Resonance parameters of the first $1/2^{+}$ state in ${}^9\mathrm{Be}$ and astrophysical implications

Spectra of the ${}^9\mathrm{Be}$($e,e^{\prime }$) reaction have been measured at the Superconducting Darmstadt Electron Linear Accelerator at an electron energy of $E_0=73$ MeV and scattering angles of ${93}^{°}$ and ${141}^{°}$ with high-energy resolution up to excitation energies of $E_x=8$ MeV. The astrophysically relevant resonance parameters of the first excited $1/2^{+}$ state of ${}^9\mathrm{Be}$ have been extracted in a one-level approximation of $R$-matrix theory, resulting in resonance energy $E_R=1.748(6)$ MeV and width ${\Gamma }_R=274(8)$ keV, which are in good agreement with the latest ${}^9\mathrm{Be}$($\gamma ,n$) experiment but with considerably improved uncertainties. However, the reduced $B(E1)$ transition strength deduced from an extrapolation of the $(e,e^{\prime })$ data to the photon point is smaller by a factor of two. Implications of the new results for possible production of ${}^{12}\mathrm{C}$ in neutron-rich astrophysical scenarios are discussed.

Figure 1

Spectra of the ${}^9\mathrm{Be}$($e,e^{\prime }$) reaction at $E_0=73$ MeV and ${\Theta }_{\mathrm{Lab}}={93}^{°}$ (top) and ${141}^{°}$ (bottom) and their decomposition. Solid lines: Fits to experimentally known resonances. Dashed lines: Radiative tail from elastic scattering. The arrows indicate the transition to the first excited state, whose asymmetric line shape is clearly visible.

Figure 2

Ratio of the measured cross sections to the Mott cross section of the transition to the $1/2^{+}$ state in ${}^9\mathrm{Be}$ as a function of momentum transfer. Data are from Ref. [12] (triangles), Ref. [7] (circles), and the present work (squares). Solid and dashed lines are theoretical predictions of the shell-model (SM) and no-core shell-model (NCSM) calculations described in the text normalized to the data.

Figure 3

Ratio of the measured cross sections of the transition to the $1/2^{+}$ state in ${}^9\mathrm{Be}$ to the Mott cross sections as a function of the squared momentum transfer. The solid line is a fit of Eq. (8) with parameters $\sqrt{B(C1,0)}=0.164(12)$ $e$ fm and $R_{\mathrm{tr}}=2.9(3)$ fm.

Figure 4

Photoneutron cross sections extracted from the present (top and middle) and older (bottom) ($e,e^{\prime }$) data [7].

Figure 5

Averaged photoneutron cross sections extracted from the ($e,e^{\prime }$) data shown in Fig. 4 in comparison with the cross sections extracted from the latest ${}^9\mathrm{Be}$$(\gamma ,n)$ experiments [6]. The solid lines are the corresponding fits with Eq. (5) with the parameters given in the text.

Figure 6

Contributions of the lowest-lying states (i) in ${}^9\mathrm{Be}$ to the $\alpha (\alpha n,\gamma ){}^9\mathrm{Be}$ reaction rate.

Figure 7

The ratio of the present rate to the latest NACRE compilation [13]. Deviations ranges from $+25\%$ to $-60\%$ depending on the temperature.