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[pbutkiewicz5]

for the lowest level in the 2D multiplet of the free La atom j=3/2
for the highest level in the 2D multiplet of the free La atom j=5/2
so |l+s|=5/2 and |l-s|=3/2 by adding both we have 2l=4 so l=2 and s=1/2 if we substitute into the equation
gJ = 1 + (j(j + 1) + s(s + 1) – l(l + 1)) / (2j(j + 1)) we obtain
for the lowest level in the 2D multiplet of the free La atom gJ=0.8
for the highest level in the 2D multiplet of the free La atom gJ=1.2

The exact Lande g-factor for metallic lanthanum cannot be determined precisely because in a solid-state environment, electron interactions, hybridization, and band structure effects alter the atomic energy levels and magnetic properties. Unlike isolated atoms, where gJ is well-defined by quantum numbers
L,S,J, in a metal, electron delocalization and screening effects modify these values, making gJ
dependent on the material’s electronic structure and experimental conditions. Additionally, I could not find any published studies that explicitly report the Landé g-factor for metallic lanthanum.
Source: chat gpt.

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