Solar neutrino flux

For some experiments, the solar neutrino flux and the rate of decay of the proton being extreme examples, tire count rate is so small that observation times of months or even years are required to yield rates of sufficiently small relative uncertainty to be significant. For high count rate experiments, the limitation is the speed with which the electronics can process and record the incoming infomiation. 

Table 5.3. Outline of stellar structure and evolution Solar neutrino fluxes expected and detected in different experiments ... 

Table 5.4. Solar neutrino fluxes from heavy water experiments...

TABLE 12.3 Predicted Solar Neutrino Fluxes (Bahcall and Pena-Garay)... 

The solar neutrino problem was identified by the first results of Davis et al. using the Cl detector at the Homestake Mine. Davis et al. observed only about one-third of the expected solar neutrino flux as predicted by standard models of the sun, which assume 98.5% of the energy is from the pp chain and 1.5% of the energy is from the CNO cycle. The final result of the Cl detector experiment is that the observed solar neutrino flux is 2.1 + 0.3 SNU compared to the predicted 7.9 + 2.4 SNU, where the solar neutrino unit (SNU) is defined as 10-36 neutrino captures/second/target atom. The GALLEX and SAGE detectors subsequently reported solar neutrino fluxes of 77+10 SNU and 69+13 SNU, which are to be compared to the standard solar model prediction of 127 SNU for the neutrinos detected by these reactions. 

Detectors using gallium > 0.2 MeV), chlorine (Ej/ 0.8 MeV), and Cerenkov effect in water > 7 MeV) measure significantly lower neutrino rates than are predicted from solar models. The deficit in the solar neutrino flux compared with solar model calculations could be explained by oscillations with Am < 10 eV causing the disappearance of Pq. 

Anselmann P, Hampel W, Heusser G et al (1992b) Implications of the GALLEX determination of the solar neutrino flux. Phys Lett B 285 390 Arima A, lacheUo F (1975) Collective nuclear states as representations of a SU(6) group. Phys Rev Lett 35 1069... 

TABLE III Calculated Solar Neutrino Fluxes and Cross Sections for the Reaction i/9 + 37CI->3 Ar + e... 

The K-II data were also of interest in connection with a possible time variation of the solar neutrino flux because the data-taking time extended over a period in which sunspot activity, reflecting the solar magnetic cycle, rose steeply from a minimum value at the end of solar magnetic cycle 21 to a maximum value approximately 15 times larger at the peak of solar cycle 22, as shown in Fig. 6. The time dependence of the K-II data is shown in Fig. 7, in which the data are separated into five time intervals, each approximately 200 live detector days. The reduced chi-squared value calculated under the assumption of a constant flux with respect to time is 0.40, which corresponds to a confidence level of 81% in the validity of the assumption. 

FIGURE 7 Plot from the K-II detector of the solar neutrino flux in five time intervals, each approximately 200 live detector days, from January 1987 through April 1990. The earliest two points are Ee > 9.3 MeV, and the latest three points are with Eg > 7.5 MeV. 

TABLE V Summary of Recent Measured and Calculated Solar Neutrino Fluxes... 

Fig. 5.3. Energy spectrum of solar neutrinos predicted from a standard solar model (e.g. Bahcall et al. 1982), omitting the undetectably small flux due to the CNO cycle. Fluxes are in units of cm-2 s-1 MeV-1 for continuum sources and cm-2 s-1 for line sources. Detectors appropriate in various energy ranges are shown above the graph. Courtesy J.N. Bahcall.

Neutrinos inform us almost instantaneously of what is happening in the Sun s core. However, the main interest of this solar cardiograph is hardly to detect some failure in the Sun s cycle. In capturing solar neutrinos, the aim of contemporary physics is rather to catch the Sun in the act of nuclear transmutation. By measuring the neutrino flux, we may check our understanding of the Sun as a whole and at the same time analyse the relationship between this strange particle and more commonplace forms of matter. 

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. 

Table 5.1. Solar neutrinos confronting prediction with detection. The unit of flux is the SNU, or solar neutrino...

Expected Solar Neutrino Sources, Energies, and Fluxes... 

The sun is a major source of neutrinos reaching the surface of Earth due to its close proximity. The sun emits 1.8 x 1038 neutrinos/second, which, after an 8-min transport time, reach the surface of Earth at a rate of 6.4 x 1010 neutrinos/s/cm2. The predictions of the standard solar model for the neutrino fluxes at the surface of Earth due to various nuclear reactions are shown in Table 12.3. 

Figure 12.18 Log-log plot of predicted neutrino fluxes from various solar nuclear reactions. The energy regions to which the neutrino detectors are sensitive are shown at the top. [From Bahcall (from Bahcall website).]...

Stellar nucleosynthesis The reaction, 4He + JHe - 7Be + photon, happens at the center of the Sun and other stars. The 7Be decay thatfollows is an important factor in the so-called solar neutrino puzzle. Although 7Be is rather rare at the solar center, decaying to 7Li with its 8-week halflife, there is rather a huge mass of 7Be at any given time at the solar center because 7Be is stable against breakup into smaller nuclear particles. That mass of7Be can be reliably calculated. But evidence of neutrinos from the Sun shows that the neutrino flux expected from that mass of 7Be does not entirely arrive at the Earth. 

The nonzero mass of the neutrino also can explain why the measured flux of the solar neutrinos is a few times smaller than the one predicted by the theory of thermonuclear generation of solar energy. If mv 0, the electron neutrinos may transform into other types of neutrinos4 that are not recorded by the modern detectors. 

The sun with a central temperature of 15.7 million degrees, (Tg0 = 15.7) burns by p-p chains. Slightly more massive star (with central temperature Tq > 20) burns H by the CNO cycle also. Davis et al.s solar neutrino experiment [23], which in 1968 had only an upper limit of the neutrino flux, itself put a limit of less than 9% of the sun s energy is produced by the carbon-nitrogen cycle (the more recent upper limit [36] is 7.3%, from an analysis of several solar neutrino experiments, including the Kamland measurements). Note however that for the standard solar model, the actual contribution of CNO cycle to solar luminosity is 1.5% [15]). In CNO cycle, nuclei such as C, N, O serve as catalysts do in a chemical reaction. The pp-chain and the CNO cycle reaction sequences are illustrated in Figs. 4 and 10. 

Fig. 4. The p-p chain starts with the formation of deuterium and 3 He. Thereafter, 3He is consumed in the sun 85% of the time through ppl chain, whereas pp II and pp III chains together account for 15% of the time in the Bahcall Pinsonneault 2000 solar model. The pp III chain occurs only 0.02% of the time, but the 8B f3+-decay provides the higher energy neutrinos (average Ev = 7.3 MeV). The net result of the chains is the conversion of four protons to a helium, with the effective Q-values (reduced from 26.73 MeV) as shown, due to loss of energy in escaping neutrinos. See [38,37] for updated branching ratios and neutrino fluxes for BPS2008(AGS) model...

A measurement of CN-cycle neutrino flux (with an expected total flux of about 5 x 108 cm 2 s-1) would test an assumption of the Standard Solar Model that during the early pre-main-sequence Hayashi phase the Sun became homogeneous due to convective mixing and that subsequent evolution has not appreciably altered the distribution of metals [38]. 

An area that was pioneered by nuclear chemists is the search for solar neutrinos. Although main-sequence stars, of which the Sun is a typical representative, have for decades been believed to derive their energy from the series of fusion reactions mentioned above, there was no direct observational evidence for this until Raymond Davis in the 1960s undertook to measure the flux of neutrinos from the Sun which accompany these reactions (Davis et al. 1968 Cleveland et al. 1998). The experiment involved measuring the number of Ar atoms (35.0 d) formed by neutrino capture in Cl in a tank of perchloroethylene. With only a few atoms of Ar per month extracted from over 600 t of liquid, this was indeed the ultimate low-level radiochemical separation. Nevertheless, the experiment was successful in detecting the neutrinos, but ever since the first data appeared in 1968, the measured neutrino flux persisted in being only one third of what was expected from model calculations, and this so-called solar neutrino puzzle literally gave rise to a whole new field — neutrino astronomy. 

Christiansen JA, Hevesy G, Lomholt S (1924) Recherches, par une m hode radiochimique, sur la circulation du bismuth dans Torganisme. Compt Rend 178 1324 Cleveland BT, Daily T, Davis R Jr et al (1998) Measurement of the solar electron neutrino flux with the Homestake chlorine detector. Astrophys 1496 505... 

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