Instabilities in neutrino systems induced by interactions with scalars

If there are scalar particles of small or moderate mass coupled very weakly to Dirac neutrinos, in a minimal way, then neutrino-anti-neutrino clouds of sufficient number density can experience an instability in which helicities are suddenly reversed. The predicted collective evolution is many orders of magnitude faster than given by cross-section calculations. The instabilities are the analogue of the ``flavor-angle" instabilities (enabled by the Z exchange force) that may drive very rapid flavor exchange among the neutrinos that emerge from a supernova. These exchanges do require a tiny seed in addition to the scalar couplings, but the transition time is proportional to the negative of the logarithm of the seed strength, so that the size of this parameter is comparatively unimportant. For our actual estimates we use a tiny non-conservation of leptons; an alternative would be a neutrino magnetic moment in a small magnetic field. The possibility of a quantum fluctuation as a seed is also discussed. Operating in the mode of putting limits on the coupling constant of the scalar field, for the most minimal coupling scheme, with independent couplings to all three $\nu$, we find a rough limit on the dimensionless coupling constant for a neutrino-flavor independent coupling of $G<10^{-10}$, to avoid the effective number of light neutrinos in the early universe being essentially six. If, on the other hand, we wish to fine-tune the model to give a more modest excess (over three) in the effective neutrino number, as may be needed according to recent WMAP analyses, it is easy to do so. \pacs{13.15.+g}Comment: 10 pages, 4 figures, comments on alternative seeds adde

The multi-angle instability in dense neutrino systems

We calculate rates of flavor exchange within clouds of neutrinos interacting with each other through the standard model coupling, assuming a conventional mass matrix. For cases in which there is an angular dependence in the relation among intensity, flavor and spectrum, we find instabilities in the evolution equations and greatly speeded-up flavor exchange. The instabilities are categorized by examining linear perturbations to simple solutions, and their effects are exhibited in complete numerical solutions to the system. The application is to the region just under the neutrino surfaces in the supernova core.Comment: 9 pages, 3 figure

Speed-up of neutrino transformations in a supernova environment

When the neutral current neutrino-neutrino interaction is treated completely, rather than as an interaction among angle-averaged distributions, or as a set of flavor-diagonal effective potentials, the result can be flavor mixing at a speed orders of magnitude faster than that one would anticipate from the measured neutrino oscillation parameters. It is possible that the energy spectra of the three active species of neutrinos emerging from a supernova are nearly identical.Comment: 8 pages, 4 figure

Plasma effects on resonant fusion

We investigate the effects of plasma interactions on resonance-enhanced fusion rates in stars. Starting from basic principles we derive an expression for the fusion rate that can serve as a basis for discussion of approximation schemes. The present state-of-the-art correction algorithms, based on the classical correlation function for the fusing particles and the classical energy shift for the resonant state, do not follow from this result, even as an approximation. The results of expanding in a perturbation solution for the case of a weakly coupled plasma are somewhat enlightening. But at this point we are at a loss as to how to do meaningful calculations in systems with even moderate plasma coupling strength. Examples where this can matter are: the effect of a possible low energy $^{12}$ C +$^{12}$ C resonance on X-ray bursts from accreting neutron stars or on supernova 1A simulations; and the calculation of the triple $\alpha$ rate in some of the more strongly coupled regions in which the process enters, such as accretion onto a neutron star.Comment: 10 pages, 1 figur

Evolution speed in some coupled-spin models

We investigate the time evolution of some models with N spins and pairwise couplings, for the case of large N, in order to compare evolution times with "speed limit" minima derived in the literature. Both in a (symmetric) case with couplings of the same strength between each pair and in a case of broken symmetry, the times necessary for evolution to a state in which the simplest initial state has evolved into a nearly orthogonal state are proportional to 1/N, as is the speed limit time. However the coefficient in the broken symmetry case comes much closer to the speed limit value. Introducing a different criterion for evolution speed, based on macroscopic changes in occupation, we find a corresponding enhancement in rates in the asymmetric case as compared to the symmetric case.Comment: 6 pages, 4 figures. Correction of numerous mistakes. One model made simpler. A superior algorithm used to solve the second exampl