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Electrons, Muons and Pauli Exclusion

Put in a possibly oversimplified way, lepton universality says that electrons, muons, and taus all behave in the same way except for mass effects. The question is “Does this apply to Pauli exclusion?”

Due to the Pauli exclusion principle, only two electrons can be in the s orbital, and hence in the ground state of regular beryllium, two electrons are in the s orbital, and two electrons are in the p orbital. My question is what happens in the ground state of dimuonic beryllium, with two muons and two electrons. Are all four particles in s orbitals, or are two in s orbitals and two in p orbitals?

A similar question can be asked about muonic lithium, which would be easier to create experimentally.

i.e., in muonic lithium, with one electron replaced by a muon, can all three leptons be in the s orbital?

Jim Graber
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    Pauli exclusion just says there can't be a doubling of a fermion state. The muon s orbital is a distinct state from the electron s orbital due to the different mass, so I see no reason at all why you would expect Pauli exclusion to play any role. – ACuriousMind Dec 20 '15 at 16:04
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    Lepton universality only means that the all leptons couple to the electroweak field in the same manner: the "equations of motion" are the same, so to speak. But as the masses are not, the "dynamics" are different. The PEP only applies to undistinguishable particles, and if two particles have different masses, you can tell them apart. Thus, the PEP sais nothing about mixed bounded states: a $\mu$ and a $e$ may share quantum numbers. – AccidentalFourierTransform Dec 20 '15 at 16:06
  • Electrons, muons and taus do not "behave the same way". For one thing, electrons are stable as far as we know, muons have a very interesting mesoscopic decay time, which would allow us to build practical muon storage rings (they have been proposed for quite some time) and tau particles are comparatively short lived. That, together with just their bremsstrahlung's profiles makes them rather different, in practice. – CuriousOne Dec 21 '15 at 00:34
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    Possible duplicate of Capacity of an orbital to hold muons and electrons – John Rennie Dec 21 '15 at 09:21

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