Diffusion Coefficients of Nucleons in the Inhomogeneous Big Bang Model
There is a strong possibility that a first order QCD phase transition from the quark-gluon plasma to the confined hadronic matter had occurred in the early universe when the temperature was about 100 MeV. This phase transition might have produced isothermal baryon number fluctuations [1,2,3]. Applegate and Hogan [2,3] have suggested that the characteristic size of these fluctuations could be such that protons would not be able to diffuse across them before the onset of nucleosynhthesis, but the neutrons would as they have no electrical charge and therefore suffer less scattering. Their calculations have shown that the difference in the mean free paths of neutrons and protons and the resultant diffusive segregation influences the formation of the light elements very significantly.In ref.  the diffusion coeffficients were calculated using a mobility formula and the Einstein relation between mobility and the diffusion coefficient . We calculate the diffusion coefficients in the framework of relativistic kinetic theory  in the temperature range 108 ≤ T ≤ 5.109 °K, assuming all particles to be classical. For these temperatures neutrons and protons are no longer in equilibrium with respect to weak interactions and as a result they retain their identity for diffusive segregation to take place.Neutrons are scattered by electrons through the interaction of their magnetic moments and by protons due to nuclear interaction.Protons,on the other hand, undergo Coulomb scattering by electrons and are also scattered by neutrons.With these elementary cross-sections as input we calculate the neutron-electron and neutron-proton diffusion coefficients using the first order Chapman-Enskog expressions .
KeywordsDiffusion Coefficient Early Universe Anomalous Magnetic Moment Einstein Relation Hadronic Matter
Unable to display preview. Download preview PDF.
- E. M. Lifshitz and L. P. Pitaevskii, Physical Kinetics( Pergamon Press, Oxford, 1981 ).Google Scholar
- S. R. de Groot, W. A. van Leeuwen and Ch. G. van Weert,Relativistic Kinetic Theory (North Holland,Amsterdam,1980)Google Scholar
- S. Weinberg,Gravitation and Cosmology (Wiley,New York, 1972).Google Scholar
- D. N. Schramm private communication.Google Scholar