Theoretical investigation of the effects of intramolecular electron-spin relaxation on Stern-Gerlach deflections

The exact solution of a random walk model for electron spin flips in a magnetic field is presented and applied to the Stern-Gerlach (SG) deflection of a spin-1/2 molecule. It is found that when the intramolecular spin-relaxation time τ is much longer than t, the residence time of the molecule in the magnetic gradient, the SG deflection spectrum is unaffected, whereas when τ is much shorter than t, the two-line splitting pattern collapses to that of a single line, neither shifted nor broadened with respect to the line profile at zero field gradient. SG band profiles at intermediate values of λ = τ/t are especially interesting. In the range 2.0 > λ > 0.5, the M_s = ± 1/2 SG bands are not shifted from their peak position at large λ, however they are strongly broadened asymmetrically toward zero deflection. This broadening assumes the nature of a broad peak at λ ≈ 0.5, which then narrows substantially and rapidly shifts to the position of zero deflection for λ between 0.3 and 0.01. Examples are given of the SG spectra of molecules exhibiting extreme values of λ.