八极声子的一个可解模型
A solvable model for octupole phonons
摘要：
本文提出了一个描述闭壳层核八极声子的可解模型，该模型是用壳层模型粒子空穴激发表示的.在单粒子能量和两体相互作用的简单假设下，导出了八极声子的能量和波函数的封闭表达式。特别地，它表明八极声子的分量与Wigner $3j$系数成正比。证明了该解析波函数在具有与三维谐振子相一致的$LS$壳闭包的轻核中是完全有效的，而在由于自旋-轨道相互作用而具有$jj$壳闭包的重核中是有效的.可解模型的属性进行了比较与一个现实的壳模型计算$^{208}$铅的结果。
英文摘要：
A solvable model is proposed for the description of octupole phonons in closed-shell nuclei, formulated in terms of shell-model par\-ticle--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 $^{208}$Pb.
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