Shell-Model Structure ofTi48Studied via the (d,t) and (α,α′) Reactions

Measurements of the ${}_{}{}^{49}{}_{}{}^{}\mathrm{Ti}\mathrm{}(d,t)\mathrm{} {}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}$ reaction have been carried out at 18 MeV with an energy resolution of about 10 keV. Single-particle strength distributions for $l=0,2,\mathrm{and} 3$ have been obtained up to excitation energy of 7 MeV in ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}$. About 85% of the $l=3\mathrm{}$ strength is found in states below 3.6 MeV, and the total $l=3\mathrm{}$ strength is consistent with the sum rule limit for $1f_{\frac{7}{2}}$ transfer to $T=2\mathrm{}$ states. About three quarters of the sum rule limit for the $l=2\mathrm{}$ strength (assumed be $1d_{\frac{3}{2}}$) and half the limit for the $l=0,2\mathrm{}{s}_{\frac{1}{2}}$ strength is observed, with lower limits for the centroid energies of 5.36 and 5.17 MeV for the $1d_{\frac{3}{2}}$ and $2s_{\frac{1}{2}}$ hole, respectively. Measurements of inelastic $\alpha$ scattering on ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}$ have also been carried out at an incident energy of 28.5 MeV with a resolution of 18 keV. These measurements provide many new spin-parity assignments for natural parity states in ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}$. In combination with the pickup measurements, they provide identification for the centroids of the $J^{\pi }={\mathrm{}(2,3,4,5)\mathrm{}}^{-}$ states of the (${f_{\frac{7}{2}}}^9\times {d_{\frac{3}{2}}}^{-1\mathrm{}}$) multiplet.