Effects of Atomic-Scale Electron Density Profile and a Fast and Efficient Iteration Algorithm for Matter Effect of Neutrino Oscillation

Mihai Horoi,Adam Zettel

doi:10.3390/universe6010016

Abstract

In a recent article, we noticed that the electron density in condensed matter exhibits large spikes close to the atomic nuclei. We showed that the peak magnitude of these spikes in the electron densities, 3–4 orders larger than the average electron plasma density in the Sun’s core, have no effect on the neutrino emission and absorption probabilities or on the neutrinoless double beta decay probability. However, it was not clear if the effect of these spikes is equivalent to that of an average constant electron density in matter. We investigated these effects by a direct integration of the coupled Dirac equations describing the propagation of flavor neutrinos into, through, and out of the matter. We proposed a new iteration-based algorithm for computing the neutrino survival/appearance probability in matter, which we found to be at least 20 times faster than some direct integration algorithms under the same accuracy. With this method, we found little evidence that these spikes affect the standard oscillations probabilities. In addition, we show that the new algorithm can explain the equivalence of using average electron densities instead of the spiked electron densities. The new algorithm is further extended to the case of light sterile neutrinos.

Highlights

The results of the solar and atmospheric neutrino oscillation experiments were recognized by a recent Nobel prize
These effects were mostly considered in electron plasma [4,5], such as the Sun or supernovae, and their use is extended to condensed matter, such as the Earth crust and inner layers [6,7,8]
The results show that 85% of the electron density in the cell resides in the spikes, while only 15% is located in the volume that has lower-than-average density

Summary

Introduction

The results of the solar and atmospheric neutrino oscillation experiments were recognized by a recent Nobel prize. The mixing of the neutrino mass eigenstates in vacuum and in dense matter seem to be well established in describing the propagation of neutrinos from source to detecting devices These effects were mostly considered in electron plasma [4,5], such as the Sun or supernovae, and their use is extended to condensed matter, such as the Earth crust and inner layers [6,7,8]. We investigate if the results of this approach (see Reference [9]) can be extended to the analysis of the effects of nonadiabatic transitions of the neutrinos through condensed matter, where the electron densities near the atomic nuclei are orders of magnitude larger than those in the Sun’s core. We use the evolution of the flavor amplitudes (see Equation (11) below), avoiding the complicated evolution of the fictitious in-medium mass eigenstates

Neutrino Oscillations in Condensed Matter

The Iterations Algorithm

The Connection to the Integration Method

The Case of Light Sterile Neutrinos

Findings

Conclusions