NEUTRINO 72

I .

HUNGARY 1972

OMKDK-TECHNOINFORM

EUROPHYSICS CONFERENCE

BALATONFÜRED, HUNGARY, 11-17 JUNE 1972

organized by

THE HUNGÁRIÁN PHYSICAL SOCIETY

PROCEEDINGS VOLUME I.

A. FRENKEL

_ Editors

G. MARX

)

MTA

KIK

OMKDK-TECHNOlNFORM

8 0 7 7 S 7

magyar

KÖNYVTARA

Distribution:

OMKDK TECHNOINFORM BUDAPEST 8. P.O.B. 12

HUNGARY

Felelős kiadó : M a rx G yörgy

Készült az O M K D K házi sokszorosító ü z ^ é b ^ T Budapest, VIIU Reviczky u. 6.-

Felelős vezető : Janoch G yula

jiví. lliD. AKADÉMIA Ki-iíiVIÁRA j

I

Sitting: T. D. Lee, G. L. Radicati, R. P. Feynman, B. Pontecorvo, V. F. Weisskopf,F. Reines, C. L. Cowanand P. Budini

ORGANIZING COMMITTEE

J . B e 11 ( G e n e v a )

T . D e G r a a f ( G r o n i n g e n ) A . F i l i p p o v ( D u b n a ) J . N i l s s o n ( G ö t e b o r g )

B . K u c h o w i t z ( W a r s a w ) J . P e t r a s ( B r a t i s l a v a )

H . P i e t s c h m a n ( V i e n n a ) B . P o n t e c o r v o ( D u b n a ) H . P r i m a k o f f ( P h i l a d e l p h G .T a v k h e 1 i d z e ( M o s c o w ) S . W e i n b e r g ( M . I . T . ) Y a .B .Z e 1 d o v i c ( M o s c o w )

G . M a r x ( B u d a p e s t ) S e c r e t a r y

A . F r e n k e l ( B u d a p e s t ) P r o c e e d i n g s S e c r e t a r y P . G n U d i g ( B u d a p e s t ) T e c h n i c a l S e c r e t a r y

ÁSS ISTANTS

E . G a j z á g ó A . P a t k ó s

L . G á l f i A . S e b e s t y é n

J . P . H a r n a d C s . S ü k ö s d P . H a s e n f r a t z A . S . S z a l a y

C .S z e g ő

R e p o r t o n the B r o o k h a v e n S o l a r N e u t r i n o E x p e r i m e n t R . D a v i s Jr., J . C . E v a n s , V . R a d e k a a n d L . C . R o g e r s

A r e the s o l a r n e u t r i n o - e x p e r i m e n t s s u g g e s t i v e of the e x i s t e n c e a r e s o n a n c e in the H e 3 + H e 3 s y s t e m ? / d i s c u s s i o n r e m a r k /

V . N . F e t i s o V a n d Y . S . K o p y s o v S o l a r n e u t r i n o s : T h e o r y J .N .fíahaall

T h e b a c k g r o u n d e f f e c t s in s o l a r n e u t r i n o e x p e r i m e n t s R . D a v i s , A.W. W o l f e n d a l e a n d E . C . M . Y o u n g

T h e i n v e s t i g a t i o n of the b a c k g r o u n d in the s o l a r n e u t r i n o p r o p o r t i o n a l c o u n t e r s / d i s c u s s i o n r e m a r k /

I .R .B a r a b a n o V a n d A . A . P o m a n s k y

N e w a p p r o a c h e s to t he s o l a r n e u t r i n o p u z z l e K. Lande, G . B o z o k i , C . L . L e e a n d E . F e n y v e s D o u b l e b é t a d e c a y

E .F i o r i n i

N o t e o n U n i v e r s i t y of C a l i f o r n i a , I r v i n e d o u b l e - b e t a - d e c a y e x p e r i m e n t

M . M o e , D . L o w e n t h a l a n d F . R e i n e s L e p t o n c h a r g e c o n s e r v a t i o n G . M a r x

N o t e o n e l e c t r o n s t a b i l i t y a n d t he P a u l i p r i n c i p l e / d i s c u s s i o n r e m a r k /

F . R e i n e s a n d H . W . S o b e l

R e m a r k on s t a b i l i t y of / d i s c u s s i o n r e m a r k / F .R e i n e s

N e u t r i n o e x i t a t i o n of n u c l e a r l e v e l s in 12C

H . U b e r a l l , B . A . L a m e r s , J .B .L a n g w o r t h y a n d F .J .K e l l y A n t i n e u t r i n o - e l e c t r o n s c a t t e r i n g

H . S . G u r r , F . R e i n e s a n d H . W . S o b e l T h e L e p t o n é r a of t he B i g B a n g T. de G r a a f

C o s m o l o g i c a l l i m i t o n n e u t r e t t o m a s s / d i s c u s s i o n r e m a r k / G . M a r x a n d A . S . S z a l a y

F i e l d - p a r t i c l e a s p e c t s of the c o s m o l o g i c a l n e u t r i n o p r o b l e m / d i s c u s s i o n r e m a r k /

H .K u c h o w i e z

R e v i e w of the e x p e r i m e n t a l s i t u a t i o n o n n e u t r a l c u r r e n t s C . B altay

D i s c u s s i o n

S e a r c h f ór n e u t r a l c u r r e n t s in " G a r g a m e l l e "

A a o h e n , B r u s a e l s , C E R N , P a r i s ( E . P . ), M i l á n , Orsay, L o n d o n (UCL) C o l l a b o r a t i o n

S e c o n d e l á s s c u r r e n t s in w e a k i n t e r a c t i o n s H .P i e t s o h m a n n

I n d u c e d t e n s o r i n t e r a c t i o n a n d s e c o n d - c l a s s c u r r e n t s B . E m a n a n d D . T a d i o

N u c l e a r b e t a - d e c a y e x p e r i m e n t s a n d s e c o n d - c l a s s w e a k c u r r e n t E . V a t a i

T h e o r e t i c a l a p p r o a c h e s to K1-. d e c a y N. P a V e r

T h e d e c a y K L 2\i / R eview/

A . D . D o l g o V , L .B .O k ú n , V . I . Z a k h a r o v R e v i e w of the k£ -*■ y+ + p p u z z l e R .J .O akea

M u o n p h y s i c s V. L. T e l e g d i

C o n c l u s i o n s o f t he f i r s t p a r t of the N e u t r i n o '72 E u r o p h y s i c s C o n f e r e n c e , B a l a t o n f ü r e d

B . P o n t e c o r v o

S c a l i n g p r o p e r t i e s in w e a k a nd e l e c t r o m a g n e t i c p r o c e s s e s

T . D. Lee 1

D i s c u s s i o n 25

P r e l i m i n a r y r e s u l t s o n the r a t i o of a n t i n e u t r i n o to n e u t r i n o t o t á l c r o s s - s e c t i o n s

A a c h e n , B u s s e l s , CERN, P a r i s ( E . P . ) , M i l á n , O r s a y , L o n d o n (UCL)

C o l l a b o r a t i o n 29

H y p e r o n p r o d u c t i o n b y a n t i n e u t r i n o s in G a r g a m e l l e

A a e h e n , B r u s s e l s , CERN, P a r i é (E.P. ), M i l á n , O r s a y , L o n d o n (UCL)

C o l l a b o r a t i o n 39

N e u t r i n o p h y s i c s at B a t a v i a : p r o s p e c t s a n d p r o g r e s s

B . C . B a r i e h 49

W h a t n e u t r i n o s c a n t e l i us a b o u t p a r t o n s

R . P . F e y n m a n 75

D i s c u s s i o n 97

D e e p - i n e l a s t i c l e p t o n - n u c l e o n s c a t t e r i n g

J . K u t i 101

R e p o r t o n W b o s o n m o d e l of w e a k i n t e r a c t i o n s w i t h m a x i m a i C P v i o l a t i o n

R . E . M a r s h a k 129

V i r t u a l n e u t r i n o e f f e c t s

P . B u d i n i 149

C a l c u l a t i o n o f s t a t i c Q u a n t i t i e s in W e i n b e r g ' s m o d e l

W ,A .B a r d e e n , R . G a s t m a n s a n d B . L a u t r u p 163

A n a l y t i c r e n o r m a l i z a t i o n a nd e l e c t r o n - a n t i n e u t r i n o s c a t t e r i n g

Z . H o r v á t h a n d G . P S o s i k 175

A p p l i c a t i o n of t w i s t o r t h e o r y in w e a k i n t e r a c t i o n s / d i s c u s s i o n r e m a r k /

Z . P e r j é s 183

A t h e o r y of u n i v e r s a l w e a k i n t e r a c t i o n s of l e p t o n s

A . T . F i lippov 185

C o s m i c r a y n e u t r i n o s

R . R e i n e s , H . H . C h e n , H . S . G u r r , W . R . K r o p p , P .B .L a n d e o k e r , J . F . L a t h o r p , W . G . S a n d i e , H . W . S o b e l - M . F . C r o u c h - J .P .F .S e l l s o h o p , D . B o u r n e ,

H . C o x e l l , D . K r a m e r , B .S .M e y e r ' 199

A n a n a l y s i s o f c o s m i c r a y m u o n n e u t r i n o e x p e r i m e n t s

J . L . O s b o r n e , A .W . W o l f e n d a l e a n d E . C . M . Y o u n g 223

p a g e S e a r c h fór n e w l e p t o n i c p r o c e s s e s u n d e r g r o u n d

G . L . C a a a i d a y 239

A t m o s p h e r i c n e u t r í n ó i n d u c e d m u o n f l u x a n d t he n e u t r i n o n u c l e o n i n t e r a c t i o n s a t h i g h e n e r g i e s

Z . K u n a s t 253

P r o s p e c t s fór the d e t e c t i o n o f h i g h e r o r d e r w e a k p r o c e s s e s a n d the s t u d y of w e a k i n t e r a c t i o n s at h i g h e n e r g y

U . C l i n e 273

C o n c l u s i o n IX

V . F . W e i s s k o p f 319

L I S T O F P A R T I C I P A N T S 3 35

n e u t r i n o' 7 2 (opening address)

G . M a r x , D e p a r t m e n t o f A t o m i c P h y s i c s , R o l a n d E ö t v ö s U n i v e r s i t y i n Budapest

We may now celebrate the 40th anniversary of the discovery o f neut­

rin o . The understanding of weak forces acting in Natúré was always d i - r e c t ly connected with the in vestigation of th is t in ie s t and sim plest piece of matter. The four decades of neutrino research form a b r i l l i a n t

success story. P a u li to ld at the beginning of neutrino Science th at n eu t- rin os would never be detected. Bút Fred Reines and Clyde Cowan taught us the way of experimenting with neutrinos. To-day sophisticated n eutrino eyes are watching at the glowing of d iffe re n t sources in several la b o ra - t o r ie s .

NEUTRINO EXPERIIÍENTS

from reacto rs: Hanford 1953

Savannah River 1955

Brookhaven 1956

from accelerators: Brookhaven 1962

CERN 1964-

Batavia 1973

from cosmic rays: Home Stake 1965

Kolar Gold F ield 1967

Utah 1969

2

Doing fundamental research i s a hard job in our age. Fór tremen- dous e f f o r t s Natúré pays on ly w ith v e ry f a i n t and v e r y p r o v is io n a l r e ­ s u lt s . Bút weak; in te r a c tio n s helped us in o b ta in in g va lu a b le b i t s o f exact in form atio n about the fundamental p r o p e r tie s o f m atter. The l a s t

d is c o v e ry o f a s t r i c t co n servatio n law was th at o f the le p to n ic charges /1952/. The G V C theorem b u i l t a b rid g e from e l e c t r i c i t y to b éta decay /1957/* The weak in t e r a c t io n taught us, what was the e s s e n tia l d if fe r e n - ce between l e f t and r ig h t /1956/* p o s it iv e and n e g a tiv e /1957/» pást and fu tu re /1964/.

The U n iverse i s crowded by n eu trin o s. They are more p l e n t y f u l , than protons or e le c tr o n s . N eu trin os are nőt on ly the sim p le s t, bút a ls ó the most common forms o f m atter. We lea rn ed them to know e a r l i e r , than the neutrons or p o s itro n s or mesons. Bút n eu trin o Science i s fa r from bein g

clo sed . Just the o p p o site statement i s tru e : i t i s g e t t in g more and more p u z zlin g in the re c e n t y ea rs. We have s e v e ra l we11-fo rm u láted question s, which are w a itin g f ó r answer. We d is co v ered the muon lon g ago, bút we

d id nőt understood i t up to now. / I t s e x is te n c e c o n tr a d ic ts sharply a l l o f our c la s s ic ideas about the o r ig in o f p a r t i e l e masses./ On the other hand, we t r i e d hard, bút we are unable to d is c o v e r the W boson. /Con-

sequ en tly we s t i l l do nőt know, i f f i e l d th e o ry i s v a l i d anywhere bút quantum electro d y n a m ics, or n ő t./ And we have a ls ó naw p u z zle s : We ob- served the decay o f the K£ meson in tő ” , what we did nőt want to observe. /We lea rn ed , th a t Natúré i s asymmetric w ith re s p e c t to time r e v e r s a l , bút the on ly statement we are able to form u late is th at this

asymmetry i s superweak and almost u n ob servab le./ We did nőt observe the decay o f ^k£ in tő what we needed d e s p e ra te ly . /In th is

h ide-and-seek game around the ^k£ meson we do nőt see, i f th ere i s any connection between the p o s it iv e and n e g a tiv e su rp rise s/ . The neu^"

rin o eyes do nőt see the sunshine e it h e r .

We have these t r ic k y probléma, because we asked Natúré on the s o p h is tic a te d language o ffe r e d by the modern experim ental technique.

Bút the system atic knowledge about weak in te r a c tio n s and the experimen­

t a l a b i l i t y to handle neu trinos w i l l help us at the new fr o n t ié r a o f ex act Science, what we have reached: a t the deep i n e l a s t i c f r o n t i e r in ­ sid e the hadrons, a t the supernova s in g u la r it y in the la t é s t e l l a r evo - lu tio n and a t the B ig Bang s in g u la r it y a t the beginn in g o f tim e. There are good hopes, th a t the t i n y neu trinos may show the way to the pioneera in these v i r g i n lands.

The l i t t l e o ld n eu trinos may come again to the h ead lin es o f s c ie n - t i f i c Journals. F e e lin g t h i s , P r o f Zatsepin c a lle d a s p e c ia liz e d meeting t o Moscow in 1969* in order to discuss the problems o f cosmic n eu trin os.

P r o f.B e r n a r d in i and P r o f.R a d ic a t i c a lle d another m eeting on s t e l l a r neut­

r in o s to Cortona in 1970. On the Cortona conference we agreed to organ ize the t h ir d European neu trin o conference in Hungary.

In our o rg a n izin g work we enjoyed the sponsorship o f the European P h y s ic a l S o c ie t y , the p o s it iv e in t e r e s t o f the J o in t I n s t it u t e o f Nuc­

l e a r Research /Dubna/, CERN /Geneva/, In te r n a tio n a l Centre f ó r T h e o r e ti­

c a l Ph ysics / T r ie s te / . The main sources o f the fin a n c ia l support were the Hungárián Academy o f S cien ces, the Hungárián P h y s ica l S o c ie ty , the Roland Eötvös U n iv e r s ity and the C en tral Research In s t it u t e in Budapest. Bút the Hungárián e f f o r t s were nőt enough, to overcome a l l the d i f f i c u l t i e s in the o rg a n izin g work. We made a stro n g use o f the T ria n g le C o lla b o ra tio n . This s c i e n t i s t 's co-op s ta rte d fo u r years ago, accordin g t o the su ggestion o f W a lter T h ir r in g . The corners o f the o r ig in a l T ria n g le were formed by the p a r t i e l e ph ysics groups in Vienna, B r a tis la v a and Budapest, bút in the meantime a ls ó oth er nearby s c i e n t i f i c cen ters jo in e d us.

This i s about the o rg a n iza tio n o f t h is con feren ce. Let the Moscow, Cortona and B alaton M eetings be fo llo w e d by s e v e ra l N eutrino Conferences!

THE TRIANGLE COLLABORATION

IN PART/CLE PHYSICS

REPORT ON THE BROOKHAVEN SOLAR NEUTRINO EXPERIMENT*

R .D a v is J r . , J .C .E v a n s , V.Radeka and L .C .R o g e r s , Brookhaven N a t io n a l L a b o r a to r y , Upton

(Abstract)

A solar neutrino experiment has been in progress since 1967 to observe neutrinos from the sün by the neutrino capture reaction

37 37

C l(v ,e ") Ar. 380,000 lit e r s o f perchloroethylene, C2C1^, are used as a neutrino capturing médium. The radioactive 37Ar (35.1-day h a l f - l i f e ) is removed from the iiq u id by purging with hélium gas, p u rified , and counted in a small low -level proportional counter. Argon-37 decay events are characterized by the energy o f the event, and the rise-tim e o f the counter pulse. The results o f s ix experiments performed during the la st two years w i l l be given. The 37Ar production rate in the detector was 0.18 + 0.10 per day, close to the production rate expected from cosmic ray muons. The experiment places an upper lim it on ^the

37 —36 — 1 3 7 “ 1

production o f Ar by solar neutrinos o f 1 x 10 sec ( Cl atom) This lim it can be compared to the currently predicted rate o f 9 x 10 *“36

-1 37 -1

sec ( Cl atom) from solar model calculations o f Bahcall and Ulrich, and Abraham and Iben.

A solar neutrino detector based upon the neutrino capture reaction

37 - 37

C l(v ,e ) Ar was b u ilt in 1964-1967 and has been operating since early 1967. The i n i t i a l experiments [1] showed that the to tá l flux-cross section

— 36 —1 37 —1

product was less than 3 x 10 sec .( Cl atom) . This conclusion was

Research performed under the auspices o f the U.S. Atomic Energy Commission.

6

substantiated by additional experiments performed during the period 1968-1970, and reported in a series o f reports [2 ]. In these experiments the 37Ar

decay events were characterized in the proportional counter by observing the energy o f the Auger electrons emitted follow ing the decay. The recent

experiments that w ill be reported here, the 37Ar decay event in the counter is characterized by the energy (pulse height) and rise-tim e o f the pulse [3 ].

This added discrimination fó r 37Ar events has lowered the counter background fór 37A r-lik e events permitting a more sen sitive search to be made fó r the neutrino radiation from the sün.

This report w i ll present a b r ie f summary o f the c r it ic a l experimental tests that have been performed to demonstrate the e ffic ie n c y o f recovering 37Ar from 380,000 lit e r s o f perchloroethylene, the rise-tim e counting system, and the observations that have been made over the la s t two years.

The detector was arranged so that i t could be shielded with a water shield with an average thickness of about 2 meters to elim inate the e ffe c t of

fást neutrons from the surrounding rock. Three experiments w i ll be reported with this water shield in piacé.

»

T h e D e t e c t o r

The detector consists o f a 380,000 l i t e r tank o f perchloroethylene (C2C14) , a pumping system fó r circu la tin g the liq u id and purging the liquid with hélium gas, and a gas absorption system fó r removing argon from the

circulatin g hélium gas. The detector is located at a depth of 4400 hg/cm 2 in the Homestake Gold mine at Lead, South Dakota. The arrangement o f the apparatus underground is shown in F ig. 1, and a schematic diagram o f the extraction system is shown in Fig. 2.

Argon-37 produced in the liq u id is removed by purging with hélium gas.

Two 1700 liter/m in pumps circu late liqu id from the tank through a series of

40 eductors that draw hélium from the gas space at the top of the tank, and distribute i t through the liq u id in the form o f small bubbles. The

20,000 lit e r s o f hélium in the tank at 1.3 atmospheres pressure is circulated through the liq u id every 2 minutes by the pumping system. TVo eductors are used to draw the hélium from the tank through a condenser at -35°C, a

molecular sieve adsorption trap, a charcoal trap cooled to 77°K, and fin a lly returning the hélium to the tank. Hélium flows through the extraction system at a rate o f 310 liters/m in. The hélium flow rates depend upon the gas

pumping rates o f the eductors, and these rates have remained constant at the values given above.

The e ffic ie n c y fó r extracting argon from the 380,000 lit e r s o f was tested in several ways.

(1) In es<h experiment a measured volume (0.05 to 0.10 cm ) o f iso to p ica lly3 pure 36Ar is introduced intő the tank to serve as a ca rrier gas and to measure the argon recovery achieved in each experiment [1].. The 36Ar ca rrier is introduced at the beginning o f the period of irrad iation and is recovered several months la te r by the hélium purge. The 36Ar content of the hélium gas in the tank was analyzed, and from the re la tiv e volumes of the gas and liq u id phases we calculate that approximately 95 percent

36 36

o f the Ar introduced dissolves in the liq u id . The recovery of Ar as a function o f the volume o f hélium circulated through the system was measured. The volume o f argon remaining in the tank decreases

exponentially with the volume o f hélium circulated [1 ]. With the fixed flow rates, a 95 percent recovery can be obtained in a 22 hour period.

37 37

(2) An analogous test was made with Ar. A sample o f Ar a c tiv ity in hélium gas was prepared, introduced intő the tank, recovered during 22 hours o f operation extending over a 2 day period, and counted. The 37Ar

8

a c tiv ity introduced was 10.0 dis Ar/day, and the recovered sample

contained 11.0 + 1.8 dis 37Ar/day corrected to the time i t was introduced.

This experiment was performed May 19, 1972, and the counting of this sample and the analysis is nőt yet complete. However, this preliminary

result does demonstrate the recovery o f 37Ar is consistent with recovery based on the 36Ar ca rrier method.

(3) The 380,000 l i t e r tank is provided with a reentrant pipe that extends to the center o f the tank. A Ra-Be neutron source was placed in this source tűbe to produce 37Ar in the liq u id by the successive nuclear

35 35 37 37

reactions Cl(n,p) S followed by Cl(p,n) Ar. The y ie ld fó r this -7 37

neutron source test was 7.4 x 10 Ar atoms per neutron, and i t was shown that the 37Ar produced was removed in successive purges along with

36 3 7

the Ar carrier [1 ]. The y ie ld of Ar a c tiv ity obtained in this

experiment was compared to sim ilar neutron irrad iation s o f containers of perchloroethylene with smaller diameters. These yield s ( Ar atoms/ 37 neutron) and diameters were: 3.0 x 10 7, 29 cm; 6 .A x 10~7, 120 cm;

7.4 x 10 7, 600 cm.

These experimental tests demonstrate that 37Ar produced in the 380,000 lit e r s of perchloroethylene is e ffic ie n t ly removed by the hélium

purge. This result is en tirely reasonable based upon the chemical behavior of argon. The neutrino capture process forms an argon ion that reco ils from its parent C^Cl^ molecule. The argon ion rapidly reaches thermal energy in the

liq u id , capturing an electron from adjacent m°lecu les becoming a

37 37

neutral Ar atom. This neutral Ar atom is id en tica l chemically with the dissolved 36Ar carrier atoms present in the liq u id at a concentration o f 5 x 109 atoms/cm3. The recovery o f 36Ar from the liq u id is therefore a valid measure o f the 37Ar recovery. Our colleagues at Brookhaven [4] have made a

37

search fó r the formation o f complex argon-C^Cl^ ions in a high pressure mass spectrometer source. No evidence was obtained in these experiments fó r the formation of stable C Cl Ar+ ions. Evidence was found fó r a charge transfer

m n

process that proceeds with a rate c o e ffic ie n t at least two orders o f magnitude greater than an upper lim it fó r the rate c o e ffic ie n t fór the reactions

producing Ar-CmCln+ . This is evidence fó r rapid charge transfer in the gas phase and supports the assumptions made above concerning the charge transfer process in the liq u id phase.

Counting

The entire argon sample recovered from the tank was placed in a small proportional counter that has already been described [1 ], In the experiments reported here the rise time of the pulse and the pulse height was measured fó r each pulse. The 2.8 keV Auger electron produced in the electron-capture

;

decay o f 37Ar has a rangé in the counter gas o f approximately 0.1 mm. Hie ion pairs produced in the gas are localized in a small volume o f the counter, and therefore they reach the center wire nearly at the same time giving a fást risin g pulse. Background events from more energetic Compton-electrons, betas or muons in passing through the counter gas, produce ion-pairs more widely spaced, and hence reach the center wire over longer periods o f time

givin g a slower risin g pulse. By measuring the rise-tim e o f the pulse one can distinguish 37Ar decay events, X-ray absorption events, and tritium decays from background events produced by gamma radiation, betas, and muons.

A fá st charge-sensitive pream plifier with a 6 nsec pulse rise-tim e response feeds an Ortec model 410 timing f i l t e r am plifier that integrates (10 nsec) and d iffe re n tia te s (10 nsec) the charge pulse. The shaped pulse is then fed to a pulse-stretching am plifier fó r acceptance by an analóg to d ig ita l converter. This d ig ita l Information is plotted on a y-axis o f a two

10

parameter p lo t and is designated the amplitude o f the d iffe re n tia te d pulse (ADP). The pulse from the pream plifier is alsó separately routed to a conventional RC shaping spectroscopy am plifier and subsequently analyzed by a second analóg to d ig it a l converter. This d lg it a l Information is displayed on the X-axis as the energy. The arrangement is shown schematically in Fig. 3.

Each time the counter functions the ADP and pulse height (energy) is w ritten on a paper tape along with the clock time, and a sequence o f te s t pulses fó r ADP and pulse height (energy). The system is autómatically checked once every 1000 minutes with the test pulses, and at this time the anti-coincidence counter rate is recorded. The counting system is capable o f recording , events from four separate counters.

The counters are calibrated with an "^Fe X-ray source. The location o f region o f fa s t-ris in g X-ray pulses is determined by recording on a separate pulse height analyzer the ADP pulses gated in coincidence with a narrow

energy region selected by a sin gle channel analyzer. This measurement is carried out at several d iffe re n t energies to define the region o f X-ray pulses. The lines drawn on the two parameter p lo t define the X-ray region.

The indicated region contains approximately 95 percent o f the fá st X-ray pulses. The location o f the position o f 37Ar on the lin ear energy scale was

55 37

determined from the Fe X-ray peak p o sition . The Ar resolution ( f u l l width at h a lf maximum, fwhm) was taken as 1.45 times the "^Fe resolution.

The discrimination against pulses produced by gammas, was measured by piacing a 6°Co source near the counter and recording the ADP pulse distribútion

corresponding to particular energies. The fra ction o f the area under the ADP spectrum ex teriő r to the X-ray region is a measure o f the e ffe c t iv e rejectio n of pulses arising from energetic betas, gammas, and muons. In the experiments

reported here there was a va riation in the rejectio n ra tio that depended upon counter f i l l i n g (argon pressure, percent CH^) and the dimensions o f the counter.

The lowest rejectio n ratio was 82 percent, and the highest achieved was 99 percent.

R e s u l t s

Three experimental runs (Nos. 18, 19, and 20) were made with the

unshielded tank, as in a l l previously reported experiments. The two-parameter e

plots fór these three runs are shown in Figs. 4 and 5. The periods o f counting are indicated on the plots, and correspond approximately to a h a l f - l i f e o f 37Ar (35.1 days). I t may be observed that 5, 9, and 3 counts,

respectively, were observed with the correct ADP and an energy within the half-width o f the 37Ar peak position . The samples were counted fó r

additional periods to see i f these 37A r-lik e events decayed away with the 35.1-day h a l f - l i f e period. The data are summarized in Table 1 where the nunfoer o f fá st counts observed in the energy in tervals 1 to 2.4 keV, 2.4 to 3.2 keV (fwhm) , and 3.2 to 7 keV are given. I t may be seen that there was sa tisfa ctory decay in runs 18 and 19 to a background counting rate o f « 2 and ^ 3 counts per 36 days, respectively, bút l i t t l e evidence fó r decay in run 20.

Following these experiments the tank chamber was flooded with water to provide a neutron sh ield. Fást neutrons above 1 MeV energy can produce 37Ar in the liq u id by the successive reactions mentioned e a r lie r . A small flu x o f fá st neutrons arises from spontaneous fis s io n o f 238U and (a,n) reactions from alpha decays o f the uránium and thorium and th eir daughters present in the rock. The fást neutron flux was measured by a sen sitive radiochemical technique based upon the ^Ca(n,ot) ~^Ar reaction. These

measurements indicated that the 37Ar production in the 380,000 l i t e r tank was about 0.04 37Ar atom per day, too small to be observed. However, the water shield should completely eliminate any possible fást neutron background from the rock w a ll.

production rate from muons in 380,000 lit e r s o f at a depth o f 4400 hg/cm is approximately 0.12 + 0.04 per day. Argon-37 can alsó be2 produced by cosmic ray produced muon-neutrinos, v^, by the reaction

37 Cl(v^,p ) Ar. _ 37 The production rate from this process was estimated to be 0.024 per day [5 ].

Somé attention was devoted to the p o s s ib ility that there is 37Ar in the earth's atmosphere. In the processing o f the 380,000 lit e r s o f C^Cl^ an excess o f 40Ar is found in each experiment, and this is attributed to the inleakage o f atmospheric argon. Quantities o f 37Ar have been found in the atmosphere that are two orders o f magnitude higher than the amount produced by cosmic ray interactions [6 ]. The le v e l was high during the period

corresponding to our run no. 19, however the sp e c ific a c tiv ity was a factor o f ten below that observed in the run 19 argon. The a ir in the Homestake mine was monitored during the period March (19 71) to March (1972) bút the 37Ar content was in generál low, <0.15 dis/min l i t e r o f argon.

Conclusions

The cosmic ray muon background must be subtracted from the 37Ar production rate lim it o f 0.18 + 0.10 given above. The resulting rate that could be attributed to solar neutrinos is then 0.06 + 0.11 37Ar atoms per day. We then conclude that the solar neutrino production rate is less than 0.2 37Ar atoms/day. The corresponding flux-cross section product lim it is

then,

This lim it can be compared to the currently calculated flux-product from standard solar models o f

„oí _ i q -j _ 1

I<|>o (th e o re tic a l) = 9.1 x 10 sec ( Cl atom)

14

The s i g n i f i c a n c e of this d i s c r e p a n c y b e t w e e n o b s e r v a t i o n s w i l l b e d i s c u s s e d by Dr. J. N. B a h c a l l i n a p a p e r p r e s e n t e d at this c o n f e r e n c e .

O u r c o n c l u s i o n s m a y b e s u m n a r i z e d as f ollows:

(1) The to tá l flux-cross section product fó r solar neutrino capture in

37 8 7

Cl is a factor o f 9 below the to tá l (B , Be , and PeP) rate

predicted by standard solar model calculations, and below the rate predicted from ^Be decay and PeP reaction neutrinos

8 6 •“ 2 1

(2) The flu x of B solar neutrinos is less than 10 cm” sec

(3) The s ü n p r o d u c e s less t h a n 3 p e r c e n t o f its e n e r g y b y the CNO ^cycle.

A c k n o w l e d g e m e n t

The authors would lik e to acknowledge the s k i l l f u l technical

assistance o f Mr. John Galvin during the en tire period o f these in vestigation s.

R e f e r e n c e s

[1] R. Davis J r ., D. S. Harmer, and K. C. Hoffman, Phys. Rév. L ett. 20, 1205 (1968).

[2] R. Davis, Proc. Moscow Conf. on Neutrino Physics and Neutrino Astro- physics, Moscow 2 , 99 (1969); l l t h In t. Conf. on Cosmic Rays, Budapest, Acta Physica Acad. Sci. Hung. 29^ Suppl. 4, 371 (1970); Cortona Conf.

on Astrophysical Aspects o f Weak Interactions, Accad. Naxionale dei Lincei 157, 59 (1971).

[3] R. Davis J r ., V. Radeka, and L. C. Rogers, Bull. Am. Phys. Soc. I I 16, 631 (19 71); R. Davis J r ., ib id I I 17, 527 (1972).

[4] J. J. Leventhal and L. Friedman (to be published).

[5] E. C. M. Young, A. W. Wolfendale, and R. Davis J r ., paper presented at Balatonfured Conference.

[6] H. H. L oo sli, H. Oeschger, and W. Wiest, J. Geophys. Rév. ^5, 2895 (1970), and priváté communication from H. Oeschger.

[7] J. N. Bahcall and K. Ulrich, Ap. J. 170, 479 (1971).

[8] Z. Abraham and I . Iben, J r ., Ap. J. 170, 157 (1971).

16

Table 1

Summary of Results Without Water Shield

Fást Counts Run

No. Exposure Period Counting Period 1.0-2.4 keV Ar37 FWHM

2.4-3.2 keV 3.2-7 keV

18 Apr 12 to Nov 14 I 39 days 10 5 5

(1970) I I 35 ff

9 5 9

I I I 34 tt

12 3 6

. IV 36 If

6 1 9

V 39 ff

11 2 11

19 Nov 14 (1970) I 36 days 6 9 3

to Mar 6 (1971) I I 39 II

5 5 13

I I I 37 II

7 5 12

IV 41 II

20 4 8

V 37 ff

20 3 8

VI 36 ff

7 3 5

VII 34 ff

5 4 8

20 Mar 6 to June 17 I 40 days 3 3 2

(1971) I I 30 ff

7 1 2

I I I 37 ff

15 3 7

IV 38 ff

8 0 3

V 51 ft

13 1 6

* VI 36 ff

7 3 3

Table 2

Summary o f Results With Water Shield

Run

No. Exposure Perlőd Counting Perlőd

Fást Counts 1.0-2.4 keV

Ar37 FWHM

2.4-3.2 keV 3.2-7 keV

21 Jan 17 to Oct 2 I 39 days 5 0 7

(1971) I I 34 " 8 1 8

22 Oct 2 to Dec 13 I 35 days 6 2 3

(1971) 11 36 " 9 2 5

I I I 40 " 9 3 6

23 Dec 13 (1971) I 40 days 4 3 5

to Mar 2 (1972)

18

COUNTER

20

3

• wc n Í L

o

o

o o

in ^{o u i ou~>}

3snnd *ddia Hd m

22

LO b>

L 3 CT)

3sind 'jdia ' i dm

ARE THE SOLAR-NEUTRINO EXPERIMENTS SUGGESTIVE OF THE EXISTENCE OF A RESONANCE IN THE H e 3 + H e 3 SYSTEM ? (üISCUSSION REMARK)

V . N . F e t i s o v , P . N . L eb ed ev P h y s ic a l I n s t i t u t e , Moscow, Y u .S . K o p y so v, I n s i t i t u t e f ó r N u c le a r R e sea rch , Moscow / P re sen te d by A.E.Chudakov/

As i s known according to Davis at a l . [ l ] the experimental counting r a t e o f s o l a r neutrinos

(^6)

i) 10

o.*

($í'5')*IO*

j e t' a r o r i ' [ % ] •

This discrepancy causes us to analyse the methods o f c a lc u - l a t i o n o f c ro ss s e ctio n s in chains o f n u clear re a c tio n s o f the hydrogen c y c le in the Sun which le ad to emission o f n eu trin osi

The usual nonresonance method o f e x t r a p o la t in g the cross sec­

tio n o f the He^(He^, 2p)He/|’ process measured only up to 80 keV[3]

to the re g io n o f lower en ergie s arouses somé s u s p i t i o n . We w i l l show that in the Be6 nucleus in the v i c i n i t y o f the threshold o f break-up in t ő 2He one can expect the ex istence o f a narrow l e v e l w ith 7

0 t T - l

pendence o f the re a c tio n cross section ( 1 ) ,

Now turn to the experimental data on the l e v e l s o f the L i^

and He^ n u c le i* According to the a n a ly s is [ 4 ] in He^ there e x is t d ip ó lé s t a t e s w ith 2 ' -

1

1 - 1

>

( H e * 2 p ) H e- *

( o / j H z

( i )

( ² )

( 3 )

24

and a lower monopolé exclted s ta t e w ith

1"

E*= 20.2 MeV. From the experimental data on photonuclear reactlons In L t 6 [ 5 ] and írom the experiments [ 6 ] on q u a s l f r e e s c a t t e r ln g o f protons by LI*7 i t is knovin th a t at E * - 18f20 MeV in the L i^

nucleus there are e x c lt a t lo n s w ith the

ls*p3>

responding in c lu s t e r terms to the d i p ó lé e x c l t a t l o n o f an -

C. /L

p a r t i e l e in L i [7J . Using the data on the speetrum o f He we f l n d that when go Ing from the d ip ó lé Inner e x c I t a t Ion of the

- c l u s t e r to the monopolé one the corresponding l e v e l w ith

V=

T - 0

(Li

Since Be and He have Is o s p in

T-

o(

1

5 . 5 MeV a r l s e s j u s t from the s im ila r e x c l t a t l o n o f the quasldeu­

t e r o n j > ] . Add Ing ~ 3«5 MeV to the energy o f the monopolé e x c l t a t l o n of the

o(

o f 2 He^ or 2H^ c l u s t e r s . The reduced wldth o f decay o f t h is sta te v la the He^+ZN channel due t o b rea k -u p of the - c l u s t e r must be much smaller than the reduced wldth o f decay v la the 2He^ and 2H^

channels. In a d d lt lo n , we note th a t there a re In d lc a tlo n s o f the

/- y -

ex lstan ce of a p o s lt I v e -p a r L t y l e v e l In L i at E ^ 15.8 MeV [9]«

Beturnlng to the astrophys Icjal aspect o f the developed a rg u - ments fa v o u rln g the ex istence o f new l e v e l s In n u c le l with A=6,

we may assume that the 0 - l e v e l o f the Indlcated natúré f a l l s

wLthln the re g io n o f the Gamov peak located in the regLon o f

6 *>

20 KeV above the threahold o f break-up o f Be Lnto 2He . In such a caae, I f the p o a lt lo n o f the resonance

Eh

T aatLafy the condltLons ^ ^

a r e the poal.ti.on and the h a l f - w i d t h of the Gamov peak) one can expect a conaLderable Lncreaae in the reactLon r a t e ( 1 ) and, aa a oonsequence, a decrease Ln the neutrLno yLeld vLa the channela

( 2 ) and ( 5 ) .

FLg. i shows the r s t l o La the product

y'^HOKires.

o f the croaa aectLon by the v e l o o l t y averaged over the Maxwell dLatrLbutLon a t the temperature of the S u n T ^ s l . ^ . i O ^ ' K

[2]

mum e f f e c t the reduced wLd-oh o f the entrance cbűnnel was tökén t o be equal to the WLgner ILmLt 31 ^ f ó r the channel radlus

K B =^.4 f a .

The uuoreaae Ln the countLng r a t e due to a drastLc enhance- ment Ln the r a t e o f the reactLon ( 1 ) can be estLmated f ó r the Davis* d e te c to r by eq. — foó) [ l O ] • In the moat fa v o u r -

res. nonn*.

a b l e case the countLng ra t e thus evaluated may decreaaed by a f a c t o r o f 16.

We a l s ó note that Ln the case o f the resonance wLth

t

One may attempt to fLnd the accurate posL tlon o f new l e v e l s Ln the nucleL w ith

A=6

* (f>)+*

26

The authora w ish to thank D rs. ri.A.Eramzhyan and Y u .F .S n L r- nov f ó r v a lu a b le d iac u a sio n o f the L l s t r a o t u r e .

A fter t h is conference p r o fe a s o r A #E.Chudakov kLndly Lnform- ed us that in an unpablLahed paper by Ponler [ l l } a p o s s l b l e exp la n atio n o f the Davis* ejcperinents by the Lnfluence o f a reaonance in the He^+He^ system was a l a o dLacuaaed.

REFERENCES

1. R.Davis J r . f L.C .Rogers and V.Radeka, B u l l . Ámor.

Phys. Sqc* 16 (1971) 631.

2 . J .N .B a h c a ll, R .K .U lr ic h , Ap. J . 170 (1971) 593.

3. M.R.Dwarakanath, H.W inkler, Phys. Rév. C4 (1971) 1532.

4 . C.Werntz, W.Meyerhof, N u c l . Phys. A121 (1968) 38.

5. I.V.Kurdymov, Yu.F.Smirnov, K .V .S h itik o v a, S .K h .E l-S a - marai, Phys. L e t t . 51B (1970) 165.

6 . J .P .C a rro n , I.C .J a c m a r t , M.Riou, C.Ruhla, I . T e i l l a c , C .C a v erz asio , K.Strauch, Phys. Rév. L e t t . 7 (1961) 261.

7« V .A .V a rta n ia n , G.E.Dogotar’, R.A.Eramzhan, A bstrac ts o f r e p o r t s submited to IV I n t e r n a t io n a l Gonference on High Energy P h ysics and Nuclear S tru c tu re , p . 108,D l-5988,Dubna, 1971.

8 . A .N .B o ja r k in a , I z v e s t i j a AN SSSR, s e r . f i z . 28(1964) 338.

9* W .C.Barber, J.G oldenberg, G .A .P eterson, Y .T o rizu k a, N u c l. Phys. 41 (1963) 461.

10. J .N .B a h c a ll, N .A .B a h c a ll, R .K .U lr ic h , A p .J . 156 (1969) 559.

11. W.A.Fowler, p r e p r in t 0AP-274, 1972.

The m ost im portant fact about the subject I am review in g is that there is a la rg e discrepancy between calculation and observation, the la tter being rep resen ted by the Brookhaven experim ent Dr. Davis has just described. The origin o f this discrepancy is unknown. I have at-

tempted to organ ize this review so that you can see fó r y ou rself what is being tested and how. The fir s t two sections concerning cross sec- tions and solar m odels are based on a r e v ie w a rtic le by m y s e lf and R . L . Sears that w ill appear in the Annual R eview o f Astronom y and A s tro p h y s ic s , V ol. 10. The last two sections include m y personal

opinion as of M ay 1972 on the questions of whether or nőt solar neutrinos reach the earth and on what one should do next to under stand the o rigin of the discrepan cy between theory and experim ent.

The basic reason fór doing solar-n eutrin o experim ents (and the associated th eoretical calculations) is to test quantitatively the theories o f nuclear en ergy generation in stars and o f s te lla r evolution. Because of the sm all photon mean fr e e path in stella r m a tériá i, photons (which are the subject of conventional astronom y) come to us from the outer- m ost la yers o f a star. Neutrinos, because of their la rg e mean fre e paths ( » a stella r radius under norm ál astronom ical conditions), can reach us fro m the deep in terio r of a star w here the tem perature is highest and the nuclear reactions, which are believed to be responsible fó r en ergy generation and stellar evolution, occu r. We of course know

R esearch sp on sored by th e N a t io n a l S c ie n c e F o u n d a tio n , G rant GP-16147 A 1.

30

m ore about the sün than any other star because o f its prox im ity and because of the fact that it is in the sim p lest stage of stella r evolution

(the quiescent main sequence phase). The Brookhaven Solar Neutrino experim en t of R. Davis, J r. , and his colleagues which is designed to ob serve solar neutrinos is th erefore a c r itic a l test o f the theories of

stella r evolution and nuclear energy generation in stars.

II. CROSS SECTIONS FÓR N E U TR IN O C A P T U R E

The ob served counting rate in any neutrino experim ent is the - 2

-

,

in tegrál o f neutrino flux per unit en ergy in terva l, (p dE (in cm sec ), E

tim es absorption cross section (in cm ) o f the target. The counting 2 rate is

J

sose o f the most frcqu en tly discussed tcrg ets are lis t e d in Table 1.

Fór the convenience o f the user, ve fo llo w the standard p ractice o f g iv in g the cross sections evercged over the appropriate neutrino energy

spectrum associated -vrith a pa rticu la r source ( e . g . , or decays).

S cattering cross sections fc r the rea ction v + e~ -* v ' + e" are a v a il- able as a function o f energy in sevcra l sources ( e . g . , Bahcall 196Ud,

Reines & Kropp l^oU, Ponteccrvo & Zatsepin 1970).

Because o f the surprising resu lts o f the VTC l experiment, the

question has erieen as to vhether or nőt the calculated absorption croso

sections (Bahcall 195Ua,b, 1966) fó r th is experiment could be the cause o f the discrepancy betveen theoi-y and observation. In our opinion, th is is nőt poEBible. The cross sections fó r the neutrinos from p + e + p -*•

h ♦ v , V 13» , and 150 a l l depend only on the ground state transition

37 37

from C l to A. This ground state transition is the inverse of the

37 — 37 37

v e ll-s tu d ie d laboratory decay o f A ( i . e . , e + A -* C l + v ) and a negligible error (< 10$) is introduced by the translation of the labora­

tory experiments intő neutrino absorption cross. sections using the established theory o f nuclear béta decey (e .g ., Konopinski 1966) .

The evaluation by Bahcall (l96Ua,b) of transitions from the ground state of 37C1 to various excited states of ^ A increaced the calculated crosB section fór this reaction by a factor of eighteen. This theoret­

ic a l stép caused considerable discussion vhen i t vas f i r s t made bút

sübsequent experimental atudies have confirmed the accuracy of the o r l-

ginal calculation.. In fact, the diBcovery (by Kardy & V errall I96U, Reeder, Poskanzer & Esterlund I96I+) o f the isotope 20Ca17 ( whoBe exia” 37

tence and decay l i f e t i c e vere predicted by Bahcall 196Ua,b) has made

32

absorption possible the calculation af the cross sections fór Cl neutrino/from

essentially experimental data (see Bahcall 1966) . The essential point

37 V7

to recognize is that ^ C a ^ is the mirror nucleus to ypl-2 0 > 1 ,e *»

37 T7

nuclear structure of Ca is the same as that o f C l because of the

v e ll established synimetry betveen neutrona and protons in nuclear

37 V7

physics. Béta decays frcza ^ Ca to the excited states of the mirror nucleus of 37 Rre ajval°S °’>i3 to neutrino-induced tranaitions

37 37

from Cl to the excited states of A. Thus, the measuremento (Poskanzerj McPhercon, Eoterlund & Reeder 1906) of the decay rateö of ^C a -» 4*

e** + v a llc v ona to largely de tenni na experimant&lly the required ^ C l

absorption cross sections. I t should be noted alsó that about five per- cent of the to tál B cross section arises frotn the ground state tran si-

8

37 37

tion betveen Cl and A and about six ty -fiv e percent from a s u p e r a l l o w e d

transition vhose absolute value is knovn on the basis of generál nuclear

physics considerations (the precise location of the analogue lev e l, vhich is d iffic u lt to calculate or measure to better than two hundred

kev, is unimportant since the cross section muot be averaged over the

• g

neutrino speetrum of B vhich is lU MeV broad). The remaining twenty-

five percent is parcelled out among various excited státe transitions;

the parcelling is constrained experimentally by a number of measured parameters including the measured (Poskanzer et a l 1966) branching ratios in the ^C a decay, the spins and paritien o f the states

(Goosman & Kavanagh 1967), and the observed to tál ^Ca and decay lifetim es. Bahcall (1966) estimát ed an overall uncertainty of the

O

order of ten percent in the calculated cross section fór B neutrino absorption by 37Cl and this estimate s t i l l seems reasonable,

m . SOLAR MODEIfí

III. K CONSTRUCTION (3F STANDARD SOLAR MODEIS

One does nőt need a detailed model.of the internál constitution o f the sün to predict the to tál number of solar neutrinos reaching the earth per cm2 per sec. In fact, this to tá l number is 2 h j(25 MeV • Un

(1 au)2) - 101 1 cm’ 2 sec”1, since on the average the basic fusion reac­

tion Up -* a + 2 c+ + 2v releases ~ 25 MeV. However, the proposed methods

A

of detection recocrd only a portion of the neutrino energy spectrum, which ranges trcm z e ro to more than 10 MeV, and the cross section fór detection

34

depends strongly on the neutrino energy. Moreover the form o f the neu­

trin o energy spectrum is a se n sitive function o f temperature, den sity,

and composition ( e . g . , the .production ra te o f the important high-energy neutrinos from B decay, f i r s t discussed by Fowler (1958) and Cameron8

(l9 p S ), va ries roughly as T

13

e f f ő rt has gone in tő the construction o f accurate so la r models and the coraputation o f the neutrino energy spectra they imply.

Table 2 iü u s tr a te s the main process cu rren tly b e lie v e d to conrvert H to He in the sün, the protcn-proton chain. The form o f tha neutrino

\

energy spectrum depends on the r e la tiv e frequencies o f the three branches

by vhich the chain is cccpieted and a d e ta iled solar model is required to determine the branchlng r a t io s .

Ve s h a ll b r i e f l y desc^ibe the construction o f solar models because the present disagreement betveen calculations and observation may de- pend on one or more assuaptions or parameters o f the models. The stan­

dard theory o f main-sequence stars (Schvarsschild I958, Cox fi: G iu li 1963, Chiu 19-53) assumes, at each point in the s ta r, ( i ) hydrostatic equilibrium betvreen g ra v ita tio n a l fo rce and pressure gradient (r a d ia l,

fór a spherically symmetric s t a r), ( i i ) energy transport "by radiation and convection, and ( i i i ) energy production by bydrogen burning. These assumptions may be stated as four first-ord er ordinary d iffe re n tia l equations, together with appropriate boundary conditions and constitu­

tive relation s. The latter include ( i ) the equation o f state which connects prescure, density, and temperature; ( i i ) the radiative opacity (which is a function o f chemical composition); and ( i i i ) the nuclear

energy-generation rate, involving the cross sections fó r the several reactions (see Cleyton 19S8 fór a clear and a thorough treatment txf

the nuclear reaction processes). As described by Schwarzschild (1958,

pp. 96-8) the only data required to obtain a solar model are the to tál mass and the distribution of chemical composition throughout the star.

We forego a deocription of the standard numerical techniques (see, e .g «, Sears & Brownlee 19^5» Kippenhahn, Weigert Se Hofmeister 19^7); the re­

sults that emerge from the computer include the march of physical variables throughout the star, the to tál radius and luminosity (ergs per second), the distribution of the energy-production processes, and

the central temperature. The calculated neutrino spectrum is detér-

mined by numerical in tegratio n crver masa ^bI^{ís ü b} .

In the case o f the sün the t o t á l mass is accurately known ( I.989 x 10

33

p r io r i. The conventional assumption in most recent vork. has been to

adopt a homogeneoua i n i t i a l composition and then to construct an evolu- tio n a ry sequence o f models (Schvrarzschild 1958, pp. 98-IO O ). In any one evolved model the helium/hydrogen r a t io is g rea te st a t the center

and f a l l s o f f to the primőr d ia i value Beme distance av*ny from the center, v it h the usual asouaption o f no rrbíing. A further dátum requ ired, then,

is the age o f the sün, usually taken as about Ív.7 x 109 years (see

Bahcall & Shaviv I908 fó r r e fe re n c e s ). One constructs an evolution ary

sequence o f a half-dozen or so models, ending v it h "th e" so lar model, vhich is required to have the present-day luminosity a ft e r U.7 x 10 q

y ears. In the case o f the sün a s t r i c t requirement on the computed radius is nőt u seful because the calculated value depends on the uncer**

ta in structure o f the convective envelope; fa rtu n ately th is uncertainty does nőt s ig n ific a n tly a ffe c t the calculated deep in t e r io r structure

(Schvarzochild 19í$> pp. lUlj— ^j Sears 196^ ).

36

•* ' 0 and Z, respectively the mass fractions of tydrogen, hélium, and heavier

elments (Z » 1-X-Y); thus orúy tvo free parameters appaar. Once values of the composition parameters axe adcpted, a solar model can be ob­

tained. I f the luminosity of the model d iffe rs from the observed lumi- noslty then one uoually changes sligh tly one of the composition párá­

mé ters—because the calculated luminosity is sensitive to Z via the opacity (roughly, L ~ ^**^) and is sensitivo to X and Y via the opacity

and the mean atomic veight per free p a r iid é in the perfect-gas equa-

7 5 "

tion of state (roughly, )• Hence one approach (Sears 196U, 1966, Bahcall & Shaviv 1963, Bahcall, Bahcall & Ulrich 1969) has been to adopt the value of Z/X given by spectroscopic observations o f the solar photosphere and to pick successive values of Y, computing an evolutionary sequence fór each, u n til a sequence is obtained in vhich the fin a l model reproduces the observed luminosity. Note' that this approach yields Y, the primordial hélium content of the sün, as a theoretical resu lt vhich can be conpared vith chromospheric determina-

38

tio n s, solar cosmic rays, and the prlm ordial abundance from a v a r ie ty o f cosmologies. Another approach, advocated by Iben (19^8, 1 9 6 ^ ), has been to adopt ab i n i t i o a value o f Y th at one b e lie v e s in on the basis

o f othsr astron caical evidence and to vary Z u n til one obtaina a luml- nosity f i t .

III. 2 RESULTS CiF STANDARD SOLAR MODELS III. 2.1 Review o f Re cent Models

The e a rlie st det&llsd so la r model used t o calculate solar neutrino

fluxes vas described by Bahcall, Fowler, Iben & Sears (1963) . Another early model was used by Pochoda & Reeves ( I96U) to estlmate a neutrino

energy spectrum. The f i r s t systeca tic study o f solar models fó r the purpose o f predictin g neutrino fluxes and th e ir u n certain ties was that

of Sears (190*0 • The baslc parameters o f his p referred Model J vere an i n i t i a l conposition parameter z/X » 0.028; the mass (1.939 x 1 0 ^ g );

and the age o f I+.5 x 10^ years. The equation o f sta te was th at o f an ideál gas, including electron-degeneracy pressure; the opacity was based

on the tables o f K e ller & Meyerott (1955); and the energy-generation rate [including the small g ra v ita tio n a l contraction term (Schwarzschild

» T

1958# Eq. 12.10)] involved the pp-chain and the CN cycle, with the cross section factors In the former from Parker, Bahcall & Fowler ( I96U). Aa

described in the preceding section the model was fitte d to the observed Bolar luminosity, 3»90 x 10 33 erg sec” . The resulting i n it ia l hélium

8 8

content waa Y ■ 0.27 and the resulting B neutrino flux was <p( B)

7 - 2 « l

1*9 x 10 cm sec • The principal p aramé tér 0 of this (19

6

contrlbution from the Be electron-capture neutrinos, led to a predicted 7

number o f neutrino captures at the earth of Z(<p<r) = 36 SNU.

Bolar models obtained by Ezer & Cameron (1965) and by Weymann &

Sears (1965) contained minor improvements, primarily in the use o f Los Alamos opacities (Cox & Stewart 1966, Cox, Stewart & E ilers 1966) .

Since these are lower than the Keller-Meyerott opacities in the deep in-

; .

terio r the resulting hélium contents and neutrino fluxes were slig h tly reduced compared to those of Sears ( I96I+). Bahcall (1966) combined

fluxes he calculated with the aid of the improved solar models and new

7 8

experimental Information on the maos-37 system and on the B e (p ,r) B