Why magnetic dipole transition intens...

Why magnetic dipole transition intensity is so low in absorption spectra compared to the electric dipole transition.

In optical process, both electric and magnetic dipole moment respond to the EM wave, causing additional energy

H'=H_E+H_M,

where H_E=pE and H_M=μB.

One can estimate the order of the magnitude difference by taking the ratio:

R=(pE/μB)².

In EM wave, one has E/B=C/n, where C is the speed of light, and n is the refractive index.

For charge transfer optical process, it is reasonable to assume that p~eA=1.6e-19×1e-10 =1.6e-29Cm.

For magnetic dipole moment μ, Bohr magneton is always a good estimation for the order of magnitude.

Therefore, the ratio between the typical oscillator strength of electric charge transfer and magnetic dipole excitation is:

R~(1.6 e-29*3e8/9.24e-24/n)²=(5.2×10²/n)² >> 1
.

This is the reason that the magnetic dipole transition is normally not intense.