The Role of Neutron -Decay in Astrophysics

THE ROLE OF NEUTRON β-DECAY IN ASTROPHYSICS J. Byrne

To cite this version:

J. Byrne. THE ROLE OF NEUTRON β-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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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

3 2 2 ftn=2Tv ln2/G|g^cos 6c (1+3 A )

where the symbols have their usual meaning. The value of t appropriate to condit ions 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 elec tron 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

2 2 =4Ia/e \/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 C3-32 JOURNAL DE PHYSIQUE

g gA to the pion-nucleon coupling constant nm '

It is known that, in the &decay of many mirror nuclei, g is reduced (7) and this phenomenon has been described in tern of a generalized Adberger-Treiman relation appropriate to nuclear matter (8). An analogy is drawn with the electrical polarizability of a dielectric medium to introduce the concept of an axial polarizability of nuclear matter, caused by the nucleon-A-isobar transition induced by the pion field. Thus in condensed systfns with density approaching nuclear mtter p-- 2.5~ 10" eY3,g could be quenched by as mch as 3% with a corresponding increase in the llfetlme 04 the neutron.

52. Helium Abundance and the Number of Neutrino Species

To trace the path from big bang to light elen?ent nucleosynthesis in the early universe (9) one need only investigate developments below a temperature of about 10°K since above this temperature strong and electromagnetic interactions maintain the populations of the relevant particle species in a state of thermal equilibrium. firthemre, the expansion time t"l~-~secis much greater then the lifetime of heavy unstable particles and at this epoch only electrons, positrons, photons, nucleons and neutrinos remin.

The statistical balance by mass of neutrons and protons is mintained at its equilibrium value -(M -M )c2/kT X/X =e n p " P through the action of the weak processes

n+e+ =p+ e, n+ ve which at terrrperatures >ldaK proceed mch faster than free neutron decay

n-t p+e-+Ce

However, the condition of thermal equilibrium ensures that these weak reaction rates can be computed using themdynamics alone, once the characteristics of free neutron decay are hown.

Since the characteristic weak scattering times increase as T5with falling tern perature, in canparison with the expansion time which goes as T-2, a point is reached at which these weak reactions can no longer maintain X,/X at its equilibrium value. At this freeze-out temperature ~~~10'OK (t=lsee) the neu-&inos decouple from matter and X /X decays with+a time characteristicof free neutron decay. At T=3x10" K (t=10 see)%& remaining e- pairs annihilate to photons, and thereafter matter and radiation stay in equilibrium until atoms form at ~~4xl0~K(t=0.5~10~~). At this point the universe switches over from radiation domination to matter domination and the photons decouple frcm the matter giving rise to the 2.9K microwave background we observe today.

The onset of nucleosynthesis can be fixed quite precisely near T=109K (.t=200sec) when deuterium formed in the key reaction remains stable against photodisintegration in the thermal radiation field. This is followed by a chain of strong interaction processes p+d -t3He+y, n+3~e+'He+y etc. whose inmediate effect is the ccjnversion of virtually all free neutrons into helium. Knowing the relevant temperatures, the expansion rate of the universe and the lifetime of the neutron, a simple calculation arrives at a value 25% for the 'He/H mass ratio in very good accord with observation (10). Some further nuclear physics input leads to a 2x10i3% abundance of deuterium by mass and lesser amount of heavier elements up to Li. The Coulcmb barrier and the gaps at mass nunbers 5 and 8 inhibits synthesis of heavier species through (n,a), (p,a) and (ci,ci) reactions.

The conclusion then is that the helium abundance is determined by (a) n and p rrasses (b) the binding energy of the deuteron and (c) the ratio of the neutron lifetime to the characteristic expansion time.

where G is the gravitational constant andpthe density. Since helium is synthesised in the era of radiation domination where baxyonic matter contributes of the energy density,p is determined by the temperature and the nmhr of particle species which are relativis tic at that temperature. In particular any significant increase in the measured value of the neutron lifetime leads to a corresponding increase in helium synthesis and conversely. Suppose finally that there exist other families of massless, or aWst massless, neutrinosover and above the three known families. These particles would also con- tribute to the density and the universe would expand correspondly faster between freeze out and nucleosynthesis. Over this reduced period of time fewer neutrons would decay and mre helium would be produced. On these grounds existing limits on helium abundances would appear to rule out more than one additional fmily of light tm-component neutrinos; indeed the same evidence would seem to point to the conclusion that knownneutrinospecies cannot he four cmponent particles (11). $3. The Solar Neutrino Problem

The proton-proton cycle of thermonuclear reactions is believed to be the predominant source of solar energy, the end-point of which is the fusion of four protons into a helium nucleus with the release of positrons, photons and neutrinos. The failure to observe mre than about 3% of the predicted capture rate of solar neutrinos in a 37~1target leading to an isobaric analogue state in 37~constitutes 'the solar neutrino problem'. (12). In the first step of the chain two protons cwbine to form a deuteron generating neutrinos with energy 60.42MeV, insufficient to trigger the j7c1 detector. This is a weak interaction whose rate determines the speed of the cycle. The pe-p react ion,

which occurs with a branching ratio of 0.25%, is an alternative to the pp process, generating neutrinosof energy <1.44MeV which are detectable in ' "21. The next step in the cycle is the fusion of hydrogen and deuterium to '~e at which stage the process branches with fusion of 3~e+3~eto form 'He (91%), or fusion of 3~e+4~eto form 7~eis). Approximately 1%of the latter branch results in the fomtion of 'B whose 6 -decay generates the 14.lKeV neutrinos to which the 7~1detector primarily responds. The predicted rat&~ofneutrino counting based on the standard solar mdel is (7.6 * 3.3) SNU (13), where 1 neutrino interactions per target atom per second. Of the 3.3 WU error on the predicted rate, 1 SNLJ derives from the estimted error in the neutron lifetime.

The role of neutron $-decay in all this sterrs from the fact that the governing p-p reaction is nothing other than inverse neutron &decay with the spectator proton providing the energy, while the pe-p reaction is the corresponding electron capture C3-34 JOURNAL DE PHYSIQUE transition. However, since the two protons can react weakly only when they scatter in the singlet state because of the Pauli principle, and because the deuteron can exist only in the triplet state, this is a pure Gamow-Teller transition with a rate proportional to gAT. Apart f ran meson exchange effects of order 1%this process can be calculated precisely knowing the temperature and the neutron lifetime.

The reason for the sensitivity of the neutrino rate to uncertainties in the value of the neutron lifetime is the following. If the neutron lifetime is reduced, the p-p at pe-p reactions go faster in the same proportion. However, the solar luminosity is fixed so the increased rate of the weak interaction must be compensated by a reduction in temperature. It turns out that in these circmtances the relative number of 'B nuclei is reduced with a corresponding reduction in the predicted rate of neutrino captures. Hence one contribution to solving the solar neutrino problem would be the demonstration that the neutron lifetime had ken substantially over- estimated.

94. Supernova Core Collapse

The feature which most distinguishes a Type I fma Type I1 supernova is the absence of hydrogen in its spectrum. It is therefore believed to be an exploding white dwarf with mass exceeding the Chandrasekhar limit of 21.5 solar masses (14). Type I1 supernovae are observed only in galactic spiral arms close to the presumed site of star formation. They are assumed to be massive stars, of order 10-100 solar masses, which have rapidly evolved to the stage where their nuclear fuel is ex- hausted. When the core mass exceeds the Chandrasekhar limit, the pressure of degenerate electrons can no longer support it and gravitational collapse sets in, releasing vast amounts of energy in the form of neutrinos over a time scale = sec, determined by the elementary weak interaction rates.

The main problem has been to disolss how this enelgy is transferred to the outer layers of the star causing the explosion (15). Originally it was believed that this was caused by nxsnen-tum transfer from the neutrinos (16) but the discovery of the neutral current processes(l7)

opened up the possibility of coherent neutrino-nuclear scattering with cross-section proportional to A2 leading to neutrino trapping inside and outside the core. Thus the proposed mechanism does not work.

The accepted picture of a Type I1 supernova is the following. There is a large envelope of hydrogen enclosing successive layers of helium, carbon, oxygen and silicon. Rese surround an iron-nickel core which is supported by the pressure of a degenerate electron gas with adiabatic index y=4/3. When the core temperature reaches T-10'~photodisintegration of the core nuclei sets in and these are dissociated into neutrons, protons and alpha particles. At a tanperatwe T=l0l0K and density p=lO1Ogm/cm electron captures can occur

and removal of the electron pressure causes the core to collapse. Since neutron @-decay is inhibited at density ~40~gtn/an~and essentially ceases for p>2x10~gm/m~ the core converts into a degenerate neutron gas with adiabatic index 512. Yhen the density reaches nuclear matter density of p=2.5x101 4gm/cm3 the collapse stops and the neutron star is formed; at this point there is a hydrodynamic 'bounce' or pressure wave which spreads outwald from the core carrying energy into the outer layers of the star. At the same tim further neutrinos are released from the core via the (neutral current) neutrino brems~trahlun~process

and the (charged current) modified URCA processes which so closely resemble the p-p and pe-p solar reactions.

Current theories as- (18) that the outgoing shock wave neutronizes material in its path through electron captures

the pressure deficit being balanced by the inverse reaction

caused by neutrinos released fmthe shocked layers. The net result is that the shock wave propagates outward without damping and the outer layers of the star are blown away.

Whether these ideas prove to be correct or not remains to be seen; in the present context the chief interest lies in the fact that every significant reaction rate is proportional to the rate of neutron decay modified by various complicating factors such as high density and (within the degenerate neutron core) high magnetic fields.

55. Synthesis of Neutron-Fich Kuclei

Because of the absence of stable nuclei withmass numbers 5 and 8 and the relative- ly low density at the onset of big bang nucleosynthesis, nucleimore massive than 11B cannot be synthesized in significant abundances in the early universe. Although elements in the range up to the iron peak at A=60 are synthesized by charged particle reactions during the slow progress of stellar evolution thrwgh successive steps of thermonuclear burning from hydrogen to silicon, elements with A>60 can be synthesized only through neutron capture. It is therefore necessary to identify suitable neutron sources.

At this point two time scales must be recognised: namely T~ the mean interval betwerlneutron captures on a givennucleus, and TB the mean @-decay lifetime of nuclei in the reaction chain. kclei synthesized in chains for which T >>T are called (slow) s-process nuclei (19) ; if rc .;ir a we have (rapid) r-procesg nuglei (20). Studi:? of s-process nuclear abundances have led to the identification of the reaction Ne(a,n) 25hig in the convective heliun layers of themally pulsed stars as the principal neutron source (21). However, s-process nucleosynthesis takes place over such vast time scales that the resulting nuclei are confined to that region of the nuclidic chart close to the stability line; thus the precise ratesat which the weak decays proceed are unimportant. Conversely, to synthesize r-process neutron-rich nuclei, extremely intense short-lived neutron sources are required, lasting no more than perhaps a few seconds. Furthermore to reach observed abundances with such a source requires the presence of substantial nmbers of heavy (A=60) seed nuclei which can proceal to higher Z by %-decay.

For these reasons a site for synthesis of r-process nuclei has ken posblated (22) in the deep interior of a supernova near the mass-cut between the forming neutron star and the ejected matter. The mantle is assumd to expand adiabatically frm conditions of peak temperature T =3x101 'K and density po=lol 'gm/cm3 with time de- pendent density determined accor8ing to expo11pntial law P=Poe-t/T where T is a simple multiple of the free-fall time (~ITG~)-'.This n~delresembles the big bang in saw respects except that the presence of a substantial nwhr of species of seed nuclei, perhaps 20 or more, leads to a rore mre complex network of reactions.

It turns out then, as in the big bang, that the resulting abundances of r-process nuclei are detemined essentially by the neutron-proton mass ratio X / at the freeze out tefiperature ~~'10'OK; this in turn is fixed by the rates 8f %he elenen- tary weak reactions C3-36 JOURNAL DE PHYSIQUE

+ e-+p +n+ve' e +n+p+ve' n -tp+e-+Ge Agreenent with observed abundances can be obtained with freeze-out values of X /X in the range 4-8 but only for a very restricted range of values of To and po (237.

There are several objections to this scenario not only in respect of its sensitivity to the initial conditions but particularly because, at an assumed mass ejection rate of 0.2 solar rrasses per supernova, it could lead to over-production of r-process nuclei by factors > lo3. Explosive helium burning in massive stars initiated by the outgoing shock-wave in a super-nova has been suggested as an alternative slte (24). In such a mdel however it is necessary to input the lifetime of each one of same thousands of nuclei participating in the reaction chain; frml the @-stability line up to the neutron drip-line. In these circumstances the highly uncertain values of nuclear ratrix eleri-entsbecome all impartant, and the simple dependence of the process on weak elen~ntaryreactions allied to neutron B-decay is lost.

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