Distorted-Wave Born-Approximation Analysis of theZr90(d,α)Y88andY89(He3,α)Y88Reactions

Abstract

The levels of $^{88}\mathrm{Y}$ have been studied with the $^{90}\mathrm{Zr}(d,\ensuremath{\alpha})$ and $^{89}\mathrm{Y}(^{3}\mathrm{He},\ensuremath{\alpha})$ reactions with 30-to 40-keV resolution at 15-MeV incident energy. The ($d,\ensuremath{\alpha}$) angular distributions for transitions to eight prominent levels below 2.2 MeV have been measured over $15\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}\ensuremath{\theta}\ensuremath{\le}150\ifmmode^\circ\else\textdegree\fi{}$. The reliability of parameters entering distorted-wave Born-approximation calculations was checked in detail. The ($d,\ensuremath{\alpha}$) calculations include the finite-range correction of Chant and Mangelson. The two-nucleon form factors (f.f.) were generated by the oscillator-expansion technique of Drisko and Rybicki, and the effect of residual interaction on the f.f. and angular distributions was studied. An attempt has been made to determine the ($d,\ensuremath{\alpha}$) absolute normalization constant based on local zero-range calculations, and limits of $20\ensuremath{\le}D_{0}^{}{}_{}{}^{2}\ensuremath{\le}30$ have been set. Two-nucleon f.f. generated by the Bayman-Kallio method were compared with the Drisko-Rybicki f.f. The ($^{3}\mathrm{He},\ensuremath{\alpha}$) angular distributions for eight strongly populated levels below 1.7 MeV were measured over $20\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}\ensuremath{\theta}\ensuremath{\le}125\ifmmode^\circ\else\textdegree\fi{}$. Spectroscopic factors and ${l}_{n}$ transfers have been extracted with both local zero-range and nonlocal finite-range calculations. The ($^{3}\mathrm{He},\ensuremath{\alpha}$) results were compared with ($d,\ensuremath{\alpha}$) results to determine unique parities and narrow ${J}^{\ensuremath{\pi}}$ limits for the levels studied. $^{3}\mathrm{He}$ and $\ensuremath{\alpha}$ elastic scattering on $^{89}\mathrm{Y}$ have also been measured and optical-model potentials have been determined. Good agreement between this work and the recently reported $^{85}\mathrm{Rb}(\ensuremath{\alpha},n\ensuremath{\gamma})^{88}\mathrm{Y}$ results is seen for the level energy and ${J}^{\ensuremath{\pi}}$ assignments made.