In a typical EPR experiment, the transitions require that the static magnetic field $$B_0$$ is oriented perpendicular to the microwave field $$B_1$$ (perpendicular mode). This is determined by the transition rules either in the classical or in the quantum mechanical description. However, there are cases where EPR transitions are observed when $$B_0$$ is oriented parallel to $$B_1$$ (parallel mode). Quite numerous studies can be found in the literature where EPR transitions in both modes (dual-mode EPR) are feasible. In the majority of cases, dual-mode EPR studies are typically applied in $$S>1/2$$ systems where non-zero transition probabilities for the parallel mode are the result of the state mixing provided by the zero-field splitting interaction. On the other hand, the observation of parallel-mode EPR signals in $$S=1/2$$ systems becomes feasible when strong hyperfine interaction between the electronic and nuclear spin is present, as has been theoretically predicted for the hydrogen atom having a hyperfine coupling constant of $$A_0=1420$$ MHz (Weil in Concepts Magn Reson Part A 28:331, 2006). Herein, we report the first dual-mode X-band EPR experiments of hydrogen atom (both isotopes $$^1$$ H and $$^2$$ H) encapsulated in polyhedral oligomeric silsesquioxane cages. We extend the theory to the case of deuterium and we extract analytical formulas for transition probabilities. For the forbidden transitions, this study revealed a first-order dependence of resonance fields on the nuclear g-factor, $$g_{\mathrm{n}}$$ , and the existence of a clock transition with $$f=307$$ MHz.

中文翻译：

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封装在 POSS 笼中的原子氢的平行模式 EPR

在典型的 EPR 实验中，转换要求静磁场 $$B_0$$ 垂直于微波场 $$B_1$$（垂直模式）。这是由经典或量子力学描述中的跃迁规则决定的。但是，在某些情况下，当 $$B_0$$ 与 $$B_1$$ 平行（平行模式）时，会观察到 EPR 转换。在文献中可以找到相当多的研究，其中两种模式（双模式 EPR）的 EPR 转换都是可行的。在大多数情况下，双模式 EPR 研究通常应用于 $$S>1/2$$ 系统，其中并行模式的非零转换概率是零场分裂相互作用提供的状态混合的结果. 另一方面，当电子和核自旋之间存在强超精细相互作用时，在 $$S=1/2$$ 系统中观察并行模式 EPR 信号变得可行，正如理论上预测的具有 $$S=1/2$$ 的超精细耦合常数的氢原子$A_0=1420$$ MHz（Weil in Concepts Magn Reson Part A 28:331, 2006）。在此，我们报告了封装在多面体低聚倍半硅氧烷笼中的氢原子（同位素 $$^1$$H 和 $$^2$$H）的第一个双模式 X 波段 EPR 实验。我们将理论扩展到氘的情况，并提取了跃迁概率的分析公式。对于禁止跃迁，这项研究揭示了共振场对核 g 因子 $$g_{\mathrm{n}}$$ 的一阶依赖性，以及 $$f=307$ 的时钟跃迁的存在$兆赫。