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The Role of Neutron -Decay in Astrophysics

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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 HAL Id: jpa-00224021 https://hal.archives-ouvertes.fr/jpa-00224021 Submitted on 1 Jan 1984 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. JOURNAL DE PHYSIQUE Colloque C3, supplement au n°3, Tome 45, mars 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 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 <X >=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 polari- zability 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 uni- verse (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 equili- brium 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 life- time 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.
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