Astrophysical S factor for the ${}^7\mathrm{Li}$($d,n_0$)${}^8\mathrm{Be}$ and ${}^7\mathrm{Li}$($d,n_1$)${}^8\mathrm{Be}$ reactions

The absolute astrophysical S factor and cross section for the ${}^7\mathrm{Li}$($d,n_0$)${}^8\mathrm{Be}$ and ${}^7\mathrm{Li}$($d,n_1$)${}^8\mathrm{Be}$ reactions have been determined using deuteron beams with energies between 45 and 80 keV. The slope of the S factor is consistent with zero in the $n_0$ case but is slightly negative in the $n_1$ case. The S factor for the sum of both neutron groups at c.m. energies below 70 keV is $S(E)=5400(\pm 1500)-37(\pm 21)E$ keV b, where E is the c.m. energy in keV.

Figure 1

The measured total neutron spectrum for the ${}^7\mathrm{Li}$($d,n$)${}^8\mathrm{Be}$ reaction at an incident deuteron energy of 80 keV in the fitting region between 2 and 14 MeV. (a) The low-energy end of the fitting region; (b) the high-energy end. The legend in (b) is the same as that in (a). The energy calibration used for the x axis is uncertain to ±0.5 MeV and was determined by pinpointing the channel corresponding to the 14-MeV endpoint energy of the $n_0$ state, dividing that channel number by the energy to obtain a calibration factor, and applying that calibration factor to all channels in the spectrum.

Figure 2

Measured energy-integrated yields for (a) ${}^7\mathrm{Li}$($d,n_0$)${}^8\mathrm{Be}$ and (b) ${}^7\mathrm{Li}$($d,n_1$)${}^8\mathrm{Be}$ plotted at the incident beam energy. The error bars include statistical and systematic uncertainties. The solid lines were obtained by assuming an S factor that varies linearly with deuteron energy; the dashed lines were obtained by assuming a constant S factor (zero slope).

Figure 3

Comparison of the constant S(E) result (solid line) and the linear, nonzero-slope S(E) result (dotted line) for the (a) $n_0$ and (b) $n_1$ groups. In the $n_1$ case, the slope of the S factor makes a significant difference in the value of S(0).

Figure 4

Results of the present measurement (solid line) along with the previous data of Refs. 1, 3, and [4]. The line assumed by Ref. 1 is based on data from Ref. 2. The points for Ref. 4 were computed by assuming their differential cross-section data at ${90}^{°}$ were isotropic, multiplying them by 4π to get the total cross section, and finally using the total cross section to deduce the S factor. It should be noted that the data for Refs. 1, 3, and [4] include all neutron groups whereas the present result is for the $n_0$ and $n_1$ groups only. The dot-dashed line is the present result + 75,000 keV b, resulting from the best fit of a line with slope equal to the present slope of −37 b to the two lower energy points of Ref. 3.

Figure 5

Results of the present measurement (circular points) along with the previous data of Refs. 1, 3 and [4]. The points for Ref. 4 were computed by assuming their differential cross-section data at ${90}^{°}$ were isotropic and then multiplying them by 4π to get the total cross section. The line representing Ref. 1 was obtained by using the S-factor result they presented to compute the cross section. It should be noted that the data for Refs. 1, 3 and [4] include all neutron groups whereas the present result is for the $n_0$ and $n_1$ groups only.