A general theory for magnetic linear dichroism (MLD) is presented. The derivation uses a perturbation approach together with the rigid shift approximation and includes terms in the Boltzmann population of the ground state and in the band shape function which are proportional to the square of the magnetic field strength. A six term expression for the MLD is obtained. The different terms result from the Zeeman splitting of the ground and/or excited states, the population redistribution of the ground state, or the intermixing of electronic states. Expressions for each of the six terms are given. They are functions of the electric dipole transition moments polarized parallel and perpendicular to the magnetic field and of the magnetic moments of the ground and/or excited states. Estimates are made of their relative importance for conditions of possible experimental importance. Computer simulations of the MLD band shapes for diamagnetic and paramagnetic species as a function of bandwidth and temperature are given. The effects of the varying contribution of the zeroth, first, and second derivatives of the assumed Gaussian band shape function are illustrated. The application of the method of moments to the quantitative analysis of an MLD spectrum is also discussed. Finally, the present theory is applied to atomic spectroscopy, e.g., atoms isolated in matrices. It is shown that the results of an MLD experiment combined with the results of a magnetic circular dichroism (MCD) experiment should provide an unambiguous assignment of the total angular momentum of excited electronic states in atoms.
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