Description of one-particle one-hole configurations coupled to the $3^{-}$ yrast state in the doubly magic nucleus ${}^{208}\mathrm{Pb}$

In ${}^{208}\mathrm{Pb}$, 14 states at $E_x\approx 6.0\mathrm{MeV}$ are identified as members of a multiplet where the one-particle one-hole configuration $g_{9/2}{p}_{1/2}$ is coupled to the $3^{-}$ yrast state. The coupling is described by the geometry of the recoupling of three spins and the large coupling strength of the one-particle one-hole configurations to the strongly collective $3^{-}$ yrast state.

Figure 1

The multiplets $g_{9/2}{p}_{1/2}\otimes 3_1^{-},g_{9/2}{f}_{5/2}\otimes 3_1^{-}$, and $i_{11/2}{p}_{1/2}\otimes 3_1^{-}$ in ${}^{208}\mathrm{Pb}$ predicted by Eq. (9). A factor $F^{\mathrm{adjust}}$ [Eqs. (15) and (16)] is applied to nearly reproduce the known members for $g_{9/2}{p}_{1/2}\otimes 3_1^{-}$ (Table 1). The members $j_p^{+1}{j}_h^{-1}J\otimes 3_1^{-}$ with $J\le j_p-\frac{1}{2}$ and $J\ge j_p+\frac{1}{2}$ are marked by a rhombus and a square, respectively. The SSM excitation energies [Eq. (8)] are shown by the dotted lines.

Figure 2

Similar to Fig. 1 but for $j_{15/2}{p}_{1/2}\otimes 3_1^{-}$. The SSM energies for the configurations with $g_{9/2}{p}_{1/2},g_{9/2}{f}_{5/2},i_{11/2}{p}_{1/2}$, and positive parity are shown for convenience.

Figure 3

Positive-parity states identified at $4.0<E_x<6.3\mathrm{MeV}$. The excitation energies and spins below $E_x=6.2\mathrm{MeV}$ are from Ref. [4]; excitation energies and spins above are from Ref. [1]. The 14 members of the two multiplets ${\left[g_{9/2}{p}_{1/2}\right]}_J\otimes 3_1^{-}$, $J=4,5$ [Eq. (8)], denoted as $g9p1\left(x\right)3^{-}$ are connected by the thick drawn and dashed lines. The $3^{+}$ and $4^{+}$ members from ${\left[i_{11/2}{p}_{1/2}\right]}_J\otimes 3_1^{-}$ are also shown. The corresponding calculations are illustrated in the lower part of Fig. 1. An asterisk marks states known as particle-hole configurations with annotation $l2j$. The circles with plus signs mark the four pairing vibration states; open circles mark the other configurations of unknown types. The SSM energies of particle-hole configurations are shown on the right. The multiplets of the six lowest particle-hole configurations are completely identified. The $1{}^{+}$ member from the seventh and the $5{}^{+}$ member from the eighth particle-hole configuration is missing, and only the $2{}^{+}$ member from the ninth configuration is identified. Not yet identified states are marked by a question mark at the position $E_x$ calculated by the SDI to first order [13]. Alternatingly, the dashed and dotted lines connect the members of each particle-hole multiplet.