Answer to Question #85948 in Atomic and Nuclear Physics for sajita

Question

. A tank of C2Cl4 (containing 37Cl) is used as a neutrino detector to
measure the flux of neutrinos produced in the sun. A neutrino has a
cross-section for interacting with matter of approximately 10 fb.
a. Write down the nuclear decay that occurs when a 37Cl nucleus
interacts with a solar neutrino (Hint: try rearranging beta decay
equations).
b. Assuming there is a material with approximately 1024 protons
per cm3
: what is the probability that the neutrino will interact
when travelling through 10 m of detector?

Answer 1

a) Chlorine decays into argon and an election:

$$^{37}\text{Cl}+v_e\to ^{37}\text{Ar}+e^-,$$

then argon captures elections of specific energies that can be used to detect an interaction with electron neutrino:

$$^{37}\text{Ar}+e^-\to ^{37}\text{Cl}+v_e.$$

b) The probability that the neutrino will interact with a proton increases with energy and depends on cross section (the cross-section actually is proportional to the energy). Calculate it using protons per volume density, cross-section and thickness:

$$P=\rho\sigma z=(1024\text{ cm}^{-3})\cdot (10\cdot 10^{-39}\text{ cm}^2)\cdot 1000\text{ cm}=$$ $$=1.024\cdot 10^{-32}.$$