What makes electron scattering more useful than alpha particle scattering for resolving the structure of the nucleus?

Question

I hear of a lot of people say that electron scattering is more useful than scattering with heavier particles like the $\alpha$ particle, but I'm not sure why this is the case. This is the first Born approximation for quantum mechanical scattering:

$$\frac{d\sigma}{d\Omega} = \left(\frac{m}{2\pi\hbar^2}\right)^2\left|\int e^{i\vec{q}\cdot \vec{r}}V(\vec{r})d^3{r}\right|^2$$

where $\sigma$ is the scattering cross section, $m$ is the mass of the incident particle, $\vec{q}$ is the change in momentum between incoming and outgoing particle states and $V(\vec{r})$ is the perturbing potential.

The only difference the electron would make in this formula as opposed to an $\alpha$ particle that I can see would be the lower mass factor out front, but this would actually lower the differential cross section significantly, and I don't see why that would be a good thing. There would also be a change in the factor infront of the potential function due to the smaller charge of the electron compared to the alpha particle, but this would not change the order of magnitude the same way the smaller electron mass would.

So what about an electron makes it so much more attractive for use than an $\alpha$ particle?

Answer 1

Electron scattering is more useful than alpha scattering for at least a couple of reasons:

• The electron is a point particle so its de Broglie wavelength ($\lambda=h/p$) and hence resolution is just inversely proportional to its momentum. Higher electron energies allow us to probe the nucleus in finer and finer detail. An alpha particle is most definitely not a point particle, so its resolution is limited by its rms charge radius of about $1.7\,\mathrm{fm}$. Things get messy when you probe smaller scales with alpha particles.

• Electron-nucleus interactions are cleaner than alpha-nucleus interactions at higher energies, although this comes with the potential disadvantage that electrons don't interact directly with electrically neutral but strongly interacting nuclear constituents (neutrons, gluons). Electrons do, however, indirectly interact with gluons and are the major source of information about gluons inside nuclei. Also, if one does want a strongly interacting probe, a proton is a smaller, simpler, and better option than an alpha particle.

Answer 2

The electron has much less mass than the alpha particle, which makes it easier to push its velocity up to the highest level possible. High velocities mean high energies and short wavelengths for the electron, and with an accelerator like SLAC it was possible to get an effective wavelength for the electron at the end of the beam line that was much much smaller than the measured diameter of a proton. This allowed the researchers to "look" at the insides of a proton.

In this picture, you can think of the SLAC as having been an electron microscope with a beam tube 10,000 feet long instead of 36 inches long.