- #1
Einj
- 470
- 59
Hi everyone. I have a question about the calculation of Rutherford cross section in the context of QED. I know how to compute it using the usual four potential:
$$
A_\mu(q)=(\frac{e}{q^2},0,0,0)
$$
and taking the matrix element to be:
$$
\mathcal{M}=\bar u_{s'}(p')\gamma_\mu u_s(p)A^{\mu}(q).
$$
I was wondering if it is possible to compute it also by considering it as the process e+γ→e, i.e. taking the matrix element to be:
$$
\mathcal{M}=e\bar u_{s'}(p')\gamma_\mu u_s(p)\epsilon^\mu,
$$
where [itex]\epsilon^\mu[/itex] is the photon polarization.
In this case I got (if I did everything correctly):
$$
\frac{1}{2}\sum_{spin}|\mathcal{M}|^2=2e^2q^2.
$$
My question is: how should I now integrate this to obtain the cross section? In order words, what is the phase space for this weird 2→1 process?
Thanks
$$
A_\mu(q)=(\frac{e}{q^2},0,0,0)
$$
and taking the matrix element to be:
$$
\mathcal{M}=\bar u_{s'}(p')\gamma_\mu u_s(p)A^{\mu}(q).
$$
I was wondering if it is possible to compute it also by considering it as the process e+γ→e, i.e. taking the matrix element to be:
$$
\mathcal{M}=e\bar u_{s'}(p')\gamma_\mu u_s(p)\epsilon^\mu,
$$
where [itex]\epsilon^\mu[/itex] is the photon polarization.
In this case I got (if I did everything correctly):
$$
\frac{1}{2}\sum_{spin}|\mathcal{M}|^2=2e^2q^2.
$$
My question is: how should I now integrate this to obtain the cross section? In order words, what is the phase space for this weird 2→1 process?
Thanks