  The Lande g factor describes the response of an atomic energy level to an
external perturbation by a uniform and constant magnetic field. In the case of
many-electron systems, the leading term is given by the interaction
mu_B*(L+2S.B), where L and S are the orbital and spin angular momentum
operators, respectively, summed over all electrons. For helium, a long-standing
experimental-theoretical discrepancy for P states motivates a reevaluation of
the higher-order terms which follow from relativistic quantum theory and
quantum electrodynamics (QED). The tensor structure of relativistic corrections
involves scalar, vector, and symmetric and anti-symmetric tensor components. We
perform a tensorial reduction of these operators in a Cartesian basis, using an
approach which allows us to separate the internal atomic from the external
degrees of freedom (magnetic field) right from the start of the calculation.
The evaluation proceeds in a Cartesian basis of helium eigenstates, using a
weighted sum over the magnetic projections. For the relativistic corrections,
this leads to a verification of previous results obtained using the
Wigner-Eckhart theorem. The same method, applied to the radiative correction
(Bethe logarithm term) leads to a spin-dependent correction which is different
for singlet versus triplet P states. Theoretical predictions are given for
singlet and triplet 2P and triplet 3P states and compared to experimental
results where available.
