THE ROLE OF NEUTRON β-DECAY IN ASTROPHYSICS

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THE ROLE OF NEUTRON β-DECAY IN ASTROPHYSICS

J. Byrne

To cite this version:

J. Byrne. THE ROLE OF NEUTRONβ-DECAY IN ASTROPHYSICS. Journal de Physique Collo- ques, 1984, 45 (C3), pp.C3-31-C3-36. �10.1051/jphyscol:1984307�. �jpa-00224021�

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Colloque C 3 , supplement au n ° 3 , Tome 4 5 , m a r s 1984 page C3-31

THE ROLE OF NEUTRON P-DECAY IN ASTROPHYSICS

3. Byrne

School of Mathematical and Physical Sciences, University of Sussex, Brighton, Sussex, U.K.

Résumé- Nous discutons les influences possibles de la désintégration béta du neutron en astrophysique et détaillons quelques cas où ce processus est d'im- portance cruciale.

Abstract- We discuss possible influences on neutron g-decay in astrophysical systems and detail a number of instances where the process is of crucial impor- tance.

§1. Neutron g-decay

The lifetime T =t /ln2 of the neutron is given by ftn=2Tv3 ln2/G|g^cos26c (1+3 A 2)

where the symbols have their usual meaning. The value of t appropriate to conditions in a terrestrial laboratory is 925±11 sec(l). This is a critical parameter in astrophysics because at temperaturesT^jLO1°K of interest, nucleons and leptons are the only weakly interacting particles present and the time scale of change between successive states of thermal equilibrium is set by neutron g-decay and allied weak reactions.

The principal effect of an intense magnetic field or radiation field on T is the modification of the phase space factor f due to quantization of the outgoing electron states (2). The critical magnetic field at which quantum effects dominate is that for which the energy of Larmor precession H.eB /m c is equal to the electron rest-mass m c2. Thus B =4.414x10*3G. In fields of this order f is increased by about 30%. Similar effects occur in intense radiation fields; in a thermal field at temperature T the relevant parameter X=E/B takes the value

<X2>=4Ia/e2\/M? V 15 (hc)^)

At a temperature T=:1010K, X2 =1 and the neutron lifetime will again be reduced by about 30%.

Of course if the neutron is placed in a degenerate electron gas at densities ^2xl09

gm/cm3, eg. inside a neutron star, neutron g-decay will be totally inhibited.

The vector current in g-decay is conserved (CVC); thus no renormalization of g is expected. It has however been suggested that in intense radiation or magnetic fields B-1016G,6 would be quenched, ie. reduced to zero (4). The notion is that the spontaneously broken synmetry parameterized by 6 would revert to the symmetric phase rather as the superconducting phase of a metal goes to normal in a magnetic field. This effect has been proposed as an explanation for the enhanced decay of

35A, although opinions are divided (5,6). However, fields of this magnitude are not normally encountered in astrophysics.

The axial current is not conserved but is believed to be partially conserved (PCAC).

This result finds its expression in the Goldberger-Treiman relation which connects

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984307

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C3-32 JOURNAL DE PHYSIQUE

gA t o t h e pion-nucleon coupling constant g nm '

I t is known t h a t , i n t h e &decay of many m i r r o r nuclei, g is reduced (7) and t h i s phenomenon has been described i n t e r n of a generalized Adberger-Treiman r e l a t i o n appropriate t o nuclear matter (8). An analogy is drawn with t h e e l e c t r i c a l polari- z a b i l i t y of a d i e l e c t r i c medium t o introduce t h e concept of an a x i a l p o l a r i z a b i l i t y of nuclear matter, caused by t h e nucleon-A-isobar t r a n s i t i o n induced by t h e pion f i e l d . Thus in condensed s y s t f n s with density approaching nuclear mtter p-- 2 . 5 ~ 10"

eY3,

g could b e quenched by as m c h a s 3% with a corresponding increase i n the l l f e t l m e 04 t h e neutron.

52. Helium Abundance and t h e Number of Neutrino Species

To t r a c e t h e path from b i g bang t o l i g h t elen?ent nucleosynthesis i n t h e e a r l y universe (9) one need only i n v e s t i g a t e developments below a temperature of about 10°K since above t h i s temperature s t r o n g and electromagnetic i n t e r a c t i o n s maintain t h e populations of t h e relevant p a r t i c l e species i n a s t a t e of thermal equilibrium.

f i r t h e m r e , the expansion time t " l ~ - ~ s e c is much g r e a t e r then t h e l i f e t i m e of heavy unstable p a r t i c l e s and a t t h i s epoch only e l e c t r o n s , positrons, photons, nucleons and neutrinos r e m i n .

The s t a t i s t i c a l balance by mass of neutrons and protons is m i n t a i n e d a t its e q u i l i - brium value

-(M -M )c2/kT X / X = e n p

" ^P

through t h e action of t h e weak processes

n+e+ =p+ e, n+ v e

which a t terrrperatures > l d a K proceed m c h f a s t e r than f r e e neutron decay n-t p+e-+Ce

However, t h e condition of thermal equilibrium ensures t h a t t h e s e weak reaction rates can be computed using themdynamics alone, once t h e c h a r a c t e r i s t i c s of f r e e neutron decay a r e hown.

Since t h e c h a r a c t e r i s t i c weak s c a t t e r i n g times increase a s T5 with f a l l i n g tern perature, i n canparison with t h e expansion time which goes as T-2, a point is reached a t which t h e s e weak r e a c t i o n s can no longer maintain X,/X a t its equilibrium value. A t t h i s freeze-out temperature ~ ~ ~ 1 0 ' OK (t=l s e e ) t h e neu-&inos decouple from matter and X /X decays with+a time c h a r a c t e r i s t i c o f f r e e neutron decay. A t T=3x10"

K (t=10 see)%& remaining e - p a i r s a n n i h i l a t e t o photons, and t h e r e a f t e r matter and r a d i a t i o n s t a y i n equilibrium u n t i l atoms form a t ~ ~ 4 x l 0 ~ K ( t = 0 . 5 ~ 1 0 ~ ~ ) . A t t h i s point t h e universe switches over from radiation domination t o matter domination and t h e photons decouple frcm t h e matter giving rise t o t h e 2.9K microwave background we observe today.

The onset of nucleosynthesis can be fixed q u i t e p r e c i s e l y near T=109K (.t=200sec) when deuterium formed i n t h e key reaction

remains s t a b l e against photodisintegration i n t h e thermal r a d i a t i o n f i e l d . This is followed by a chain of s t r o n g i n t e r a c t i o n processes p+d -t3He+y, n + 3 ~ e +'He+y etc.

whose inmediate e f f e c t is t h e ccjnversion of v i r t u a l l y a l l f r e e neutrons i n t o helium.

Knowing t h e relevant temperatures, t h e expansion r a t e of t h e universe and t h e l i f e - time of the neutron, a simple calculation a r r i v e s a t a value 25% f o r t h e 'He/H mass r a t i o in very good accord with observation (10). Some f u r t h e r nuclear physics input leads t o a 2x10i3% abundance of deuterium by mass and l e s s e r amount of heavier elements up t o Li. The Coulcmb b a r r i e r and t h e gaps a t mass nunbers 5 and 8

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The conclusion then is t h a t t h e helium abundance is determined by (a) n and p rrasses (b) the binding energy of t h e deuteron and ( c ) t h e r a t i o of t h e neutron l i f e t i m e t o t h e c h a r a c t e r i s t i c expansion time.

where G is t h e g r a v i t a t i o n a l constant a n d p t h e density. Since helium is synthesised i n t h e e r a of r a d i a t i o n domination where baxyonic matter contributes of t h e energy density,p is determined by t h e temperature and t h e n m h r of p a r t i c l e species which are r e l a t i v i s t i c a t t h a t temperature. I n p a r t i c u l a r any s i g n i f i c a n t increase i n t h e measured value of t h e neutron l i f e t i m e l e a d s t o a corresponding increase i n helium synthesis and conversely.

Suppose f i n a l l y t h a t t h e r e e x i s t o t h e r f a m i l i e s of massless, o r a W s t massless, neutrinosover and above t h e t h r e e known families. These p a r t i c l e s would a l s o con-

t r i b u t e t o t h e density and t h e universe would expand correspondly f a s t e r between f r e e z e out and nucleosynthesis. Over t h i s reduced period o f time fewer neutrons would decay and mre helium would be produced. On these grounds e x i s t i n g l i m i t s on helium abundances would appear t o r u l e out more than one additional f m i l y of l i g h t tm-component neutrinos; indeed t h e same evidence would seem t o point t o t h e conclusion t h a t knownneutrinospecies cannot he four cmponent p a r t i c l e s (11).

$3. The Solar Neutrino Problem

The proton-proton cycle of thermonuclear r e a c t i o n s is believed t o be t h e predominant source of s o l a r energy, t h e end-point of which is t h e fusion of four protons i n t o a helium nucleus with t h e r e l e a s e of positrons, photons and neutrinos. The f a i l u r e t o observe mre than about 3% of t h e predicted capture r a t e of s o l a r neutrinos i n a 3 7 ~ 1 t a r g e t leading t o an i s o b a r i c analogue state i n 3 7c o n s t i t u t e s ' t h e s o l a r ~

neutrino problem'. (12).

In t h e f i r s t s t e p of t h e chain two protons c w b i n e t o form a deuteron

generating neutrinos with energy 60.42MeV, i n s u f f i c i e n t t o t r i g g e r t h e j7c1 detector.

This is a weak i n t e r a c t i o n whose r a t e determines t h e speed of t h e cycle. The p e - p r e a c t ion,

which occurs with a branching r a t i o of 0.25%, is an a l t e r n a t i v e t o t h e p p process, generating neutrinosof energy <1.44MeV which are d e t e c t a b l e i n ' "21.

The next s t e p i n t h e c y c l e is t h e fusion of hydrogen and deuterium t o ' ~ e

a t which s t a g e t h e process branches with fusion of 3 ~ e + 3 ~ e t o form 'He (91%), o r fusion of 3 ~ e + 4 ~ e t o form 7 ~ e is). Approximately 1% of t h e l a t t e r branch r e s u l t s in t h e f o m t i o n of 'B whose 6 -decay generates t h e 14.lKeV neutrinos t o which t h e

7 ~ 1 detector primarily responds.

The predicted r a t & ~ o f neutrino counting based on t h e standard s o l a r m d e l is (7.6 *

3.3) SNU (13), where 1 neutrino i n t e r a c t i o n s per t a r g e t atom per second.

Of t h e 3.3 WU e r r o r on t h e predicted r a t e , 1 SNLJ d e r i v e s from t h e e s t i m t e d e r r o r i n t h e neutron l i f e t i m e .

The r o l e of neutron $-decay in a l l t h i s sterrs from t h e f a c t t h a t t h e governing p-p reaction is nothing o t h e r than inverse neutron &decay with t h e spectator proton providing t h e energy, while t h e p e - p reaction is t h e corresponding electron capture

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t r a n s i t i o n . However, s i n c e t h e two protons can r e a c t weakly only when they scatter i n t h e s i n g l e t state because of t h e P a u l i p r i n c i p l e , and because t h e deuteron can e x i s t only i n the t r i p l e t s t a t e , t h i s is a pure Gamow-Teller t r a n s i t i o n with a r a t e proportional t o gAT. Apart f r a n meson exchange e f f e c t s of order 1% t h i s process can be c a l c u l a t e d p r e c i s e l y knowing t h e temperature and the neutron l i f e t i m e .

The reason f o r t h e s e n s i t i v i t y of t h e neutrino r a t e t o u n c e r t a i n t i e s i n t h e value of the neutron l i f e t i m e is the following. I f t h e neutron l i f e t i m e is reduced, t h e p-p a t p e - p reactions go f a s t e r i n t h e same proportion. However, t h e s o l a r luminosity is f i x e d so t h e increased r a t e of t h e weak i n t e r a c t i o n must be compensated by a reduction i n temperature. I t t u r n s o u t t h a t i n these c i r c m t a n c e s t h e r e l a t i v e number of 'B nuclei is reduced with a corresponding reduction i n t h e predicted r a t e of neutrino captures. Hence one contribution t o solving t h e s o l a r neutrino problem would be t h e demonstration t h a t t h e neutron l i f e t i m e had k e n s u b s t a n t i a l l y over-

estimated.

94. Supernova Core Collapse

The f e a t u r e which most distinguishes a Type I f m a Type I 1 supernova is t h e absence of hydrogen i n its spectrum. It is therefore believed t o be an exploding white dwarf with mass exceeding t h e Chandrasekhar l i m i t of 21.5 s o l a r masses (14).

Type I1 supernovae a r e observed only i n g a l a c t i c s p i r a l arms close t o t h e presumed site of s t a r formation. They a r e assumed t o be massive s t a r s , of order 10-100 s o l a r masses, which have rapidly evolved t o t h e s t a g e where t h e i r nuclear f u e l is ex- hausted. When t h e core mass exceeds t h e Chandrasekhar l i m i t , the pressure of degenerate e l e c t r o n s can no longer support it and g r a v i t a t i o n a l collapse sets i n , releasing v a s t amounts of energy i n t h e form of neutrinos over a time s c a l e = sec, determined by t h e elementary weak i n t e r a c t i o n r a t e s .

The main problem has been t o d i s o l s s how t h i s enelgy is t r a n s f e r r e d t o t h e outer layers of t h e star causing t h e explosion (15). Originally it was believed t h a t t h i s was caused by nxsnen-tum t r a n s f e r from t h e neutrinos (16) but t h e discovery of t h e n e u t r a l current processes(l7)

opened up t h e p o s s i b i l i t y of coherent neutrino-nuclear s c a t t e r i n g with cross-section proportional t o A2 leading t o neutrino trapping i n s i d e and outside t h e core. Thus t h e proposed mechanism does not work.

The accepted p i c t u r e of a Type I1 supernova is t h e following. There is a l a r g e envelope of hydrogen enclosing successive l a y e r s of helium, carbon, oxygen and s i l i c o n . R e s e surround an iron-nickel core which is supported by t h e pressure of a degenerate electron gas with a d i a b a t i c index y=4/3. When t h e core temperature reaches T - 1 0 ' ~ photodisintegration of t h e core nuclei sets i n and t h e s e are

d i s s o c i a t e d i n t o neutrons, protons and alpha p a r t i c l e s . A t a t a n p e r a t w e T=l0l0K and density p=lO1Ogm/cm electron captures can occur

and removal of t h e e l e c t r o n pressure causes t h e core t o collapse. Since neutron

@-decay is i n h i b i t e d a t d e n s i t y ~ 4 0 ~ g t n / a n ~ and e s s e n t i a l l y ceases f o r p>2x10~gm/m~

t h e core converts i n t o a degenerate neutron gas with a d i a b a t i c index 512. Yhen the d e n s i t y reaches nuclear matter density of p=2.5x101 4gm/cm3 t h e collapse s t o p s and t h e neutron star is formed; a t t h i s point t h e r e is a hydrodynamic 'bounce' o r pressure wave which spreads outwald from t h e core carrying energy i n t o t h e o u t e r l a y e r s of t h e s t a r . A t t h e same tim f u r t h e r neutrinos a r e released from t h e core v i a t h e ( n e u t r a l current) neutrino b r e m s ~ t r a h l u n ~ process

and t h e (charged c u r r e n t ) modified URCA processes

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Current t h e o r i e s as- (18) t h a t t h e outgoing shock wave neutronizes m a t e r i a l i n its path through electron captures

t h e pressure d e f i c i t being balanced by t h e inverse reaction

caused by neutrinos released f m t h e shocked l a y e r s . The net r e s u l t is t h a t t h e shock wave propagates outward without damping and t h e o u t e r l a y e r s of t h e s t a r are blown away.

Whether these ideas prove t o be correct o r not remains t o be seen; i n t h e present context t h e chief i n t e r e s t lies i n t h e f a c t t h a t every s i g n i f i c a n t reaction r a t e is proportional t o t h e r a t e of neutron decay modified by various complicating f a c t o r s such a s high density and (within t h e degenerate neutron core) high magnetic f i e l d s .

55. Synthesis of Neutron-Fich Kuclei

Because of t h e absence of s t a b l e nuclei withmass numbers 5 and 8 and t h e r e l a t i v e - l y low density a t t h e onset of b i g bang nucleosynthesis, n u c l e i m o r e massive than

1 1

B cannot be synthesized i n s i g n i f i c a n t abundances i n t h e e a r l y universe. Although elements i n t h e range up t o t h e i r o n peak a t A=60 a r e synthesized by charged par- ticle reactions during t h e slow progress of s t e l l a r evolution t h r w g h successive s t e p s of thermonuclear burning from hydrogen t o s i l i c o n , elements with A>60 can be synthesized only through neutron capture. I t is therefore necessary t o i d e n t i f y s u i t a b l e neutron sources.

A t t h i s point two time s c a l e s must be recognised: namely T~ t h e mean i n t e r v a l betwerlneutron captures on a givennucleus, and T B t h e mean @-decay l i f e t i m e of

nuclei i n t h e reaction chain. k c l e i synthesized i n chains f o r which T >>T are c a l l e d (slow) s-process nuclei (19) ; i f rc .;r iwe have (rapid) r-procesg nuglei (20).

a

Studi:? of s-process nuclear abundances have led t o t h e i d e n t i f i c a t i o n of t h e reac- t i o n Ne(a,n) 25hig i n t h e convective heliun l a y e r s of t h e m a l l y pulsed stars as t h e p r i n c i p a l neutron source (21). However, s-process nucleosynthesis takes place over such v a s t time s c a l e s t h a t t h e r e s u l t i n g nuclei are confined t o t h a t region of t h e n u c l i d i c c h a r t close t o t h e s t a b i l i t y l i n e ; thus t h e p r e c i s e r a t e s a t which t h e weak decays proceed a r e unimportant. Conversely, t o synthesize r-process neutron-rich n u c l e i , extremely intense short-lived neutron sources a r e required, l a s t i n g no more than perhaps a few seconds. Furthermore t o reach observed abundances with such a source r e q u i r e s the presence of s u b s t a n t i a l nmbers of heavy (A=60) seed n u c l e i which can proceal t o higher Z by %-decay.

For these reasons a site f o r synthesis of r-process nuclei has k e n p o s b l a t e d ( 2 2 ) i n t h e deep i n t e r i o r of a supernova near t h e mass-cut between t h e forming neutron star and t h e ejected matter. The mantle is assumd t o expand a d i a b a t i c a l l y f r m conditions of peak temperature T =3x101 'K and d e n s i t y p o = l o l 'gm/cm3 with time de- pendent density determined accor8ing t o expo11pntial law P=Poe-t/T where T is a simple multiple of t h e free-fall time ( ~ I T G ~ ) - ' . This n ~ d e l resembles t h e b i g bang i n s a w r e s p e c t s except t h a t t h e presence of a s u b s t a n t i a l n w h r of species of seed nuclei, perhaps 20 o r more, leads t o a r o r e mre complex network of reactions.

I t t u r n s o u t then, as i n t h e b i g bang, t h a t t h e r e s u l t i n g abundances of r-process n u c l e i a r e detemined e s s e n t i a l l y by t h e neutron-proton mass r a t i o X / a t t h e t a r y weak reactions freeze out tefiperature ~ ~ ' 1 0 ' O K ; t h i s i n turn is fixed by t h e r a t e s 8f% he elenen-

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e-+p +n+v +

e' ^{e +n+p+v}e ' n -tp+e-+Ge

Agreenent with observed abundances can be obtained with freeze-out values of X /X i n t h e range 4-8 but only f o r a very r e s t r i c t e d range of values of To and po (237.

There a r e several objections t o t h i s scenario not only i n respect of its s e n s i t i v i t y t o t h e i n i t i a l conditions but p a r t i c u l a r l y because, a t an assumed mass e j e c t i o n r a t e of 0.2 s o l a r rrasses per supernova, i t could lead t o over-production of r-process nuclei by f a c t o r s > l o 3 . Explosive helium burning i n massive s t a r s i n i t i a t e d by the outgoing shock-wave i n a super-nova has been suggested as an a l t e r n a t i v e slte (24). I n such a m d e l however it is necessary t o input t h e l i f e t i m e of each one of same thousands of n u c l e i p a r t i c i p a t i n g i n t h e reaction chain; f r m l t h e @ - s t a b i l i t y l i n e up t o t h e neutron drip-line. In these circumstances t h e highly uncertain values of nuclear r a t r i x eleri-entsbecome a l l impartant, and t h e simple dependence of the process on weak e l e n ~ n t a r y r e a c t i o n s a l l i e d t o neutron B-decay is l o s t .

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