1\mathrm{H}$, ${}^2\mathrm{H}$, and ${}^{12}\mathrm{C}$ and deuteron breakup (solid lines) and instrumental background (dashed lines).

Figure 2

Data (open circles) for the structure functions $A(q^2)$ [29, 30] and $B(q^2)$ [30, 31, 32] of elastic electron-deuteron scattering. Present results are shown as stars. The solid lines are polynomial fits to the data.

Figure 3

Double-differential cross sections of the ${}^2\mathrm{H}(e,e^{\prime })$ reaction with errors (hatched bands) extracted from the spectra of Fig. 1. The gray bands and dashed lines are EFT($\mathrm{\pi ̸}$) and potential model calculations, respectively, explained in the text.

Figure 4

Top: Total cross section of the $\gamma d\to pn$ reaction. Data are from 6 (open stars), 7 (open square), 8 (open circles), 9 (solid squares), 10 (solid star), and 11 (open triangles). Bottom: cross sections deduced from the present experiment (solid dots) in the BBN energy regime. The error bars correspond to the uncertainties of the cross section and energy determination. The model results are decomposed into $M1$ and $E1$ parts. Potential model and EFT($\mathrm{\pi ̸}$) calculations (solid, dashed, and dotted lines) agree within line thickness.