Determining the strength of undetectable particle-hole configurations by complete spectroscopy of negative parity states inPb208

Abstract

In the doubly magic nucleus $^{208}\mathrm{Pb}$, many states contain fractions of particle-hole configurations whose strength can be determined from experiment. However, some configurations are not excited in a directly detectable way. Their strengths can be determined by observing an ensemble of states which consists entirely of an equivalent set of configurations with a given spin and parity among which only one or two configurations are not detected. Examples for spins ${2}^{\ensuremath{-}}$--${5}^{\ensuremath{-}}$ are evaluated. Excitation energies of states in $^{208}\mathrm{Pb}$ are determined with a precision down to 100 eV by experiments on the $^{208}\mathrm{Pb}$$(p,{p}^{\ensuremath{'}})$ and $^{207}\mathrm{Pb}$$(d,p)$ reactions with the Q3D magnetic spectrograph (Maier-Leibnitz-Laboratorium, Garching, Germany). Six doublets with distances between the states of less than 2 keV are resolved. 72 negative parity states below ${E}_{x}=6.1$ MeV are identified. They correspond to 70 states predicted by the schematic shell model without residual interaction below ${E}_{x}=6361$ keV. The ${1}^{\ensuremath{-}}$ and ${3}^{\ensuremath{-}}$ yrast states appear in addition. Six new spins are assigned to negative parity states, three new spins to positive parity states, and two spins suggested by the Nuclear Data Sheets are verified. The state at ${E}_{x}=4953$ keV is identified as the 3${}^{+}$ member of the configuration ${g}_{9/2}$${i}_{13/2}$. Among about hundred states, the configuration mixing for unnatural parity is shown to be less than for natural parity.