Modification of the transition rate in the hydrogen atom placed in finite space

Cheon, Il–Tong

doi:10.1007/s004600050102

Cited by 6 publications

(3 citation statements)

References 15 publications

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“…The photon propagator for plane parallel plates as given in this subsection had been used in [97] for the calculation of boundary dependent contributions to the anomalous magnetic moment of the electron, and in [98,99] for the calculation of boundary dependent level shifts of a hydrogen atom. It will be applied to calculate the radiative corrections to the Casimir force in Sec.4.5.…”

Section: The Photon Propagator In Plane Parallel Geometrymentioning

confidence: 99%

New developments in the Casimir effect

2001

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We provide a review of both new experimental and theoretical developments in the Casimir effect. The Casimir effect results from the alteration by the boundaries of the zero-point electromagnetic energy. Unique to the Casimir force is its strong dependence on shape, switching from attractive to repulsive as function of the size, geometry and topology of the boundary. Thus the Casimir force is a direct manifestation of the boundary dependence of quantum vacuum. We discuss in depth the general structure of the infinities in the field theory which are removed by a combination of zeta-functional regularization and heat kernel expansion. Different representations for the regularized vacuum energy are given. The Casimir energies and forces in a number of configurations of interest to applications are calculated. We stress the development of the Casimir force for real media including effects of nonzero temperature, finite conductivity of the boundary metal and surface roughness. Also the combined effect of these important factors is investigated in detail on the basis of condensed matter physics and quantum field theory at nonzero temperature. The experiments on measuring the Casimir force are also reviewed, starting first with the older measurements and finishing with a detailed presentation of modern precision experiments. The latter are accurately compared with the theoretical results for real media. At the end of the review we provide the most recent constraints on the corrections to Newtonian gravitational law and other hypothetical long-range interactions at submillimeter range obtained from the Casimir force measurements.

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Section: The Photon Propagator In Plane Parallel Geometrymentioning

confidence: 99%

New developments in the Casimir effect

2001

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“…if x , ify and if z may explicitly be written as (11) where we have further split the integrals into their radial I R ≡ ∞ 0 R * nf,lf (r)R ni,li (r)r 3 dr and angular (I θφx ≡ π 0 2π 0 Y * lf,mf Y li,mi sin(θ ) cos(φ) sin(θ ) dθ dφ, etc) components. Explicit formulae for the radial and angular integrals in ( 9), ( 10) and ( 11) may be then obtained using ( 4) and ( 6) respectively.…”

Section: Exact Non-integral State-to-state Transition Rate Formulaementioning

confidence: 99%

“…As a check on the validity of these expressions, they may be easily converted to their equivalent atomic counterparts. For example the decay rate for the n i = 2, l i = 1 → n f = 1, l f = 0 transition in hydrogen may be calculated using the present treatment by substituting parameter values relevant to this atomic transition yielding 6.2 × 10 8 s −1 compared to literature values [10,11] of 6.3 × 10 8 s −1 . Decay of the 'Rydberg' atomic hydrogen n i = 10, l i = 0 and n i = 10, l i = 1 states are more complicated because they involve addition of rates over a greater number of decay channels and also transitions involving other l and m values ( l = ±1 and m = 0, ±1).…”

Section: Exact Non-integral State-to-state Transition Rate Formulaementioning

confidence: 99%

Gravitational eigenstates in weak gravity: I. Dipole decay rates of charged particles

Ernest¹

2009

J. Phys. A: Math. Theor.

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The experimental demonstration that neutrons can reside in gravitational quantum stationary states formed in the gravitational field of the Earth indicates a need to examine in more detail the general theoretical properties of gravitational eigenstates. Despite the almost universal study of quantum theory applied to atomic and molecular states very little work has been done to investigate the properties of the hypothetical stationary states that should exist in similar types of gravitational central potential wells, particularly those with large quantum numbers. In this first of a series of papers, we attempt to address this shortfall by developing analytic, non-integral expressions for the electromagnetic dipole state-tostate transition rates of charged particles for any given initial and final gravitational quantum states. The expressions are non-relativistic and hence valid provided the eigenstate wavefunctions do not extend significantly into regions of strong gravity. The formulae may be used to obtain tractable approximations to the transition rates that can be used to give general trends associated with certain types of transitions. Surprisingly, we find that some of the high angular momentum eigenstates have extremely long lifetimes and a resulting stability that belies the multitude of channels available for state decay.

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The modified decay width of the radioactive nucleus

Cheon

2007

Eur. Phys. J. A

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Modification of the transition rate in the hydrogen atom placed in finite space

Cited by 6 publications

References 15 publications

New developments in the Casimir effect

New developments in the Casimir effect

Gravitational eigenstates in weak gravity: I. Dipole decay rates of charged particles

The modified decay width of the radioactive nucleus

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