Measurement of the ${}^2\mathrm{H}(p,\gamma ){}^3\mathrm{He}$ $S$ factor at 265–1094 keV

Recent astronomical data have provided the primordial deuterium abundance with percent precision. As a result, big bang nucleosynthesis may provide a constraint on the universal baryon to photon ratio that is as precise as, but independent from, analyses of the cosmic microwave background. However, such a constraint requires that the nuclear reaction rates governing the production and destruction of primordial deuterium are sufficiently well known. Here, a new measurement of the ${}^2\mathrm{H}{(p,\gamma )}^3\mathrm{He}$ cross-section is reported. This nuclear reaction dominates the error on the predicted big bang deuterium abundance. A proton beam of 400–1650 keV beam energy was incident on solid titanium deuteride targets, and the emitted $\gamma$ rays were detected in two high-purity germanium detectors at angles of ${55}^{\circ }$ and ${90}^{\circ }$, respectively. The deuterium content of the targets has been obtained in situ by the ${}^2\mathrm{H}({}^3\mathrm{He},p){}^4\mathrm{He}$ reaction and offline using the elastic recoil detection method. The astrophysical $S$ factor has been determined at center of mass energies between 265 and 1094 keV, addressing the uppermost part of the relevant energy range for big bang nucleosynthesis and complementary to ongoing work at lower energies. The new data support a higher $S$ factor at big bang temperatures than previously assumed, reducing the predicted deuterium abundance.

Figure 1

Astrophysical $S$ factor of the ${}^2\mathrm{H}(p,\gamma ){}^3\mathrm{He}$ reaction as a function of the center of mass energy $E$. The symbols correspond to the experimental data of studies past 1990 by Refs. [13, 14, 15, 16, 17, 18, 19]. The solar fusion II [21] fit curve is shown in black. The theoretical ab initio $S$ factor by Ref. [22] is shown in blue.

Figure 2

Schematic view of the experimental setup with the beam entering from the left side. Left panel: Experimental setup showing the target chamber, the two HPGe detectors and the silicon detector seen from the top. Right panel: Setup including vacuum components and electronic devices seen from the side. For clarity, the copper pipe is shown in the right panel but omitted in the left panel. See text for details.

Figure 3

$\mathrm{\Delta }E-E$ histogram of the elastic recoil detection analysis with the Bragg chamber, at the center of the visible beam spot of target No. 4. See text for details.

Figure 4

Pulse height spectra of the silicon detector used for determining the ${}^{1,2}\mathrm{H}$ content in the ERD runs, for target No. 4, inside and outside the respective proton beam spot. The two runs have similar incident charge but the spectra were not normalized.

Figure 5

Top: Pulse height spectra in the in situ silicon particle detector of a ${}^{241}\mathrm{Am}$ source (blue; spectrum taken without the 50-$\mu \mathrm{m}$ nickel foil) and the no-source background (gray). The inset shows the region of interest with a smaller binning. Bottom: Pulse height spectrum from the irradiation of the deuterated titanium sample No. 4 with a ${}^3\mathrm{He}^{2+}$ beam. The expected energy range for protons from the ${}^2\mathrm{H}({}^3\mathrm{He},p){}^4\mathrm{He}$ reaction, after passing the 50-$\mu \mathrm{m}$ nickel foil, is given by red lines.

Figure 6

$\gamma$-ray spectra at the lowest and highest energies studied, $E=265$ and 1094 keV, respectively, and at a representative intermediate energy $E=535\mathrm{keV}$. The shaded areas inside the insets show the beam energy and detector angle dependent region of interest for the ${}^2\mathrm{H}(p,\gamma ){}^3\mathrm{He}$ peak. See text for details.

Figure 7

Ratio of the efficiency-corrected yields $Y^{*}$ of both HPGe detectors as a function of center-of-mass energy $E$. The ab initio predicted yield ratio is shown as a solid line [22, 43, 44]. The dashed curve and shaded area are a constant fit to the data and its uncertainty. See text for details.

Figure 8

Experimental $S$ factor data from the present work for the two different targets used. The inner error bar is the statistical error, the outer error bar reflects statistical and systematic errors combined in quadrature. Previous fits [17, 21] and the present new fit are also shown (shaded area for the error band [17, present]). Previous data in this energy range [11, 17] are also included. The lower panel shows the BBN sensitive energy range (light gray: 95% of the area, dark gray: 68% of the area). See text for details.

Figure 9

Residuum of the $S$-factor data [13, 14, 15, 16, 17, 18, 19, and present work] with respect to the solar fusion II fit [21]. The ab initio theory curve by Marcucci [22], the Mossa et al. fit [17], and the present fit are also shown (blue, black, and red, respectively). The standard deviation $\left(1\sigma \right)$ of the present fit is given by thin red lines. The error bars for the data points are only statistical.