As a realistic model of a quantum system of matter, this paper investigates the gravitational-wave effects on a hydrogen-like atom using a first-principles approach. By formulating the tetrad formalism of linearized gravity, we naturally incorporate gravitational-wave effects through minimal coupling in the covariant Dirac equation. The atomic electron transition rates induced by the gravitational wave are calculated using first-order perturbation theory, revealing a distinctive selection rule along with Fermi’s golden rule. This rule can be elegantly understood in terms of gravitons as massless spin-2 particles. Our results suggest the existence of gravitons and may lead to a novel approach to probing ultra-high-frequency gravitational waves.

中文翻译：

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引力波诱导的类氢原子的原子电子跃迁


作为量子物质系统的真实模型，本文使用第一性原理方法研究了引力波对类氢原子的影响。通过制定线性引力的四元形式，我们自然地通过协变狄拉克方程中的最小耦合来整合引力波效应。引力波引起的原子电子跃迁速率是使用一阶微扰理论计算的，揭示了一个独特的选择规则以及费米黄金法则。这个规则可以用引力子作为无质量的自旋 2 粒子来优雅地理解。我们的结果表明引力子的存在，并可能导致一种探测超高频引力波的新方法。