“Oscillator strength”的意思、由来-开放百科全书

In spectroscopy, oscillator strength is a dimensionless quantity that expresses the probability of absorption or emission of electromagnetic radiation in transitions between energy levels of an atom or molecule.^[1]^[2] The oscillator strength can be thought of as the ratio between the quantum mechanical transition rate and the classical absorption/emission rate of a single electron oscillator with the same frequency as the transition.^[3]

Theory

the reduced Planck constant. The quantum states

1,2, are assumed to have several

Thomas–Reiche–Kuhn sum rule

To make equations of the previous section applicable to the states belonging to the continuum spectrum, they should be rewritten in terms of matrix elements of the momentum

. In absence of magnetic field, the Hamiltonian can be written as

, and calculating a commutator

in the basis of eigenfunctions of

results in the relation between matrix elements

Next, calculating matrix elements of a commutator

in the same basis and eliminating matrix elements of

, we arrive at

where

are oscillator strengths for quantum transitions between the states

and

. This is the Thomas-Reiche-Kuhn sum rule, and the term with

has been omitted because in confined systems such as atoms or molecules the diagonal matrix element

due to the time inversion symmetry of the Hamiltonian

. Excluding this term eliminates divergency because of the vanishing denominator.^[4]

Sum rule and electron effective mass in crystals

In crystals, the electronic energy spectrum has a band structure

. Near the minimum of an isotropic energy band, electron energy can be expanded in powers of

where

is the electron effective mass. It can be shown^[5] that it satisfies the equation

Here the sum runs over all bands with

. Therefore, the ratio

of the free electron mass

to its effective mass

in a crystal can be considered as the oscillator strength for the transition of an electron from the quantum state at the bottom of the

band into the same state.^[6]

See also

References

1. ^{{cite book|author=W. Demtröder|title=Laser Spectroscopy: Basic Concepts and Instrumentation|url=https://books.google.com/books?id=dNx1OLgn1xcC|accessdate=26 July 2013|year=2003|publisher=Springer|isbn=978-3-540-65225-0|page=31}}
2. ^{{cite book|author=James W. Robinson|title=Atomic Spectroscopy|url=https://books.google.com/books?id=BNqp0RO7DXcC&pg=PA26|accessdate=26 July 2013|year=1996|publisher=MARCEL DEKKER Incorporated|isbn=978-0-8247-9742-3|pages=26–}}
3. ^{{cite journal|last1=Hilborn|first1=Robert C.|title=Einstein coefficients, cross sections, f values, dipole moments, and all that|journal=American Journal of Physics|volume=50|issue=11|year=1982|pages=982|issn=0002-9505|doi=10.1119/1.12937|arxiv=physics/0202029|bibcode = 1982AmJPh..50..982H }}
4. ^{{cite book|author1=Edward Uhler Condon|author2=G. H. Shortley|title=The Theory of Atomic Spectra|url=https://books.google.com/books?id=hPyD-Nc_YmgC|accessdate=26 July 2013|year=1951|publisher=Cambridge University Press|isbn=978-0-521-09209-8|page=108}}
5. ^{{cite journal |doi=10.1103/PhysRev.97.869|title=Motion of Electrons and Holes in Perturbed Periodic Fields|journal=Physical Review|volume=97|issue=4|pages=869|year=1955|last1=Luttinger|first1=J. M.|last2=Kohn|first2=W.|bibcode=1955PhRv...97..869L}}
6. ^{{cite book|publisher=Springer|location=Berlin | doi=10.1007/978-3-642-91116-3_3| chapter=Elektronentheorie der Metalle| title=Aufbau Der Zusammenhängenden Materie| pages=333| year=1933| last1=Sommerfeld| first1=A.| last2=Bethe| first2=H.| isbn=978-3-642-89260-8}}