Nonexponential decay law of the 2P-1S transition of the H-atom
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910615602200576 |
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| author | Giacosa, Francesco Kyzioł, Krzysztof |
| author_facet | Giacosa, Francesco Kyzioł, Krzysztof |
| contents | We evaluate numerically the survival probability $P(t)$ for the unstable 2P excited state of the hydrogen atom, which decays into the ground-state 1S emitting one photon ($τ\sim 1.595$ ns), thus extending the analytic study of Facchi and Pascazio, Physics Letters A 241 (1998). To this end, we first determine the analytic expression of the spectral function of the unstable state, which allows for an accurate evaluation of $P(t)$. As expected, for short and long times $P(t)$ shows deviations from the exponential law: a `Zeno' region occurs at extremely short times (up to $\sim 0.3$ attosec, followed by a longer `anti-Zeno' domain (up to $\sim 50$ attosec); at long times above $125 τ$, the decay law scales as $t^{-4}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06905 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonexponential decay law of the 2P-1S transition of the H-atom Giacosa, Francesco Kyzioł, Krzysztof Quantum Physics High Energy Physics - Phenomenology We evaluate numerically the survival probability $P(t)$ for the unstable 2P excited state of the hydrogen atom, which decays into the ground-state 1S emitting one photon ($τ\sim 1.595$ ns), thus extending the analytic study of Facchi and Pascazio, Physics Letters A 241 (1998). To this end, we first determine the analytic expression of the spectral function of the unstable state, which allows for an accurate evaluation of $P(t)$. As expected, for short and long times $P(t)$ shows deviations from the exponential law: a `Zeno' region occurs at extremely short times (up to $\sim 0.3$ attosec, followed by a longer `anti-Zeno' domain (up to $\sim 50$ attosec); at long times above $125 τ$, the decay law scales as $t^{-4}$. |
| title | Nonexponential decay law of the 2P-1S transition of the H-atom |
| topic | Quantum Physics High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2408.06905 |