Reconciling Coulomb breakup and neutron radiative capture

The Coulomb-breakup method to extract the cross section for neutron radiative capture at astrophysical energies is analyzed in detail. In particular, its sensitivity to the description of the neutron-core continuum is ascertained. We consider the case of ${}^{14}\mathrm{C}(n,\gamma ){}^{15}\mathrm{C}$ for which both the radiative capture at low energy and the Coulomb breakup of ${}^{15}\mathrm{C}$ into ${}^{14}\mathrm{C}+n$ on Pb at 68 MeV/nucleon have been measured with accuracy. We confirm the direct proportionality of the cross section for both reactions to the square of the asymptotic normalization constant of ${}^{15}\mathrm{C}$ observed by Summers and Nunes [Phys. Rev. C 78, 011601(R) (2008)], but we also show that the ${}^{14}\mathrm{C}-n$ continuum plays a significant role in the calculations. Fortunately, the method proposed by Summers and Nunes can be improved to absorb that continuum dependence. We show that a more precise radiative-capture cross section can be extracted selecting the breakup data at forward angles and low ${}^{14}\mathrm{C}-n$ relative energies.

Figure 1

Reduced radial ground-state wave functions of ${}^{15}\mathrm{C}$ obtained with the three potentials given in Table 1, labeled by their diffuseness.

Figure 2

Phases shifts in the ${}^{14}\mathrm{C}-n p$ wave for the four different potentials described in Table 1.

Figure 3

Breakup cross section for ${}^{15}\mathrm{C}$ impinging on Pb at 68 MeV/nucleon as a function of the ${}^{14}\mathrm{C}-n$ relative energy $E$. The calculations, folded with the experimental energy resolution, have been obtained with twelve different descriptions of ${}^{15}\mathrm{C}$. The color correspond to the different bound states (see Fig. 1) while the line types distinguish the different descriptions of the $p$ continuum (see Fig. 2). Experimental data are from Ref. [14] and correspond to the selection over the whole experimental angular range ($\mathrm{\Theta }<6^{\circ }$).

Figure 4

Role of the description of the ${}^{14}\mathrm{C}-n$ continuum on breakup calculations illustrated by the dimensionless function $S_0^1\left(1\right)$ introduced by Typel and Baur [26, 27].

Figure 5

Cross sections for the radiative capture ${}^{14}\mathrm{C}(n,\gamma ){}^{15}\mathrm{C}$ as a function of the ${}^{14}\mathrm{C}-n$ relative energy $E$. Calculations with the twelve different descriptions of ${}^{15}\mathrm{C}$ are shown in the same line type and color code as in Fig. 3. The experimental data are from Ref. [15].

Figure 6

Breakup calculations scaled to the RIKEN experimental data [14] ($\mathrm{\Theta }<6^{\circ }$). Calculations with the 12 different descriptions of ${}^{15}\mathrm{C}$ are shown in the same line type and color code as in Fig. 3.

Figure 7

Theoretical radiative-capture cross sections, multiplied by the scaling factor extracted from ${}^{15}\mathrm{C}$ Coulomb-breakup measurements, are confronted with the experimental data of Reifart et al. [15].

Figure 8

Theoretical breakup cross sections for ${}^{15}\mathrm{C}$ scaled to the data of Ref. [14] limited to $E=0.5\mathrm{MeV}$ in the ${}^{14}\mathrm{C}-n$ continuum ($\mathrm{\Theta }<6^{\circ }$).

Figure 9

Theoretical radiative-capture cross sections multiplied by the scaling factor extracted from ${}^{15}\mathrm{C}$ Coulomb breakup limited to 0.5 MeV in the ${}^{14}\mathrm{C}-n$ continuum.

Figure 10

Theoretical radiative-capture cross sections multiplied by the scaling factor extracted from ${}^{15}\mathrm{C}$ Coulomb breakup selected at forward angles ($\mathrm{\Theta }<2.1^{\circ }$) and limited to $E=0.5\mathrm{MeV}$ in the ${}^{14}\mathrm{C}-n$ continuum.