Solar Neutrinos?

What Have We Learned About Solar Neutrinos?

by JOHN N. BAHCALL

The apparent deficit of solar neutrinos may be caused by physical processes beyond the Standard Model.

HIRTY YEARS AGO Ray Davis—then working at Brookhaven and now at Pennsylvania—suggested it was practical Tto build an experiment to detect solar neutrinos if the event rate I calculated was correct. The proposal was based upon his Texperience at the Savannah River reactor trying to detect antineutrinos using a tank filled with 3,000 gallons of perchloroethylene (C2 Cl4, a common cleaning fluid), and on calculations that I had done of the event rate to be expected in a 100,000 gallon tank.

10 FALL 1994 These calculations were in turn based upon nuclear physics estimates of the neutrino capture rates and so- Chlorine lar model calculations of the neu- Comparisons between the predicted fluxes of the standard trino fluxes. Ray was confident that solar model and the four operating 8.0±1.0 he could build and successfully op- solar neutrino experiments. The unit erate the 100,000 gallon tank, ex- used for the three radiochemical 2.55±0.25 tracting the few radioactive atoms of experiments is a solar neutrino unit, Water argon produced each month due to or SNU, which equals one event per 36 neutrino capture by chlorine atoms second per 10 target atoms. 1.0±0.14 (37Cl → 37Ar) in this huge detector. Following the experimenters, the Kamiokande result is expressed in Thirty years later it is clear that he terms of a ratio to the expected 0.51±0.07 was right and the then-abundant event rate. Predictions shown in this Gallium 73±19 skeptics were wrong. figure and quoted elsewhere in this At the time this chlorine experi- article are from the Bahcall- ment was proposed, the only moti- Pinsonneault 1992 standard solar vation either of us presented for per- model with helium diffusion. The 132±7 forming a solar neutrino experiment observed rates are less than the was to use neutrinos “to see into the expected rates for all four experiments. 79±12 interior of a star and thus directly ver- TheoryExperiment 1σ Errors ify the hypothesis of nuclear ener- gy generation in stars.” The hypoth- esis being tested was that stars like the Sun shine by fusing protons to neutrino experiments were discussed are not accessible in laboratory ex- form alpha particles, positrons, neu- by Ken Lande in the Fall 1992 Beam periments. Such searches for new trinos, and thermal energy. Line; they are summarized in the physics are based upon quantitative The original goal of demonstrat- table on the next page. The results of discrepancies between the predic- ing that proton fusion is the origin of these experiments represent a tri- tions for and the observations of so- sunshine has been achieved. Solar umph for the combined physics, lar neutrinos. As the experiments and neutrinos have now been observed chemistry, and astronomy commu- the theoretical predictions have in four different experiments with (to nities because they bring to a suc- steadily improved over the past three usual astronomical accuracy) fluxes cessful conclusion the development decades, these discrepancies have res- and energies that are in rough agree- (which spanned much of the twen- olutely refused to go away, convinc- ment with the expected values. The tieth century) of a theory of how or- ing many of us who work in this field observed rates in all of the solar neu- dinary stars—those like the Sun— that we have been witnessing the dis- trino experiments are only about a shine. covery of new physics in an unex- factor of 2 or 3 less than expected (see pected context. chart on this page). Moreover, the OST OF THE CURRENT Although thirty years ago I was fact that the neutrinos indeed come interest in solar neutrinos a skeptic about the theory of stellar directly from the Sun was established Mis focused on an applica- evolution and did not believe in any by one of these experiments tion of this research that was not explanation of astronomical phe- (Kamiokande), which showed that even discussed when the Homestake nomena that required changing con- electrons scattered by interacting chlorine detector was proposed. Sci- ventional physics, my preconcep- neutrinos recoil in the forward di- entists have realized that they can tions have since been shaken by the rection—away from the Sun. The use solar neutrinos for studying as- robustness of the theory and by the characteristics of the operating solar pects of the weak interactions that combined results of the four solar

BEAM LINE 11 Operating Solar Neutrino Experiments

Name Target Mass Threshold Detector Type Location (tons) (MeV)

Homestake 37Cl 615 0.86 radiochemical Black Hills, South Dakota

Kamiokande H2O 680 7.5 electronic Japanese Alps (Kamiokande) registers both electron neutrinos and (with much reduced GALLEX 71Ga 30 0.2 radiochemical Gran Sasso, Italy sensitivity) muon or tau neutrinos. Do electron neutrinos change SAGE 71Ga 57 0.2 radiochemical Caucasus their flavor, or “oscillate,” into hard- Mtns., Russia to-detect muon or tau neutrinos dur- ing their journey from the interior of the Sun to the Earth? The simplest neutrino experiments. I now think it version of the standard electroweak is most likely that we are witnessing model answers “No.” Neutrinos evidence for new physics in these ex- have zero masses in the Standard periments. Model, and lepton flavor does not Solar neutrino observations are of- change. However, solar neutrinos can ten compared to a combined theo- reveal physical processes not yet dis- retical model, the standard solar covered in the laboratory because, for model plus the Standard Model of certain processes, these experiments electroweak interactions. A solar are 1011 times more sensitive than model is required to predict how terrestrial neutrino experiments. many—and with what energies— Their increased sensitivity is due neutrinos are produced in the Sun’s largely to the fact that the elapsed interior. The observed luminosity of time in the rest frame of a (finite- the sun (due to the same nuclear mass) neutrino is proportional to the processes that produce solar neutri- ratio of the target–detector separa- nos) and the other observational con- tion to the neutrino energy; this ra- straints on the solar model (includ- tio is much larger for neutrinos orig- ing the Sun’s known age, mass, inating in the Sun. Moreover, solar chemical composition, and its many neutrinos traverse a far greater precisely measured seismological fre- amount of matter than their labo- quencies) limit the calculated fluxes ratory counterparts. to fairly narrow regions, at least by astrophysical standards (see box on HE FIRST, and for two next page). decades the only, solar neu- The standard electroweak mod- Ttrino experiment uses a chlo- el—or some modification of the Stan- rine detector to observe electron-type dard Model—is required to determine neutrinos via the reaction v + 37Cl − e what happens to neutrinos as they → e + 37Ar. The 37Ar atoms produced pass through the Sun and interplan- by this neutrino capture process are etary space on their way from the so- extracted chemically from the 615 lar interior to earthbound detectors. tons of perchloroethylene in which The observed discrepancies might oc- they were created; they are then cur if neutrinos decay in transit, or counted using their characteristic if they change from one species to an- radioactivity in small, gaseous pro- other before reaching the detectors. portional counters. The threshold The three radiochemical detectors energy is 0.8 MeV, which means (see register only electron neutrinos, figure on the next page) that this while the only electronic detector experiment is sensitive to the rare

12 FALL 1994 SOLAR NEUTRINO FLUXES

he spectrum of solar neutri- nos that is predicted by the high-energy 8B neutrinos, as well as threshold is at least 7.5 MeV. The Tstandard solar model is to the lower energy pep and 7Be neu- probability of detecting muon or tau shown in the graph below. The basic low-energy neutrino fluxes, trinos formed by electron capture on neutrinos by their scattering of atom- 7 from pp and pep neutrinos, are two fusing protons and on Be nuclei. ic electrons is only about 17 percent most closely related to the total Like all solar neutrino experiments, of the equivalent probability of de- solar luminosity and are calculated the chlorine experiment is performed tecting electron neutrinos at the en- to an estimated accuracy of about deep underground (in the Homestake ergies for which Kamiokande is sen- 1 percent. These reactions initiate gold mine, in Lead, South Dakota) in sitive. the nuclear fusion chain in the Sun order to avoid cosmic-ray induced Two gallium experiments are in and produce neutrinos with a max- imum energy of 0.4 MeV (pp neu- events that might be confused with progress, GALLEX (located in the trinos) or an energy of 1.4 MeV true neutrino events. Gran Sasso underground laboratory (pep neutrinos). Electron-capture In the Kamiokande experiment, about an hour’s drive from Rome) by 7Be ions produces the next which is carried out in Kamioka and SAGE (in an underground cham- most abundant source of neutri- mine in the Japanese Alps, neutrino- ber excavated beneath the Andyrchi nos, a 0.86 MeV neutrino line, electron scattering, v + e → v' + e', mountains in the North Caucasus whose flux has an estimated theo- occurs inside the fiducial mass of region of Russia). Performed by two retical error of 6 percent. Neutrinos 8 680 tons of ultrapure water. The scat- international collaborations, these from the beta decay of B can have energies as high as 14 MeV; tered electrons are detected by the experiments provided the first ob- they are rare and their flux is cal- Cerenkov light that they produce servational information about the culated to an estimated accuracy while speeding through the water. low-energy neutrinos from the basic of only 15 percent. The fact that the neutrinos are com- proton-proton fusion reaction. Both → 2 + ν ing directly from the Sun was estab- experiments use neutrino absorption pp: p + p H + e + e lished by this experiment, which by gallium atoms to produce germa- − 7l → − 7l pep: p + e + p → 2H + ν showed that the electrons were nium, ve + Ga e + Ge, which e scattered in the forward direction, has a threshold of only 0.2 MeV for − 7 7Be: 7Be + e → Li + ν relative to the Sun. Only the rare, neutrino detection. Such a low e high-energy 8B solar neutrinos can threshold allows the detection of the 8 8 → 8 + ν B: B Be + e + e be detected in the Kamiokande low-energy pp neutrinos, for which experiment, for which the detection the flux is known to an accuracy of

Water Gallium Chlorine The energy spectrum of neutrinos from 12 the pp chain of interactions in the Sun, 10 as predicted by the standard solar pp model. Neutrino fluxes from continuum 1010 sources (such as pp and 8B) are given in the units of counts per cm2 per second per MeV. The line fluxes (pep and 7Be) 108 7 7 are given in neutrinos per cm2 per sec- Be Be pep ond. The pp chain is responsible for 8B Flux 6 more than 98 percent of the energy gen- 10 eration in the standard solar model. Neu- trinos produced in the carbon-nitrogen- 104 oxygen CNO chain are not important energetically and are difficult to detect 2 experimentally. The arrows at the top of 10 the figure indicate the energy thresholds 0.1 0.3 1 3 10 for the ongoing neutrino experiments. Neutrino Energy (MeV)

BEAM LINE 13 in the boxes on pages 15 and 16, the least radical solutions are: at least three of the four experiments are wrong, or something unexpected happens to neutrinos after they are created in the solar interior. The lat- (Thomas J. Bowles) ter solution requires a slight but im- LANL portant generalization of the simplest Containers of gallium in the SAGE 1 percent. The GALLEX and the SAGE version of the standard electroweak experiment, which detects solar experiments use radiochemical pro- theory. neutrinos down to a threshold energy of 0.2 MeV cedures to extract and count a small I use only the published results of number of atoms from a large detec- the four ongoing solar neutrino ex- tor, similar to what is done in the periments and the most robustly pre- Homestake chlorine experiment. dicted neutrino fluxes from pub- All four solar neutrino experi- lished standard solar models. As a ments yield fluxes significantly less measure of the uncertainty in the than predicted and well outside the predictions, I use the total range of combined errors (see chart on page the calculated neutrino fluxes from 11). One fact is immediately appar- the 11 recently-published solar mod- ent: the disagreement between the- el calculations carried out by differ- ory and experiment seems to depend ent research groups using indepen- upon the threshold for neutrino de- dent stellar evolution codes and tection, being a factor of about 3.1 for employing a wide range of possible the Homestake chlorine experiment input parameters and approximations (0.8 MeV threshold) and only 2.0 for to the stellar physics. the Kamiokande water experiment Some particle physicists have ex- (7.5 MeV threshold). These two ex- pressed skepticism about the solar periments are primarily sensitive to neutrino problem because the cal- the same neutrino source, the rare, culated flux of high-energy neutrinos high-energy 8B solar neutrinos; their from 8B beta-decay depends strong- sensitivity to threshold energy sug- ly upon the central temperature of gests that some physical process, in the Sun. A related concern is being addition to the familiar nuclear beta- discussed among nuclear physicists, decay, changes the energy spectrum who are using recent experiments of these neutrinos before they reach and new calculations to determine the detectors. whether the 9 percent uncertainty estimated by CalTech physicists for HE MARKED discrepancies the production cross section of 8B between predicted and mea- nuclei in the Sun is indeed valid. The Tsured neutrino fluxes is calculated flux of 8B neutrinos is known as the “solar neutrino prob- proportional to this cross section. lem.” It cannot be “solved” by mak- I personally believe that the pre- ing plausible changes in the standard viously estimated nuclear physics solar model or by postulating that uncertainties are reasonable. But for only one or two solar neutrino ex- the purposes of the present argu- periments are incorrect. As I argue ment—and to allay skepticism—I

14 FALL 1994 The Chlorine-Water Problem

HE HOMESTAKE AND THE KAMIOKANDE solar neu- of the capture rates from three different neutrino sources is trino experiments are not consistent with each other the simplest expression of the “solar neutrino problem.” It is Tunless some physical process—not included in stan- independent of the solar model used. dard electroweak theory—affects the energy spectrum of 8B Although the best estimate for the residual capture rate neutrinos. The argument leading to this conclusion goes as for pep, 7Be and CNO solar neutrinos is negative, the physi- follows: cal capture rate for any set of neutrino fluxes has to be posi- The most recent result of the Kamiokande experiment for tive definite. Adopting the conservative procedure used by the rare 8B neutrinos is the Particle Data Group in analogous discussions (for − − example, upper limits to neutrino masses), we find: Flux (8B) = (2.89 ± 0.41) × 106 cm 2s l, (1) Rate in Cl(pep + 7Be + CNO) < 0.68 SNU (95% conf.). (5) where I have combined quadratically (both here and below) the statistical and systematic errors. I have shown else- We can refine this result by utilizing the fact that the flux where that if standard electroweak theory is correct, then of neutrinos from the pep reaction is directly related to the the shape of the energy spectrum from 8B solar neutrinos basic pp reaction, which is the initiating fusion reaction that must be the same (to 1 part in 105) as the shape deter- produces nearly all of the solar luminosity in standard solar mined by laboratory experiments. The absorption cross sec- models. The total spread in the calculated capture rates for tion is known accurately for 8B neutrinos with a standard pep neutrinos for the 11 recently published standard solar energy spectrum incident on a 37Cl nucleus. Therefore, if models (calculated with different codes and input parame- standard electroweak theory is correct, the capture rate in ters) is 0.22 ± 0.01 SNU. Subtracting this accurately-known the Homestake chlorine experiment from the 8B neutrino pep flux from the the upper limit for the three neutrino sour- flux observed in the Kamiokande experiment should be ces shown in (5), we obtain:

Rate in Cl (8B) = (3.21 ± 0.46) SNU, (2) Rate in Cl(7Be + CNO) < 0.46 SNU (95% conf.). (6) where 1 SNU = 1 neutrino capture per 1036 target atoms per The 7Be neutrino flux is predicted with reasonable accu- second. But the observed rate in the chlorine experiment racy; the results from the 11 different standard solar models from all neutrino sources is yield the value

Obs Rate in Cl = (2.55 ± 0.25) SNU. (3) SSM Rate in Cl(7Be) = 1.1± 0.1 SNU. (7)

Subtracting the rate due to 8B neutrinos as determined Thus the upper limit on the sum of the capture rates from by the Kamiokande experiment (2) from the rate due to all 7Be and CNO neutrinos is significantly less than the lowest neutrino sources (3), we find that the best estimate for the value predicted for 7Be neutrinos alone, by any of the 11 capture rate in the chlorine experiment from all sources recent standard solar models. I did not subtract the CNO except 8B neutrinos, assuming standard electroweak theory neutrino capture rate from the sum of the two rates because to be correct, is the conflict between the measurements and the standard models (solar and electroweak) is apparent without this Obs Rate in Cl(pep + 7Be + CNO) = Ð0.66 ± 0.52 SNU, (4) additional step and because the estimated rate from CNO where CNO represents the sum of all neutrino-producing neutrinos, 0.4 ± 0.08 SNU, is more uncertain than for the reactions in the CNO cycle. This negative value for the sum other neutrino fluxes being considered.

BEAM LINE 15 The Gallium Problem

HE GALLEX AND THE SAGE gallium solar neutrino experiments have reported consistent neutrino capture rates (respectively, 79±12 SNU and T73±19 SNU). From the weighted average of their results, the best esti- mate for the gallium rate is

Obs Rate in Ga = 77 ±10 SNU. (8) will assume that all of the published laboratory measurements and theo- All standard solar models yield essentially the same predicted event rate retical nuclear physics calculations from pp and pep neutrinos, 74 ± 1 snu. Subtracting this rate from the total 7 8 are wrong and that the cross section observed rate, one finds that the residual rate from Be and B solar neutrinos 8 in gallium is small, for B production in the Sun has somehow been adjusted to yield the Rate in Ga(7Be + 8B) = 3 ±10 SNU, (9) flux measured for these high-energy neutrinos in the Kamiokande ex- which implies that the upper limit on this rate is periment. This implies that the lab- Rate in Ga(7Be + 8B) < 22 SNU (95% conf.). (10) oratory nuclear physics measure- 7 8 7 ments are in error by a factor of 2, not This combined Be and B rate is less than the predictions from Be neutri- 8 nos alone for all 11 recently-published standard solar models. by 9 percent. Since I adopt the B Moreover, one should take account of the 8B neutrino flux that is observed neutrino flux measured in the in the Kamiokande experiment, which in the gallium experiments translates to Kamiokande experiment, the 8B flux used in the following discussion is Rate in Ga(8B) = 7.0+7 SNU, (11) -3.5 independent of any solar-model where the quoted errors are dominated by uncertainties in the calculated neu- uncertainties (including the sensi- trino absorption cross sections and I have assumed that the shape of the tive temperature dependence). This energy spectrum of 8B solar neutrinos is the same as measured in the labora- 8 7 procedure removes a principal rea- tory. Subtracting this rate for B neutrinos from the combined rate of Be and son for skepticism. Even this extreme 8B neutrinos, one again finds that the best-estimate flux for 7Be neutrinos is negative. assumption does not avoid the ne- cessity for new physics, as we shall 7 +11 Rate in Ga( Be) = Ð4Ð12 SNU. (12) see. The argument described here, Following the same statistical procedure as described earlier, one can set a most of which was developed in a 7 conservative upper limit on the Be neutrino flux using the gallium and the slightly different form by Hans Bethe Kamiokande measurements: and myself in 1990, avoids all un- Rate in Ga(7Be) < 19 SNU (95% conf.). (13) certainties associated with the so- lar model calculation of the 8B flux. The predicted rate given by the 11 standard solar models is We pointed out that taking the mea- 8 SSM Rate in Ga(7Be) = 34 ± 4 SNU. (14) sured rate for B neutrinos from the Kamiokande experiment implies an The discrepancy between these two equations is a quantitative expression 8B event rate in the Homestake ex- of the gallium solar neutrino problem. periment that is slightly in excess of The present results for the gallium experiments are close to being in conflict the total measured rate from all neu- with a model-independent, unrealistically conservative upper limit on the count- trino sources. In other words, a par- ing rate. This minimum counting rate of 80 SNU is calculated assuming only that the Standard Model is correct and that the Sun is currently producing tial rate exceeds the total rate, which nuclear fusion energy at the same rate at which it is losing photon energy from makes no sense unless something the surface. To reach the lower limit of 80 SNU in a solar model, one must set happens to the lower-energy part of equal to zero the rates of all nuclear reactions that produce 7Be in the sun. We the 8B electron neutrino flux—that know that this limit cannot be satisfied in practice because we observe high part of the flux which is visible in the 8 8 7 energy B neutrinos and B is produced by proton capture on Be—and Homestake chlorine experiment but because the cross section for creating 7Be has been measured in the labora- not in the Kamiokande water exper- tory to be competitive with the other solar fusion rates. iment. This direct comparison of two experiments—independent of any so- lar model considerations—suggests

16 FALL 1994 One of the large containers of gallium used in the GALLEX solar neutrino experiment, which is located in the Gran Sasso underground laboratory in Italy.

that a new physical process causes Bruno Pontecorvo in an epochal pa- the discrepancy between the exper- per, and matter-enhanced neutrino iments. oscillations, the MSW effect, a beau- There are actually two solar neu- tiful idea discovered by Lincoln trino problems: the chlorine-water Wolfenstein and also by Stanislav problem and the gallium problem. In Mikheyev and Alexei Smirnov. the box on page 15, I show why the Other solutions have been proposed measured rates of the chlorine and for the solar neutrino problem that the water experiments are inconsis- involve new weak interaction phys- tent with each other, unless some ics, such as neutrino decay, rotation collaboration new physical process—not includ- of the neutrino magnetic moment,

ed in the standard electroweak mod- and matter-enhanced magnetic mo- GALLEX el—changes the shape of the energy ment transitions. spectrum of 8B neutrinos in transit If new physics is required, then the to the detector. In the box on page 16 MSW effect, which provides a nat- I argue that the gallium experiments ural extension of the simplest ver- are inconsistent with robust predic- sion of standard electroweak theory, tions of the standard solar model. is in my view the most likely can- Let me assume for purpose of dis- didate. According to this explanation, The regions in mass and mixing angle cussion that a correct solar neutrino electron neutrinos are transformed space that are consistent with all four experiment must yield a rate for the into muon or tau neutrinos as a re- solar neutrino experiments. This figure, 7Be neutrino flux that is consistent sult of their interaction with elec- prepared by Naoya Hata and Paul (at the 95% confidence level) with trons in the Sun. The MSW effect Langacker, shows two possible solutions nothing happening to solar neutrinos only occurs if neutrinos have an of the solar neutrino problem that make after they are created (i.e., the stan- “identity crisis”—i. e., the neutrinos use of the MSW effect. Both solutions correspond to some neutrinos having a dard electroweak theory) and with produced in nuclear beta decay are mass of order 0.003 eV. the value of the 7Be neutrino flux mostly electron neutrinos but have that is predicted by the standard so- a non-vanishing probability (de- 10–3 lar model. If these assumptions are scribed by a mixing angle θ) of be- both correct, then at least three of ing either a muon or a tau neutrino. 10–4 the four operating solar neutrino ex- Non-zero neutrino masses are re- periments must be wrong. Either the quired for this effect to occur in a Homestake or the Kamiokande ex- plausible manner, but the masses and 10–5

periment must be wrong in order to mixing angles indicated by experi- ) avoid the chlorine-water problem ment are within the range expected 2

(see box on page 15) and both the on the basis of grand unified theories. –6

(eV 10

GALLEX and SAGE experiments must If the MSW effect is the explanation 2 m

be wrong in order to avoid the gal- of the solar neutrino problem, then ∆ lium problem (see box on page 16). the Homestake, Kamiokande and the 10–7 two gallium experimental results can HE TWO MOST POPULAR all be explained (see graph) if at least

mechanisms for explaining one neutrino coupled to the electron 10–8 SAGE and GALLEX the solar neutrino problem neutrino has a mass m and a mix- Kamiokande Homestake T − 2 5 2

via new physics are vacuum neutri- ing angle θ that satisfy: m ∼ 10 eV Combined Solution 2 −2 2 −5 2 no oscillations, first discussed in this and sin 2θ ∼ 10 or m ∼ 10 eV 10–9 2 10–4 10–3 10–2 10–1 100 connection by Vladimir Gribov and and sin 2θ ∼ 0.6. sin22θ

BEAM LINE 17

New solar neutrino experiments new experimental data. Finally, the- now under construction will soon oretical physicists have invented new

test the proposition that new phys- physical processes that extend the ics is required, independent of un- standard electroweak model in plau- certainties due to solar models. The sible ways and which, in addition

first of these experiments (the Sud- to explaining the operating experi- bury Neutrino Observatory, or SNO, ments, make testable predictions for and Super Kamiokande) are expect- the next round of solar neutrino ex- ed to become operational in 1996 and periments. Important limits on the

to increase the counting rates by two magnitudes of possible non-standard orders of magnitudes over those ob- neutrino interactions have already served in the four pioneering solar been established by the existing ex- neutrino experiments. (see “New So- periments. After the new experi- lar Neutrino Detectors,” by Ken ments begin operating, we should Lande, Fall 1992 Beam Line, page 9, finally learn whether or not we have

for a brief discussion of these exper- stumbled by accident upon new par- Artist's conception of the Super iments). These two experiments and ticle physics while trying to test the Kamiokande detector now under another called ICARUS (being devel- theory of how the Sun shines. construction in the Japanese Alps. This oped at CERN) can determine the huge tank, containing 50,000 tons of shape of the 8B solar neutrino ener- ultrapure water viewed by over 11,000 gy spectrum and whether or not elec- phototubes, will be used to search for tron neutrinos have oscillated into proton decay and to detect solar some other kind of neutrino. And a neutrinos, among other goals. (The 60 foot humpback whale is shown only liquid scintillator detector named for size comparison and is not a part of BOREXINO will provide the first di- this experiment!) rect measurement of the crucial flux of 7Be neutrinos. In the meantime, scientists and engineers can take great satisfaction that thirty years of their collective efforts have provided direct experi- mental confirmation, in the form of measured neutrinos, of the theory of how ordinary stars shine. Physicists and chemists have collaborated to perform extraordinarily sensitive ex- periments that measure accurately the event rates produced by solar neutrinos. Astrophysicists have suc- cessively refined their calculations of solar models until they are in agreement with a wealth of detailed (non-neutrino) solar observations. Their theoretical calculations of the neutrino interaction rates have been steadily improved with the help of

18 FALL 1994