The hyperfine structure Stark effect I. Theory

1968 ◽  
Vol 305 (1480) ◽  
pp. 125-138 ◽  
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.

scholarly journals The Stark effect with minimum length

2017 ◽  
Vol 32 (02n03) ◽  
pp. 1750010 ◽  
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.

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

Atoms ◽  
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.

The hyperfine structure Stark effect - III. The 2 P ½ level of aluminium

1974 ◽  
Vol 338 (1612) ◽  
pp. 95-100 ◽  
Keyword(s):  
Electric Field ◽  
Frequency Shift ◽  
Hyperfine Structure ◽  
Stark Effect ◽  
Ground Level ◽  
Tensor Polarizability ◽  
Atomic Beams ◽  
Quadratic Stark Effect ◽  
Stark Operator

The quadratic Stark effect in the hyperfine structure of the 2 P ½ ground level of aluminium has been investigated by the method of atomic beams. A frequency shift caused by the application of an electric field has been interpreted in terms of an effective Stark operator, and the associated tensor polarizability α ten ( J = ½, F = 3) has a measured value of (8.13±0.72) × 10 –4 a 3 0 . The case of J = ½ is a special one in that the theoretical value of α ten ( J = ½, F = 3) vanishes in the absence of hyperfine structure effects. The inclusion of the hyperfine structure operator in a calculation of the tensor polarizability has led to a small theoretical value in agreement with experiment.

Hyperfeinstruktur, Stark-Effekt und Lebensdauern in den angeregten 5d6s6p y2D3/2,5/2 -Zuständen des Lanthan I-Spektrums/ Hyperfine Structure, Stark-Effect and Lifetimes of the Excited 5d6s6p y 2D3/2,5/2-States of the Lanthanum I Spectrum

1970 ◽  
Vol 25 (11) ◽  
pp. 1537-1545 ◽  
Author(s):  
A. Hese ◽  
G. Büldt
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Hyperfine Interaction ◽  
Detailed Analysis ◽  
Hyperfine Structure ◽  
Stark Effect ◽  
Homogeneous Electric Field ◽  
Intermediate Coupling ◽  
Quadratic Stark Effect ◽  
Measured Change

The levelcrossing method has been used for an investigation of the hyperfine structure and lifetimes in the excited 5d6s6p y 2D3/2, 5/2-states of Lanthanum I. From a detailed analysis of the measured change in intensity of the resonance light the following hyperfine interaction constants and lifetimes were deduced:Applying an additional homogeneous electric field parallel to the usual magnetic field the constants β of the quadratic Stark effect in the y 2D-states were derived from the observed shifts of the levelcrossing signals:The experimental results are interpreted theoretically by the concept of intermediate coupling using appropriate eigenvectors. The observed lifetimes and the β-values are compared with the Bates and Damgaard approximation.

Stark-Effekt-Untersuchung der Hyperfeinstruktur des 3 2P3/2-Zustands von Natrium mit der Level-crossing-Methode / Stark-Effect Investigation of the Hyperfine Structure of the 3 2P3/2-State of Sodium by Level-Crossing-Method

1970 ◽  
Vol 25 (2) ◽  
pp. 196-201
Author(s):  
D. Zimmermann
Keyword(s):  
Electric Field ◽  
Hyperfine Structure ◽  
Stark Effect ◽  
Oscillator Strengths ◽  
Experimental Result ◽  
Level Crossing ◽  
Quadratic Stark Effect ◽  
Fluorescence Light ◽  
Measured Change ◽  
Lower Limits

Abstract The level-crossing-method has been used for an investigation of the hyperfine structure of the first excited 3 2P3/2-state of sodium applying an additional electric field parallel to the usual mag. netic field. By means of a detailed analysis of the measured change in intensity of the scattered fluorescence light due to the electric field the constant β of the quadratic Stark-effect of the 3 2P3/2-state of sodium was deduced to be β= (10.8± 1.2) kc/s·(kV/cm)2. The experimental result will be discussed with respect to a determination of upper and lower limits for oscillator strengths of transitions between the 3 2P3/2-state and S-states in the sodium spectrum.

The hyperfine structure Stark effect II. The ground levels of samarium, europium and aluminium

1968 ◽  
Vol 305 (1480) ◽  
pp. 139-148 ◽  
Keyword(s):  
Hyperfine Structure ◽  
Stark Effect ◽  
Ground Level ◽  
Field Approximation ◽  
Central Field ◽  
A Value ◽  
Coupling Approximation ◽  
Atomic Beams ◽  
Quadratic Stark Effect ◽  
Stark Operator

The quadratic Stark effect in the hyperfine structure of the ground levels of samarium, europium and aluminium has been investigated by the method of atomic beams. Frequency shifts caused by the application of an electric field have been interpreted, to second order in perturbation theory, in terms of an effective Stark operator with which is associated a parameter called the tensor polarizability, α ten. . In the LS coupling approximation the results for five lines in samarium give a value α ten. ( 7 F ; J ═ 6) ═ – 3·64 ± 0·17 a 0 3 . Measurements on one line in europium give, for the ground level, α ten. ( J ═ 7 / 2 ) ═ 0·0141 ± 0·0007 a 0 3 . In the IJ coupling and LS coupling approximations the theory of the Stark effect in hyperfine structure has been tested and confirmed, but on the more stringent assumption that the central-field approximation is also valid, an attempt to evaluate a parameter α ten. (4 f ) common to both samarium and europium has only limited success. This result leads to the expected conclusion that in the rare earths the central-field model breaks down. Measurements on one line in aluminium give α ten. ( J ═ 3/2) ═ α ten. (3 p ) ═ – 8·15 ± 0·40 a 0 3 . In the course of this work new values of the hyperfine structure interaction constants and of the g -factor have been found for the 3 p 2 P 3/2 level of 27 Al. These results are A ═ + 94·27767 ± 0·00010 Mc/s, B ═ + 18·91526 ± 0·00070 Mc/s, gj ═ 1·33474 ± 0·00005.

Perturbation theory for the Stark effect in the hyperfine structure of alkali-metal atoms

1975 ◽  
Vol 11 (6) ◽  
pp. 1784-1786 ◽  
Author(s):  
Taesul Lee ◽  
T. P. Das ◽  
R. M. Sternheimer
Keyword(s):  
Perturbation Theory ◽  
Alkali Metal ◽  
Hyperfine Structure ◽  
Stark Effect ◽  
Metal Atoms

The evolution and revival structure of angular momentum quantum wave packets

1999 ◽  
Vol 77 (7) ◽  
pp. 491-503 ◽  
Author(s):  
Marcis Auzinsh
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Wave Packet ◽  
Electric Field ◽  
Stark Effect ◽  
Wave Packets ◽  
Zeeman Effect ◽  
Permanent Magnetic Field ◽  
Stark Effects ◽  
Quadratic Stark Effect

In this paper, a coherent superposition of angular-momentum states created by absorption of polarized light by molecules is analyzed. Attention is paid to the time evolution of wave packets representing the spatial orientation of the internuclear axis of a diatomic molecule. Two examples are considered in detail. Molecules absorbing light in a permanent magnetic field experiencing the Zeeman effect and molecules absorbing light in a permanent electric field experiencing the quadratic Stark effect. In a magnetic field, we have a wave packet that evolves in time exactly as a classical dipole oscillator in a permanent magnetic field (classical-physics picture of the Zeeman effect). In the second case, we have a wave packet that goes through periodical changes of shape of the packet with revivals of the initial shape. This is pure quantum behavior. The classical motion of angular momentum in an electric field in the case of a quadratic Stark effect is known to be a periodic. Solutions obtained for wave packet evolution are briefly compared with Rydberg-state coherent wave packets and harmonic-oscillator wave packets. Zeeman and Stark effects in small molecules continuously attract the attention of researchers, theoreticians, as well as experimentalists. These investigations allow us to obtain a deeper understanding of the interaction of molecules with stationary external fields and also can be used as a practical tool to measure different molecular characteristics, such as permanent electric or magnetic dipole moments, intramolecular perturbations, etc. It is worthwhile analyzing these effects as an evolution of wave packets. All this motivates a comparison of the quantum and classical picture of Zeeman and Stark effects in molecules.PACS No.: 33.55.Be

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