An algebraic approach based on unitary algebras to calculate Franck–Condon factors (FCF’s) is presented. The method is based on the unitary group approach, which consists in adding a scalar boson to the $$\nu $$ ν -D harmonic oscillator space, taking advantage of the transformation brackets connecting the energy, coordinate and momentum representations. In this scheme the solutions are given in terms of an expansion of harmonic oscillator functions. In this way the overlaps are expressed in terms of simple scalar product of the eigenvectors. As a benchmark to illustrate our approach the case of two 1D-Morse potentials is presented. Discussions concerned with both non-Condon contributions and the harmonic limit are included. FCF’s involving the 1D-Morse and asymmetric double Morse potentials are also considered. As an application, the FCF’s involving the S–S stretching in the $$\hbox {S}_2\hbox {O}$$ S 2 O molecule are described in terms of two Morse potentials.

中文翻译：

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一种计算 Franck-Condon 因子的代数方法

提出了一种基于幺正代数的代数方法来计算 Franck-Condon 因子 (FCF)。该方法基于酉群方法，该方法包括将标量玻色子添加到 $$\nu $$ ν -D 谐振子空间，利用连接能量、坐标和动量表示的变换括号。在这个方案中，解决方案是根据谐波振荡器函数的扩展给出的。这样，重叠就用特征向量的简单标量积来表示。作为说明我们方法的基准，介绍了两个 1D-Morse 势的情况。包括与非 Condon 贡献和谐波限制有关的讨论。还考虑了涉及 1D-Morse 和非对称双 Morse 势的 FCF。作为应用程序，