The theoretical predictions for the ^(37)Cl solar-neutrino experiment are summarized and compared with the experimental results of Davis, Harmer, and Hoffman. Three important conclusions about the sun are shown to follow

Bahcall, John N.

Bahcall, Neta A.

Shaviv, Giora

English

Caltech Authors - Main

VoLUME 20, NuMBER 21 PHYSICAL REVIEW LETTERS 20MAY 1968 
product for the carbon-nitrogen cycle to be 3.5 
xl0-35 sec-1 per Cl37 atom, based on this cycle 
being the only source of the sun's energy. With 
the limit given above one can conclude that less 
than 9% of the sun's energy is produced by the 
carbon-nitrogen cycle. 
It is possible to improve the sensitivity of the 
present experiment by reducing the background 
of the counter. However, background effects 
from cosmic-ray muons will eventually limit the 
detection sensitivity of the experiment at its 
present location. Detailed studies of the cosmic-
ray background are in progress. 
The authors would like to thank Professor 
W. A. Fowler and Professor John N. Bahcall for 
their initial and continual encouragement in plan-
ning this experiment. We would like to acknowl-
edge Professor A. G. W. Cameron's constant in-
terest extending over many years. We are in-
debted to the Homestake Mining Company for al-
lowing us to build the experiment in their mine, 
and for their generous assistance in solving 
many technical problems in the construction of 
the apparatus. We would like to acknowledge the 
many useful suggestions and direct assistance 
from the members of the staff of Brookhaven Na-
tional Laboratory. 
*Research performed under the auspices of the U. S. 
Atomic Energy Commission. 
tPermanent address: Georgia Institute of Technolo-
gy, Atlanta, Georgia. 
1J. N. Bahcall, W. A. Fowler, I. Iben, Jr., and R. L. 
Sears, Astrophys. J. 137, 344 (1963). 
2R. L. Sears, Astrophys. J. 140, 153 (1964). 
3P. Pochoda and H. Reeves, Planetary Space Sci. 12, 
119 (1964). 
4J. N. Bahcall, Phys. Rev. Letters 12, 300 (1964); 
17, 398 (1966). 
5D. Ezer and A. G. W. Cameron, Can. J. Phys. 43, 
1497 (1965), and 44, 593 (1966); and private communi-
cation. 
6J. N. Bahcall, N. Cooper, and P. Demarque, Astro-
phys. J. 150, 723 (1967); G. Shaviv, J. N. Bahcall, 
and W. A. Fowler, Astrophys. J. 150, 725 (1967). 
7 --J. N. Bahcall, N. Bahcall, W. A. Fowler, and 
G. Shaviv, Phys. Letters 26B, 359 (1968). 
8J. N. Bahcall and G. Shaviv, to be published. 
9For recent summary see F. Reines, Proc. Roy. Soc. 
(London) 310A, 104 (1967). 
10J. N. Bahcall, Phys. Rev. 135, B137 (1964). 
11R. Davis, Jr., Phys. Rev. Letters 12, 303 (1964); 
R. Davis, Jr., and D. S. Harmer, CERN Report No. 
CERN 65-32, 1965 (unpublished). 
12The circuit used in this work was designed by Mr. 
R. L. Chase and Mr. Lee Rogers of Brookhaven Nation-
al Laboratory. 
13J. N. Bahcall, N. A. Bahcall, and G. Shaviv, follow-
ing Letter [Phys. Rev. Letters 20, 1209 (1968)]. 
PRESENT STATUS OF THE THEORETICAL PREDICTIONS 
FOR THE 36Cl SOLAR-NEUTRINO EXPERIMENT* 
John N. Bahcallt and Neta A. BahcalU 
California Institute of Technology, Pasadena, California 
and 
Giora Shaviv§ 
Cornell University, Ithaca, NewYork 
(Received 8 April 1968) 
The theoretical predictions for the 37Cl solar-neutrino experiment are summarized 
and compared with the experimental results of Davis, Harmer, and Hoffman. Three 
important conclusions about the sun are shown to follow. 
The experiment of Davis, Harmer, and Hoff-
man, 1 • 2 designed to detect solar neutrinos with a 
37Cl target, has prompted a continuing investiga-
tion3-7 of the accuracy with which the flux of neu-
trinos produced by nuclear reactions in the sun's 
interior can be predicted. We report here calcu-
lations of the solar-neutrino fluxes made using 
the more accurate rate for the proton-proton re-
action recently derived by Bahcall and May8 and 
the improved determination of the abundance ra-
tio of heavy elements to hydrogen recently ob-
tained by Lambert and Warner.9 We also discuss 
some of the important, recognized uncertainties 
that influence the predictions of the solar-neutri-
no fluxes and conclude that the present results of 
Davis, Harmer, and Hoffman1 are not in obvious 
conflict with the theory of stellar structure. We 
show, however, that a counting rate of less than 
0.03X 10-35/ 37Cl atom sec would cast serious 
doubt on the correctness of current ideas con-
1209 
VoLUME 20, NuMBER 21 PHYSICAL REVIEW LETTERS 20MAY 1968 
Table I. Some important quantities for five solar models. 
Su T c 
Model (1o-25 MeV b) X y z (106 OK) 
A 3.36 0.715 0.258 0.027 15.7 1.7 
1.6 
1.5 
1.4 
1.6 
B 3.36 0.768 0.217 0.015 15.2 
c 3.78 0.764 0.221 0.015 14.9 
D 3.93 0.800 0.190 0.010 14.5 
E 3.63 0.740 0.240 0.020 15.2 
cerning the way nuclear fusion reactions produce 
the sun's luminosity. We then enumerate some 
of the most important experiments that are nec-
essary to limit the uncertainties in the theoreti-
cal predictions. Finally, we show that the exper-
iment of Davis, Harmer, and Hoffman implies 
the following: (1) that the sun does not derive 
most of its radiated energy from the CNO cycle, 
(2) the heavy-element mass fraction in the sun 
is probably less than 2 %, and (3) the primordial 
helium content was of the order of 22% by mass. 
The latter two inferences depend upon the validi-
ty of current theoretical models for the solar in-
terior. 
In Table I we list some important quantities de-
rived from five evolutionary models for the sun 
that were obtained by numerically integrating the 
relevant equations of stellar structure10 as de-
scribed in Ref. 7. In Table II we give the neutri-
no fluxes and predicted counting rates for the ex-
periment of Davis, Harmer, and Hoffman1•2 that 
were calculated from the same solar models. 
The quantities X, Y, Z, T c• and Pc of Table I 
are, respectively, the primordial hydrogen 
mass fraction, the primordial helium mass frac-
tion, the heavy-element (atomic number greater 
than four) mass fraction, the central tempera-
ture, and the central density. It is assumed that 
the heavy-element abundance observed on the 
surface of the sun is the same as the primordial 
(and present) heavy-element abundance in the 
center of the sun. This assumption requires fur-
ther theoretical investigation, but is supported 
by the agreement between our inferred helium 
abundance [cf. conclusion (3)] and rocket mea-
surements of the helium abundance in solar cos-
mic rays (cf. Ref. 9). The neutrino fluxes from 
the various neutrino-emitting isotopes11• 12 are 
given in columns two through six of Table II; the 
neutrinos from the reaction 1H + 1H- 2D + e- + v 
are represented by the flux cp ve H + 1 H) and those 
from the reaction 1H+ 1H+e- - 2D+ v are repre-
sented by the flux «Pv(lH+e-+ 1H). The quanti-
ties L:;ali(«PvO'v) and l:;an but B(«PvO'v) are the 
predicted capture rates per 37Cl atom. The 
cross sections are taken from the work of Bah-
call.5•12 All of the models listed in Tables I and 
II have a luminosity, after 4.7X 109 yr of nuclear 
burnil,lg, that equals the solar luminosity13 of 
3.83 x 1093 erg/sec within ±0.2 %; all of the nucle-
ar parameters, with the exception of the rate of 
the proton-proton reaction, are taken from the 
recent review by Fowler, Caughlan, and Zim-
merman.14 
Model A was constructed for a heavy-element 
mass fraction of Z= 0.027 and a low-energy 
cross -section factor14 for the proton -proton reac-
tion of S11 =3.36Xl0-25 MeV b. A similar model 
was regarded a& their most probable one by Bah-
call and Shaviv7 and has been used by Davis, 
Harmer, and Hoffman1 in discussing the results 
of their experiment. The present model A, and 
Table II. Neutrino fluxes and counting rates from five solar models. 
10-7(/1 (BB) 1o-9q~ (iBe) 10-9fP (13N) 10-1ofP (1H + 1H) fP (1H +e- + 1H) l:;(fPI}') I; (q~ VuJ.) v v v v v 
all all but B 
Model (cm-2 sec-1) (cm-2 sec-1) (cm-2 sec-1) (cm-2 sec-1) (108 cm-2 sec-1) (10-35 sec-1) (1o-35 sec-1) 
A 1.35 4.7 1.1 6.0 1.6 2.1 0.27 
B 0.69 3.4 0.3 6.2 1.7 1.1 0.16 
c 0.47 2.9 0.2 6.4 1.7 0.77 0.13 
D 0.25 2.1 0.1 6.5 1.7 0.44 0.10 
E 0.70 3.7 0.4 6.3 1.6 1.1 0.17 
1210 
VoLUME 20, NuMBER 21 PHYSICAL REVIEW LETTERS 20MAY 1968 
all other models discussed in this Letter, differ 
from the one selected as most probable by Bah-
call and Shaviv7 in that three rather small ef-
fects not previously included have been taken ac-
count of in the present work. These effects are 
the Debye-Hiickel correction to the equation of 
state, 15 the contributions of electron conduction 
to the opacity, 16 and partial conversion of 160 to 
14N via the reactions 1S0(1H, y)17 F(J3+v)l70(1H, 
a)14N. The net result of the inclusion of these ef-
fects has been to increase the predicted counting 
rate calculated from model A by about 15% com-
pared with the most probable model of Ref. 7. 
Since the work of Bahcall and Shaviv was com-
pleted, two important experimental data have be-
come available. The two data are the improved 
measurement of the mass ratio of heavy ele-
ments to hydrogen on the surface of the sun9 and 
the redetermination of the neutron lifetime .17 
Model B was constructed using the mass ratio of 
heavy elements to hydrogen of 0.019 obtained by 
Lambert and Warner,9 and the traditional value14 
for the proton cross -section factor, S 11 = 3. 3 6 
x 10-25 MeV b. Note that L)an('Pa) is lowered by 
about a factor of 2 when the newer composition 
is used. Model C was constructed using the val-
ues of the low-energy proton cross-section fac-
tor S11 =3.78X10-25 MeV band its logarithmic 
derivative (dlnSu/dE)E=o= 11.2 MeV-t, de-
rived recently by Bahcall and May .8 The result 
quoted above differs from the previous value for 
S11 mainly because Bahcall and May used the 
newer lifetime measurement for the neutron17; 
small changes were also introduced because of 
their more accurate calculations of the nuclear 
matrix element and beta-decay phase-space fac-
tors, and their treatment of radiative correc-
tions. Note that the 12.5% increase in S11 from 
model B to model C decreased the predicted 
counting rate by 32%. 
Model C yields our most probable theoretical 
results. We find that18 
~ ('Pa) 1 most probable 
_ x -ss -1 sl7 ( 1) 
- (0.75 ± 0.3) 10 sec 0_043 keV b" 
The quantity S17 is the low-energy cross-section 
factor for the reaction 7Be(lH, y)8 B. If we use in 
Eq. (1), as we have throughout Table II, the val-
ue of 0.043 keV b obtained for S17 by Parker/9 
the most probable predicted counting rate is 
about a factor of 2 larger than the probable up-
per limit set by Davis, Harmer, and Hoffman.1 
However, the preliminary results of Vaughn et 
al.20 suggest that Parker's value may requirere-
vision downward. The error estimate in Eq. (1) 
was made by constructing models D and E in 
which Z and S11 were chosen equal to their prob-
able extreme values.8 •9 The opacities used in 
all of the above-described calculations were ob-
tained in the usual way7 by interpolation within 
published tables of Cox, Stewart, and Eilers.21 
As an additional check, J. N. Stewart and A. N. 
Cox kindly supplied us with opacity tables for 
precisely the solar composition of heavy ele-
ments that was obtained by Lambert and War-
ner.9 A recalculation of model C using this 
more direct approximation to the solar opacity 
yielded values for the most important quantities 
that were within a few percent of the values list-
ed in Tables I and II. 
It is apparent from Eq. (1) that there is no ir-
reconcilable discrepancy between our predic-
tions and the experiment of Davis, Harmer, and 
Hoffman1 when the uncertainties in the various 
parameters that enter the calculation are taken 
into account.22 
The neutrino flux from the reaction 1H + 1H + e-
-
2D + v is very nearly model independent as may 
be seen in Table II. Hence we can predict a low-
er limit on the counting rate that is consistent 
with current ideas about the way nuclear fusion 
reactions produce the sun's liminosity. We find 
(cf. Ref. 12) that 
('Pa)only 1H+ 1H+e-- 2D+v 
=0.03Xl0-35 sec-1 • (2) 
It is important to measure accurately several 
crucial quantities in order that the relationship 
between the observed and predicted counting 
rates may more clearly reveal the adequacy or 
inadequacy of the current theory of stellar interi-
ors. The quantities of most importance are , 
(1) the neutron lifetime from which the axial-vec-
tor coupling constant, and hence the rate of the 
proton-proton reaction, are determined,S (2) the 
low-energy cross section for 7Be(1H, y)8 B to 
which the predicted counting rate is directly pro-
portional, and (3) the heavy-element abundance 
on the surface of the sun. 
We now list several conclusions that can be 
drawn from the results of the experiment of Da-
vis, Harmer, and Hoffman. First, the sun does 
not derive most of its radiated energy from the 
CNO cycle since this implies, independent of 
1211 
VOLUME 20, NUMBER 21 PHYSICAL REVIEW LETTERS 20MAY 1968 
the theory of stellar models (cf. Ref. 5), a count-
ing rate of 3.5X10-35 sec-1/ 37Cl atom. Second, 
if the usual theory of stellar interiors is correct, 
then the heavy-element abundance Z must be 
less than 2% by mass in order for the predicted 
neutrino-capture rate not to exceed the observed 
value. Third, assuming the measured value9 of 
z;x~ 0.019, we can deduce the primordial heli-
um abundance of the sun by requiring that the 
calculated luminosity of our solar models equals, 
after 4. 7 X 109 yr of nuclear burning, the observed 
solar luminosity. We find Y==0.22±0.03, where 
the uncertainty in Y reflects the uncertainties in 
the parameters that characterize various solar 
models. 
We are grateful toR. Davis, Jr., R. P. Feyn-
man, William A. Fowler, P. Goldreich, D. L. 
Lambert, R. M. May, and F. Reines for stimu-
lating and informative conversations, and to 
J. N. Stewart and A. N. Cox for supplying us with 
opacity tables for the Lambert-Warner solar 
composition. 
*Supported in part by the National Science Founda-
tion [GP-7976, formerly GP-5391] and the Office of 
Naval Research [Nonr-220(47)]. 
t Alfred P. Sloan Foundation Fellow. 
tAlso at Tel Aviv University, Tel Aviv, Israel. 
§Also supported by the National Science Foundation 
[GP-6928] with Cornell University. 
1R. Davis, Jr., D. S. Harmer, and K. C. Hoffman, 
preceding Letter [Phys. Rev. Letters 20, 1205 (1968)]. 
2R. Davis, Jr., Phys. Rev. Letters 12, 303 (1964). 
3J. N. Bahcall, W. A. Fowler, I. Iben, Jr., and R. L. 
Sears, Astrophys. J. 137, 344 (1963). 
4R. L. Sears, Astrophys. J. 140, 477 (1964). 
5J. N. Bahcall, Phys. Rev. Letters 17, 398 (1966). 
6J. N. Bahcall, M. Cooper, and P. Demarque, Astro-
phys. J. 150, 723 (1967); G. Shaviv, J. N. Bahcall, 
and W. A~owler, Astrophys. J. 150, 725 (1967); J. N. 
Bahcall, N. A. Bahcall, W. A. Fowler, and G. Shaviv, 
Phys. Letters 26B, 359 (1968). 
· 7J. N Bahcall and G. Shaviv, to be published. 
8J. N. Bahcall and R. M. May, Astrophys. J. Letters 
152, 37 (1968). 
-en. L. Lambert, Nature 215, 43 (1967), and Monthly 
Notices Roy. Astron. Soc. 138, 143 (1967), and Obser-
vatory 87, 228 (1968); D. L. Lambert and B. Warner, 
Monthly Notices Roy. Astron. Soc. 138, 181, 213 (1968); 
1212 
B. Warner, Monthly Notices Roy. Astron. Soc. 138, 
219 (1968); D. L. Lambert, private communications. 
10M. Schwarzschild, Structure and Evolution of the 
Stars (Princeton University Press, Princeton, N.J., 
1958). 
11J. N. Bahcall, Science 147, 115 (1965). 
12J. N. Bahcall, Phys. R~135, B137 (1964), and 
Phys. Rev. Letters 12, 300 (1964). 
13R. Stair, W. R. Waters, and H. T. Ellis, spring 
meeting of the Optical Society of America, 1967, Ab-
stract THG15 (unpublished); R. Stair and H. T. Ellis, 
"The Solar Constant Based on New Spectral Irradiance 
Data from 3100 to 5300 Angstroms" (to be published); 
A. J. Drummond, J. R. Hickey, W. J. Sholes, and 
E. G. Lane, paper presented at the Fifth Aerospace 
Sciences Meeting, American Institute of Aeronautics 
and Astrophysics, New York, January, 1967 (unpub-
lished); H. Neckel, Z. Astrophys. 65, 133 (1967). 
14w. A. Fowler, G. R. Caughlan, and B. A. Zimmer-
man, Ann. Rev. Astronomy Astrophys. 5, 525 (1967). 
15see, for example, L. D. Landau and E. M. Lifshitz, 
Statistical Physics (Pergamon Press, London, Eng-
land, 1968) p. 232. The corrected pressure can be 
written in the form P ""P0[1-4.4X 10-2(3 +X)312PV2/(5X 
+3)T6312 ], where P 0 is the pressure ofa perfect gas, p 
is the density in g/cm3, and T 6 is the temperature in 
units of 106oK. We have assumed in the above formula 
that Z«X. For consistency, the Debye-HUckel correc-
tion must also be taken into account in calculating the 
entropy. 
16We use the analytic approximation of C. B. Hasel-
grove and F. Hoyle, Monthly Notices Roy. Astron.. Soc. 
119, 112 (1959), to the results of L. Mestel, Proc. 
Cambridge Phil. Soc. 46, 331 (1950). 
17c. J. Christensen, A. J. Nielsen, A. Bahnsen, W. K. 
Brown, and B. M. Rustach, Phys. Letters 26B, 11 
(1967). -
180nly the 8B contribution to the counting rate is pro-
portional to S 17 , but this is almost all of the total pre-
dicted counting rate for the most likely models (of. Ta-
ble II). 
19P. D. Parker, Astrophys. J. 145, 960 (1966), and 
Phys. Rev. 150, 851 (1966). Cf. the results of R. W. 
Kavanagh, Nucl. Phys. 15, 411 (1960). 
2°F. J. Vaughn, R. A. Chalmers, D. A. Kohler, and 
L. F. Chase, Jr., Bull. Am. Phys. Soc. 12, 1177 
(1967). -
21A. N. Cox and J. N. Stewart, Astron. J. 67, 113 
(1962), and Astrophys. J. Suppl. Q, 22 (1966); A. N. 
Cox, J. N. Stewart, and D. D. Eilers, Astrophys. J. 
Suppl. 11, 1 (1966). 
22A fuller discussion of these uncertainties is given 
in Refs. 6 and 7. 


Present Status of the Theoretical Predictions for the ^(37)Cl Solar-Neutrino Experiment

http://authors.library.caltech.edu/33199/1/BAHprl68.pdf

Present Status of the Theoretical Predictions for the ^(37)Cl Solar-Neutrino Experiment

Abstract

Similar works

Full text

Available Versions

Caltech Authors - Main