Study of the (d, p) Reaction on the Even-ABarium Isotopes 130-138

The ($d, p$) reactions on ${\mathrm{Ba}}^{130,132,134,136,138}$ have been investigated with 12.0-MeV deuterons from the Argonne Tandem Van de Graaff accelerator. Proton spectra were recorded in a broad-range magnetic spectrograph. Many new levels were observed. The ground-state $Q$ values (in MeV) for the ($d, p$) reactions (including the odd-$A$ targets) are found to be 5.269 for $A=130, 4.977$ for $A=132, 4.746$ for $A=134, 6.886$ for $A=135, 4.680$ for $A=136, 6.398$ for $A=137, \mathrm{and} 2.493$ for $A=138\mathrm{}$. Proton angular distributions were measured for states up to an excitation energy of about 3 MeV. The observed angular momentum transfers were $l_n=0, 1, 2, 3, \mathrm{and} 5$, which correspond to the population of states of the $3s_{\frac{1}{2}}$ and $2d_{\frac{3}{2}}$ configurations below the closed neutron shell at $N=82\mathrm{}$ and the $2f_{\frac{7}{2}}$, $3p_{\frac{3}{2}}$, $3p_{\frac{1}{2}}$, $1h_{\frac{9}{2}}$, and $2f_{\frac{5}{2}}$ configurations above it. From the observed $l$ values, it was possible to assign spins in some isotopes from a knowledge of the spin in other isotopes by taking account of systematic shifts in the $Q$ values of levels and also from shell-model expectations. Distorted-wave Born-approximation calculations were used to extract absolute spectroscopic factors. The problems and uncertainties arising in such calculations were studied in some detail. They derive, in part, from the need to use a sharp radial cutoff to fit the experimental angular distributions; calculations with nonlocal potentials and finite-range approximations did not yield satisfactory fits. Another source of uncertainty is the dependence of the spectroscopic factors upon the geometric parameters of the bound-state potential well. The results are interpreted with the help of pairing theory; centers of gravity and single-particle energies are deduced.