Why anomalous Zeeman effect is more common? Gone through many books, searched on Google, but couldn't find the answer.
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The "anomalous" Zeeman effect is the name for the Zeeman effect with more than three - symmetrically distributed – sublines of the original lines.
Without the spin, one would expect 3 lines in the pattern only because the transition may change a single type of the spin $S$ only, by $\pm 1$, roughly speaking, from the spin of the photon. Quantum mechanically including the spin, there are transitions between many different states with various values of $L,S$ and other parts of the angular momentum, and they're allowed quantum mechanically as long as the total $J$ angular momentum is conserved.
One gets the "normal" Zeeman effect in the real world only for some simple – perhaps vanishing etc. – arrangements of $L,S$, which is rare, so most of the real-world Zeeman effects are those that were called "anomalous" because they couldn't have been explained without the spin.