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Neutrino Oscillations for Dummies / SurprizingFacts

About neutrino oscillations almost all geeks have heard. About this phenomenon written a lot of professional literature and a lot of popular articles, but only the authors of textbooks believe that the reader understands the theory of the field, and even the quantum, and the authors of popular articles are usually limited to phrases in the style: "The particles fly-fly, and then BAC and turn into others ", with a different mass (!!!). We will try to figure out where this most interesting effect comes from and how it is observed with the help of huge installations. And at the same time we learn how to find and extract several desired atoms from 600 tons of matter.
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Another neutrino

In the previous article I told how in 1932 the very idea of ​​the existence of neutrinos appeared and how this particle was discovered 25 years later. I recall that Raines and Cowen registered the interaction of antineutrinos with a proton

 $  bar { nu} + p  to n + e ^ + $ "data-tex =" inline

. But even then many scientists believed that neutrinos can be of several types. A neutrino actively interacting with an electron was called electron, and a neutrino interacting with a muon, respectively, is muon. The experimenters had to figure out whether these two states differ or not. Lederman, Schwartz and Steinberger conducted an outstanding experiment. They investigated a beam of pions from an accelerator. Such particles readily dissociate into muons and neutrinos.

 $  pi  to  mu +  nu $ "data-tex =" display

If the neutrino does have different grades, then the muon must be born. Further everything is simple: we put a target on the way of the created particles and investigate how they interact: with the birth of an electron or a muon. Experience has unambiguously shown that electrons are almost never born.

 $  nu_ { mu} + p  rightarrow n +  mu \  nu_ { mu} + p  nrightarrow n + e $ "data-tex =" display

So, now we have two types of neutrinos! We are ready to proceed to the next step in the discussion of neutrino oscillations.

This is some "wrong" Sun

In the first neutrino experiments an artificial source was used: a reactor or an accelerator. This made it possible to create very powerful particle flows, because interactions are extremely rare. But where it was more interesting to register natural neutrinos. Of special interest is the study of the particle flux from the sun.

By the middle of the XX century it was already clear that the sun does not burn firewood – they counted and it turned out that there was not enough firewood. Energy is released in the nuclear reaction in the very center of the Sun. For example, the main process for our star is called a "proton-proton cycle", when four helium atoms are collected from four protons.

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You can notice that at the first step the particles of interest are born. And here neutrino physics can show all its power! For optical observation, only the surface of the Sun (the photosphere) is accessible, and the neutrino passes unimpeded through all the layers of our star. As a result, the detected particles come from the very center, where they are born. We can "observe" the nucleus of the Sun directly. Naturally, such studies could not help attracting physicists. In addition, the expected flux was almost 100 billion particles per square centimeter per second.

The first such experiment was put by Raymond Davis in America's largest gold mine, the Homestake mine. The installation had to be buried deep beneath the ground in order to protect itself from the powerful flow of cosmic particles. Neutrinos can pass through one and a half kilometer of rock without problems, but the rest of the particles will be stopped. The detector was a huge barrel filled with 600 tons of tetrachloride – compounds of 4 chlorine atoms. This substance is actively used for dry cleaning and is cheap enough.

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This method of registration was proposed by Bruno Maksimovich Pontecorvo. When interacting with neutrinos, chlorine is converted to an unstable isotope of argon,

 $  nu_ {e} + {} ^ {37} Cl  to {} ^ {37} Ar + E ^ - $ "data-tex =" display

Which captures an electron from the lower orbitals and decays back on average in 50 days.

 $ {} ^ {37} Ar + e ^ {-}  to {} ^ {37} Cl +  nu_ {E} $ "data-tex =" display

But! On the day, only about 5 neutrino interactions are expected. In a couple of weeks, only 70 originating argon atoms will be typed, and they must be found! Find a few dozen atoms in a 600 ton drum. A truly fantastic task. Once every two months, Davis blew the barrel with helium, blowing out the formed argon. The repeatedly purified gas was placed in a small detector (Geiger counter), where the number of decays of the resulting argon was considered. This is how the number of neutrino interactions was measured.

Almost immediately it turned out that the neutrino flux from the Sun is almost three times lower than expected, which caused a great furore in physics. In 2002, Davis and Kosiba-san shared the Nobel Prize for a significant contribution to astrophysics, in terms of detecting cosmic neutrinos.

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A small note: Davis registered neutrinos not From the proton-proton reaction, which I described above, but from slightly more complex and rare processes with beryllium and boron, but this does not change the essence.

Who is to blame and what to do?

So, the neutrino flux is three times smaller than expected. Why? You can suggest the following options:

  1. The model of the Sun is not true. Despite the long-term optical observations, we absolutely do not understand how the Sun works. The total neutrino flux is less than expected;
  2. Something is wrong with the neutrinos themselves. For example, they change their type along the way to Earth (
     $  nu_e  to  nu_  mu $ "data-tex =" inline

    ) and can no longer interact with the birth of an electron. The general flow

     $  nu_e +  nu_  mu $ "data-tex =" inline

    has not changed.

These unstable neutrinos

A year before the results of the Davis experiment, the already mentioned Bruno Pontecorvo develops a theory of how neutrinos can change their type in a vacuum. One consequence is that different types of neutrinos must have different masses. And with what reason is it that the particles should take and change their mass on the fly, which, generally speaking, should be preserved? Let's understand.

We can not do without a small introduction to quantum theory, but I will try to make this explanation as transparent as possible. It will take only basic geometry. The state of the system is described by the "state vector". If there is a vector, then there must be a basis. Let's look at the analogy with the color space. Our "state" is green. In the basis of RGB, we write this vector as (0, 1, 0). But here in CMYK basis almost the same color will be written already in another way (0.63, 0, 1, 0). Obviously, we do not and can not have a "main" basis. For different needs: images on the monitor or printing, we must use our coordinate system.

What are the bases for the neutrino? It is perfectly logical to decompose the neutrino flux into different types: the electronic (19459008)  $  nu_e $ "data-tex =" inline

), muonic (

 $  nu_  mu $ "Data-tex =" inline

) and tau (

 $  nu_  tau $ "data-tex =" inline

). If the flux of exclusively electronic neutrinos flies from the Sun, then this state (1, 0, 0) in such a basis. But as we have already discussed, neutrinos can be massive. And have different masses. This means that the neutrino flux can also be expanded in terms of mass states:

 $  nu_1,  nu_2,  nu_3 $ "data-tex =" inline

with masses

 $ m_1 , M_2, m_3 $ "data-tex =" inline

respectively.

The whole salt of the oscillations is that these bases do not coincide! The blue on the picture shows the types (sorts) of neutrinos, and the red states with different masses.

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That is, if an electronic neutrino appeared in the neutron decay, Three mass states (projected

 $  nu_e $ "data-tex =" inline

on

 $  nu_1,  nu_2,  nu_3 $ "data-tex = "Inline

). But these states propagate at different rates, since the pulses are the same, and the masses are different. As a result, the state vector begins to slightly rotate. The neutrino interacts depending on the type (

 $ e,  mu,  tau $ "data-tex =" inline

). Therefore, when we want to calculate how the neutrino will manifest itself, we need to design our state vector on the

 $  nu_e,  nu_  mu,  nu_  tau $ "data-tex =" inline

). And in this way it will be possible to register one or another type of neutrino. We will obtain such a probability wave for the electron neutrino, depending on the distance traveled:

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How much the type will change will be determined by the relative angles of the described coordinate systems (shown in the previous figure

] and the mass differences. </p>
<p> If you are not afraid of the terminology of quantum mechanics, and you had enough patience to finish reading it. </p>
<math> <img src=

Up to this point, a simple formal description can be found in Wikipedia.

But how is it really?

The theory is, of course, good. But until now we can not decide which of the two options is implemented in nature: the sun is "not that" or the neutrino is "not like that." We need new experiments that will finally show the nature of this interesting effect. Literally, in a nutshell, I will describe the main settings that played a key role in the research.

Kamioka Observatory

The history of this observatory begins with the fact that they tried to find the decay of a proton. That's why the detector got the proper name – "Kamioka" (Kamioka Nucleon Decay Experiment). But finding nothing, the Japanese quickly reoriented to a promising direction: the study of atmospheric and solar neutrinos. We have already discussed the origin of solar radiation. Atmospheric ones are produced in the decays of muons and pions in the Earth's atmosphere. And while they reach the Earth they manage to oscillate.

The detector began to type data in 1987. With dates they were wildly lucky, but about this next article πŸ™‚ The installation was a huge barrel filled with pure water. The walls were paved with photomultipliers. The main reaction by which neutrinos were caught was the knocking out of an electron from water molecules:

 $  nu_e + e_ {in  space atom} ^ -  to  nu_e + e_ {free } ^ - $ "data-tex =" display

A fast-moving free electron glows in the water in a dark blue color. This radiation and recorded the photomultiplier on the walls.

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The experiment confirmed the deficit of solar neutrinos and added to this the deficit of atmospheric neutrinos.

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Gallium experiments

Almost immediately after the launch of Kakiokande in 1990, two gallium detectors began operating. One of them was located in Italy, under the mountain of Grand Sasso in a laboratory with the same name. The second one is in the Caucasus, in the Baksan Gorge, under the Andy rchi mountain. Especially for this laboratory in the gorge was built the village of Neutrinos. The method itself was proposed by Vadim Kuzmin, inspired by the ideas of Pontecorvo, back in 1964.

 $ {} ^ {71} Ga +  nu_e  to {} ^ {71} Ge + e ^ - $ "data-tex =" display

When interacting with neutrinos, gallium turns into an unstable isotope of germanium, which decays back into gallium on an average of 16 days. Over a month, several dozen germanium atoms are formed, which must be extracted very carefully from gallium, placed in a small detector, and counted the number of decays back into gallium. The advantage of gallium experiments is that they can catch very low-energy neutrinos that are inaccessible to other installations.

All the above experiments showed that we see less neutrinos than expected, but this does not prove the presence of oscillations. The problem can still be in the wrong model of the Sun. The SNO experiment put the last and boldest point in the problem of solar neutrinos.

Sudbury Observatory

In the Kreighton mine, Canadians built a huge "star of death."

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An acrylic sphere surrounded by a photomultiplier and filled with 1000 tons of heavy water was placed at a depth of 2 km. This water differs from the usual one in that ordinary hydrogen with one proton is replaced by deuterium, a compound of a proton and a neutron. It was deuterium and played a key role in solving the problems of solar neutrinos. Such an installation could record both the interactions of the electronic neutrinos and the interactions of all other types! Electronic neutrinos will destroy deuterium with the birth of an electron, while all other types of electrons can not give birth. But they can slightly "push" deuterium so that it falls apart into its component parts, and the neutrino will fly further.

 $  nu_e + d  to p + p + e ^ - \  nu_  alpha + d  to p + n +  nu_  alpha,  space  Alpha = e,  mu,  tau) $ "data-tex =" display

The fast electron, as we have already discussed, glows when moving in an environment, and the neutron must be captured rather quickly by deuterium, while emitting a photon. All this can be registered with the aid of photomultipliers. Physicists finally got the opportunity to measure the total flux of particles from the Sun. If it turns out that it coincides with expectations, then electronic neutrinos go to others, and if it is less than expected, then the wrong model of the Sun is to blame.

The experiment began work in 1999, and measurements have confidently indicated that there is a deficit of the electronic component

 $  frac {N_e} {N_ {total}} = 0.34 $ "data-tex =" display

Let me remind you that almost exclusively electronic neutrinos can be produced in a star. So the rest turned out in the process of oscillations! For these works Arthur MacDonald (SNO) and Kadzita-san (Kamiokande) received the Nobel Prize in 2015.

Almost immediately, at the beginning of the zero, other experiments began to study oscillations. This effect was also observed for man-made neutrinos. The Japanese experiment KamLAND, located all the same in Kamioka, already in 2002 observed oscillations of electronic antineutrinos from the reactor. And the second, also Japanese, experiment K2K for the first time recorded a type change in neutrinos created with the help of an accelerator. As a distant detector, the well-known Super-Kamiokande was used.

Now more and more installations are engaged in the study of this effect. Detectors are being built on Baikal, in the Mediterranean, on the South Pole. There were installations near the North Pole. All of them catch neutrinos of cosmic origin. Accelerating and reactor experiments are in progress. The parameters of the oscillations themselves are refined, attempts are made to learn something about the magnitude of the neutrino masses. There are indications that it is through this effect that the preponderance of matter over antimatter in our universe can be explained!

Under the spoiler a small remark for the most thoughtful.

The 2015 award was issued with The formulation "for the discovery of neutrino oscillations, showing the presence of their mass." In the circle of physicists such a statement caused some confusion. When measuring solar neutrinos (SNO experiment), we are insensitive to the mass difference. Generally speaking, the mass can be zero, and the oscillations remain. This behavior is explained by the interaction of neutrinos with the matter of the Sun (the Mikheev-Smirnov-Wolfenstein effect). That is, there are oscillations of solar neutrinos, their discovery is a fundamental breakthrough, but this has never indicated the presence of mass. In fact, the Nobel Committee issued a prize with the wrong wording.
Oscillations in a vacuum manifest themselves for atmospheric, reactor and accelerator experiments.

I want to note that they also change their flavors and quarks in the same way, only this effect is much weaker for them.

PS I continue to try the feathers in popular articles, so I will be grateful for the comments / comments / inquiries. How will I find the time, next time I plan to write how the astrophysical object was first observed not through electromagnetic radiation.
Spoiler – with the help of neutrinos:)

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