Can the Selection Rule Δl = ±1 Be Applied to Helium Transitions?

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SUMMARY

The selection rule Δl = ±1 can be applied to Helium transitions despite the presence of electrostatic interactions and multiple electrons. This conclusion is supported by the analysis of transition rules derived from Einstein's A and B coefficients, as well as the wavefunction of Hydrogen. The discussion highlights the distinction between triplet-singlet transitions, which are forbidden (ΔS=0), and the applicability of Δl = ±1 in Helium. Understanding these principles is essential for accurate predictions of atomic transitions in multi-electron systems.

PREREQUISITES
  • Understanding of atomic transition rules, specifically ΔS and Δl
  • Familiarity with Einstein's A and B coefficients
  • Knowledge of wavefunctions in quantum mechanics
  • Basic principles of electrostatic interactions in multi-electron atoms
NEXT STEPS
  • Study the derivation of selection rules for multi-electron atoms
  • Explore the implications of electrostatic interactions on atomic transitions
  • Learn about the application of Einstein's A and B coefficients in atomic physics
  • Investigate the wavefunction models for Helium and other multi-electron systems
USEFUL FOR

Students and researchers in atomic physics, quantum mechanics enthusiasts, and anyone studying the behavior of multi-electron atomic transitions.

Niles
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Hi

I am reading about transition in Helium, and I have come across a question. It is clear that triplet-singlet transition are not allowed, i.e. ΔS=0. But in my book (Foot's Atomic Physics) it says that Δl = ±1. This is what I don't understand. The selection rule Δl = ±1 we derived for Hydrogen, where there was no electrostatic interaction and only a single electron making the transition. In Helium we *do* have an electrostatic interaction and two electrons -- then how can we reuse Δl = ±1 again?Niles.
 
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In a textbook I find that the rule of transition can be deducted by Einstein's A,B cofficients,and use the wavefunction of hydrogen.
 

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