The model passes a validation test based on a spherically symmetric solution. The model is adjusted by fitting to it the sum of spherical radiations emitted by the composing “stars.” The huge ratio distance/wavelength needs to implement a numerical precision better than the quadruple precision. In a previous work, the general applicability of this representation has been proved. This analytical model is based on an explicit representation for axisymmetric source-free Maxwell fields.
Here, an analytical model is built to simulate that field in an axisymmetric galaxy. The Maxwell radiation field is an essential physical characteristic of a galaxy. The ORM methodology for the cavity model presented in this article can potentially be used for two-electron systems in a quantum dot. Even for the sharp transition, the ORM results again agree very well with the analytic results at least for the ground state when a commonly used approximation in the ORM is removed. The ORM results in the zeroth order approximation diverge significantly in the region of the shallow-deep transition (i.e., for the values of the radius where the shallow-deep transition occurs) when the dielectric constant is high and as a result the transition is sharp. The results of the ORM agree well with the results obtained by the analytic solution when the shallow-deep transition is not too sharp (i.e., when the dielectric constant is not too large) for all values of the cavity radius. The sharpness of the transition depends on the value of the dielectric constant of the medium. The energy levels of the hydrogenic atom in a spherical cavity exhibit a shallow-deep instability as a function of the cavity radius. The results obtained by the ORM are compared with a known exact analytic solution. The nonmonotonic dependence of the laser field-caused energy shift on the nuclear charge is a counterintuitive result.Ī solution to the problem of a hydrogenic atom in a homogeneous dielectric medium with a concentric spherical cavity using the oscillator representation method (ORM) is presented. We also find that the shift has a nonmonotonic dependence on the nuclear charge Z : as Z increases, the absolute value of the shift first increases, then reaches a maximum, and then decreases. We find that the absolute value of the shift increases monotonically as the unperturbed binding energy of the Rydberg electron increases. The second effect is a shift of the energy of the Rydberg electron, also calculated analytically. In the radiation spectrum, this precession would manifest as satellites separated from the spectral line at the Kepler frequency by multiples of the precession frequency. We calculate analytically the precession frequency and show that it differs from the case of a hydrogenic atom/ion. The first effect is the precession of the orbital plane of the Rydberg electron. We find two primary effects of the high-frequency laser field on circular Rydberg states. For obtaining analytical results, we use the generalized method of the effective potentials. In this study, we study a helium atom or a helium-like ion with one of the two electrons in a Rydberg state, the system being under a high-frequency laser field. It was shown that the motion of the Rydberg electron is analogous to the motion of a satellite around an oblate planet (for a linearly polarized laser field) or around a (fictitious) prolate planet (for a circularly polarized laser field): it exhibits two kinds of precession – one of them is the precession within the orbital plane and another one is the precession of the orbital plane. In the literature, there were studies of Rydberg states of hydrogenic atoms/ions in a high-frequency laser field.
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