Class ConstDensityMatterSolver๏ƒ

class ConstDensityMatterSolver๏ƒ

Solver class for constant density material.

This class is used to obtain effective mass eigenstates and an effective mixing matrix due to matter effects for neutrinos passing through a block of material of constant density.

The method used here is to first construct the effective Hamiltonian

\[\begin{equation} \frac{1}{2E} Diag(m^2_i) - \sqrt(2)G N_e \mathbf{U}_{ei} \otimes \mathbf{U}_{ie}^\dagger \end{equation}\]
where \( \mathbf{U} \) is the supplied mixing matrix and \( Diag(m^2_i) \) is a diagonal matrix with the specified mass eigenvalues on the diagonal. We then calculate the eigenvalues \( m_i^\prime \) and eigenvectors, summarised in the matrix \( V_{ij} \). These can then be passed to a propagator class to get the oscillation probabilities in the presence of such matter effects.

See Barger for more details.