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Journal of the Physical Society of Japan

Stark Effect of the Lymann Alpha Line by a Rotating Electric Field

Tsutomu Ishimura

Published Aug 1, 1967• 16 citations
Publisher

Abstract

Wave functions of a hydrogen atom perturbed by an electric field are calculated under the assumption of a first-order Stark effect. It is assumed that the strength of the perturbation field is constant and its direction rotates around a fixed axis with a constant angular velocity. The ground state of the atom is not affected by the perturbation field. The energy level of the first excited state of the perturbed atom splits into nine sub-levels. The Lymann alpha line emitted from the perturbed atom consists of seven components. In the case where the angular velocity of the field rotation is small, the structure of the line is similar to that of the line emitted from an atom perturbed by a static field. In the case where, the angular velocity is large, it is similar to that of the line emitted from an unperturbed atom.

DOI
10.1143/jpsj.23.422

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Wave functions of a hydrogen atom perturbed by an electric field are calculated under the assumption of a first-order Stark effect. It is assumed that the strength of the perturbation field is constant and its direction rotates around a fixed axis with a constant angular velocity. The ground state of the atom is not affected by the perturbation field. The energy level of the first excited state of the perturbed atom splits into nine sub-levels. The Lymann alpha line emitted from the perturbed atom consists of seven components. In the case where the angular velocity of the field rotation is small, the structure of the line is similar to that of the line emitted from an atom perturbed by a static field. In the case where, the angular velocity is large, it is similar to that of the line emitted from an unperturbed atom.
The intensity distribution in the core region of the Lyman-$\ensuremath{\alpha}$ line of hydrogen perturbed by neutral hydrogen atoms in the presence of an external cone-rotating electric field has been evaluated using an impact approximation. It was found that the line shape in this region can be described as the sum of four Lorentzian profiles representing contributions coming from transitions between various Stark and Berry sublevels of the resonance and ground states of the hydrogen atom. The effects due to Berry's phase are shown to produce a Lorentzian-shaped feature on each side of the Lyman-$\ensuremath{\alpha}$ line, with maxima located at frequencies linearly dependent on the angular frequency with which the electric field rotates about the laboratory fixed zzz axis, as well as on the cosine of the polar angle that the field makes with respect to this axis. The remaining two Lorentzian profiles are due to the Stark effect, and their maxima are located on both sides of the Lyman-$\ensuremath{\alpha}$ line at frequencies corresponding to the Stark shift.
General equations are presented for determining the field-dependent variation of the wavefunctions, matrix elements and intensities of dipole transitions between Stark levels of a hydrogen atom in a field range where the fine-structure effects may be neglected. The Sturm-series resolution for the reduced Coulomb-Green function is used to derive analytical expressions for the first-order corrections in terms of parabolic quantum numbers of initial and final states. Simple forms of these expressions as functions of the upper-state quantum numbers are presented explicitly for the Lyman and Balmer series. The selective action of the dc electric field on the intensity of Stark components of hydrogen lines is revealed in numerical calculations for both and types of emitted radiation. This selectivity may cause, in particular, enhancement of the high-frequency and damping of the low-frequency Stark -lines of the Lyman series.
The profile of a hydrogen emission line is investigated on the assumption that the hydrogen atom is perturbed by passing ions. Provided that the ions do not approach to within ten times the average atomic radius the electric field of the ion may be assumed homogeneous and the matrix elements calculated for the usual Stark effect may be used. For a collision at low velocity or with close approach, the adiabatic approximation is valid, and the profile depends solely on the total phase shift produced by the collision. The Fourier analysis of the wave train may be carried through exactly for certain values of this phase shift. Nonadiabatic transitions are examined for the lowest lines, and an exact solution given for this case also. For higher lines a modified Born approximation is used. The Weisskopf collision broadening formula is shown to hold only in certain cases, and the dispersion curve smearing function for impact broadening is shown to lead in some instances to incorrect results.
The nonlinear low-field Stark effect in the level n=2 of hydrogen has been investigated. \nThe experiment employed the level crossing technique, measuring the position of the crossings between the Zeeman states: \n2P3/2, mj=-3/2 and 2P1/2, mj=1/2; and \n2P3/2, mj=-3/2 and 2S1/2, mj=1/2; \nas the electric field was varied from 0 to 500 kV/m. \nA beam of atomic hydrogen, produced by thermal dissociation, was subjected to parallel electric and magnetic fields. Lymman –α (Lyα) resonance radiation was generated in an electrodeless microwave discharge lamp. The profile of the Lyα line emitted by the lamp has been investigated experimentally. \nThe level crossings were detected as changes of the Lyα resonance fluorescence intensity observed in a certain direction. The crossing positions were determined from the observed crossing signals of Lorentzian profile by a least squares computer programme. \nThe experimental results for the crossing positions as afuction of the electric field have been compared with theoretical calculations. The theoretical values were obtained by numerical diagonalization of the matrix of the eigenstates |2ℓjFmF> for perturbation by combined electric and magnetic fields. Radiative corrections were included. \nTheoretical values and experimental results agreo within the experimental uncertainties of 2%.
Abstract We consider an isolated two-electron Rydberg atom/ion, where the average distance of the inner electron from the nucleus is much smaller than the average distance of the outer Rydberg electron from the nucleus. We calculate analytically the shape of any spectral line emitted by the inner electron under the rotating electric field of the outer electron—by using the O 4 symmetry of hydrogenic atoms/ions. By applying the obtained analytical expressions to the example of the Ly-alpha line, we arrive, in particular, to a peculiar result . Namely, as the spectral line splits into several components, the most intense components exhibit a quadratic Stark effect with respect to the electric field of the outer electron (though it is linear with respect to the dipole moment of the inner electron), while one would intuitively expect a linear dependence on the electric field of the outer electron since the subsystem Z + e is hydrogenic. We provide a physical explanation of this peculiar result.