Filling of Electronic States - usual filling sequence: - consider ...
Filling of Electronic States - usual filling sequence: - consider ... Filling of Electronic States - usual filling sequence: - consider ...
Relative orientation of L and S in one electron atoms - two possibilities: quantization of total angular momentum J for the two possibilities of coupling between L and S phys4.10 Page 7 Precession of angular moments without external field: - the magnitude and direction of J is conserved - L and S precess around J with external magnetic field B: - J precesses around B - J z is quantized - L and S precess around J - this gives rise to the anomalous Zeeman effect phys4.10 Page 8
LS coupling - in many electron atoms the total angular momentum J is the vector sum of the individual orbital angular moments L i and spin angular moments S i in most of the many electron atoms - the individual orbital angular moments L i are observed to couple to a resultant orbital angular moment L - the individual spin angular moments S i couple to the resultant spin angular momentum S - the moments then interact via the spin orbit coupling to form the total angular momentum J the angular momentum magnitudes L, S, J and their z-components L z , S z , J z are quantized in the usual way with their respective quantum numbers phys4.10 Page 9 quantization rules: note that the resultant angular moment quantum numbers are indicated by capital letters, whereas the individual electron quantum numbers are not capitalized note: - L and M L quantum numbers are always integer or 0 - all other quantum numbers are half integer for an odd number of electrons - and integer or 0 for an even number of electrons - for L > S the total angular momentum J can have 2S + 1 different values - for L < S the total angular momentum J can have 2L + 1 different values phys4.10 Page 10
- Page 1 and 2: Filling of Electronic States - usua
- Page 3: Spin orbit coupling in hydrogen - n
- Page 7 and 8: - for S > L the multiplicity is giv
- Page 9 and 10: Helium (He, Z = 2 ) spectrum: selec
Relative orientation <strong>of</strong> L and S in one electron<br />
atoms<br />
- two possibilities:<br />
quantization <strong>of</strong> total<br />
angular momentum J for<br />
the two possibilities <strong>of</strong><br />
coupling between L and S<br />
phys4.10 Page 7<br />
Precession <strong>of</strong> angular moments<br />
without external field:<br />
- the magnitude and direction <strong>of</strong> J is conserved<br />
- L and S precess around J<br />
with external magnetic field B:<br />
- J precesses around B<br />
- J z is quantized<br />
- L and S precess around J<br />
- this gives rise to the anomalous Zeeman<br />
effect<br />
phys4.10 Page 8
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