Identification of rotating and vibrating tetrahedrons in the heavy nucleus 208Pb

Ten known states in the heavy nucleus 208Pb at \(2.6 < E_{x} < 7.9\) MeV are described by rotating and vibrating tetrahedrons. The \( 3^{-}\) and \( 4^{+}\) yrast states are the first members of the rotational band. A \( 2^{\pm}\) doublet state with the \( 2^{+}\) yrast state as one member and the newly recognized \( 2^{-}\) yrast state as the other member, the \( 1^{-}\) yrast state, and the third \( 0^{+}\) state are the heads of the three elementary tetrahedral rotating and vibrating bands. The newly recognized state at \( E_{x} = 4142\) keV was assigned spin 2 in 1975 and is suggested to have negative parity by the absent 208Pb \((\alpha, \alpha')\) excitation. Four more states at \(5.7< E_{x}< 7.9\) MeV are identified as the next members of the three elementary tetrahedral rotating and vibrating bands. The ambiguous spin assignment to the state at \(E_{x}= 7020\) keV is settled with \( 3^{-}\), the state at \( E_{x} = 7137\) keV is assigned \( 4^{-}\).