Stark patterns observed in helium

This paper is mainly a report of further observations on the Stark-effect in helium made with a view to establishing various definite Stark patterns for the series lines. It thus appears as an extension to an earlier paper in which it was pointed out that a plan for Stark patterns is contained implicitly in the Bohr perturbation theory of the Stark-effect as developed by Kramers to predict connections between the hydrogen fine structure and the components observed in high fields. This plan, which on the perturbation theory might be expected to make its appearance in helium, receives somewhat detailed support from the present data, and will be outlined in later paragraphs. It should be stated now, however, that while the detailed analyses here given may be regarded as an extension to the observations by Stark and Nyquist, they offer definite reasons for a rather extensive revision of the complex analyses reported by Takamine and Kokubu. Soon after his discovery of this effect Stark suggested that it might be found to be of the same nature for the various members of a single spectral series. He noted, in particular, that on the early plates certain principal and sharp series lines of helium were merely displaced without being split by the applied electric field. In the following paper Stark and Kirschbaum gave the results of a more complete examination of the Stark-effect for the series lines of orthohelium, parhelium, lithium, and the doublets of calcium. With the single exception of the parhelium line λ 3614, which appeared to be double, they found all principal and sharp series lines simply displaced. The two components of each calcium doublet were shifted in the same direction, and by nearly the same amounts.

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The stark effect of the fine-structure of hydrogen

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

10.1098/rspa.1928.0100 ◽

1928 ◽

Vol 119 (782) ◽

pp. 313-334 ◽

Cited By ~ 26

Keyword(s):

Fine Structure ◽

Hydrogen Atom ◽

Electric Field ◽

Quantum Dynamics ◽

Stark Effect ◽

Energy Levels ◽

Structure Theory ◽

Weak Electric Field ◽

Classical Dynamics ◽

Balmer Series

One of the earliest successes of classical quantum dynamics in a field where ordinary methods had proved inadequate was the solution, by Schwarzschild and Epstein, of the problem of the hydrogen atom in an electric field. It was shown by them that under the influence of the electric field each of the energy levels in which the unperturbed atom can exist on Bohr’s original theory breaks up into a number of equidistant levels whose separation is proportional to the strength of the field. Consequently, each of the Balmer lines splits into a number of components with separations which are integral multiples of the smallest separation. The substitution of the dynamics of special relativity for classical dynamics in the problem of the unperturbed hydrogen atom led Sommerfeld to his well-known theory of the fine-structure of the levels; thus, in the absence of external fields, the state n = 1 ( n = 2 in the old notation) is found to consist of two levels very close together, and n = 2 of three, so that the line H α of the Balmer series, which arises from a transition between these states, has six fine-structure components, of which three, however, are found to have zero intensity. The theory of the Stark effect given by Schwarzschild and Epstein is adequate provided that the electric separation is so much larger than the fine-structure separation of the unperturbed levels that the latter may be regarded as single; but in weak fields, when this is no longer so, a supplementary investigation becomes necessary. This was carried out by Kramers, who showed, on the basis of Sommerfeld’s original fine-structure theory, that the first effect of a weak electric field is to split each fine-structure level into several, the separation being in all cases proportional to the square of the field so long as this is small. When the field is so large that the fine-structure is negligible in comparison with the electric separation, the latter becomes proportional to the first power of the field, in agreement with Schwarzschild and Epstein. The behaviour of a line arising from a transition between two quantum states will be similar; each of the fine-structure components will first be split into several, with a separation proportional to the square of the field; as the field increases the separations increase, and the components begin to perturb each other in a way which leads ultimately to the ordinary Stark effect.

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The Stark effect with minimum length

International Journal of Modern Physics A ◽

10.1142/s0217751x17500105 ◽

2017 ◽

Vol 32 (02n03) ◽

pp. 1750010 ◽

Cited By ~ 2

Author(s):

H. L. C. Louzada ◽

H. Belich

Keyword(s):

Perturbation Theory ◽

Energy Spectrum ◽

Hydrogen Atom ◽

Electric Field ◽

Stark Effect ◽

Heisenberg Algebra ◽

Uniform Electric Field ◽

Minimum Length

We will study the splitting in the energy spectrum of the hydrogen atom subjected to an uniform electric field (Stark effect) with the Heisenberg algebra deformed leading to the minimum length. We will use the perturbation theory for cases not degenerate (n[Formula: see text]=[Formula: see text]1) and degenerate (n[Formula: see text]=[Formula: see text]2), along with known results of corrections in these levels caused by the minimum length applied purely to the hydrogen atom, so that we may find and estimate the corrections of minimum length applied to the Stark effect.

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Classical Description of Resonant Charge Exchange Involving the Second Flavor of Hydrogen Atoms

Atoms ◽

10.3390/atoms9030041 ◽

2021 ◽

Vol 9 (3) ◽

pp. 41

Author(s):

Eugene Oks

Keyword(s):

Perturbation Theory ◽

Electric Field ◽

Charge Exchange ◽

Cross Sections ◽

Stark Effect ◽

Uniform Electric Field ◽

Hydrogen Atoms ◽

Additional Tool ◽

Classical Description ◽

Resonant Charge Exchange

We studied the consequences of the existence of the second flavor of hydrogen atoms (SFHA)—the existence proven by atomic experiments and evidenced by astrophysical observations—on the resonant charge exchange. We found analytically that there is indeed an important difference in the corresponding cross-sections for the SFHA compared to the usual hydrogen atoms. This difference could serve as an additional tool for distinguishing between the two kinds of hydrogen atoms in future experiments/observations. We also show that the SFHA does not exhibit any Stark effect—whether in a uniform or a non-uniform electric field—in any order of the perturbation theory.

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Effects of an Applied Electric Field on Silicon Nanocrystals Photoluminescence

MRS Proceedings ◽

10.1557/proc-1145-mm01-07 ◽

2008 ◽

Vol 1145 ◽

Author(s):

Alexandre Lacombe ◽

David Barba ◽

Félix Beaudoin ◽

François Martin ◽

Guy G. Ross

Keyword(s):

Electric Field ◽

Ion Implantation ◽

Current Density ◽

Gate Voltage ◽

Applied Electric Field ◽

Silicon Nanocrystals ◽

Stark Effect ◽

Charge Carriers ◽

Wavelength Shift ◽

Quantum Confined Stark Effect

AbstractThe photoluminescence (PL) of silicon nanocrystals (Si-nc) obtained by ion implantation in the oxide layer of a MOS structure was measured during the application of a slowly varying electric field generated by biasing the gate electrode. As a result, both PL intensity enhancement and quenching have been observed. These reproducible intensity modulations exhibit a hysteresis effect when the applied electric field is varied and persist even after it is removed. The behavior of the current density and the absence of wavelength shift in the PL spectra during gate voltage sweeps suggest that these modulations are related to the motion of charge carriers rather than to field-induced mechanisms such as quantum-confined Stark effect (QCSE).

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Development of Field-Controlled Smart Optic Materials (ScN, AlN) with Rare Earth Dopants

Advances in Science and Technology ◽

10.4028/www.scientific.net/ast.82.38 ◽

2012 ◽

Vol 82 ◽

pp. 38-43 ◽

Cited By ~ 1

Author(s):

Hyun Jung Kim ◽

Yeon Joon Park ◽

Glen C. King ◽

Sang H. Choi

Keyword(s):

Refractive Index ◽

Rare Earth ◽

Electric Field ◽

Rare Earth Elements ◽

Applied Electric Field ◽

Stark Effect ◽

Wide Band ◽

Active Optics ◽

Main Research ◽

Functional Capabilities

Development of the fundamental materials for field-controlled spectrally active optics is essential for new concept of optics, such as: membrane optics, filters for LIDARs, windows for sensors and probes, telescopes, spectroscopes, cameras, light valves, light switches, flat-panel displays, etc. The dopants of rare earth elements create a number of absorption and emission band structures and can easily be incorporated into many high quality crystalline and amorphous hosts. In wide band-gap semiconductors, like ScN and AlN with rare earth dopants, the existing deep levels can capture or emit the mobile charges, and can be ionized with the loss or capture of the carriers. This is a fundamental basis for smart optic materials. ScN and AlN doped with rare earth elements (Er, Ho) were tested under an applied electric field to characterize spectral and refractive index shifts by the Stark Effect. Decrease in refractive index under an applied electric field was observed as a shift in absorption coefficient using a variable angle spectroscopic ellipsometer. Under an electric field, mobile carriers are redistributed within the space charge region (SCR) to reveal this electro-refractive effect. The main research goal is to facilitate concept demonstration and testing of field-controlled spectrally smart active optics for optical multi-functional capabilities in a selected spectral range.

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The hyperfine structure Stark effect I. Theory

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1968.0109 ◽

1968 ◽

Vol 305 (1480) ◽

pp. 125-138 ◽

Cited By ~ 121

Keyword(s):

Perturbation Theory ◽

Electric Field ◽

Hyperfine Structure ◽

Stark Effect ◽

Free Atom ◽

Uniform Electric Field ◽

Theory Approach ◽

Tensor Form ◽

Quadratic Stark Effect ◽

Effective Operators

A theory of the quadratic Stark effect is presented. It is aimed at a description of the hyperfine structure of a free atom in a uniform electric field. A perturbation theory approach is adopted and extensive use is made of effective operators. In spherical tensor form these can be written as the sum of a scalar and a tensor of rank two. Associated scalar and tensor polarizabilities are defined and their properties are discussed. A variety of applications of the theory are given.

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The perturbation theory model of a spherical oscillator in electric field and the vibrational stark effect in polyatomic molecular species

Spectrochimica Acta Part A Molecular and Biomolecular Spectroscopy ◽

10.1016/j.saa.2006.05.010 ◽

2007 ◽

Vol 66 (4-5) ◽

pp. 985-993 ◽

Cited By ~ 4

Author(s):

Irina Petreska ◽

Gjorgji Ivanovski ◽

Ljupčo Pejov

Keyword(s):

Perturbation Theory ◽

Electric Field ◽

Molecular Species ◽

Stark Effect ◽

Theory Model ◽

Spherical Oscillator

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Asymmetry observed in the stark components of H α

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

10.1098/rspa.1931.0099 ◽

1931 ◽

Vol 132 (819) ◽

pp. 257-265 ◽

Cited By ~ 6

Keyword(s):

Fine Structure ◽

Electric Field ◽

External Electric Field ◽

Electric Fields ◽

Wave Equations ◽

Stark Effect ◽

Numerical Results

This paper is a report of observations on H a which show an asymmetry in the displacements as well as in the intensities of its Stark components. The early theoretical treatments of the Stark effect in hydrogen neglected the fine structure and gave symmetrical displacements of the components in moderate electric fields (about 40,000 v./cm.). So far as the writer is aware, no observations have been made which would lead one to deny this symmetry. Using the wave equations of Darwin and Dirac, Schlapp has reconsidered the hydrogen-like atom in an external electric field and under the influence of the forces which cause fine structure. In the case of H a numerical results were calculated for two limiting cases, (i) where the effect of the electric field is small compared with the fine structure (for fields less than 300 v./cm.), and (ii) where the fine structure is small compared with the Stark effect (fields above 10,000 v./cm.). The displacements were not calculated for the intermediate region, but the connections between the two sets of components are given.

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DRIFT VELOCITY OF HOT ELECTRONS IN n-TYPE GERMANIUM

Canadian Journal of Physics ◽

10.1139/p62-114 ◽

1962 ◽

Vol 40 (9) ◽

pp. 1056-1066 ◽

Cited By ~ 22

Author(s):

Robert Barrie ◽

R. R. Burgess

Keyword(s):

Field Strength ◽

Electric Field ◽

Drift Velocity ◽

Applied Electric Field ◽

Applied Field ◽

Hot Electrons ◽

High Fields

The drift velocity of electrons in n-type germanium has been measured as a function of applied electric field at lattice temperatures of 77° K and 295° K. Three directions of applied field were used, viz. (100), (110), and (111) crystal directions. The range of field strength was from 500 v/cm to 75 kv/cm. A longitudinal anisotropy was observed at 77° K but not at 295° K. All specimens showed saturation of the drift velocity at high fields. At 77° K, all (100) specimens exhibited a breakdown effect, the cause of which is not known. The results are analyzed on the basis of an extension of Stratton's theory to the case of a many-valley semiconductor.

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