Mixing strength in the two lowest $0^{-}$ states in ${}^{208}\mathrm{Pb}$

With a resolution of 3 keV, the two lowest $0^{-}$ states in ${}^{208}\mathrm{Pb}$ are identified by measurements of the reaction ${}^{207}\mathrm{Pb}$$(d,p)$ with the München Q3D magnetic spectrograph in the region $E_x=5.2\text{−}5.7$ MeV where the average level spacing is 6 keV. Precise relative spectroscopic factors are determined. Matrix elements of the residual interaction among one-particle one-hole configurations in a two-level scheme are derived for the two lowest $0^{-}$ states in ${}^{208}\mathrm{Pb}$. The off-diagonal mixing strength is determined as $110\pm 10\text{(experimental)}\pm 15\text{(systematic)}$ keV. Measurements of the reaction ${}^{208}\mathrm{Pb}$$(p,p^{\text{'}})$ via isobaric analog resonances in ${}^{209}\mathrm{Bi}$ support the structure information obtained.

Figure 1

Two lowest $0^{-}$ configurations in ${}^{208}\mathrm{Pb}$, neutron particle-hole configurations $s_{1/2}{p}_{1/2}$ and $d_{5/2}{f}_{5/2}$, are separated from the next higher configurations by a large gap $\Delta ,$ allowing us to discuss the simple case of two-level configuration mixing in the $\underline{|1,0^{-}\rangle }$ and $\underline{|2,0^{-}\rangle }$ states at $E_x=5280,5599$ keV. Residual interaction $v$ is decomposed into m.e. $v_{11}$ and $v_{22}$ describing the shift of the two levels and m.e. $v_{12}=v_{21}$ describing the level repulsion.

Figure 2

${}^{207}\mathrm{Pb}$$(d,p)$ spectrum taken at $\Theta ={30}^{°}$ for $E_x=5.23\text{−}5.36$ MeV. The 5280 $0^{-}$ state (marked •) is resolved from the two neighbors in 4–7 keV distance. It is displayed on a logarithmic scale because the background is 1/2000 of the maximum peak, but many levels with 1% of the maximum are clearly resolved. Curves show the fit by the computer code GASPAN [10], where the energies are taken from Table and only the centroid of all energies together and the peak heights are varied. The widths and tails are interpolated from a table generated by inspection of several strong, rather isolated peaks in the whole spectrum covering about 1.2 MeV, nearly ten times more than shown. A weak contamination line from ${}^{23}\mathrm{Na}$ is identified near $E_x=5.31$ MeV.

Figure 3

${}^{207}\mathrm{Pb}$$(d,p)$ spectrum taken at $\Theta ={25}^{°}$ for $E_x=5.54\text{−}5.65$ MeV. The 5599 $0^{-}$ state (marked •) is well isolated. For other details, see Fig. 2.