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Introduction
Up to recently the neutrinos, the 3 neutral out of the 12 fundamental fermions, out of which all matter is made,
were assumed to be massless particles. But recent results from the atmospheric and solar neutrino
experiments [1] indicate the existance of neutrino oscillations and therefore require non-zero neutrino
masses. Although we now know that neutrinos have masses, we still do not know, which ones. The reason for this
is, that these oscillation experiments are only sensitive to differences between squared masses
 (and mixing
parameters) of different neutrinos, but not to its absolute mass values. On the other hand not only for
particle phyiscs but also for cosmology it is very important to know the value of the neutrino masses:
- Particle physics
We have a very precise understanding of the elementary particles and their interactions
by the so-called Standard Model. The neutrinos are assumed to be massless in this model.
But this Standard Model neither explains the pattern of the fermion masses nor
the mixing between the quarks (6 out of the 12 fundamental fermions). The parameters
describing masses and mixing have to be determined by experiments.
This unsatisfactory situation calls for an extended theory beyond the Standard Model.
In most of such new theories the neutrinos get masses naturally in agreement with the
experimental findings mentioned above. Since neutrinos are much lighter than the other
fermions their masses are of special interest for these theories.
Knowing the neutrino mass values and their mixing might
help us to find the right theoretical description out of all possible theories.
Concerning the neutrino mass generation in such models
it is of special interest whether the neutrino masses are hierarchical
or nearly degenerated
In the latter case residual small differences between the various nearly
degenerated neutrino masses is the reason for the neutrino oscillation signals
observed with solar and atmospheric neutrinos. From the
observed in these experiments the two cases
cannot be distinguished. To solve this problem a sensitivity on the neutrino mass itself of
 1 eV/c² is required.
- Cosmology
According to the big bang theory there exists a huge amount of neutrinos in the universe left over
from the big bang, like the photons of the so-called cosmic microwave background radiation, which were
discovered more than 30 years ago. The ratio of theses relic neutrinos to atoms is about one billion to one,
therefore even very small neutrino masses a very important. From different observations we know, that
a large amount of non-visible, so-called Dark Matter, contributes more to the total matter in the universe,
than all stars, even more than all the atoms in the universe together. It is very interesting to know,
especially for the still open questions of structure formation and the evolution of the universe, whether
neutrinos contribute to this dark matter in a significant way or not. Also the answer to this requires a
sensitivity on the neutrino mass of
1 eV/c² .
The only way to determine neutrino masses without the requirement of further assumptions are the
so-called direct mass measurements, of which the investigation of the endpoint region of the
tritium  decay spectrum is the most sensitive one: Tritium undergoes a
decay into a Helim ion emitting an electron antineutrino and an electron. The
electron energy spectrum, the so-called spectrum, is senstive to
the value of the electron(anti-)neutrino mass at its upper end at
E0 = 18.6 keV (s. figure 1). The
measurement of the neutrino mass is therefore nothing else but the extremely precise determination
of the shape of the spectrum in the region just below the endpoint
E0.
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