In a scientific paper, I need for my Bachelor thesis, the differential cross section for photo pair production
$\gamma\gamma\to e^{+}e^{-}$
is given as follow:
$\mathrm{d}\sigma = \frac{r_{0}^{2}\mathrm{d}\vec{p}_{+}\mathrm{d}\vec{p}_{-}}{2\epsilon_{+}\epsilon_{-}\omega_{1}\omega_{2}(1-\cos(\theta))}(B+4A-4A^{2})\delta(\vec{k}_{1}+\vec{k}_{2}-\vec{p}_{+}-\vec{p}_{-})\delta(\omega_{1}+\omega_{1}-\omega_{2}-\epsilon_{+}-\epsilon_{-})$
where $r_{0}$ is the classic electron radius,
$A=\big(\frac{1}{x_{1}}+\frac{1}{x_{2}}\big )$ and $B=\big(\frac{x_{1}}{x_{2}}+\frac{x_{2}}{x_{1}}\big )$.
$x_{1}$ and $x_{2}$ are relativistic invariants:
$x_{1}=-2p^{(4)}_{+}k^{(4)}_{1}$ and $x_{1}=-2p^{(4)}_{+}k^{(4)}_{2}$
with the four momenta:
positron: $p_{+}^{(4)}=(\vec{p}_{+},i\epsilon_{+})$, electron: $p_{-}^{(4)}=(\vec{p}_{-},i\epsilon_{-})$,
photon 1: $k_{1}^{(4)}=(\vec{k}_{1},i\omega_{1})$, photon 2: $k_{2}^{(4)}=(\vec{k}_{2},i\omega_{2})$
The problem now is that these quantities are written in natural units $m=c=\hbar=1$, but I need this in SI-Units. But how can I rewrite this formula in SI units? A first step is to write for example
$p_{+}^{(4)}=(\vec{p}_{+},i\epsilon_{+}/c)$ and
$\hbar k_{1}^{(4)}=(\hbar\vec{k}_{1},i\omega_{1}\frac{\hbar}{c})$.
But this is not enough since B is dimensionless, but A is not. How is A+B defined as an example?
The paper cites the book "Quantum electrodynamics" from Akhiezer (1965), but I don't find the book on the internet or in a library.
Can anybody help me?