In the helium transition lines, 1s2p 3P2 -> 1s2 1S0 and 1s2p 3P1 -> 1s2 1S0 are named intercombination line, 1s2s 3S1 -> 1s2 1S0 named fobidden line, and 1s2s 3S1 -> 1s2 1S0 named resonance line, I want to know why so named?
The 1s2p 3P2 -> 1s2 1S0 and 1s2p 3P1 -> 1s2 1S0 lines are called intercombination lines because the initial and final spin states are different (triplet and singlet respectively). These transitions do not violate the $\Delta L = 0,1$ selection rule, but they do violate the $\Delta S = 0$ selection rule. Sometimes they are called semi-forbidden lines.
The 1s2s 3S1 -> 1s2 1S0 line is called forbidden (more precisely electric-dipole-forbidden) because it violates the $\Delta L = 1$ selection rule (for transitions involving S-states $\Delta L$ cannot be zero, while for higher angular momentum states it can). This transition can still occur (as a magnetic dipole transition) but with much lower probability.
The 1s2s 3S1 -> 1s2 1S0 is called a resonance line because at low densities the 1s2s 3S1atomic state decays (very slowly) via magnetic dipole transition to 1s2 1S0. However, when the density of atoms and electrons reaches a certain value, the rate of the transition is sharply increased due to collisions with electrons. In fact, the knowledge of this radiative transition rate allows to determine the electron density in plasma.
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