High-Resolution Study ofCo56by (d,α) and (He3,p) Reactions

Abstract

Levels of ${\mathrm{Co}}^{56}$ up to 4.4-MeV excitation have been studied by the direct ${\mathrm{Ni}}^{58}(d,\alpha ){\mathrm{Co}}^{56}$ reaction at a deuteron energy of 17 MeV. Experimental resolution of 9 to 12 keV permitted investigation of many previously unknown states. ${\mathrm{Fe}}^{54}({\mathrm{He}}^3,p){\mathrm{Co}}^{56}$ spectra at $E_{{\mathrm{He}}^3}=18\mathrm{}$ MeV were taken in order to supplement an earlier low-resolution study at the same energy. The total experimental resolution obtained for this reaction was 16 keV and permitted investigation of previously unresolved doublets. Accurate (±0.3%) excitation energies were obtained for about 80 ${\mathrm{Co}}^{56}$ levels. ${\mathrm{Ni}}^{58}(d,\alpha ){\mathrm{Co}}^{56}$ angular distributions obtained by other investigators with 12- and 15-MeV deuterons had presented serious difficulties in the attempted analysis with distorted-wave Born-approximation (DWBA) calculations. At 17 MeV, given $L$ values led to characteristic shapes which could be recognized empirically and crudely fit by "conventional" DWBA curves. Stock et al. had shown in 1967 that finite-range corrections become less important and DWBA results more reliable for (${\mathrm{He}}^3,\alpha$) if $V_{{\mathrm{He}}^3}+V_n\approx V_{\alpha }$. We generalized this prescription to two-nucleon transfers and found similarly positive results, provided that the radii of all real wells were kept near $1.2A^{\frac{1}{3}}$ fm. With this "well-matching" prescription our microscopic DWBA calculations were improved to the point that the correlation of $L=0, 2, 4, 6$ curves to positive-parity states became unambiguous. In the study of individual ${\mathrm{Co}}^{56}$ states we used ($p,{\mathrm{He}}^3$) and (${\mathrm{He}}^3,t$) results of other investigators together with our own data to suggest $J^{\pi }$ assignments or narrow $J^{\pi }$ limits for 46 states. It was found particularly useful to investigate the $\frac{\sigma (d,\alpha )}{\sigma (p,{\mathrm{He}}^3)}$ ratio for given $L$ transfer. As expected on theoretical grounds, cross sections for $J^{+}$ (odd) levels showed large and nearly constant ratios. Ratios for transition strengths to known $J^{+}$ (even) states were significantly smaller and vanished for $T_{>}$ states. The properties of 15 low-lying levels could be correlated with those of states predicted in recent shell-model calculations by J. McGrory. The importance of two-particle-two-hole configurations in most of these states was demonstrated. Remaining discrepancies might be explained by a sizable four-hole-two-particle strength in ${\mathrm{Ni}}^{58}$(g.s).