The reaction ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}(d,d^{\prime }){}_{}{}^{10}{}_{}{}^{}\mathrm{B}$ was investigated to determine the isobaric-spin violation in exciting the lowest $T=1\mathrm{}$ state of ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$ at an excitation energy of 1.74 MeV. The extent and nature of the isobaric-spin-forbidden reaction was obtained by measuring yield curves at laboratory angles of 30, 45, and 77°, using deuteron bombarding energies from 5 to 12 MeV and at 140° from 6.5 to 16 MeV. Simultaneously, data were obtained on the nearby isobaricspin-allowed $T=0\mathrm{}$ state at 2.15 MeV. Generally, broad structure dominates the excitation functions at all angles but tends to disappear at higher bombarding energies. Angular distributions of deuterons leading both to the $T=0\mathrm{}$ and $T=1\mathrm{}$ states were obtained at five bombarding energies between 6.5 and 12.0 MeV. The angular distributions both for the forbidden ($T=1\mathrm{}$) and allowed ($T=0\mathrm{}$) state are characterized by a trend to forward peaking with increasing bombarding energies although much less so for the $T=1\mathrm{}$ state. The total cross sections were measured, and the ratios of the forbidden yield to allowed yield were found to decrease linearly from 0.69% at 6.5 MeV to 0.16% at 12 MeV. In an attempt to describe the angular distributions in terms of a direct-reaction mechanism, distorted-wave Born-approximation (DWBA) calculations were performed assuming collective excitations for the residual nucleus. No clear physical interpretation could be derived from these calculations. Indications are that the reaction ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}(d,d^{\prime }){}_{}{}^{10}{}_{}{}^{}\mathrm{B}$ proceeds through states very high in the compound nucleus ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, where the isobaric-spin violation originates in Coulomb mixing of $T=1\mathrm{}$ and $T=0\mathrm{}$ states of the same spin and parity. In view of the very small yield of deuterons leading to the lowest $T=1\mathrm{}$ state in ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$, and in view of the background difficulties anticipated and experienced, a specialized charged-particle detection system was used, consisting of a position-sensitive gas proportional counter mounted on the focal surface of a broad-range magnetic spectrograph. This constitutes the first observation of the lowest $T=1\mathrm{}$ state in ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$ by the present reaction.

[NUCLEAR REACTIONS ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}(d,d^{\prime })$, $E=5-16\mathrm{}$ MeV; measured $\sigma (E,\theta )$; ratio isobaric-spin allowed-forbidden. Enriched targets. DWBA analysis; $\theta =10-{150}^{\circ }$.]

• Received 24 September 1973

DOI:https://doi.org/10.1103/PhysRevC.9.102