Hydrogen 1s 3s transition frequency

[neilparker62]

Good day

With reference to the following article: https://hal.archives-ouvertes.fr/hal-00506468

The measured frequency is given as 2922742936.729(13)MHz but right at the end of the article, the following is written:

"The hyperfine structure of the 1S level is well known and that of the 3S level is evaluated from the Fermi formula with the Breit correction to be 52 609.4 kHz. After correction of the hyperfine splitting, the frequency of the 1S-3S transition is:

(1S − 3S) = 2 922 743 278.678 (13) MHz "

So which of these frequencies is the 'actual' frequency of a photon emitted following an electron transition from 3s to 1s ? Also if I subtract the two frequencies, I get about 340 MHz which doesn't seem to relate to the +-53MHZ referred to. What are the remaining components making up the 340MHz difference ?

 

[DrClaude]

So which of these frequencies is the 'actual' frequency of a photon emitted following an electron transition from 3s to 1s ?

The point is that there is no such thing as the transition from 3s to 1s. The actual transition is between two F levels, one in the 3s hyperfine manifold, the other in the 1s hyperfine manifold. The measured frequency is the frequency they actually measured, so corresponding to a real transition in hydrogen. The second frequency is the hypothesized transition frequency one would get if there where no hyperfine interaction.

Also if I subtract the two frequencies, I get about 340 MHz which doesn't seem to relate to the +-53MHZ referred to. What are the remaining components making up the 340MHz difference ?

You have to take into account the hyperfine shift of the ground state also.

 

[neilparker62]

Something like this then (?)

Measured energy + ground state Lamb shift + hyperfine splitting = Dirac energy 1s - 3s

The ground state lamb shift is + because we are subtracting the 1s energy from the 3s energy.

A diffraction based experiment by Gerhard Herzberg in the 50s attempted to determine the ground state lamb shift by subtracting measured energy from the Dirac energy of the (unresolved) 1s-2p transition in Deuterium so I'm presuming this is something similar except for the further inclusion of hyperfine splitting.

I'm just interested in the experimental side of things and know nothing about the theory of hyperfine splitting nor of Lamb shift other than that (from what I can make out) they are component parts of transition energy for which the major constituent is the Dirac energy. In any calculations I do, I just look up values for Lamb shift, hyperfine splitting etc. Hence the second part of my query - I would just like to know the component parts of the +-340MHz hyperfine splitting.