the zeeman effect (; ), named after the dutch physicist pieter zeeman, is the effect of splitting a spectral line into several components in the presence of a static magnetic field. it is analogous to the stark effect, the splitting of a spectral line into several components in the presence of an electric field. also similar to the stark effect, transitions between different components have, in general, different intensities, with some being entirely forbidden (in the dipole approximation), as governed by the selection rules. since the distance between the zeeman sub-levels is a function of the magnetic field, this effect can be used to measure the magnetic field, e.g. that of the sun and other stars or in laboratory plasmas. the zeeman effect is very important in applications such as nuclear magnetic resonance spectroscopy, electron spin resonance spectroscopy, magnetic resonance imaging (mri) and mÃ¶ssbauer spectroscopy. it may also be utilized to improve accuracy in atomic absorption spectroscopy. a theory about the magnetic sense of birds assumes that a protein in the retina is changed due to the zeeman effect.the magnetic compass mechanisms of birds and rodents are based on different physical principles. journal of the royal society when the spectral lines are absorption lines, the effect is called inverse zeeman effect. thumb|420px|zeeman splitting of the 5s level of rb-87, including fine structure and hyperfine structure splitting. here f = j + i, where i is the nuclear spin. (for rb-87, i = 3/2) ==nomenclature== historically, one distinguishes between the normal and an anomalous zeeman effect that appears on transitions where the net spin of the electrons is not 0, the number of zeeman sub-levels being even instead of odd if there is an uneven number of electrons involved. it was called "anomalous" because the electron spin had not yet been discovered, and so there was no good explanation for it at the time that zeeman observed the effect. at higher magnetic fields the effect ceases to be linear. at even higher field strength, when the strength of the external field is comparable to the strength of the atom's internal field, electron coupling is disturbed and the spectral lines rearrange. this is called the paschen-back effect. in the modern scientific literature, these terms are rarely used, with a tendency to use just the "zeeman effect". ==theoretical presentation== the total hamiltonian of an atom in a magnetic field is :h = h_0 + v_m,\ where h_0 is the unperturbed hamiltonian of the atom, and v_m is perturbation due to the magnetic field: :v_m = -\vec{\mu} \cdot \vec{b}, where \vec{\mu} is 
Foundational_quantum_physics Quantum_magnetism Spectroscopy