# Why do we need such a good vacuum?

Matter-wave interference experiments with molecular beams require a good vacuum. Otherwise, collisions with gas particles would prevent the molecular beam from propagating freely from the source to the detector. At atmospheric pressure air molecules only fly for about $$60 \mathrm{nm}$$ before they collide with another particle. In our experiments even larger molecules need to fly more than $$2 \mathrm{m}$$ without collision. A closer inspection shows that this is only possible at pressures as low as $$10^{-8} \, \mathrm{mbar}$$ which is a hundred billion times lower than atmospheric pressure.

Such an ultra-high vacuum can be achieved using a two-stage system. Backing pumps (scroll and piston pumps) reduce the pressure to a hundred-thousandth of the atmospheric pressure. For the final pressure we additionally use turbo molecular pumps.

Extra: Mathematical background

The mean free path $$\ell$$ in a thermalised gas can be approximated by:

$$\ell = \frac{k_{\rm B}T}{\sqrt 2 \pi (r_1 + r_2)^2 p}$$,

where $$k_{\rm B}$$ is the Boltzmann constant, $$T$$ the absolute temperature in Kelvin, $$r$$ the molecular radii in meter and $$p$$ the pressure in Pascal.

For different values of the velocity and small-angle scattering the coefficients change. The Van-der-Waals cross-section can easily be a hundred times larger than the geometrical cross-section.

Extra: Lab techniques

## Scroll pumps (backing pumps)

From an atmospheric pressure of 103 mbar down to 10−2 mbar for the generation of a low or medium vacuum

Scroll pumps are gas transfer pumps; they transport gases out of the chamber. They consist of two nested spirals of which one is movable. Due to the eccentric movement the spacing between the spirals is periodically increased and decreased. Thereby, the gas is sucked into the pump, compressed and emitted at the centre of the spirals. In  the animation you can track a free space from the rim to the centre of the spiral but not the other way around. Hence, the gas is consistently pumped in one direction. These pumps work in the hydro-dynamical regime where the mean free path is smaller than the typical size of the vacuum chamber.

## Turbo-molecular pumps

From 10-2 mbar for the generation of ultra-high vacuum

These pumps resemble an aircraft turbine and consist of static and rotating paddle wheels. The rotor blades rotate about 1000 times per second hence reaching the velocity of the gas particles (300 m/s – 400 m/s). The molecules struck by the blades are decelerated and kicked towards the next lower rotor stage and then removed by a backing pump. These pumps work in the molecular flow regime where the value of the mean free path is greater than the typical size of the vacuum chamber therby allowing particles to move ballisticly from one wall to the other.

## Sorption pumps

Even lower pressures can be achieved by pumps that do not remove the material but bind the residual gas on a surface. Two types of gas-binding pumps are often combined:

### Ion-getter-pumps

From 10−7  mbar, for the generation of ultra-high vacuum at existing high vacuum

In ion-getter-pumps air molecules are ionized by electron collisions and then accelerated in an electric field towards a binding surface.

### Titanium-sublimation pumps

From 10−7  mbar, for the generation of ultra-high vacuum at existing high vacuum

Titanium is an excellent getter, that is a material that chemically binds molecules such as oxygen, nitrogen or carbon dioxide. If enough particles stick to the surface, a new titanium layer is deposited and the captured particles are buried.