Dear students, ladies and gentlemen,
As the only living Nobel laureate in physics in the Federal Republic of Germany,
and consequently a member of a rapidly dwindling species of beings,
I wondered whether it might not be more worthwhile, instead of holding a scientific lecture,
to speak about the causes for this rapid decline in Nobel laureates in the Federal Republic,
which might have been a more important subject, but since this is a political topic,
and as the representatives of my ministry of education and cultural affairs,
the Bavarian Ministry of Education and Cultural Affairs, aren't in any case here at this conference,
I thought that I would perhaps speak instead about a more pleasant topic, and hold a scientific lecture.
I would like to speak to you about neutrinos, and perhaps first say some words about the history of neutrinos.
If we speak in Europe about history, about any subject, then we usually start with the ancient Greeks,
but where neutrinos are concerned, history starts approximately in the year 1933,
exactly when is a little difficult to say, as the hypothesis of neutrinos that Pauli formulated cannot be dated very precisely.
It underwent some change, including with Pauli himself,
and it was actually first conceived a little differently to how we know it today,
but I believe that 1933 is perhaps a good year from which we can say that this hypothesis was applicable.
A hypothesis that requires us to assume – and this was Pauli's assumption
– that we have beta decay from a nucleus with the atomic number Z, for instance,
to a nucleus with an atomic number Z+1 while emitting an electron,
that requires us to assume that, after the initial and final conditions have been well defined here relating to its energy,
that also the radiation emitted, in other words, in this case the beta radiation, possesses a well-defined energy.
But as all of you are certainly aware, this is not the case,
but instead, the emitted beta particles have an energy distribution with a maximum energy
that we can actually ascribe to this energy difference, here with some corrections,
in other words, mass differences, but there are also very much lower energies.
From this dilemma, which initially might have looked like a violation of the laws of the conservation of energy and impulse,
and spin also played a role, Pauli found a way out of this dilemma through this neutrino hypothesis
in which he said, not only is a beta particle emitted, an electron, but also another particle, a neutrino.
The beta decay can then perhaps be formulated
so that, within this nucleus, a neutron is converted into a proton while emitting these two other particles.
This should be an electron-neutrino, more precisely – and this is this horizontal line – an electron-antineutrino.
Whether this is anti, or not anti, is a question of definition that was introduced later.
We have very secure assumptions today, very secure measurements,
or let us say, measurements that are secure to a certain extent about these neutrinos,
and I would like to speak a little in today's lecture about some of the more modern concepts of these neutrinos,
although in no way about all of them.
The sum of our experimental information
– and we must, always in the final analysis, rely on experiments,
irrespective of all the clever things the theoreticians tell us, we need to check and see whether everything they say is correct –
is largely contained in quantum numbers, which we refer to today as lepton numbers.
Excuse me if I'm doing everything here in English and holding my lecture in German after Mr. Wegener made such an effort,
I also wish to do the same with language and instead of using the otherwise usual broken English in this lecture,
I would like to use a visible English.
Now, these lepton numbers that you see here, we ascribe them to the electron and muon neutrinos that we know today.
And we are already familiar today with 4 such lepton types,
in other words, electrons, negatively-charged electrons and the related electron neutrinos,
as well as muons and related muon neutrinos, which can be characterised by these quantum numbers L(e) and L(Mu),
and for these particles here there are then of course the corresponding antiparticles
with the corresponding quantum numbers with reversed signs.
In fact, today we are aware of
– and I've indicated this modestly with this dot – at least one further type of lepton, the so-called tauons,
and these also include neutrinos, but this situation is very new and as yet unclarified in all its details,
and I'm not going to use these tauons any further in my lecture, but everything I say can also then be generalised easily.
Now a few words about the neutrino sources that are available to us today.
I should perhaps also say something about these lepton numbers, as I've been given ten extra minutes' speaking time.
I've written an example here, where you see that there is a law of conservation for these neutron-electron-numbers,
in other words, these nucleons here, they have a lepton number of 0, and then here you see,
for example, on the left-hand side stands the lepton number 0, and then it must also stand on the right-hand side
if there is a law of conservation, and you see that this is correct.
Here, for example, for the e minus you have here a 1 and for the Nu superscript e, the anti-electron neutrino,
you have a minus 1, and 1 and minus 1 together make 0, in other words,
the same stands on both the left-hand side and the right-hand side of this equation.
Now, a word about the neutrino sources that are available to us today.
I have listed the most important here, so we have for now the fission reactors
that are currently a topic of great public interest.
These fission reactors produce, besides hazardous radioactive emission, to a far greater extent neutrinos
– (this might indicate some scope for potential political demonstrations in the future!) –
in the range of 2 to 8 MeV.
They have fluxes of the magnitude of 10^13.
And these flux figures that I've given here, at a distance of around 5 metres from the heart of such a reactor
– we can't in any case get any closer because there are big shieldings there –
so these are the fluxes for the strongest reactors we have today.
Then we have the meson factories that supply us with neutrinos,
and while they supply us with electron and anti-neutrinos here, the reactors supply us with muon neutrinos.
They also deliver other particles, but these are the interesting ones, albeit with very much lower intensities.
And then we have the high-energy accelerators, which for their part operate in other energy ranges,
and also supply us with fluxes, and which are also very appropriate for measurements.
And finally, one of our most important, or perhaps one of our most important sources of neutrinos, the Sun.
I've listed them here a little more specifically because I'm going to come back to them later.
We distinguish here primarily the low-energy neutrinos from the Sun.
These are neutrinos with high intensities, occurring at almost 10^11 in the flux.
These are those neutrinos, and these are now normal electron neutrinos
that play a role in the Sun's main fusion process, in other words simply the fusing of two protons.
Then there are other high-energy neutrinos.
And these are the only ones that are accessible to measurement today,
or should actually be accessible, let me say, with high energies,
and are produced as a sideshow, a transition from 8 B, 8 boron, to 8 beryllium, but with only quite low intensities.
As far as this point is concerned, this last reaction,
which, as I said, is the only one that is currently accessible to direct measurement
– this will probably change in the not too distant future – I'll come back to speak about it briefly later.
So much for neutrino sources.
Let me point out once again that accelerators and nuclear fission reactors are the main sources available to us today.
And now a few words about the unique properties of neutrinos.
Neutrinos are perhaps almost the most remarkable particles that we have in nature today,
and I'd like to briefly explain some of these remarkable properties – although in no way all of them.
First, the properties in the upper part here, the properties of interactions,
namely the interactions that these neutrinos participate in.
And in order to demonstrate this to you, I've written up a couple of further particles here,
in other words, nucleons, such as the proton, that participate in all interactions known to us,
in other words, in the strong interaction, in the electromagnetic interaction,
in the weak interaction and also in the gravitational interaction.
Physicists then have an esoteric super-weak interaction
– but this also reaches the limits, gets very close to the limits, I would say, goes beyond the limits of our knowledge,
which is why I'm not mentioning them at all.
And I'm also not going to mention gravitation from now on,
because it's so weak compared to the other interactions that I can dispense with it here for our purposes.
Now, the electrons, they're already somewhat more limited insofar as, due to their charge,
they still participate in the electromagnetic interaction, and then naturally also in the weak interaction,
although not really until the gravitational interaction.
Even weaker are the neutrinos, which also, because they carry no charge, only participate in the weak interaction.
So, neutrinos are unique in form insofar as they participate in neither the electromagnetic nor the strong interaction,
and for this reason enable us to make an isolated study particularly of the properties of the weak interaction.
What weak interaction means, is something that even a physicist
who is familiar with this area sometimes needs to get clear about again and again.
Weak interaction means that this neutrino has almost no interaction.
We are familiar with weak interaction in the case of beta decay,
because beta decay arises through weak interaction, but what this really means – weak – is
that, after observing beta decay in the laboratory on its own – something that's sometimes difficult even for the initiate
– we need to, so to speak, reverse the beta decay process, and ask ourselves how likely this process is.
To make clear to you how small the probability of this process is,
I would first like to say that the Earth in its entirety is almost transparent to neutrinos.
They pass through it as if they were nothing.
This means, for example, the Sun emits neutrinos, and if you have the Sun overhead,
you see these neutrinos arriving where you are standing.
But if the Sun is located on the opposite side, when it's night-time on our side of the Earth,
then the neutrinos arrive here with precisely the same flux, with the same strength, as if the Earth weren't there at all.
If I really wanted to influence them, the neutrinos
– if I really in other words wished to create a weak interaction, so that they actually produced some type of reactions,
then I need to put some type of material in their path that roughly corresponds to the magnitude of a light-year of lead.
These are of course enormous volumes, and you can see with this statement
that it isn't easy to prove such particles in the laboratory,
because if the Earth is transparent to such neutrinos,
how can I then, in a detector of the magnitude of perhaps 1 cubic metre or so, have a chance of seeing such particles.
I can only have this chance naturally if I have enough of such particles so that,
despite the low probability that exists here, I perhaps have a chance of occasionally making one of these many particles react.
The aspect of neutrinos – and there are many other aspects that I'll not go into now –
that's particularly interesting to us here, is the question concerning the rest mass of neutrinos.
Normal theoreticians – and I've referred to this here, I've described this here as conventional theory –
assume that the neutrinos – and all of them, whether electron neutrinos or muon neutrinos –
that these neutrinos have no rest mass.
In other words, they behave in the same way as we also conventionally assume to be the case with photons.
Also our photons, our light quanta, possess no rest mass.
The experimental situation here doesn't look good at all.
We have firstly an upper limit at 35 electron volts for the electron neutrinos,
and for the muon neutrinos, the situation looks significantly worse: here we have a limit of 650 keV.
Nevertheless, we assume in the theory that the rest masses are 0
– that they will not be as high as these upper limits – a lot of cosmological arguments exist for this.
I believe that we can assume today that the masses for neutrinos are certainly below around 15 electron volts.
Otherwise there would be quite strange consequences for all our cosmological theories,
although it's something that's no longer quite so certain.
In any case, the mass limits that we know today are relatively high,
and we can now ask ourselves, is it rational to assume
that the masses are really precisely zero, or could perhaps an infinite mass apply to the neutrinos.
I will now give you a fairly short list of potential plausible or less plausible reasons
as to why we could assume that the rest mass of neutrinos is actually different to zero.
First, it should be said that the theoretical arguments which we have, and which compel us to assume
that the rest mass is zero
– that they are significantly less imperative than is the case for example with the parallel, analogous case of photon rest mass.
The photon rest mass is based on the fact that we assume an electromagnetic gauge invariance for our equations,
and this is a gauge invariance that is generally applicable for the so-called Hamilton function.
And from this assumption – that the Hamilton function is invariant in relation to such an electromagnetic gauge invariance –
this often of necessity implies not only a rest mass 0 of the photon,
but also the conservation of the electric charge,
and this is a law that has been extremely well verified in nature through experiments.
This means that there are extremely stringent and hard arguments here for the zero rest mass of the photon,
while in the case of the neutrino, it is in no way as imperative and as hard.
Here, too, there are symmetry arguments, which I mention only by name, without explaining them,
especially so-called gamma 5 invariance, which leads us to a zero rest mass of the neutrino in the theory,
but these invariances also no longer apply generally for the so-called Hamilton function,
but only for the wave function and the corresponding equation for the neutrino itself.
In other words, they are essentially less general, and we wouldn't be so unhappy if we had to relinquish this,
while we would be very unhappy if we had to relinquish these gauge invariances in the electromagnetic sector.
So, our arguments here for a zero rest mass in the theoretical area
are not so wildly convincing through to their final consequence.
Then, a perhaps somewhat weak argument that I would nevertheless like to present is
that it is nevertheless interesting to point out that the muon's mass is very different to the electron's mass,
while we assume so-called mass inequality for the related neutrinos, albeit with a zero mass in this case.
Now, this might be a coincidence, it might be that a higher symmetry is behind it,
but, of course, we don't know all of these things yet.
A further argument that I can cover only briefly because it's somewhat extensive, is
that we know from the theory of weak interaction that, in the case of the so-called hadronic contributions to this interaction,
certain symmetries exist with our quarks, which we regard today as basic building blocks.
And if we also apply, in a wholly consistent manner and entirely analogously,
such symmetries for the leptons' contributions to the weak interaction,
then we arrive of necessity at a very interesting phenomenon that was first applied as a postulate by Pontecorvo.
This is a phenomenon or assumption that the neutrinos that we observe today,
in other words the electron neutrino and the muon neutrino, are not stable particles in the classic meaning of the word,
but that the overlays are mixtures in precisely the form that Professor Wegener has already explained today for another example,
whereby the overlays or mixtures of two stable particles, which I will now refer to as Nu 1 and Nu 2,
in other words, these new neutrinos Nu 1 and Nu 2 that we do not observe,
that these neutrinos are actually stable in the sense that they have a clearly-defined mass.
Expressed in modern terms, one would say that these neutrinos are eigenstates of the mass matrix.
I've referred to this again briefly just for the specialists here.
So, here I've written the Hamilton operator for these eigenstates of the mass matrix, and you can see immediately
– those of you who are familiar with this formalism – that here, for example, a particle Nu 1 disappears,
and here one is generated, in other words, the number of Nu 1 particles is retained, precisely as here for the Nu 2 particles.
If, by contrast, I rewrite this expression using this transformation matrix, then I get constants,
all of which I can easily calculate from what's here – they're unimportant –
and then I get here, in particular, this type of expression,
where you see that here an electron neutrino is converted into a muon neutrino.
In other words, the lepton numbers are no longer retained here.
This is, so to speak, the symmetry that's destroyed here, and it can be derived here quite directly
if I assume such a transformation property.
In this case, this theta here, this theta angle is simply a mixing angle about which we know nothing at all today.
It's a mixing angle that's only written here as an angle so that this entire story is nicely orthogonal.
In other words, this sine and this cosine have no angle significance in the normal way: it's simply a constant,
and they're done in this way so that each of these equations is nicely orthogonal with the others.
So, we have a mixture here: the electron neutrino is a mixture consisting of two stable neutrinos
with this mixing constant or this mixing term, this mixing angle.
A fourth reason why we arrive at the assumption, why the assumption
– that the muon and electron neutrinos have a finite rest mass – is no longer so plausible,
is the so-called solar neutrino problem.
The fact, namely, that an American group consisting of Davis and his colleagues,
based at Brookhaven National Laboratory, have, for many years, decades in fact, been searching for this solar neutrino flux
that I mentioned previously – and the fact that this flux hasn't been located –
and that at least a factor of 3 fewer neutrinos from the Sun have been observed than one would actually expect.
I'm not yet sure whether this can be called a catastrophe, because there are still a few possibilities
that it could be that the effective cross sections that are used for the solar reaction
– that they're not quite correct, that extrapolation is required and so on, but it's beginning to look quite hopeless.
We no longer really know where this flux actually is, and the assumption of a finite neutrino mass could
– as I'll show you later – immediately solve this problem.
In other words, this is a further indication, although not yet a conclusive one,
that neutrinos might actually possess a finite rest mass.
After giving you reasons why neutrinos might have a finite mass compared with the conventional assumption,
I would now like to outline for you a few of the consequences that such a finite mass would have.
First, there are lots of consequences that I will not cover in detail now,
for particle physics, elementary particle physics and for field theories, but these consequences are not groundbreaking.
So these are minor corrections which need to be applied, and which are extremely difficult to measure experimentally.
If it were otherwise, we would have long known about it.
Then there are consequences for astrophysics and cosmology.
Perhaps a brief word on this last point.
If neutrinos had a mass, then they would also naturally have an energy according to the Einstein equation,
and this could mean that the entire energy sum in the universe looks quite different to what we assume today.
This would have significant consequences for our theories, especially the Earth's origin – the question as
to whether the universe is open or closed, and whether we can actually manipulate all these things
if we had a finite neutrino mass.
So, this would have quite enormous consequences.
It could be that we – as we know very well – not only swim in a sea of neutrinos –
that you are always swimming in this sea – but that this sea is much denser,
and perhaps contains quite other particles, than we currently assume.
The second point – if neutrinos had a finite mass – then they would become unstable and susceptible to decaying radioactively,
especially if, for example, the electron neutrino or the muon neutrino have different masses
– if one is heavier than the other, then the heavier can naturally decay into a lighter one,
and a gamma quant could then be released.
These processes are extremely difficult to observe.
Assumptions about them exist today, so there are processes that people have been looking for.
The New York Times and other relevant periodicals frequently announce that such a thing has been found.
Of course, it's quite important when it happens, but such announcements are then usually retracted later.
Some people become famous in this way for a little while, before being consigned to oblivion again.
So, people are constantly looking for this decay but they haven't found it yet.
This would also have consequences for the neutrinos' normal stability
where we would then be able to attribute a decay period to the neutrino.
A lot of speculation surrounds this.
The really wonderful thing about this field is that we can still really speculate about it,
which is no longer so easy in physics today.
Someone is already working on the ideas we have today, someone who says,
"Yes, but there you've violated the second law", or "You've violated this here," or "You've missed this out,"
or "You've simply misunderstood the physics, and this is why you've arrived at such and such an idea,"
– so, this constantly happens to us nowadays.
Here, however, we can still philosophise wildly,
and there's a certain satisfaction in this, in being able to propose wild ideas about neutrinos' potential decay periods.
Now, such philosophies are not quite so wild, we need of course to examine all of the experiments
that have been done somewhere at some point to see whether we can learn something from them,
and here we can actually learn a great deal.
The fact is that, today, we have – at least in the case of electron neutrinos –
good arguments to suggest that their lifespans are very long, certainly very much longer than I need for my lecture today,
but they are also certainly potentially longer than the lifespan of the universe as we assume it today,
and, of course, it's uninteresting to then look for such periods, but it's still a somewhat open and unsolved question here.
A further argument that I'd like to present – and this is in fact the central topic of my lecture today – is
that a finite neutrino mass, and, in particular, a mass difference between the two main neutrinos
that I've presented here, electron neutrinos and muon neutrinos, such a mass difference would result in transformations,
in such a way – I've stated only the most important example here – there are other possibilities –
that an electron neutrino converts into a muon neutrino over the course of time,
that this then converts back into an electron neutron and so on and so forth.
In other words, these neutrinos oscillate, so to speak, at one moment one type is here
– if I have it in this form at the start – and then comes this type, and so on and so forth.
So, in a quite primitive image: if I have a nuclear reactor, and I have here an electron-antineutrino source,
and the neutrinos are emitted on all sides, then this neutrino will have converted into a muon neutrino after a certain time,
before becoming an electron neutrino again much further out, and so on and so forth.
And if I now install a detector somewhere here that reacts only to electron neutrinos, for example,
then I will find a maximum intensity for my electron neutrinos here, and I will find nothing here, for instance.
So the neutrinos oscillate, they oscillate as a function of time, or, as they – the masses are certainly small –
travel at practically the speed of light, they will also oscillate in this way as a function of this location.
And it is particularly these neutrino oscillations about which I would like to talk to you in a little more detail,
because we are about to conduct an experiment in this sector.
And now allow me – but I will perhaps keep it quite brief – to speak just briefly about the formalism
relating to how these oscillations arise.
So, we saw previously that we make the assumption that electron neutrinos,
for example, are a mixture of these two types of stable neutrinos Nu 1 and Nu 2, and we now ask ourselves,
"What does it look like as a function of time if I produce an electron neutrino in such a way, and it then moves through space?"
Now, the general time-dependence of a wave function in quantum mechanics can be formulated in the way that I've indicated here.
We assume the wave function at a particular time, for example, at time zero,
and then multiply it by this factor in order to derive the time-dependence,
whereby, for the sake of simplicity, I always set the atomic constants to 1,
and if I apply this consistently to this formula here, then you can see
that I derive the time-dependence for such an electron neutrino in this form here,
whereby E(1) is simply the energy that belongs to this particle Nu 1,
and E(2) is the energy that particle Nu 2 possesses, and so this is this mixing angle that is up here.
As an example, I can mention perhaps a nuclear fission reactor that emits electron-antineutrinos,
and this means that at the location or at the time zero, no muon neutrinos are there,
that is to say, electron neutrinos arise at the reactor's centre.
And now they move outwards, and the probability of then finding such an electron neutrino at time t is consequently given
by this expression here, or at least proportionally to this expression.
So this can then be written quite easily in this formula, where you can see that the mixing angle is entered here,
and then the energy difference between these two neutrinos Nu 1 and Nu 2.
This is quite analogous to a beat frequency, where you have a beat frequency of two waves with two frequencies
or with two energies – then the energy difference or frequency difference is always included in such a beat frequency.
And if you take this expression, this E(2) minus E(1) times time and then adapt it a bit
– it's quite trivial, this adaptation, assuming that the impulse term is large compared with the mass term –
then you get an expression that you can write in the following way:
distance D from the location where the neutrino is generated, divided by a length
that I refer to as the oscillation length, which simply states for me when this intensity rises and falls.
And if I then take this parameter, which is the central parameter besides the mixing angle,
in other words, M2^2 minus M1^2, the mass difference of the two neutrinos that are involved,
and if I refer to the delta as M^2, then I arrive at an oscillation length that I've written previously here in formulas.
If I state it in metres, and the energy of the neutrinos or the impulse in MeV and this mass difference in eV^2,
then I get an expression here for this oscillation length for which I will soon show you some examples.
So the important thing – as you can see – is that the thing only works if the delta M^2 is different from 0
– only then do I derive something here at all if delta M^2 is equal to 0, then this entire expression here simply becomes 0,
and then just a 1 stands here, and this is nothing special, then there is no time-dependence.
I only get a time-dependence if this expression is different from 0
– and for this, the delta M^2, in other words, the two masses of my two neutrinos, must actually be different.
Now a couple of examples of such neutrino masses, and what type of oscillation lengths are derived.
This is of course just pure speculation.
We have no idea what we can expect in this case.
So, I have three examples here: namely, I have put a reactor, a meson factory and a high-energy accelerator here on the outside,
and I will give you the oscillation lengths for two different hypothetical mass differences.
If we assume that the mass difference is 1 eV^2 or 10^-3 eV^2, then we get oscillation lengths in the following form:
for the reactor, 2.5 metres, which is a respectable difference where we can make a measurement;
for the meson factory, 25 metres, which is also reasonable; and for a high-energy accelerator, 2.5 kilometres,
which also makes sense.
If, by contrast, I assume that the mass difference is lower by a factor of 10^3,
then already in the case of the reactor I get a distance of 2.5 kilometres,
which are distances where there's simply no longer any intensity left,
because intensity declines at 1 divided by R^2 with the distance.
We can no longer measure here. The meson factory is also uninteresting, and 2,500 kilometres is really very uninteresting indeed.
Here we can no longer make a measurement.
So, we can assume that we can perhaps go down further by a factor of 100 or so,
but it's certainly already a factor of 1,000, which is certainly too much.
We can also assume with an accelerator that we can perhaps still measure at a distance of 250 kilometres,
because these neutrinos have their intensity peaks forwards, so the intensity moves in a forward direction.
And, in fact, it was once proposed that an experiment be conducted at Cern to construct a type of neutrino detector,
to place it directly before the accelerator, and to then take it away and move it behind the Jura Mountains, into Switzerland,
and to then take another look to see whether some intensity was still there, at a distance of 100 kilometres or so.
This is possible in principle perhaps, but such an experiment has not yet been carried out.
Now, as for the rest of this table, we're going to leave it aside, and I would now like to show you briefly
– and just so that you get a bit of an idea, without going into details –
what such oscillations would look like now if we measure them at a nuclear fission reactor,
and this is what we are actually intending to do in our group.
I've written a few formulas up here that define the expressions a little,
although this is perhaps not so important now, with one exception:
if we had no mixing angle, if the mixing angle were zero,
then there would also be no neutrino oscillation, the whole thing would no longer apply.
In other words, the mixing angle must have a finite value, and specifically as large a value as possible.
If possible, this makes the experiment easier,
although at the moment we don't have any theoretical ideas about this mixing angle itself,
there aren't even any respectable speculations about it.
Now, assuming that we are concerned with a point source, in other words, that the reactor is almost point-formed,
which means that it is small compared with the oscillation length, and assuming that we have maximum mixing angle,
which means in this case theta = Pi/4, and under the assumption, an arbitrary assumption,
that this mass difference exists, I have depicted here for you such neutrino oscillations,
calculated by computer as we would get them
if we work with a nuclear fission reactor, and simply modify the distance from the reactor.
Which intensity that we observe if we, so to speak, move our detector away from the reactor and locate it at various places
– D is simply the distance from the reactor's centre, a few metres or so, typically between 0 and 30 metres –
distances that one can perhaps apply simply.
I've applied this here for various energy intervals.
Let us perhaps take this first one here
– from 4 to 10 MeV, this is approximately the range of the spectrum that is available to us at a nuclear fission reactor.
And there you can see that the intensity changes in this way.
In other words, if I set up my detector at 13 metres or so, then I get very little,
and if I set it up here at 20 metres, then I get quite a lot of neutrino intensity.
And if I now vary my energy interval, then you can see that these oscillations undergo quite a vast change.
We can, in other words, measure not only as a function of distance,
but also as a function of energy in principle and that's what we actually intend to do.
Now, what does the experimental situation look like in the area where we are looking for potential finite neutrino masses,
or more precisely, for neutrino oscillations.
Before we talk about this - some preliminary remarks.
We could also naturally measure such neutrino masses in another way, in principle.
We could set up other experiments.
For example, we could measure a beta spectrum directly, and then perhaps try to become increasingly precise.
There are lots of other proposals as to what could be done,
but all of these proposals cannot compete with such direct measurements of neutrino oscillations,
because this experiment is an interference experiment.
And such an experiment is generally always very much more precise
than if we directly measure absolute amounts, more precisely, the absolute amounts of quantum-mechanical probabilities.
In other words, if at all, this oscillation experiment is superior by many magnitudes to all other direct measurements of masses.
What experiments have there been to date that are concerned with such neutrino oscillations?
To be quite precise, there haven't been any.
There are only retrospective analyses of experiments that have already been conducted, of experiments
that have been performed for purposes other than those I cite here,
and where one can naturally go back and make a retrospective analysis
in order to see what limits are derived for potential neutrino mass differences from these experiments.
At Cern, at the Gargamelle, a measurement was carried out that always assumed maximum mixing angle,
and the energies are displayed here from which we can draw the conclusion
that, given maximum mixing, the neutrino mass difference must be smaller than 1 eV^2.
This is, so to speak, now the experimental limit we have.
At Yale, they have a proposal, and they believe that with their accelerator,
in other words, the meson factory in Los Alamos, they can achieve a limit smaller than 0.5 eV^2.
Finally, at Savannah River, Professor Reines and staff
– who are actually pioneers in this area and who have been concerned with electron neutrinos for more than 30 years –
arrive at the conclusion, through the retrospective analysis of their earlier experiments,
that the mass difference should be smaller than 0.3 eV^2.
We are planning at the German-French-British high flux reactor in Grenoble, in France, at the so-called ILL,
the Institut Laue-Langevin, an experiment that is in a very advanced stage of creation.
We consist of three groups: one group from the USA from Caltech – I'm not going to read out the names,
they're written here – one group from Grenoble, from the Institut des Sciences Nucléaires, a French group,
and our group in Munich from the Technical University.
We plan to apply this reaction to prove the existence of neutrinos in precisely the same form.
This reaction is the same that Reines has been applying for decades to measure the effective cross section of this reaction.
We are however applying another measuring technology, the same reaction - but another measuring technology.
The effective cross section measured by Reines and his colleagues
– as I said, this has already been going on for decades – is in the magnitude of 10^-43 cm^2.
As a physicist, you already get the shivers when you see such figures.
Even as a physicist, I should say, these are really extremely small,
and this is precisely the statement that I made at the start, that the Earth is transparent to such neutrinos.
This effective cross section we want to measure again, because
– as I said – this measurement has stood all on its own for decades,
and it goes without saying that we must re-examine measurements like this that have such significance
– examine them again applying independent methods, in other words, applying other measurement methods.
Now, quite briefly perhaps – again just a little more for the experts –
a presentation of the change in the significant quantities included in such an experiment,
namely the energy distribution of the neutrinos or of the anti-neutrinos that are emitted from a nuclear fission reactor,
which I've stated here, and specifically for various calculations.
Such an energy distribution can be measured directly only with great difficulty.
Measurements are currently underway, but so many corrections are included that need to be combined with theory,
and the problem is simply that, with nuclear fission, we now know that around 720 different fission products arise.
And we now know the decay schemes of around 200 of these fission products,
and for the other 500 we simply have to adopt appropriate theoretical speculations, which have now advanced very far,
but which differ, and this generates such differences over the range of the antineutrino spectrum.
The effective cross section for the electron-antineutrinos is also included.
As I've drawn here, this increases quadratically with the energy, at least in this energy range, in the MeV range.
If you move to large accelerators, for instance to Cern in the GeV range,
it then changes linearly with the energy for atomic form factor reasons.
But here it goes quadratically, so to speak, meaning it is particularly the high energies that that are interesting,
although these naturally are especially the energies
where the beta particles in particular have low energies, the neutrinos high energies, and the beta particles low energies.
And if I bring these two things together, if I multiply them by each other,
then this question as to how many neutrinos I get from my reactor and what is the effective cross section –
this is in fact the quantity that particularly interests us – then it appears
that we have in the range of 4 MeV approximately a maximum of our distribution.
In other words, this is where our experimental sensitivity will then be especially good.
Now, what does such an experiment look like – at least in our case, in the case of our planned experiment.
What we do here is the following: once again, the reaction up here that I've already mentioned,
this is what we want to prove, electron-antineutrinos come from the reactor and fall into a scintillator.
This is in other words a volume that is filled with scintillation liquid.
You'll see the details and measurement data later – just the principle for now –
a specially-produced scintillation liquid made particularly for this experiment with quite special properties.
So, at this point, one of these infrequent reactions occurs with a proton.
This scintillator is particularly quite rich in protons.
This proton will now decay into a neutron and a positron.
The positron has an energy here of some MeV's.
It moves a while here before finally resting and then decaying into two gamma quanta,
and this entire hodgepodge of electromagnetic emissions that arises is then observed directly here in these multipliers.
The neutron that arises here at the same time – this neutron has energies that are relatively low,
perhaps of the magnitude of 10 keV - this is moderated, meaning it undergoes many collisions with the protons
that are in here and in other light elements.
So it will become ever slower before finally diffusing somewhere across there into a helium-3 counter,
and the helium-3, with its quite particularly high effective cross sections,
reacts to thermal neutrons in an especially strong manner, so that it is then absorbed here.
During the absorption, a tritium and a proton then arise, and these two again produce an electric impulse on the wires
that are located in this counter, allowing the existence of this neutron to be proven.
The precondition is that the neutron is thermal.
In other words, the 10 kV that it has here is too high, they must be slowed down first.
This is critical, it must be slowed down first,
because only then do we have this nice, high effective cross section, this nice high proof sensitivity that we'd like to have.
Just briefly: the pulses that we observe once here and once here,
they look approximately like this, on the proton scintillator we get an impulse distribution of this type.
The important thing in this is that we achieve resolutions of around 18 percent in the case of 1 MeV, which isn't bad.
For questions relating to background it's important, of course, to have the resolution as good as possible,
and also for the energy resolution that we'd then like to have overall.
In the case of helium-3 counters, we have impulse forms of this type.
As I've already said, a proton and a tritium arise.
So, if I catch the two of them together in the counter, if one of them doesn't fly out again,
then I get all of the energy together, which is then around 764 keV, and if one of them leaves
– this will be the proton mainly – then I get a somewhat lower impulse magnitude.
The new factor in our experiment is these helium-3 counters.
These helium-3 counters are very difficult to build, years of development at the ILL in Grenoble helped us here massively.
There they know how to do these things.
It's always a collaboration between many people that allows such complicated things to be done in the first place.
And secondly, France helped us a great deal, the country's so-called strategic reserve of helium-3 was made available to us,
so we have 400 litres of helium-3, an incredibly expensive substance, available to us.
We get anxious, of course, lest we lose some of it, or that something happens to it.
So, you no longer sleep very well if you are doing these types of experiments.
So much for these pulses and how they look, and now perhaps just a few experimental details
that are interesting mainly for the experimental physicists among you.
The neutrons need to be braked, as I've said, and this proceeds relatively slowly.
We need to wait until we have magnitudes of 200 microseconds until the mass of these neutrons is really slowed down.
In other words, we implement a delayed coincidence between the protons in the scintillator
and the neutrons in the helium-3 counter – and the delay periods – the opening of the window – are unfortunately very long,
and we actually get a lot of background noise with such lengthy times, which is the problem of this experiment.
Now, we can do a lot of things to counteract this background noise.
I mention here just one of the most important things we can do.
We have for example background noise due to the fact that lots of muons come from the cosmic radiation, very fast particles,
and these muons can make a nuisance of themselves.
They can generate a fast neutron in our counter, which is quite undesirable,
and this fast neutron creates a proton recoil when it meets the protons.
And then it looks as if we get a proton from a real event, although it's a false event.
We can eliminate such protein recoils – since we know about muon incidence, as I'm going to show you –
through pulse shape discrimination techniques, by exploiting the fact
that protons and positrons have different forms to their electrical impulses, which we observe in the scintillator.
This is simply connected with the fact that these decay times, as I've pointed out here, are different,
and that the protons interact with the molecules in another way to the positrons.
The protons generate especially long-lived molecules and the positrons more short-lived molecules,
so that the decay constants are different, and we can exploit this to separate these particles from these particles
and especially to identify these false protons.
Using this technique, we will certainly be able to reduce our risky background noise,
and this is the riskiest part of the background, by a factor of between 10 and 100.
Finally, I would like to say a little about what we expect.
First, we are using the Grenoble reactor – as I've already mentioned –
which is a really puny reactor when we think of nuclear power plant reactors.
We should perhaps make it a little clearer in the press that these type of research reactors
that we use for our neutron experiments, that they are harmless reactors compared with nuclear power plant reactors.
Their capacity is simply much lower, although it's currently the most modern research reactor that exists anywhere in the world.
So we have 57 megawatts of capacity, and we could ask, why we don't go straight to a large reactor,
we could namely go to a nuclear power reactor, to a high-capacity electrical generation reactor.
Such power reactors typically offer 3,000 megawatts of thermal output.
The thermal output is higher than the electric output by a factor of three, meaning we could almost gain a factor of 100.
The reason why we are nevertheless starting in Grenoble with this small, relatively small reactor is simply
because we are concerned there with an almost point-formed neutrino source.
The entire fuel assembly – there's only one in it – has a 40-centimetre diameter, and this is extraordinarily small,
but if you want to measure such short oscillations, you must have small dimensions.
Later, if we then perhaps go on to dimensions of 100 metres or so, measuring large distances from the reactor,
then we will of course go to one of these dangerous nuclear power reactors, but that's still in the future.
We simply intend to initially measure with two distances in Grenoble, namely 8.5 and 15 metres,
and release the energy as I've briefly outlined.
Later then, a nuclear power plant reactor with very much higher output, and then distances of perhaps 10 to 100 metres.
Then we still need to discuss the possibility of a pulsed reactor;
I particularly want to take the opportunity of this conference in Lindau to discuss this with some colleagues.
In Dubna, in the Soviet Union, there's a highly interesting new reactor, which is of a very dangerous type.
And there, there really is some concern that when one moves about in such a thing
– that it's simply in principle two atom bombs that are sub-critical,
and they can then be rotated and brought together,
and at the moment when they're brought together you have, so to speak, an atomic explosion.
But then they part them again so rapidly that the thing doesn't blow up.
Instead you get a quite strong pulse of neutrons, which leave again in good time, so to speak.
Now, it doesn't bear thinking about what would happen if such a thing were once to get stuck,
although, appropriate precautionary measures are of course available for this,
because you shouldn't assume that we scientists are potential suicide candidates,
as we are quite the opposite, at least most of us.
Now, this type of pulsed reactor would be interesting for such an experiment because,
naturally, such a strong pulse occurs only during a very short period,
and our problem with such an experiment is the background noise.
And we could then switch the apparatus off while the reactor isn't working,
and we would then get a very much better relationship between the signal and the background noise,
and this is the reason why such a pulsed reactor would be interesting in principle.
Perhaps, however, not practically, because unfortunately the beta decays occur relatively slowly
and we need to consider very precisely whether such a pulse is also long enough for us
to actually achieve a gain in the relationship between the signal and the background.
If we namely then need to leave the window open again for long enough so that the thing already delivers its next pulse,
if we have just finished with the previous measurement, then such a reactor naturally doesn't help.
These are things that we still need to discuss; we haven't talked about them yet.
Now, what we expect from such an experiment are expect count rates, signal count rates, in the most favourable scenario,
of up to around 3 impulses per hour, which sounds very hard, although it's not that bad, then background noise rates,
and this is of course what is important, of around 1 impulse per hour.
This is the aim, although it's a theoretical aim.
Around a week ago we started to record our first data.
We're not yet at this rate at the moment, but we've also not yet quite finished building the experiment,
but it does appear that the thing is not far at all from the theoretical predictions,
especially as the helium-3 counter is actually running better than we originally assumed.
Now, the shielding against background noise is naturally the alpha and omega of such an experiment,
and specifically both a shielding against the reactor and a shielding against false radiation
that comes from the cosmic radiation.
And here we've naturally taken very special measures.
Now, finally, let me show you – just to give you a very brief impression of how the measurements are running -two slides.
In the first image, I would like to show you what the core of such an apparatus looks like.
So this is the centre of the equipment, the dimensions are stated here,
which are around 80 centimetres up here, and around 130 centimetres coming out towards the top here.
We have 30 of such individual proton counters, which are these scintillation counters with their multipliers,
and which I previously showed you one schematically.
In between each of them one helium-4 multiwire counting chamber,
then a level of scintillation counters again, so a total of 30 of this type, and 4 of these helium-3 counters.
So this is the heart of the apparatus,
and this apparatus must of course now be wrapped up as carefully as possible
to shield it from external radiation so that almost no false radiation arrives.
As I said – a count rate in the whole arrangement of around 3 per hour in the most favourable scenario.
And the next image shows you how the entire arrangement then looks.
So here you see this counter again, that is, the dimension is around 1.30 metres from here to here, as I've just shown you.
The entirety is then surrounded – this is a trolley, of course,
you need to be able to push it into this shielding housing and then be able to bring it out again,
because such an apparatus has naturally its tricky aspects and all sorts of things can go wrong.
Here alone we have 132 of such multipliers located,
and getting them to all run well at the same time is simply impossible, as we know.
So, until we have everything in shape, so we can enter and exit here frequently,
it must therefore be constructed so that access is easy.
So the central apparatus is first surrounded by polyethylene, in order to slow down the neutrons,
and this is particularly light material that creates good neutron-braking,
which is then surrounded externally by a so-called veto-counter.
These are anti-coincidence counters that seal off this almost cube-formed apparatus on all six sides,
and which tell us whether a particle, a charged particle, enters from outside.
So this anti-coincidence that you see here comes next, and then come 20 centimetres of lead shielding to the outside;
this is special lead with particularly low natural radioactivity.
Natural radioactivity plays a decisive role in this experiment,
and we've conducted an incredible number of experiments to keep the activity in the material
that is used here as low as possible, a lead shielding, in other words.
And then the whole thing is inserted here, and it is then fully sealed against the outside world.
Then a second veto-counter up here, which is designated as Veto 2, so that we can again separately control and observe,
at least from up here, the muon radiation and identify it quite securely.
Now, this gives you a little impression of what these people in Grenoble,
what our group in Grenoble, is up to in the cellar below the reactor.
We sit as it were directly below the reactor; the reactor is running above us, and these are ideal shielding conditions.
We also have the advantage that nobody can see us down there, nobody visits us,
and we can work there in peace, far away from any bureaucrats who would never venture down there.
So it's a fun time that we have there, and I hope that perhaps at one of our next conferences
I can report to you on the events that occur while we're having fun down in our cellar.
Thank you very much!