• Tritium β Decay and the Neutrino Rest Mass
  
• Overview of the KATRIN Experiment

Each β decay of an atomic nucleus characterized by mass number A and charge Z produces an electron (e⁺ or e^-) and a nucleus of mass number A and charge Z−1 or Z+1. The total rest mass of the end products is a bit smaller than that of the initial system, the energy gained according to E = m�c² appears as kinetic energies of the particles in the final state.

If only two particles emerge from the decay of a nucleus which is at rest, the kinetic energy of each particle (nucleus and electron) has a unique value in order to satisfy the conservation of momentum and energy. Looking at a typical energy distribution of β electrons (see the second figure below) one immediately realizes that this is not the case, and there seems to be an apparent violation of energy conservation. Furthermore, there is a violation of conservation of the "spin" (a quantum mechanically defined sort of intrinsic angular momentum of a particle or system of particles).

Pauli resolved all of this by postulating a third, "invisible" particle emerging from the decay. Named the "neutrino" by E.Fermi -who subsequently developed a theoretical explanation- it shares the available kinetic energy with the other particles, mainly with the electron because from kinematics the much heavier nucleus receives only very little kinetic energy. The neutrino was also assigned a spin which cared for the conservation of angular momentum.

The picture shows the particles involved in tritium β beta decay. We now know that the neutrino created together with an electron is of the "electron" flavour (ν_e). Apart from the electron there are two other charged "leptons", muon (�) and tau particle (τ). Accordingly there are two other neutrinos, the muon neutrino (ν_�) and the tau neutrino (ν_τ) appearing with these heavy, instable leptons. Because of the high mass these charged leptons can only be created by particle collisions with high kinetic energies or in the decay of even higher-mass particles created by such collisions. This is only possible at accelerator machines or with particles emerging from cosmic accelerators, therefore this neutrino - charged-lepton connection became only apparent in the 1970's. It also became clear that the oppositely charged leptons are particle and anti-particle. The only stable lepton, the electron e⁻, was assigned a particle, and the neutrino created together with it became the anti-particle as indicated by the horizontal bar in the figure above.

Neutrinos were considered massless for a long time. The highest energy value of electrons in β decay is up to now indistinguishable from the value which can be calculated for a massless neutrino. Any nonzero mass value of the neutrino would lower the available kinetic energy, so a nonzero mass of the ν_e would have to be tiny. Detecting neutrinos directly is very difficult because they interact only by the "weak" force. This makes matter almost transparent to neutrinos which are abundantly available in the universe, but they pass through the sun and the earth practically unhindered.

With large detectors it was, though, possible to observe neutrinos by their rare reactions with matter. In recent years, several huge experiments (e.g. SNO, Super-Kamiokande) could show that neutrinos undergo so-called flavour oscillations, a quantum-mechanical effect which causes neutrinos to temporarily change flavour. This effect is only possible if neutrinos of different flavour have slightly different masses. If oscillations are observed, at least one kind of neutrino must have a non-zero mass. By applying very clever methods, the oscillation experiments provided much insight, but they can only set limits to the mass differences, they cannot determine the neutrino mass itself. The SNO website states (Sep 2006):

"We know that the mass of the neutrino is approximately zero, but we are unsure how large the masses of the three individual neutrino types are because of the difficulty in detecting neutrinos. This is important because neutrinos are by far the most numerous particle in the universe (other than photons of light) and so even a tiny mass for the neutrinos can enable them to have an effect on the evolution of the Universe through their gravitational effects. There are other recent astrophysical measurements that provide information on the evolution of the Universe and it is interesting to seek complementary information by direct determinations of the masses of neutrinos."

An obvious approach for a direct mass determination of the electron neutrino is to examine very precisely the end region of the β spectrum. This has been done for several decades, and the most recent efforts in Russia (Troitsk nr Moscow) and Germany (Mainz) during the 1990's both rendered an upper limit of the ν_e mass of 2.2 eV/c². Both experiments employed the so-called MAC-E filter method to determine the energy of the electron. The KATRIN experiment does this on a much larger scale, and together with a high-intensity tritium β source it is hoped to achieve a mass determination down to 0.35 eV/c², or to set an upper limit of 0.2 eV/c². An in-depth description is given in the KATRIN Design Report 2004.

• The Windowless Gaseous Tritium Source (WGTS) will consist of a 10 m long, cylindrical tube of 90 mm diameter. The gaseous tritium is inserted in the middle and pumped out at both ends
  
  
• Electrons from beta decay and remaining tritium molecules enter the transport section which has the purpose of eliminating the tritium while guiding the electrons to the spectrometers. This is achieved by a combination of mechanical and cryogenic pumps and superconducting magnets.
  
  
• The pre-spectrometer is in principle a smaller version of the main one. A static electric field provides a retarding energy of about 100 eV below E₀ and removes all electrons but a fraction of 10^-7 at the highest energies. This is necessary to minimize background in the main spectrometer due to trapped electrons.
  
  
• The main spectrometer is 23m long and 10m in diameter. It defines the analyzing potential with a precision of a few ppm. Both spectrometers operate as MAC-E-filters, i.e. electrons from the tritium source which are produced isotropically can be accepted within a large solid angle. Magnetic fields are provided by superconducting magnets on both sides of the spectrometers. Electrons are counted in an integral fashion above the retarding potential which is varied in small steps just below E₀. This adjustment is done at the tritium source which is on a moderate potential of 0...-200V. The spectrometers may be operated at a temperature down to -20�C to reduce outgassing. To minimize background, an ultra high vacuum of better than 10^-11mbar is necessary.
  
  
• Leaving the main spectrometer the electrons are guided to a detector which, from the measuring principle, needed only to be a counting device. But from previous experiments we know that recognition of background is paramount, so a rather sophisticated detecor with high position and energy resolution will have to be employed.