Valence component in the threshold photoneutron spectrum ofZr91

Abstract

Ground-state radiation widths (${\ensuremath{\Gamma}}_{\ensuremath{\gamma}0}$) for 36 ${p}_{\frac{3}{2}}$ photoneutron resonances in $^{91}\mathrm{Zr}$ have been measured from 5-225 keV above threshold at the Argonne National Laboratory threshold photoneutron facility. Reduced neutron widths (${{\ensuremath{\gamma}}_{n}}^{2}$) for the same resonances were obtained at the Oak Ridge Electron Linear Accelerator facility from total-cross-section measurements on $^{90}\mathrm{Zr}$. A strong correlation ($\ensuremath{\rho}=+0.59$) is observed between the two sets of widths. Because of a lack of knowledge of the relative phase of the compound-nucleus and valence amplitudes in the individual resonances, the average valence component cannot be deduced from the correlation analysis. However, one can obtain a mean compound-nucleus contribution by studying those resonances where the valence amplitude is expected to be negligible. By using such a procedure, an average valence component is obtained which is in excellent agreement with the average valence strength calculated from the valence model. The $s$-wave neutron strength function is ${S}^{0}=(6.2\ifmmode\pm\else\textpm\fi{}1.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ and the $p$-wave strength function is ${S}^{1}$ = (3.2 \ifmmode\pm\else\textpm\fi{} 0.8) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}4}$. The reduced photon width for $E1$ transitions is $\overline{k}(E1)=(3.2\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, in agreement with the single-particle reduced width derived from the Weisskopf model. The neutron widths are observed to follow a Porter-Thomas distribution, while the photon widths appear to follow a ${\ensuremath{\chi}}^{2}$ distribution with two degrees of freedom.[NUCLEAR REACTIONS $^{91}\mathrm{Zr}(\ensuremath{\gamma},n)$, ${E}_{\ensuremath{\gamma}}=9.0$ MeV; deduced ${\ensuremath{\Gamma}}_{\ensuremath{\gamma}0}$ of resonances. $^{90}\mathrm{Zr}$($n$, total), ${E}_{n}=5\ensuremath{-}225$ keV; measured $\ensuremath{\sigma}(E)$, deduced ${{\ensuremath{\gamma}}_{n}}^{2}$ of resonances. Determined correlation, calculated valence contribution to ${\ensuremath{\Gamma}}_{\ensuremath{\gamma}0}$; calculated strength functions.]