Low lying particle-hole states in $$^\mathbf{206 }$$Pb and $$^\mathbf{208 }$$Pb and the shell model

Abstract

The nucleus $$^{206}\mathrm{Pb}$$ 206 Pb differs from the doubly magic nucleus $$^{208}\mathrm{Pb}$$ 208 Pb by two missing neutrons. In $$^{208}\mathrm{Pb}$$ 208 Pb most states at $$E_x< 7.4$$ E x < 7.4 MeV are described by one-particle one-hole configurations. The lowest configurations with a g$$_{{ 9}/{2}}$$ 9 / 2 particle and dominant p$$_{{ 1}/{2}}$$ 1 / 2 , f$$_{{ 5}/{2}}$$ 5 / 2 , p$$_{{ 3}/{2}}$$ 3 / 2 holes and admixtures from f$$_{{ 7}/{2}}$$ 7 / 2 and a few more configurations build an ensemble of two dozen states at 3.2$$<E_x< 4.9$$ < E x < 4.9 MeV. They are described by rather complete orthonormal transformation matrices of two dozen states with spins from 2$$^-$$ - to 8$$^-$$ - to configurations. In $$^{206}\mathrm{Pb}$$ 206 Pb a similar ensemble of states is deduced from the analysis of angular distributions measured in 1969 for the $$^{206}\mathrm{Pb}$$ 206 Pb $$({{{\textit{p}}}, {{\textit{p}}}' })$$ ( p , p ′ ) reaction via the g$$_{{ 9}/{2}}$$ 9 / 2 IAR in $$^{207}\mathrm{Bi}$$ 207 Bi . An equivalent $$^{208}\mathrm{Pb}$$ 208 Pb $$({{{\textit{p}}}, {{\textit{p}}}' })$$ ( p , p ′ ) experiment was performed in 1968 at the Max–Planck–Institut für Kernphysik at Heidelberg (Germany). New spins are determined for 32 states and 22 levels in $$^{206}\mathrm{Pb}$$ 206 Pb . The comparison to corresponding states in $$^{208}\mathrm{Pb}$$ 208 Pb studied especially in 1982 yields both remarkable similarities and clear differences. Sizeable g$$_{{ 9}/{2}}$$ 9 / 2 p$$_{{ 1}/{2}}$$ 1 / 2 strength found in 4$$^-$$ - and 5$$^-$$ - states is interpreted as admixtures of $${{\textit{p}}}{_{{ 3}/{2}}}^{-2}$$ p 3 / 2 - 2 and $${{\textit{f}}}{_{{ 5}/{2}}}^{-2}$$ f 5 / 2 - 2 components to the ground state of $$^{206}\mathrm{Pb}$$ 206 Pb with dominant $${{\textit{p}}}{_{{ 1}/{2}}}^{-2}$$ p 1 / 2 - 2 character. The description of nuclear states by shell model particle-hole configurations in the lead region needs the inclusion of collective excitations at already very low excitation energies. For the two isotopes $$^{206}\mathrm{Pb}$$ 206 Pb and $$^{208}\mathrm{Pb}$$ 208 Pb a rather good agreement of excitation energies and configuration mixing is observed for states at 3.7$$<E_x< 4.7$$ < E x < 4.7 MeV.