Measurement of the ${}^{10}\mathrm{B}(\alpha ,n_0){}^{13}\mathrm{N}$ cross section for $2.2<E_{\alpha }<4.9\mathrm{MeV}$ and its application as a diagnostic at the National Ignition Facility

The National Ignition Facility (NIF) provides the opportunity to study nuclear reactions under controlled conditions at high temperatures and pressures at a level never before achieved. However, the timescale of the deuterium-tritium (DT) implosion is only a few nanoseconds, making data collection and diagnostics very challenging. One method that has been proposed for obtaining additional information about the conditions of the implosion is to activate a dopant material using the $\alpha$ particles produced from the DT fuel as a diagnostic. The yield of the activated material can give a measure of the mixing that occurs in the capsule. One of the reactions that has been proposed is ${}^{10}\mathrm{B}(\alpha ,n){}^{13}\mathrm{N}$ as it produces a radioactive reactant product with a convenient half-life of $\approx 10\min$. Although this reaction has several advantages for the application at hand, it has not seen much study in the present literature, resulting in large uncertainties in the cross section. Furthermore, for the current application, the cross section must be well characterized. With this motivation, the ${}^{10}\mathrm{B}(\alpha ,n){}^{13}\mathrm{N}$ cross section has been remeasured for $2.2<E_{\alpha }<4.9\mathrm{MeV}$ with the angle-integrated ground-state cross section reported for the first time. The present results, combined with previous measurements, allow for a determination of the cross section to a significantly higher degree of accuracy and precision than obtained previously and are shown to be consistent with thick-target measurements. Preliminary calculations are performed to test the feasibility of this reaction as a diagnostic for a NIF implosion.

Figure 1

Experimental setup. Positioned counterclockwise for the beam pipe are the HPGe, the EJ-315, the three EJ-315Ms, and the EJ-301D. The three EJ-315Ms and the EJ-301D are positioned on a swing arm to allow for additional angular distribution measurements.

Figure 2

Pulse shape discrimination plot for $\gamma$ rays and neutrons for an EJ301D deuterated liquid scintillator. The vertical axis represents the ratio of the tail pulse integral (S) to the total pulse integral (L).

Figure 3

Comparison of the efficiency curve of a $7.6\text{−}\mathrm{cm}\text{−}\mathrm{thick}\times 5.8\text{−}\mathrm{cm}\text{−}\mathrm{diameter}$ EJ-315M deuterated liquid scintillator from a simulation using mcnp-polimi (red triangles) and the efficiency curve measured using time of flight with the ${}^9\mathrm{Be}(d,n)$-thick target method [24, 25] (blue squares).

Figure 4

Example of spectrum unfolding for a measurement at $E_{\alpha }=4.84\mathrm{MeV}$ and ${\theta }_{\mathrm{lab}}={90}^{\circ }$. The top panel shows the resulting unfolded neutron energy spectrum, which is unfolded using the well-calibrated detector response model. The bottom panel shows the raw light output spectrum (red line) compared to the resulting neutron spectrum in the top panel folded with the detector response (blue line).

Figure 5

Comparison of the angular distribution measurements at $E_{\alpha }=4.63\mathrm{MeV}$ from the present measurement (blue triangles) with those of Van der Zwan and Geiger [8] (red squares). Only statistical uncertainties are shown.

Figure 6

Comparison of Legendre polynomial fits to angular distributions from the present paper (blue triangles) to that of Van der Zwan and Geiger [8] (red squares) at $E_{\alpha }=4.768\mathrm{MeV}$. The present measurements at 12 angles reveal a significantly more complex angular distribution than inferred from the three angle measurements of Van der Zwan and Geiger [8]. To illustrate, a first-order Legendre polynomial (dotted red line) is sufficient to fit the angular distribution of Van der Zwan and Geiger [8], whereas a fifth-order Legendre polynomial (blue solid line) is required to match the present data.

Figure 7

Comparison of the ${}^{10}\mathrm{B}(\alpha ,n){}^{13}\mathrm{N}$ angle-integrated cross-section measurements. Those of Gibbons and Macklin [14] (green stars) and Prior et al. [15] (pink circles) are total cross-section measurements (sum over all neutron deexcitations), whereas the present data (blue triangles) and those of Van der Zwan and Geiger [8] (red squares) are of the ground-state transition. The data of Gibbons and Macklin [14] show a large deviation from both the present measurements and those of Prior et al. [15]. The uncertainties in the present angle-integrated cross sections are estimated to be $\approx 6\%$ as described in the text and are usually smaller than the points on the plot.

Figure 8

Comparison of the thick-target yields measured by Roughton et al. [29] (orange stars) and Bair and Gomez del Campo [7] (green circles) with those calculated from the cross-section measurements of this paper (blue triangles) and that of Prior et al. [15] (pink squares). Note that the data of Roughton et al. [29] represent the thick-target yields from the ground-state transition of the ${}^{10}\mathrm{B}(\alpha ,n_0){}^{13}\mathrm{N}$ reaction, whereas those of Bair and Gomez del Campo [7] and those calculated from the cross-section data of Prior et al. [15] represent those from all transitions.