Can Neutrinos Detect the Earth's Core?

To determine whether neutrinos could prove useful in detecting the Earth's core, we examine the probability curves of several scenarios. We create a two-density model with the inner core and the rest of the planet as the mantle. We expect this simple model to be adequate in answering our questions, in that two layers is sufficient to determine the sensitivity of the oscillation and can be generalized to more layers. A detector is placed on one side of the Earth.

Theta_z is the angle the solar neutrino enters the Earth to the detector.
We plot a castle-wall density profile of the Earth through a zenith angle of 0 degrees using the PREM values:

A_mantle= 1.5 e-6 eV^2/MeV
R_core= 6400 km
A_core= 2.5 e-6 eV^2/MeV
R_core= 1200 km

We use matter potential (A) in place of density. A mass density of 3.0 g/cm^3 is equivalent to a matter potential of 5.8 e-7 eV^2/MeV.

The path angle determines the amount of matter the neutrino passes through, so the probability is now a function of zenith angle. We then create contour plots of probability as a function of zenith angle and energy using Matplotlib and adjust the radius and density parameters.

Results

The first plot shows P(theta_z, energy) with the given PREM values.

In the scenario we have adjusted core and mantle density values to
A_mantle = 0.5 e-6 eV^2/MeV
A_core = 4 e-6 eV^2/MeV
while keeping the radius of the core the same. There is a clear difference in the probability density in both the core and the mantle.

The third scenario has an adjusted core radius of R_core = 3200 km, or half the radius of the Earth. It is clear that a neutrino's P2e function changes with the radius of the core. We conclude that we can use neutrinos to detect and measure where a hard boundary exists.