A solvable model is proposed for the description of octupole phonons in closed-shell nuclei, formulated in terms of shell-model particle–hole excitations. With some simple assumptions concerning single-particle energies and two-body interactions, closed expressions are derived for the energy and wave function of the octupole phonon. In particular, it is shown that the components of the octupole phonon are proportional to Wigner 3j coefficients. This analytic wave function is proven to be exactly valid in light nuclei, which have LS shell closures that coincide with those of the three-dimensional harmonic oscillator, and to be valid to a good approximation in heavier nuclei, which have jj shell closures due to the spin–orbit interaction. The properties of the solvable model are compared with the results of a realistic shell-model calculation for ²⁰⁸Pb.

提出了一个可解模型来描述闭壳核中的八极子声子，该模型是根据壳模型的粒子-空穴激发来制定的。通过一些有关单粒子能量和两体相互作用的简单假设，得出了八极声子的能量和波函数的封闭表达式。特别地，表明八极声子的分量与维格纳3 j系数成比例。该解析波函数被证明在轻核中是完全有效的，轻核的LS壳闭合与三维谐波振荡器的LS壳闭合重合，并且在重核中具有jj的近似近似是有效的。由于自旋轨道相互作用而导致的壳封闭。将可求解模型的属性与²⁰⁸ Pb的实际壳模型计算结果进行比较。