For example, in my PhD thesis I developed a new field theoretic formulation of neutrino oscillations in dense matter which unifies neutrino refraction with non-forward scattering causing oscillation "damping". This fully relativistic approach includes antineutrino degrees of freedom and leads to a kinetic description by a "non-abelian" Boltzmann-like equation for the neutrino and antineutrino density matrices. It accounts for non-linear effects such as neutrino refraction due to self-interactions and Pauli-blocking of mixed neutrino final states. This quantum kinetic formalism can also be applied to other mixing phenomena such as polarization of the microwave background in the ambient plasma, and even to the quantum mechanical measurement problem.
Using the formalism discussed above, Georg Raffelt, Leo Stodolsky ( Max-Planck-Institut für Physik, München), Hans-Thomas Janka (Max Planck Institut für Astrophysik), Steen Hannestad (University of Aarhus) and I calculated the time scale of neutrino flavor conversion in a supernova core as a function of neutrino mixing angles and masses (see recent paper). This conversion can influence the transport properties of the neutrino gas and thus supernova evolution. By numerical simulations of the full non-linear kinetic equations, I also investigated flavor conversion outside the core where neutrino self-interactions are important. This resulted in a more reliable determination of the neutrino mixing parameter range which would render r-process nucleosynthesis in supernovae impossible. These bounds lie in a mass range where neutrinos could serve as hot dark matter and are thus cosmologically important.
Together with Michael Turner (U of C), I developed a simple analytical transport formalism for weakly interacting particles which can also be unstable. By applying it to supernova observations, we derived bounds on mass and lifetime of the tau-neutrino that complement experimental constraints.
Recently, I derived a new sum rule for the nucleon spin density structure function of hot nuclear matter which allows improved estimates of the rather poorly known weak interaction rates in dense nuclear matter. This has important implications for the cooling history of a supernova and its neutrino signal, and for astrophysical bounds on the properties of certain hypothetical particles such as axions. It shows that weak interactions are not strongly suppressed in hot, dense nuclear matter compared to the "naive" lowest order rates which result from treating the medium constituents as free particles. In a rather large collaboration with Wolfgang Keil, Thomas Janka (MPA, Garching), David Schramm,, Michael Turner (U of C), and John Ellis (CERN), we have recently incorporated this new assessment of weak interaction rates in hot nuclear matter into a numerical supernova simulation. As a result, we showed that supernova bounds on the axion mass are relaxed by about a factor of 2.
In contrast to the density structure function, the nucleon spin density structure function has a finite width which is related to the spin fluctuation rate of individual nucleons. This implies a new mode of energy transfer between neutrinos and the nuclear medium which is of comparable importance to ordinary recoil effects. In addition, weak interaction rates depend on spatial correlations of the nuclear spin- and isospin-densities. Thus, accurate measurements of the neutrino signal from a nearby supernova might provide important information on the equation of state of hot nuclear matter. Such measurements might be possible with the next generation neutrino detectors such as Super-Kamiokande which just started operation or the Sudbury Neutrino Observatory which is under construction. Motivated by that, I plan to extend these investigations and do a systematic study of weak interaction rates in nuclear matter using methods of finite temperature field theory. My goal is to treat the temporal and the usually much more familiar spatial dependence of the structure functions on an equal footing for the first time. I believe that this will allow considerable progress in the understanding of the type II supernova phenomenon.
As a first step in this direction, here is a simple
toy model for nucleon spin evolution in a hot
and dense nuclear medium I developed with Georg Raffelt.
A given nucleon is limited to
one-dimensional motion in a distribution of external, spin-dependent
scattering potentials. The figure on the left is an example for
the numerically calculated spin autocorrelation function
in frequency space at a temperature of 30 MeV, where the
external potential varies
between 10 and 30 MeV, depending on the relative orientation
of external and test particle spin. The density of scatterers
for the cases shown is 0.2, 0.4, 0.8, 1.2, 2, 4, and 12
per femtometer in descending order at the left end.
For all plausible parameter combinations mimicking the conditions in a supernova core, the width of the spin density structure function was found to be less than the temperature. This is in contrast with a naive perturbative calculation based on the one-pion exchange potential which overestimates this width and suggests a large suppression of the neutrino opacities by nucleon spin fluctuations.
I am now thinking about a more ambitious calculation of response functions in hot nuclear matter, using quantum Monte Carlo codes that implement realistic nuclear interactions in a truly many body frame work. This work is planned together with Ted Ressell (U of C).
I am performing the theoretical studies mostly in connection with the Sonderforschungsbereich Astroteilchenphysik (particle astrophysics) . To combine such studies with full blown numerical supernova simulations, I collaborate with people from the hydrodynamics group at the Max Planck Institut für Astrophysik, Garching bei München, such as Thomas Janka who is an expert in computational astrophysics.
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