Missing relativistic gamma in interaction constant

[mjo22]

As per Spence’s textbook, the electron interaction constant has a factor of relativistic mass in it. In cryoJAX conventions we scale out fundamental constants through a rescaling of the interaction constant and potential. This makes the potential and electron scattering factors simple to calculate.

I had thought the interaction constant under our rescaling was $\sigma = \lambda / 4 \pi$, but really it should be $\sigma = \gamma \lambda / 4 \pi$, where $\gamma$ is the relativistic factor.

To fix this, we can follow a similar pattern as for the wavelength:

1. We’d need to add a property like AbstractImageConfig.relativistic_gamma, that computes gamma from the voltage.
2. We would need to update the function apply_interaction_constant.

@geoffwoollard can you take a look at fixing this?

EDIT:
Probably best to call AbstractImageConfig.relativistic_gamma -> AbstractImageConfig.lorenz_factor

[mjo22]

I think it should be the following (check me on this):

$$\gamma = \frac{E_{total}}{E_{rest}} \rightarrow \frac{m_0 c^2 + eV}{m_0 c^2}$$.

Therefore in AbstractImageConfig we can add

class AbstractImageConfig(eqx.Module):

    ...

    @property
    def lorenz_factor(self):
        c = scipy.constants.speed_of_light
        m0 = scipy.constants.electron_mass
        e = scipy.constants.elementary_charge
        rest_energy = m0 * c**2
        accelerating_energy = e * (1000.0 * voltage_in_kilovolts)
        return 1 + accelerating_energy / rest_energy

[mjo22]

Moving discussion over to #419