Eur. Phys. J. C 20, 507-515 (2001)
DOI: 10.1007/s100520100687

Neutrino oscillations with three flavors in matter of varying density

T. Ohlsson^{1, 2} and H. Snellman<sup>2

1</sup>  Institut für Theoretische Physik, Physik Department, Technische Universität München, James-Franck-Strasse, 85748 Garching bei München, Germany
²  Division of Mathematical Physics, Theoretical Physics, Department of Physics, Royal Institute of Technology, 100 44 Stockholm, Sweden

tohlsson@physik.tu-muenchen.de or tommy@theophys.kth.se
snell@theophys.kth.se

(Received: 23 March 2001 / Published online: 8 June 2001 -© Springer-Verlag / Società Italiana di Fisica 2001)

Abstract
In this paper, we discuss the evolution operator and the transition probabilities expressed as functions of the vacuum mass squared differences, the vacuum mixing angles, and the matter density parameter for three flavor neutrino oscillations in matter of varying density in the plane wave approximation. The applications of this to neutrino oscillations in a model of the earth's matter density profile, step function matter density profiles, constant matter density profiles, linear matter density profiles, and finally in a model of the sun's matter density profile are discussed. We show that for matter density profiles which do not fluctuate too much, the total evolution operator consisting of n operators can be replaced by one single evolution operator in the semi-classical approximation.

© Società Italiana di Fisica, Springer-Verlag 2001