The main decay channels of the anomalous low-energy $3/2^{+}(7.8\pm 0.5\mathrm{eV})$ isomeric level of the ${}^{229}\mathrm{Th}$ nucleus, namely the $\gamma$ emission and internal conversion, inside a dielectric sphere, dielectric thin film, and conducting spherical microcavity are investigated theoretically, taking into account the effect of media interfaces. It is shown that (1) the $\gamma$ decay rate of the nuclear isomer inside a dielectric thin film and dielectric microsphere placed in a vacuum or in a metal cavity can decrease (increase) in dozen of times, (2) the $\gamma$ activity of the distributed source as a function of time can be nonexponential, and (3) the metal cavity, whose size is of the order of the radiation wavelength, does not affect the probability of the internal conversion in ${}^{229}\mathrm{Th}$, because the virtual photon attenuates at much shorter distances and the reflected wave is very weak.

中文翻译：

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介电球，薄膜和金属腔中核异构体Th229（3/2 +，7.8eV）的衰减率

异常低能的主要衰变通道 $3/{\mathrm{2个}}^{+}（7.8\pm 0.5\mathrm{电子伏特}）$ 的异构体水平 ${}^{229}钍$ 核，即 $\gamma$考虑到介质界面的影响，从理论上研究了介电球内部，介电薄膜和导电球形微腔内的发射和内部转换。结果表明（1）$\gamma$ 放置在真空或金属腔中的介电薄膜和介电微球内部的核异构体的衰变率可以降低（增加）数十倍，（2） $\gamma$ 随时间变化的分布式源的活动可以是非指数的，并且（3）大小为辐射波长量级的金属腔不影响内部转换的概率。 ${}^{229}钍$，因为虚拟光子在更短的距离处衰减，并且反射波非常微弱。