Sub-Coulomb ${}^3\mathrm{He}$ transfer and its use to extract three-particle asymptotic normalization coefficients

Data for the ${}^{13}\mathrm{C}({}^6\mathrm{Li},t){}^{16}\mathrm{O}$ reaction, obtained in inverse kinematics at a ${}^{13}\mathrm{C}$ incident energy of 7.72 MeV, are presented. A distorted wave Born approximation (DWBA) analysis was used to extract spectroscopic factors and asymptotic normalization coefficients (ANCs) for the $〈{}^{16}\mathrm{O}\mid {}^{13}\mathrm{C}+{}^3\mathrm{He}〉$ overlaps, subject to the assumption of a fixed $〈{}^6\mathrm{Li}\mid {}^3\mathrm{He}+{}^3\mathrm{H}〉$ overlap. The variation of the extracted spectroscopic factors and ANCs as a function of various inputs to the DWBA calculations was explored. The extracted ANCs were found to vary as a cubic function of the radius of the potential well binding the transferred ${}^3\mathrm{He}$ to the ${}^{13}\mathrm{C}$ core while the spectroscopic factors varied as a quartic function of the radius. The ANC values could be determined to within a factor of two for this system.

Figure 1

$\mathrm{\Delta }E$ vs. $E$ two-dimensional scatter plot for a pin detector at ${30}^{\circ }$ in the laboratory reference frame used for particle identification. A typical triton selection gate is shown by the solid lines.

Figure 2

Spectrum of tritons from the ${}^{13}\mathrm{C}({}^6\mathrm{Li},t){}^{16}\mathrm{O}$ reaction at a triton scattering angle of ${137}^{\circ }$ in the center of mass reference frame.

Figure 3

Angular distributions for the ${}^{13}\mathrm{C}({}^6\mathrm{Li},t){}^{16}\mathrm{O}$ reaction to: (a) the 6.05 MeV $0^{+}$ state, (b) the 6.13 MeV $3^{-}$ state, (c) the 6.92 MeV $2^{+}$ state, and (d) the 7.12 MeV $1^{-}$ state. The solid curves denote the results of calculations using the full (nuclear plus Coulomb) distorting potentials in both entrance and exit channels, the dotted curves calculations using the full potential in the exit channel but only the Coulomb potential in the entrance channel, the dashed curves calculations using the full potential in the entrance channel but only the Coulomb potential in the exit channel, and the dot-dashed curves calculations using only the Coulomb potential in both entrance and exit channels.

Figure 4

Angular distributions for the ${}^{13}\mathrm{C}({}^6\mathrm{Li},t){}^{16}\mathrm{O}$ reaction to: (a) the 6.05 MeV $0^{+}$ state, (b) the 6.13 MeV $3^{-}$ state, (c) the 6.92 MeV $2^{+}$ state, and (d) the 7.12 MeV $1^{-}$ state. The dashed and dotted curves denote DWBA fits with distorting potentials calculated using global parameter sets in both entrance and exit channels and the exit channel only, respectively. The solid curves denote DWBA fits with entrance and exit channel distorting potentials taken from Refs. [15, 16], respectively, repeated from Fig. 3.

Figure 5

Spectroscopic factor and ${\mathrm{ANC}}^2$ values for the $〈{}^{16}\mathrm{O}\mid {}^{13}\mathrm{C}+{}^3\mathrm{He}〉$ overlaps to: (a), (e) the 6.05 MeV $0^{+}$ state; (b), (f) the 6.13 MeV $3^{-}$ state; (c), (g) the 6.92 MeV $2^{+}$ state; (d), (h) the 7.12 MeV $1^{-}$ state as a function of $r_0$. See text for details.