THEORY OF QUASI-EQUILIBRIUM NUCLEOSYNTHESIS AND APPLICATIONS TO MATTER EXPANDING FROM HIGH-TEMPERATURE AND DENSITY

Our first purpose is construction of a formal theory of quasi-equilibr ium. We define quasi-equilibrium, in its simplest form, as statistical equilibrium in the face of an extra constraint on the nuclear populat ions. We show that the extra constraint introduces a uniform translati on of the chemical potentials for the heavy nuclei and derive the abun dances in terms of it. We then generalize this theory to accommodate a ny number of constraints. For nucleosynthesis, the most important cons traint occurs when the total number of heavy nuclei Y-h within a syste m of nuclei differs from the number that would exist in nuclear statis tical equilibrium (NSE) under the same conditions of density and tempe rature. Three situations of high relevance are (1) silicon burning, wh erein the total number of nuclei exceeds but asymptotically approaches the NSE number; (2) alpha-rich freezeout expansions of high entropy, wherein Y-h is less than the NSE number; and (3) expansions from high temperature of low-entropy matter, in which Y-h exceeds the NSE number . These are of importance, respectively, within (1) supernova shells, (2) Type II supernova cores modestly outside the mass cut, and (3) Typ e Ia supernova cores in near-Chandrasekhar-mass events. Our next goal is the detailed analysis of situation (2), the high-entropy alpha-rich neutron-rich freezeout. We employ a nuclear reaction network, which w e integrate, to compare the actual abundances with those obtained at t he same thermal conditions by the quasi-equilibrium (QSE) theory and b y the NSE theory. For this detailed comparison, we choose a high-entro py photon-to-nucleon ratio phi = 6.8, for which we conduct expansions at initial bulk neutron excess eta(0) = 0.10. We demonstrate that the abundance populations, as they begin expansion and cooling from temper ature 10 x 10(9) K, are characterized by three distinct phases: (1) NS E, (2) QSE having Y-h smaller than the NSE value, and (3) final reacti on rate-dependent freezeout modifications of the QSE. We demonstrate t hat the true final abundances are well approximated by the QSE distrib ution near the freezeout temperature T-9f = 4.0. During the expansion, the QSE distribution changes shape continuously in ways that are inde pendent of the reaction cross sections of the heavy nuclei with free l ight particles. It is this changing shape, rather than ''nuclear flows ,'' that establish the abundance pattern. The abundance pattern is act ually determined by the parameter Y-h and the degree to which it diffe rs from the NSE value owing to the slowness with which light particles can be assembled into heavy nuclei (A greater than or equal to 12). W e also detail the nature and magnitude of the freezeout corrections to the QSE distribution. The entire distribution depends less upon the v alues of heavy-element cross sections than has been heretofore thought . Our third goal is to survey the alpha-rich freezeout. We do this by less complete analysis of nine different expansions determined by the matrix of three distinct entropies (phi = 1.7, 6.8, and 17) and three distinct initial neutron excesses (eta(0) = 0.003, 0.10, and 0.1667). The trends are easily comprehended in terms of the concept of quasi-eq uilibrium, whereas they are not understandable in terms of either NSE or in terms of reaction rates. This secures for the QSE concept a majo r diagnostic capability within nucleosynthesis theory. We delineate th e key trends and also remark on the ways that order arises from disord er in this complex system. We conclude with a discussion of how such s ystems assemble heavy nuclei.