Shell-Model States and Configuration Mixing in the Ti Isotopes by the (p, d) Reaction

Abstract

The energy spectra and angular distributions of deuterons resulting from the bombardment of ${\mathrm{Ti}}^{46}$, ${\mathrm{Ti}}^{47}$, ${\mathrm{Ti}}^{48}$, ${\mathrm{Ti}}^{49}$, and ${\mathrm{Ti}}^{50}$ with 17.5-MeV protons have been measured. For even-$A$ targets, one strong transition is observed while for odd-$A$ targets a large number of levels are strongly excited. The deuteron angular distributions show that these strong transitions are due to the pickup of an $l_n=3\mathrm{}$ neutron. A number of even-$l$ transitions corresponding to the pickup of neutrons from the already filled $1d_{\frac{3}{2}}$ and $2s_{\frac{1}{2}}$ shells have also been observed. The $Q$ values for the pickup of $l_n=2\mathrm{}$ neutrons from the even-$A$ Ti isotopes show an interesting feature in that they are found to be approximately independent of the Ti isotope used. A few $l_n=1\mathrm{}$ transitions have also been observed indicating $p$-wave admixture in the ground level wave functions of the target nuclei. By comparison of the experimental result with DWBA calculation, spectroscopic factors have been calculated for the transitions observed. The spectroscopic factors and excitation energies for $l_n=3\mathrm{}$ transitions have been compared to recent theoretical predictions where it is assumed that protons and neutrons in excess of 20 can be treated as belonging to a pure ${\left(1\mathrm{}{f}_{\frac{7}{2}}\right)}^n$ configuration.