Vacuum Polarization

[Widdekind]

C.A.Bertulani's Nuclear Physics in a Nutshell (pg. 24) quotes the following formula for Vacuum Polarization in QED:

 

[math]e^2® = \frac{e^2(r_0)}{1 + \frac{2 e^2(r_0)}{3 \pi} ln \frac{r}{r_0}}[/math]

What is the electron radius r₀ ?

[ajb]

It will be the classical electron radius (I think).

 

Is what you have quoted the one loop renormalised electron charge? This is often given in terms of vacuum polarisation. It has been a while since I have looked at QED.

[Bob_for_short]

C.A.Bertulani's Nuclear Physics in a Nutshell (pg. 24) quotes the following formula for Vacuum Polarization in QED:

 

[math]e^2® = \frac{e^2(r_0)}{1 + \frac{2 e^2(r_0)}{3 \pi} ln \frac{r}{r_0}}[/math]

What is the electron radius r₀ ?

It is a sum of the most divergent diagrams. I do not have this book but I think that r₀ is not the electron radius. It is 1/Λ where Λ is the cut-off. When Λ tends to infinity, r₀ tends to zero and the electron charge gets completely screened at distant r (if it is finite at r₀=0). This is a "Moscow zero" - a result obtained by Pomeranchuk and Landau.

 

Although somewhat off-topic, you can find a similar difficulty described in my article "Atom as a 'Dressed' Nucleus" (arXiv, CEJP).

Edited August 25, 2010 by Bob_for_short

[Widdekind]

thanks for the responses !