Momentum-space detection of an Electron (EWP)

[logic smogic]

[SOLVED] Momentum-space detection of an Electron (EWP)

I know there have been plenty of questions about electrons, momentum, and wave packets recently - but my question is distinct (and comes with a picture!).

Question: If you ionize an atom and detect the resulting free electron wave packet, how should it appear in momentum space?

My understanding is that the spacially-localized electron wave packet (EWP) that is born during ionization will be of a Gaussian shape, due to:

$$\Psi(x,t) = \frac{1}{\sqrt{2 \pi \hbar}} \int^{+\infty}_{-\infty}{\phi(p)e^{i(px - Et)/\hbar} dp$$

and that it will spread as it moves away from the ion and towards the detector. But won't the detector still process it as either a delta function or a Gaussian (in position space)? And if so, why isn't the resulting detection in momentum space a Gaussian (the Fourier Transform)?

The picture below is of an EWP that was single photon ionized by an XUV attosecond pulse. It looks to me like a "Sinc" function, which means that in position space it would be a rectangular function. This is without scattering (off of the ion core). My question really is why does this picture look like this? Thanks!

 

[logic smogic]

Oh, nevermind!

I found a paper that derives the final (drift) momentum as

$$p(t_{0}) = \frac{e E}{\omega} [cos(\omega t_{0}) + \gamma]$$

which is effectively a sinc function.