Spin determination of valence and inner hole states via the 208Pb(d

Abstract

Highly excited neutron hole states in $^{207}\mathrm{Pb}$ have been studied via the (d\ensuremath{\rightarrow},t) reaction at ${\mathit{E}}_{\mathit{d}}$=200 MeV using for the first time a polarized beam, with both vector and tensor components. The determination of overlapping neutron hole response functions takes advantage of the strong characteristic features of ${\mathit{j}}_{\mathrm{\ensuremath{-}}}$=l-1/2 versus ${\mathit{j}}_{+}$=l+1/2 level analyzing powers and of the good distorted wave Born approximation (DWBA) description of the reaction. A least-squares fit analysis of the \ensuremath{\sigma}, ${\mathit{A}}_{\mathit{y}}$, and ${\mathit{A}}_{\mathit{y}\mathit{y}}$ angular distributions has allowed a determination of the high j transition spectroscopic factors contributing to the excitation energy bins up to ${\mathit{E}}_{\mathit{x}}$=14.5 MeV. The results are compared in details with those relying only on l identification, previously obtained in the 1${\mathit{i}}_{13/2}$ and 1${\mathit{h}}_{9/2}$ valence state fragmentation up to ${\mathit{E}}_{\mathit{x}}$=6.7 MeV and on the 1${\mathit{h}}_{11/2}$ strength up to \ensuremath{\sim}10 MeV. Several previous conclusions are unambiguously confirmed, in particular, the attribution of the bump around ${\mathit{E}}_{\mathit{x}}$=8.2 MeV to the 1${\mathit{h}}_{11/2}$ strength. In addition, the present experiment settles the attributions of several ${\mathit{j}}_{\mathrm{\ensuremath{-}}}$ versus ${\mathit{j}}_{+}$ valence groups and indicates that the 1${\mathit{h}}_{9/2}$ strength is spread up to \ensuremath{\sim}10.8 MeV.The analysis performed up to ${\mathit{E}}_{\mathit{x}}$=14.5 MeV gives the first determination of the 1${\mathit{h}}_{11/2}$ strength beyond the bump, and a first reliable evidence for the 1${\mathit{g}}_{7/2}$ strength, with the maximum around ${\mathit{E}}_{\mathit{x}}$=11 MeV. \ensuremath{\sim}85% of these inner hole state sum rules are exhausted in the studied excitation energy range. The spin-orbit splitting of 1h orbitals in $^{208}\mathrm{Pb}$ deduced from the strength centroids is 5.2 MeV. The experimental strength distributions and the integral characteristics of the 1${\mathit{i}}_{13/2}$, 1${\mathit{h}}_{9/2}$, 1${\mathit{h}}_{11/2}$, and 1${\mathit{g}}_{7/2}$ hole states are compared with the results from different theoretical approaches, i.e., microscopic calculations of the fragmentation and phenomenological calculations of spectral functions in a modified mean field. The comparison reports on the sharing of the valence strengths between each quasihole level and the other fragments, characterized by their centroids and widths, and on the shape of the inner hole strength distributions, the centroids and spreading widths.