Atomic form factor

In nuclear and particle physics, the form factor is a factor in the cross section for elastic collisions. It is the Fourier transform of the electrical charge distribution of the Targetteilchens (eg nucleus ) and depends on the momentum that is transferred during the dispersion. The form factor thus indicates how the scattering depends on the momentum transfer. By measurement of the form factor at different momentum transfers, conclusions can be drawn regarding the charge distribution of the target.

At inelastic collisions occur at the location of the form factor of the structure features.

Shape factor in the Rutherford scattering

The Rutherford scattering formula, which applies only to the scattering of a particle by a point charge ( Coulomb ), it can be extended for extended charge distributions. The differential cross section is then as follows from

Wherein the shape factor of the charge distribution.

It depends on the momentum transfer of the incident particle

And contains all the information about the spatial distribution of charge in the scattering center. So you can use the measurement of the cross section of certain scattering processes as a function of momentum transfer to make by subsequent comparison with theoretical models, information about the shape of the scattering potential.

In the Born approximation (ie, the potential of the interaction is so weak that initial and final states can be treated approximately as plane waves ) yields the form factor as the Fourier transform of the normalized to the total charge of the charge distribution function:


  • The imaginary unit i
  • The reduced Planck 's constant

The load distribution function is defined as:

In which

  • The static charge density
  • The atomic number and
  • The elementary charge;

It has the normalization condition


Experimental determination

For the experimental determination of the electric and magnetic form factors and to use the Rosenbluth formula for the differential cross section:


  • The Mott cross section
  • The negative square of the transferred four-momentum
  • The probability of a spin- flip in the scattering
  • The scattering angle.

It has the cross section measured at a fixed scattering angle for a plurality of so to do a Rosenbluth plot, in which is plotted on the x-axis and the y -axis. The Rosenbluth formula is then by the linear form

Being possible to calculate the magnetic and electric form factors from the slope and intercept:

  • Atomic physics
  • Nuclear physics
  • Particle Physics