We have revisited the theory of radiative and nonradiative transitions using the crude adiabatic approximation and methods of quantum electrodynamics in order to calculate the transition rates for these processes. All the integrals involving vibrational wave functions have been calculated analytically using Laguerre functions. It has been argued that the radiative transitions will be mediated by the local vibrational modes, referred to as active modes. In the case of nonradiative transitions both local and nonlocal modes contribute to the transition rates. The multidimensional theory involving all the active normal coordinates has been applied to interpret the vibronic spectra of yttrium garnet doped with Pr 3+ (YAG:Pr 3+ ) at low temperature. The Huang-Rhys parameters have been obtained for the normal frequencies observed for YAG. This approach provides a powerful technique to determine the Huang-Rhys parameters from the low temperature data, which can be used...

中文翻译：

---

重新审视多原子系统的辐射跃迁和非辐射跃迁的理论

为了重新计算这些过程的跃迁速率，我们已经使用绝热近似和量子电动力学方法重新讨论了辐射跃迁和非辐射跃迁的理论。所有涉及振动波函数的积分均已使用Laguerre函数进行了解析计算。有人认为辐射跃迁将由局部振动模式（称为活动模式）介导。在非辐射跃迁的情况下，局部模式和非局部模式都会对跃迁速率有所贡献。涉及所有活动法向坐标的多维理论已被用于解释低温下掺有Pr 3+（YAG：Pr 3+）的钇石榴石的振动光谱。已针对YAG观察到的正常频率获得了Huang-Rhys参数。