Slight deviations of the coefficient of the linear Zeeman term from the elementary Landé value arise from the following effects: ($a$) small departures from Russell-Saunders (R-S) coupling, ($b$) the motion of the nucleus, ($c$) relativity corrections, ($d$) interplay between the magnetic field and various kinds of magnetic interactions within the atom, and ($e$) the Schwinger electro-dynamical corrections. In the present paper an effort is made to estimate the magnitude of the effects ($a$), ($b$), ($c$), ($d$) with the goal of examining whether the residual discrepancy between Rawson and Beringer's measurements on oxygen and the ideal Landé value is in accord with Schwinger's formula for ($e$).

The effect ($d$) may be further divided into modulation by the magnetic field, or Larmor precession, of ($d_1$) ordinary spin-orbit, ($d_2$) spin-other-orbit, and ($d_3$) orbit-orbit interaction. The theory for $c$ and $d_1$ has already been developed by Margenau and Breit, and $d_2$ to a certain extent by Lamb, while that for $b$ was first given by Phillips. The corrections ($d$) can in each case be obtained by substituting $\mathrm{p}+\frac{e\mathrm{A}}{c}$ for p in the corresponding magnetic interaction terms in the Pauli two-component Hamiltonian function, but can also be derived more fundamentally from the four-component Dirac equation. From the standpoint of the Dirac equation, the segregation of ($c$) from other magnetic effects is rather artificial, but ($c$) has the simple physical interpretation that it is tantamount to substituting the transverse mass for the rest mass in the ordinary Zeeman energy.

The numerical estimate of effects $\mathrm{}\left(b\right)-\left(d\right)\mathrm{}$ requires knowing the wave functions in some detail. Certain rather crude approximations are made in the present paper, including omission of exchange terms in some places. However, the agreement between the calculated and observed Zeeman coefficients after all the corrections ($a-e$) are included is gratifying.

• Received 12 August 1953

DOI:https://doi.org/10.1103/PhysRev.92.1448