Benchmark on neutron capture extracted from $(d,p)$ reactions

Direct neutron capture reactions play an important role in nuclear astrophysics and applied physics. Since for most unstable short-lived nuclei it is not possible to measure the $(n,\gamma )$ cross sections, $(d,p)$ reactions have been used as an alternative indirect tool. We analyze simultaneously ${}^{48}\mathrm{Ca}(d,p){}^{49}\mathrm{Ca}$ reactions at deuteron energies of $2,13,19,$ and 56 MeV and the thermal $(n,\gamma )$ reaction at 25 meV. We include results for the ground state and the first excited state of ${}^{49}\mathrm{Ca}$. From the low-energy $(d,p)$ reaction, the neutron asymptotic normalization coefficient (ANC) is determined. Using this ANC, we extract the spectroscopic factor (SF) from the higher energy $(d,p)$ data and the $(n,\gamma )$ data. The SF obtained through the 56-MeV $(d,p)$ data are less accurate but consistent with those from the thermal capture. We show that to have a similar dependence on the single-particle parameters as in the $(n,\gamma )$, the $(d,p)$ reaction should be measured at 30 MeV.

Figure 1

Angular distributions for ${}^{48}\mathrm{Ca}(d,p){}^{49}\mathrm{Ca}$ compared to data populating the ground state: $E_d=13$ MeV (red dotted line), $E_d=19$ MeV (green dashed line), and $E_d=56$ MeV (blue dot-dashed line). Also shown are the angular distributions to the first excited state: $E_d=13$ MeV (black, thin dotted line) and $E_d=19$ MeV (black, thin dashed line).

Figure 2

$S_{\exp }(b)$ from ${}^{48}\mathrm{Ca}(d,p){}^{49}\mathrm{Ca}(g.s.)$ at $E_d=1.99$ MeV (green dots), $E_d=13$ MeV (red squares), $E_d=19$ MeV (purple diamonds), $E_d=30$ MeV (open circles), and $E_d=56$ MeV (open triangles), and from ${}^{48}\mathrm{Ca}(n,\gamma ){}^{49}\mathrm{Ca}(g.s.)$ at 25 meV (blue triangles). Also shown are the experimental uncertainties in the $(d,p)$ reaction at $1.99$ MeV (dashed lines) and at 56 MeV (long-dashed lines) and the $(n,\gamma )$ reaction (solid lines).

Figure 3

Same as Fig. 2 but now referring to the ANC $C_{\exp }^2(b)$. ANC and SF are related by Eq. (3).

Figure 4

Same as Fig. 3 but now referring to first excited state in ${}^{49}\mathrm{Ca}$.