Absolute normalization of (t,d) and (³He,d) reactions

Parameters for the d-pn, t-dn, and ³He-dp overlaps obtained from dispersion relations yield for the normalization constants for (d,p), (t,d), and (He3,d) reactions the values D²=(1.66, 3.9,and 2.9)×10⁴ MeV² fm³, respectively. These constants are employed in a comparative distorted-wave Born-approximation analysis of interrelated nucleon-transfer reactions on ⁴⁰Ca and ²⁰⁸Pb at energies near the Coulomb barrier. The relative normalization of the (t,d) and (d,p) reactions is almost independent of the wave function of the transferred nucleon and of the optical potentials. For the mirror (t,d) and (³He,d) reactions on a self-conjugate nucleus, the relative normalization depends on the ratio between root-mean-squared radii of the transferred nucleons. This ratio is calculated using a method which always yields the same relative normalization. Good consistency is found between reaction data and the normalization constants obtained from dispersion relations. NUCLEAR REACTIONS ⁴⁰Ca(d,p₀), E=3, 4, and 6 MeV. ⁴⁰Ca(³He,d₀)⁴¹Sc, E=9, 9.85, 10.7 MeV. Ca40(d, He03)K39, E=11 MeV. Measured σ(E,θ). Comparisons with ⁴⁰Ca(t, d₀)Ca41, ²⁰⁸Pb(d, t_0,1)²⁰⁷Pb, and ²⁰⁸Pb(p,d_0,1)Pb207. Deduced normalization constants for (t,d) and (³He,d) reactions.