Theory of the Quadratic Zeeman Effect

Abstract

The experiments of Jenkins and Segrè, reported in the accompanying paper, are considered theoretically. The quadratic Zeeman effect observed in absorption to large orbits in strong magnetic fields is due to the diamagnetic term in the Hamiltonian, which is proportional to the square of the vector potential and hence to the square of the magnetic field. For the alkalis, the problem involves essentially only one electron, and its spin can be ignored. $m_l$ and parity are always exactly defined, while $n$ and $l$ are not. The observed spectrum can be divided up with increasing $n$ into three regions, according as the lines are broadened asymmetrically (region I), broadened further, but nearly symmetrically (region II), and broadened so much as to overlap into a continuum (region III). It is shown that region I corresponds to $n$ being a good quantum number and $l$ a fairly good one; region II to $n$ being a fairly good quantum number and $l$ not good at all; and region III to both $n$ and $l$ breaking down completely as quantum numbers. Good quantitative agreement with the experiments is obtained as long as inter-$n$ perturbations can be neglected. When this can no longer be done (large $n$), the theory becomes prohibitively complicated, although some qualitative indications can still be obtained from it.