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The oscillator strength is the same for each sub-state .
The oscillator strength is defined by the following relation to the cross section for absorption:
Second, not all transitions have the same transition matrix element, absorption coefficient or oscillator strength.
The oscillator strength is a dimensionless quantity to express the strength of the transition.
See oscillator strength.
The sum of the oscillator strength from one sub-state to all other states is equal to the number of electrons :
This allows all three Einstein coefficients to be expressed in terms of the single oscillator strength associated with the particular atomic spectral line:
For high enough densities, all energies correspond to continuum states and some of the oscillators strengths may become negative-valued due to the Pauli-blocking effect.
If the charge, , is omitted from the electric dipole operator during this calculation, one obtains as used in oscillator strength.
The optical absorption is then essentially the product of the dipole operator matrix element (also known as the oscillator strength) and the JDOS.
The addition of the moiety to the sidewall of the nanotube disrupts the oscillator strength that gives rise to RBM feature and hence causes decay of these features.
For direct-gap semiconductors, the oscillator strength is proportional to the product of dipole-matrix element squared and that vanishes for all states except for those that are spherically symmetric.
The transition moment is related to the oscillator strength by the expression where s f is the degeneracy number of the upper state, m is the mass of the electron and ν is the transition frequency.
The first largely complete set of oscillator strengths of singly ionized iron group elements were made available first in the 1960s, and improved oscillator strengths were computed in 1976.
A time-dependent (TD) density functional theory analysis reveals that an increase in the applied field strength by and large increases the excitation energies corresponding to significant electronic transitions among frontier MOs with a concomitant decrease in their oscillator strengths.
It is similar to periodic-orbit theory, except that closed-orbit theory is applicable only to atomic and molecular spectra and yields the oscillator strength density (observable photo-absorption spectrum) from a specified initial state whereas periodic-orbit theory yields the density of states.
Atoms are considered as quantum mechanical oscillators with a discrete energy spectrum with the transitions between the energy eigenstates being driven by the absorption or emission of light according to Einstein's theory with the oscillator strength depending on the quantum numbers of the states.
For scaling systems such as Rydberg atoms in strong fields, the Fourier transform of an oscillator strength spectrum computed at fixed as a function of is called a recurrence spectrum, because it gives peaks which correspond to the scaled action of closed orbits and whose heights correspond to .