Radii of 1f/sub 7/2/ neutron orbitals in isotopes of calcium and titanium

The rms radii of the valence 1f/sub 7/2/ neutron orbitals in 4448Ca and 4647484950Ti have been investigated by the (d,t) neutron pickup reaction at energies for which the triton is below the Coulomb barrier. Angular distributions were measured on each target for one or two low-lying transitions in which a neutron is picked up primarily from the 1f/sub 7/2/ orbital. Several beam energies were employed for most of the reactions, ranging from 5.8 to 10.0 MeV. Absolute cross-sections were obtained to an accuracy of 10% or better in most cases. The results were analyzed by the DWBA method using several sets of optical parameters. The cross-section of each transition depends on the overlap integral between initial and final nuclear states which is closely related to the orbital wavefunction of the transferred neutron. Using an approximate calculation for the overlap integral which takes residual interactions between valence nucleons into account to first order, an rms radius has been inferred for the 1f/sub 7/2/ neutron orbital in each of the target nuclei. The radii for 41Ca, 44Ca, 48Ca, 49Ti, and 50Ti are found to be about 4.0 +- .15 fm, while the radii for 46Ti and 48Ti are about 3.7 +- .2 fm. The uncertainties in the DWBA analysis are considerable, however, and a constant radius of 3.95 fm is not ruled out. The results are compared with other measurements for the radius of the 1f/sub 7/2/ orbital. The combined data indicate that the radius varies with nucleon number roughly as A1+-1. While the result is consistent with no change in the radius, the theoretical uncertainties in inferring rms radii from existing transfer reaction data make it difficult to determine the variation with more precision