Hyperfine structure

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Area of ​​Expertise - Spectroscopy

The splitting of line spectra (atomic spectra) beyond the fine structure is called hyperfine structure. The split of the hyperfine structure is only around $1/1000$ the fine structure splitting. It is based on a nuclear spin effect (shell electron-nucleus coupling) and on the isotopy of the elements (nuclear mass and nuclear volume effect).

Transitions between hyperfine states are used in atomic clocks because their frequency is constant and can be generated and measured with high accuracy and with relatively simple means.

Fine structure (physics)

When looking closely at line spectra of atoms, one observes one Fine structure. This can be seen in the fact that individual lines of a spectrum are split into two or more lines that are very close together. This means that there are energy levels in the respective atom that are very close together, since each spectral line can be assigned to a distance between energy levels.

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The order of magnitude of this finer split is, however, about 10 4 times less than that of the other levels. In the case of the hydrogen atom, the change in wavelengths for H&alpha -, H&beta and H&gamma Line of the Balmer series 0.14 Å, 0.08 Å and 0.07 Å (for comparison: the wavelength of the H&alpha Line is at 6562.8 Å). This also explains the relatively late discovery of the fine structure.

This abolition of the degeneracy of the energy levels is a consequence of the somewhat different kinetic energy in the theory of relativity, the spin-orbit coupling and an effect that is described by the Darwin term.

In order to take these purely relativistic effects into account in quantum mechanics, correction terms are added to the Hamiltonian of the system. In the first order, the Hamilton operator then reads:

H = mec 2 + H0 + W.M. + W.S.B. + W.D. + .. ,

whereby mec 2 the rest energy of the electron and H0 is the non-relativistic Hamilton operator.

It is W.M. the relativistic correction term of the kinetic energy:

,

W.S.B. is the correction term for the spin-orbit coupling:

and W.D. is the so-called Darwin term as a correction of the potential energy

.

The energy shift, which is called the fine structure, is then ΔE. = E.M. + E.S.B. + E.D. (relativistic mass correction, spin-orbit coupling, Darwin term).

These correction terms occur when the relativistic Dirac equation for the atom is solved instead of the non-relativistic Schrödinger equation (or Pauli equation). In addition to the fine structure, one can also observe finer structures: the hyperfine structure.

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