bbbl67 said:
So basically, I guess even if you think the muon is going into replace the outermost layer of electrons, in actual fact it's always going into become its very own first muon level, no matter what? It couldn't care less what the electrons are doing?
It cares, especially if it is outermost. Because it is NOT required to be on its first muon level.
Consider the excited states of a hydrogen/-like atom. The one electron is not bound to be on first electron level - that is the ground state. In excited states the electron is on second, third, thirtieth et cetera electron level, and the first level is simply unoccupied.
Short of relativistic and reduced mass effects, a muon on first level is 207 times closer to nucleus than electron would be. Whereas in hydrogen-like atoms, the radius of the 2nd level is 4 times that of 1st level, the radius of 3rd level is 9 times that of first level, and the radius of 15th level is 225 times that of 1st level. Thus a muon on its 15th level is slightly further than an electron on its first.
Consider a He atom with 1 electron on its first level, and 1 muon on its 15th.
In the absence of any muon, the electron in He
+ ion would orbit at 1/2 the distance it has in H, with 4 times the energy.
For the muon orbiting well outside He
+ ion on muon´ s 15th orbital, the He+ ion looks much like H+. With one difference, though - the electron has some polarizability.
The muon on its distant orbit is 15 times slower than the electron in H would be. The electron in He+ is further 2 times faster in linear, 4 times faster in angular speed - total 60 times faster in angular speed than the muon. Over the timescale of muon orbital movement, the electron is orbiting in slowly varying field.
Now, the muo on its 15th orbital is unstable and can eventually fall to its first.
He-μ
- is 200 times smaller than He
+, thus 400 times smaller than H. The muon has the same linear speed as electron in He
+, 400 times the angular speed of electron in H. Thus an electron will simply barely feel the difference between He-μ
- and H
+, while the muon will barely feel the presence of electron.
In between, you are going to have excited states where te electron and muon orbit on the same timescale, which cannot be simplified in either above described direction.