Why the discrepancy in muonic H Bohr radius? 285 fm or 256 fm?

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Discussion Overview

The discussion revolves around the discrepancy in the Bohr radius of muonic hydrogen, with specific values cited as 285 fm and 256 fm. Participants explore the implications of these values in different contexts, particularly focusing on the role of reduced mass in determining the Bohr radius.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants note that the Bohr radius of muonic hydrogen is cited as 285 fm in certain sources, while others report it as 256 fm or 255 fm.
  • One participant suggests that both values can be correct under different contexts: 256 fm is considered the Bohr radius for an infinitely heavy nucleus, while 285 fm applies to a proton-muon atom due to the reduced mass of the muon.
  • The reduced mass of the muon when forming an atom with a proton is stated to be 0.89879 times its rest mass, influencing the Bohr radius calculation.
  • It is mentioned that the physical value of the Bohr radius for a deuteron would fall between 256 fm and 285 fm due to a larger reduced muon mass.
  • One participant expresses gratitude for the clarification regarding reduced mass in Newtonian physics.

Areas of Agreement / Disagreement

Participants do not reach a consensus on which value is definitively correct, as they acknowledge that both values are applicable in different contexts.

Contextual Notes

The discussion highlights the dependence of the Bohr radius on the assumptions regarding the nucleus's mass and the reduced mass of the muon, which may not be fully resolved in the contributions.

seattle.truth
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Some places say (including this paper) claim the bohr radius of muonic hydrogen is 285http://ethesis.unifr.ch/theses/downloads.php?file=LudhovaL.pdf

Many more peer reviewed papers say it is 256 fm, or 255 fm though. (search for '256 fm muonic' in the googlez).

So who is right? And more importantly, why is there such a massive descripancy?

Any help will be greatly appreciated. Thanks.
 
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seattle.truth said:
Some places say (including this paper) claim the bohr radius of muonic hydrogen is 285http://ethesis.unifr.ch/theses/downloads.php?file=LudhovaL.pdf

Many more peer reviewed papers say it is 256 fm, or 255 fm though. (search for '256 fm muonic' in the googlez).

So who is right? And more importantly, why is there such a massive descripancy?

Any help will be greatly appreciated. Thanks.

They are both correct under different contexts. 256 fm is the correct Bohr radius for an infinitely heavy nucleus. 285fm is the Bohr radius for a proton-muon atom. This is because the reduced mass of muon when it forms an atom with a proton is 0.89879 times its rest mass. The first value is constant (but it is not accurate for a real system), while the second value is physical and accurate, but it is only valid for a proton nucleus. The physical value is different from 285 for a Deutoron for example (and it is in between 256 and 285, because the reduced muon mass is larger.)
 
Thank you very much, sir.

I didn't know about reduced mass in Newtonian physics.

Now I'm enlightened (after doing a bit more research).
 
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