Large amplitude oscillation of cosmic field that may occur right after inflation and in the decay process of weakly interacting fields gives rise to violent particle production via the parametric resonance. In the large amplitude limit the problem of back reaction against the field oscillation is solved and the energy spectrum of created particles is determined in a semi-classical approximation. For large enough coupling or large enough amplitude the resulting energy spectrum is broadly distributed, implying larger production of high energy particles than what a simple estimate of the reheating temperature due to the Born formula would suggest.
Thermal history after inflation is studied in a chaotic inflation model with supersymmetric couplings of the inflaton to matter fields. The time evolution equation is solved in a formalism that incorporates both the back reaction of particle production and the cosmological expansion. The effect of the parametric resonance gives rise to a rapid initial phase of the inflaton decay followed by a slow second stage of the decay whose rate is given by the Born approximation. Thermalization takes place immediately after the first explosive stage for a medium strength of the coupling among created particles. As an application we calculate the time evolution of the gravitino abundance that is produced by ordinary particles directly created from the inflaton decay, which typically results in a much more enhanced yield than what a naive estimate based on the Born approximation would suggest. ͓S0556-2821͑96͒04216-6͔ PACS number͑s͒: 98.80.Cq
In the mass spectrum of the vapor from grey selenium subliming in the temperat~ue range 102 to 187 "C all possible Sen+ ions between n = 1 and 12 = 8 were detected in measurable quantities. The ions Seab, Seec, Se,+, and SesLarise mainly from ionization of the corresponding parent molecules, which are believed to be clclic. .It 175 "C the composition of the vapor is Se;, ,< 29.0%, See >, 57.57;, Se, >, 11.4%, and Ses >, 2.0%. Thermodynamic data are reported for the sublimation of these molecules. Small amounts of See+ and Selot were also detected.In the condensed state, selenium can exist in a \\:ide variety of different forms. The thermodynamically stable forin a t tempel-atures up to the melting point is grey, metallic, or hexagonal selenium (1, 2). In this variety the selenium atoins forin spiral chains (3, 4) in which adjoining atoms form normal single bonds.Red crystalline selenium is inonoclinic and two forins have been found (6, 6). The form is composed of Sea rings (7). According to Burbanli (7) Vitreous selenium is formed by rapid cooling of inolten selenium. Altl~ough various views on its structure have been proposed (12-18) i t seeins certain that the chain structure found in grey seleniuin exists in this variety but the chains have become enmeshed and intertwined. When it is dissolved in iodine the average length of the selenium chain is about 100 atoms (19). Vitreous seleni~~in transforms to grey selenium, taliing 20 days a t 43", 72 h a t 55", 12 h a t 70" (lo), and 1 h a t 100 O C (20).Red amorphous seleili~lm also contains chains of selenium atoins (21), the spirals being slightly defornled and randomly placed along the axis of the chain (22). Berthelot (23) distinguishes t\\-o varieties of amorphous selenium.Contradicting values have been given for the density of selenium vapor (34-29). I-Iolvever, all results indicate progressive dissociation into sn~aller nlolecules as the temperature rises.Vapor pressures have been measured by several methods (29-3s). Determinations involving the Knudsen technique involve a lino~\~ledge of the vapor composition and ~vill be in error if the incorrect assumption is made. I t has been proposed (30) that below 530 O C the vapor consists of Sea and between 550 and SO0 "C the vapor consists of SeG and Sez in equilibrium. AIetzger (39) has found that the average molecular weight of freely evaporating selenium is consistent with the formula Se5 ,, 6. 0 1 1 the basis of electron diffraction studies on selenium vapor a t Ion-pressures, I-1on.e and Lark-I-Iorovitz (40) propose Ses
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