# What is the order of the number of significantly scattered particles in Møller scattering?

in an electron-electron collision with a low speed and in the nonrelativistic case, approximately what fraction of electrons get significantly deflected (say more than 10 degrees)? Generally, with increasing the speed of the colliding electrons, does the number of not-deviated (reflected at 180 degrees) particles increase or decrease?

• G.Smith i meant electrons, edited it. – Ali Lavasani May 31 at 4:32
• Being reflected at 180 degrees is the maximum deviation possible, not the not-deviated case. – G. Smith May 31 at 4:32
• G.Smith what is the range of the diffraction angle? And what fraction are defelcted at 180 in the case I deacribed (a lot or a few, what are angles with the most probability)? – Ali Lavasani May 31 at 4:35
• Actually, I take back what I said. Since these are identical particles, you can’t tell whether they both turned around 180 degrees or they just kept going with no deflection. I guess the maximum deflection is 90 degrees. – G. Smith May 31 at 4:41
• The $1/\sin^4{\theta}$ means that angles near 0 and 180 are much more probable than near 90. – G. Smith May 31 at 4:43

Nonrelativistic Møller scattering reduces to Rutherford scattering (plus exchange scattering) in the relative coordinate, and the Rutherford cross sections diverges for small deflection angles. All incoming particles are, to a greater or lesser extent, scattered. That means that it is not possible to talk quantitatively about the fraction of the total particles scattered through at lease some minimal angle, because there are an infinite number scattered by very small angles $$\theta\gtrsim0$$.

• So you mean, if I have two electrons colliding with a certain velocity v, it's impossible to calculate the probabikity that the deflection angle is more than a certain amount? – Ali Lavasani May 31 at 5:11
• It doesn’t make sense to ask about this probability. Suppose they both have velocity $0.1c$ in the center-of-momentum frame. If they have an impact parameter of $10^{-10}$ meters, they are going to scatter through larger angles than if they have an impact parameter of $10^{-5}$ meters. This is why cross sections are about scattering of beams with a wide distribution of impact parameters. – G. Smith May 31 at 5:31
• @Ali Lavasani if you have a cutoff then you can certainly calculate it. But if you want to know how many electrons will be "deviated" by any amount then the answer is all of them. An electron on the moon and another on the sun will cause "deviations" to each other because the Coulomb force has infinite range. – KF Gauss May 31 at 5:55
• @G.Smith does the probability for larger scattering angles increase or decrease as the velocity of incidence increases? – Ali Lavasani May 31 at 9:58
• @KFGauss what kind of scattering is the collision between two atoms? Does it have the same behavior as moller scattering? – Ali Lavasani May 31 at 15:01