Reanalysis of radioisotope measurements of the ${}^9\mathrm{Be}(\gamma ,n){}^8\mathrm{Be}$ cross section

The ${}^9\mathrm{Be}(\gamma ,n){}^8\mathrm{Be}$ reaction is enhanced by a near-threshold $1/2^{+}$ state. Contradictions between existing measurements of this reaction cross section affect calculations of astrophysical $r$-process yields, dark matter detector calibrations, and the theory of the nuclear structure of ${}^9\mathrm{Be}$. Select well-documented radioisotope ${}^9\mathrm{Be}(\gamma ,n)$ source yield measurements have been reanalyzed, providing a set of high-accuracy independently measured cross sections without the large systematic errors from recent beamline experiments [Arnold, Clegg, Iliadis, Karwowski, Rich, Tompkins, and Howell, Phys. Rev. C 85, 044605 (2012); Utsunomiya, Katayama, Gheorghe, Imai, Yamaguchi, Kahl, Sakaguchi, Shima, Takahisa, and Miyamoto, Phys. Rev. C 92, 064323 (2015)]. A single-level Breit-Wigner fit of these corrected measurement yields are $E_R=1736.8\left(18\right)$ keV, ${\mathrm{\Gamma }}_{\gamma }=0.742\left(25\right)$ eV, and ${\mathrm{\Gamma }}_n=252\left(17\right)$ keV for the $1/2^{+}$ state, excluding a virtual state solution.

Figure 1

A selection of existing near-threshold cross section measurements of the ${}^9\mathrm{Be}(\gamma ,n){}^8\mathrm{Be}$ reaction [5, 14, 15, 16, 17, 18, 20, 21, 29]. Lines show the cross section from fitted Breit-Wigner parameters. The parameters from Barker [30] were fit to data from Kuechler et al. [27].

Figure 2

Fit Breit-Wigner parameters to the $1/2^{+}$ state. Best-fit parameters (solid circles) are $E_R=1736.8\left(18\right)$ keV, ${\mathrm{\Gamma }}_{\gamma }=0.742\left(25\right)$ eV, and ${\mathrm{\Gamma }}_n=252\left(17\right)$ keV with a ${\chi }^2/\mathrm{degree}$ of freedom of $4.70/7$. The 68% (dashed) and 95% (solid) confidence regions are shown. A fit excluding the data from Fujishiro et al. [18] was also performed, with the 95% confidence region shown by dotted lines. A virtual state would exist if $\mathrm{\Gamma }\approx {\mathrm{\Gamma }}_n>E_R-S_n$ [see Eq. (1)]. The best-fit virtual state solution for the fit including all reanalyzed radioisotoope data is shown (open squares) and is excluded with 99.3% confidence ($2.7\sigma$). If the data from Fujishiro et al. [18] is excluded, a virtual state is disfavored with 93% confidence ($1.8\sigma$). A script to calculate these likelihoods is available in the Supplemental Material [64].

Figure 3

Reanalyzed cross sections from radioisotope measurements of the ${}^9\mathrm{Be}(\gamma ,n){}^8\mathrm{Be}$ cross section. Only the cross sections for the highest-intensity photon energy of each radioisotope are shown, assuming that ratios to the cross sections at other photon energies equal the best-fit ratios. The absolute yield of the measurements by Fujishiro et al. [18] are floated. The 2.7 MeV measurement by Snell et al. [14] of the ${}^{24}\mathrm{Na}/\mathrm{Be}$ source yield was not included in the fit, but it is used to validate the contribution of higher-energy resonances as measured by Arnold et al. [21].

Figure 4

Comparison of the fitted ${}^9\mathrm{Be}(\gamma ,n){}^8\mathrm{Be}$ cross section to recent inverse Compton-scattered photon beam [5, 21] and electron scattering [29] measurements (see text).

Figure 5

Calculated rate from the two-step ${}^4\mathrm{He}(\alpha n,\gamma ){}^9\mathrm{Be}$ fusion reaction compared to previous evaluations [21, 46]. Bands show $\pm 1\sigma$ uncertainties.