In the graphic, atoms are colored blue while atoms are green. Two beams collide at the center and are scattered. Detectors can be rotated by the angle , . The paths of the incident and scattered particles are lit up by light beams; particles scattered at angles other than are not visible. The counter shows the average number of scattered atoms per second per unit solid angle.

The low-energy (around 100 meV) elastic scattering of helium atoms can be treated by the Rutherford scattering formula. The scattering amplitude in the center-of-mass system is given by [2, 3]:

,

where .

( reduced mass of , electron charge, , helium nuclear charge and wavenumber, such that kinetic energy .)

The differential scattering cross-section (also written ) is determined from the amplitude by .

For scattering, the identities of the atoms can, in principle, be distinguished. The scattering cross section for all atoms is then equal to the sum

.

For scattering, since the scattered particles are identical bosons, the scattering amplitude is given by the sum and the cross section is then

.

scattering, by contrast, involves identical fermions. The scattering amplitude is then given by the difference and

.

In simplified arbitrary units, the three cross sections are given by

,

,

.

Interpret these as the number of helium atoms hitting the detectors per second per unit solid angle , as recorded by the counter.

The most dramatic effect occurs for scattering at . The cross section has twice the magnitude of that for , but the scattering vanishes completely at .