Muonic hydrogen ground state energy

[petey_hb69]

Would the energy just be a multiple of how much bigger it is than electron?

 

[zhermes]

You could approximate it using the bohr model. You should work it out in detail to be sure, but I think you would just replace the electron mass with the reduced mass, in the numerator of the ground state energy term... so you would increase the energy by roughly a factor of 100?---maybe.

 

[Bob S]

Here in Figure 1 are the main energy levels and K x-ray energies of muonic hydrogen:

http://cern.ch/AccelConf/e94/PDF/EPAC1994_0864.PDF

This shows the K_∞ X ray energy, which is the 1s binding energy. Compare to the electronic hydrogen 1s binding energy, at about 13.60 eV.

The two biggest corrections to the muon-to-electron mass ratio (13.6 eV x 105.658/0.511 = 2812 eV) are the corrections for reduced mass and for vacuum polarization (virtual particle shielding of the bare proton charge).

Bob S