Microscopic Analysis of the (He3,t) and (He3,He3′) Reactions on1p-Shell Nuclei

The (${}_{}{}^3{}_{}{}^{}\mathrm{He},t$) and (${}_{}{}^3{}_{}{}^{}\mathrm{He}$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$′) reactions on ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ [(${}_{}{}^3{}_{}{}^{}\mathrm{He},t$) reaction only], ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, and ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ have been investigated at ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ energies varying between 40 and 50 MeV. Angular distributions were obtained for all prominent states up to excitations of 20 MeV. A microscopic analysis of these data has been carried out, using a local two-body interaction with an arbitrary spin-isospin exchange mixture. Spectroscopic factors were calculated, using intermediate-coupling wave functions for $p$-shell states, while simple $j-j$ configurations were assumed for the levels which were populated by promoting a $p$ nucleon to the $s-d$ shell. A Yukawa interaction with a range of 1.2 F was found to give the best results. The strength of the effective nucleon-nucleon interaction required to fit these data is in good agreement with recent analyses of the ($p,p^{\prime }$) and ($p,n$) reactions on light nuclei. In particular, dominant $L=0\mathrm{}$ transitions observed in the (${}_{}{}^3{}_{}{}^{}\mathrm{He},t$) reaction give values for the isospin-dependent ($V_{\mathrm{ST}}=V_{01}$) and spin-isospin-dependent ($V_{11}$) terms (converted to an effective nucleon-nucleon interaction at a range of 1.0 F) of 20.6 and 16.5 MeV, respectively, while the strengths required to fit (${}_{}{}^3{}_{}{}^{}\mathrm{He},t$) $L=2,3\mathrm{}$ transitions were generally enhanced. For inelastic transitions, the average strengths obtained for $V_{00}$, assuming a Serber exchange mixture, varied from 47.2 to 67.3 MeV, depending upon the $L$ transfer involved. A comparison of the (${}_{}{}^3{}_{}{}^{}\mathrm{He},t$) and (${}_{}{}^3{}_{}{}^{}\mathrm{He}$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$′) reactions populating analog final states (where $T_f=T_i+1\mathrm{}$) is also presented. In general, these transitions were weak; however, it was possible to observe the lowest $T=\frac{3}{2}$ levels in the mirror nuclei ${}_{}{}^9{}_{}{}^{}\mathrm{B}$-${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ and ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$-${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, and several $T=1\mathrm{}$ levels in ${}_{}{}^{12}{}_{}{}^{}\mathrm{N}$-${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$.