论文标题
八极声子的可解决模型
A solvable model for octupole phonons
论文作者
论文摘要
提出了一个可解决的模型，以描述封闭壳核中的八极核声子，该模型是根据壳模式 - 孔 - 孔 - 孔 - 孔激发的。有了一些关于单粒子能量和两体相互作用的简单假设，封闭的表达式是为八杆声子的能量和波函数得出的。特别是表明，Octupole声子的组件与Wigner $ 3J $系数成正比。事实证明，该分析波函数在光核中完全有效，在光核中具有$ ls $壳的闭合，与三维谐波振荡器相吻合，并且有效对于较重的核中的良好近似值，由于自旋 - 孔线相互作用，它们在$ jj $ shell中的闭合。将可解决的模型的属性与$^{208} $ pb的逼真的壳模计算结果进行了比较。
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.
