C14(p, n)N14Reaction and the Two-Body Force

Abstract

The ${\mathrm{C}}^{14}(p, n){\mathrm{N}}^{14}$ reaction to the ground and first two levels of ${\mathrm{N}}^{14}$ has been investigated for proton energies between 6 and 14 MeV. The angular distributions at the highest energies have been analyzed by using a finite range distorted-wave Born-approximation formalism, assuming the two-body force to be of the form ${\tau }_0·{\tau }_i(b+a{\sigma }_0·{\sigma }_i)f\left(r_{0i}\right)$, where ${\tau }_0$ and ${\sigma }_0$ refer to the isospin and spin of the incident nucleon, ${\tau }_i$ and ${\sigma }_i$ refer to isospin and spin of the extra-core target nucleons, and $f\left(r_{0i}\right)$ is the Yukawa form factor with a range of 1.4 F. Calculations employing Visscher-Ferrell wave functions for ${\mathrm{C}}^{14}$ and ${\mathrm{N}}^{14}$ gave a good fit for the $0^{+}$→$0^{+}$ transition and a reasonable value for $b$ of 9 MeV. However, the calculations for the $0^{+}$→$1^{+}$ ground-state and second-excited-state transitions yielded inconsistent values for $a$ of 7 MeV for the excited transition and 21 MeV for the ground-state transition. This latter result is not unexpected, since $\left({\tau }_0·{\tau }_i\right)\left({\sigma }_0·{\sigma }_i\right)$ is related to the Gamow-Teller $\beta$-decay operator. The fact that experimentally the ($p, n$) reaction to the ground state is not inhibited (while the corresponding $\beta$ decay is strongly suppressed) indicates that the spin and charge-exchange operator is not sufficient to account for the ($p, n$) ground-state transition. An explanation of the observed ground-state cross section in ${\mathrm{C}}^{14}(p, n)$ requires additional spin-flip mechanisms such as a tensor interaction or particle exchange.