Features of the (t,p) reaction below the Coulomb barrier of the entrance channel

The differential cross sections for the reactions ${}_{}{}^{63,65}{}_{}{}^{}\mathrm{Cu}\mathrm{}(t,p)\mathrm{}{}_{}{}^{65,67}{}_{}{}^{}\mathrm{Cu}$ were measured at $E_t=3.2, 3.0, \mathrm{and} 2.8$ MeV. For $L=0\mathrm{}$ ground-state transitions, the energy dependence of the values of the differential cross sections is strong and exponential, while the angular distribution shape, which is of a clear diffraction pattern in sharp contrast to the case of the sub-Coulomb ($d,p$) reaction, does not change with small energy variation. The reactions proceed well below the Coulomb barrier of the entrance channel, yet through a direct process. A definite difference is observed between the angular distributions for the two ground-state transitions. The zero-range distorted-wave Born approximation can reproduce the energy dependence of the differential cross sections and the trend of isotope dependence of the angular distribution. In distorted-wave Born approximation calculations, a definite nuclear optical potential is needed for the triton-nucleus channel which is below the Coulomb barrier, in sharp contrast to the sub-Coulomb ($d,p$) reaction. The triton-nucleus optical potential below the Coulomb barrier is nearly equal to the optical potential that works at energies of a few tens of MeV. The angular distribution for an $L=2\mathrm{}$ transition is forward-rising, though not diffractionlike, and can be reproduced on the whole by the zero-range distorted-wave Born approximation. It is confirmed for the first time that the ($t,p$) reaction below the Coulomb barrier of the entrance channel takes place in an extended region outside the nucleus. It is argued and concluded on various grounds that the ($t,p$) angular distribution shape below the Coulomb barrier of the entrance channel is sensitive to the radial two-neutron from factor outside the nucleus. Physical implications of the revealed features are discussed, especially on the coherence of the two-particle form factor and the proton and neutron distributions in the nuclear surface region.