Neutrino reactions

Once we assume that we are dealing with lepton scattering on point-like spin-half objects, we expect, on the basis of our results for ue —> i/e and ue —> ue [see Section 5.1 and (5.1.26 and 29)] to find that our angular distribution is a sum of two terms, with the characteristic structure of the scattering off left-handed and right-handed objects. So for neutrino reactions we expect 1 from uL —> uL and (1 — from i R —> i/R and vice versa for antineutrino reactions. [For electromagnetic reactions we would expect 1 -I- (1 - y) . ... 

The overall reaction thus converts 4 protons into 1 helium nucleus plus 2 positrons and 2 neutrinos ... 

What is needed now is some means for calculating e. To do this, it is useful to consider some component, H, which is formed only by Reaction I, which does not appear in the feed, and which has a stoichiometric coefficient of v/// = 1 for Reaction I and stoichiometric coefficients of zero for all other reactions. It is always possible to write the chemical equation for Reaction I so that a real product has a stoichiometric coefficient of +1. For example, the decomposition of ozone, 2O3 3O2, can be rewritten as 2/3O3 —> O2. However, you may prefer to maintain integer coefficients. Also, it is necessary that H not occur in the feed, that there is a unique H for each reaction, and that H participates only in the reaction that forms it. Think of H as a kind of chemical neutrino formed by the particular reaction. Since H participates only in Reaction I and does not occur in the feed, Equation (2.40) gives... 

The first reaction is a fusion of two protons to produce a 2H nucleus, a positron (e+) and a neutrino (ve). The second reaction is a proton capture with the formation of 3He and a y-ray. In the third reaction two 3He nuclei fuse to give 4He and two protons. The total energy released in one cycle is 26.8 MeV or 4.30 x 10-12 J. An important product of this process is the neutrino and it should provide a neutrino flux from the Sun that is measurable at the surface of the Earth. However, the measured flux is not as big as calculated for the Sun - the so-called neutrino deficit... 

Neutrino deficit Subatomic particles predicted to be released by the nuclear reactions on the Sun and should be detected on Earth. The number of neutrinos observed on Earth is much less than predicted by the models of solar nuclear fusion. 

Find the range of neutrino energies resulting from the reaction... 

Which of the following reactions might be used to detect such neutrinos from the Sun ... 

The first major set of nuclear reactions in stellar evolution involves hydrogenburning through the pp chains and the CN cycle or CNO bi-cycle, which liberate 6.68 MeV of energy per proton minus neutrino losses (2 neutrinos are emitted for each 4He nucleus synthesized). The first two reactions of the pp chains are... 

The fact that neutrinos are emitted during the transformation provides an opportunity for direct observation of the reactions taking place at the heart of the Sun. Note that antimatter is produced in this strange reaction, in the form of the positton or antielectron e+. The positrons generated immediately annihilate with electrons in the surrounding medium with subsequent emission of gamma rays. 

Figuratively speaking, just as hydrogen is said to bum, we may say that helium is the ash left over from the reaction. The imponderable separates from the ponderous, photons and neutrinos take flight, leaving the heavy helium ash to accumulate gradually. The ample energy disgorged (26.7 MeV) makes this reaction chain one of the most generous known. For example, thermonuclear fusion of 1 g of hydrogen releases some 20 milhon times more energy than the chemical combustion of 1 g of coal.

Fig. 5.3. Solar neutrino spectrum and detection ranges of the various underground neutrino observatories. The main part of the emission comes from the proton-proton reaction. About 3000 bilhon neutrinos pass through this figure every second. These neutrinos left the Sun eight minutes and two seconds earlier.

Neutrino detectors are placed at great depths, at the bottom of mines and tunnels, in order to reduce interference induced by cosmic rays (Fig. 5.3). Two methods of detection have been used to date. The first is radiochemical. It involves the production by transmutation of a radioactive isotope that is easily detectable even in minute quantities. More precisely, the idea is that a certain element is transformed into another by a neutrino impact, should it occur. Inside the target nucleus, the elementary reaction is... 

Historically, chlorine was the first target used to trap neutrinos. Chlorine-37 is mainly sensitive to high-energy neutrinos emanating from marginal fusion reactions (2 out of 10000) which lead to production of boron-8. On rather rare occasions, under the impact of neutrinos, chlorine-37 is transformed into radioactive argon-37 which is easy to detect by its radiation. However, the myriads of low-energy neutrinos completely escape its notice. 

Gallium can be used to detect low energy neutrinos arising in the reaction... 

Five experiments have so far detected solar neutrinos. These are Homestake (USA), GALLEX, SAGE, KAMIOKANDE and SUPERKAMIOKANDE, all set up down mines or tunnels. Detected fluxes agree qualitatively with theoretical predictions, both in numbers and energies. We may say that we have basically understood how the Sun shines. The same set of nuclear reactions invoked to explain the solar luminosity does give rise to neutrinos. 

The following stage is core collapse caused by electron capture or photodisintegration of iron. According to the traditional view, collapse leads to formation of a neutron star which cools by neutrino emission and decompression of matter when it reaches nuclear density (10 g cm ). The rebound that follows generates a shock wave which is capable of reigniting a good few nuclear reactions as it moves back out across the stellar envelope. 

Fig. 5.4. Schematic evolution of the internal structure of a star with 25 times the mass of the Sun. The figure shows the various combustion phases (shaded) and their main products. Between two combustion phases, the stellar core contracts and the central temperature rises. Combustion phases grow ever shorter. Before the explosion, the star has assumed a shell-like structure. The centre is occupied by iron and the outer layer by hydrogen, whilst intermediate elements are located between them. CoUapse followed by rebound from the core generates a shock wave that reignites nuclear reactions in the depths and propels the layers it traverses out into space. The collapsed core cools by neutrino emission to become a neutron star or even a black hole. Most of the gravitational energy liberated by implosion of the core (some 10 erg) is released in about 10 seconds in the form of neutrinos. (Courtesy of Marcel Amould, Universite Libre, Brussels.)...

The fact that neutrinos are emitted during this reaction provides an opportunity to observe directly the nuclear reactions taking place in the Sun s core. But its core is like a safe or an urn in which it zealously guards its own ashes. 

Insofar as these reactions occur relatively rapidly at the high temperatures now prevailing, the star s evolution accelerates enormously. This is exacerbated by the fact that it suffers a significant energy loss due to thermal neutrino production via the reaction... 

As the weak interaction is the slowest of all, it was the first to find itself unable to keep up with the rapid expansion of the Universe. The neutrinos it produces, which serve as an indicator of the weak interaction, were the first to experience decoupling, the particle equivalent of social exclusion. By the first second, expansion-cooled neutrinos ceased to interact with other matter in the form of protons and neutrons. This left the latter free to organise themselves into nuclei. Indeed, fertile reactions soon got under way between protons and neutrons. However, the instability of species with atomic masses between 5 and 8 quickly put paid to this first attempt at nuclear architecture. The two species of nucleon, protons and neutrons, were distributed over a narrow range of nuclei from hydrogen to lithium-7, but in a quite unequal way. 

Neutrino emitted in nuclear reaction very small 0... 

The nuclear reaction that finally stabilizes the structure of the protostar is the fusion of two protons to form a deuterium atom, a positron, and a neutrino (1 H(p,p+v)2D). This reaction becomes important at a temperature of a few million degrees. The newly produced deuterium then bums to 3He, which in turn bums to 4He in the proton-proton chain. The proton-proton chain is the main source of nuclear energy in the Sun. With the initiation of hydrogen burning... 

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