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Tuesday, February 7, 2017

Paulis Hypothesis of Beta Decay

Pauli introduced concept of third particle, a neutral particle which gets emitted in β⁻decay. This particle has the generic name of Neutrino.

The total energy is shared by 3 particles

The recoil nucleus
The Electron
The Neutrino

Because of its comparatively great mass, the recoil energy of Nucleus is very small and nearly all Kinetic Energy is shared between the Beta particle and the Neutrino.

In addition to laws of conservation of charge and energy, we must also apply the laws of conservation Linear and angular momentum to every nuclear process. Taking our reference system as the parent nucleus at rest, the vector sum of Linear Momenta of the recoil nucleus, the beta particle and neutrino must be zero.

To conserve angular momentum in β⁻decay, we note that parent and daughter nuclei are isobars; i.e. they have equal number of nucleons. Hence, the total change in nuclear angular momenta will be either zero or an integral multiple of ℏ.

The beta particle has an intrinsic spin angular momenta of 1/2ℏ.The vector sum of angular momenta of Neutrino and beta particle will be either zero or one in units of ℏ.

The present accepted theory, which is supported by experimental evidence shows that there are two types of neutrino or two components of Neutrino. It has been found that the axis of spin of neutrino is parallel to its direction of motion; one type spins according to the left hand rule with respect to its direction of motion as its axis, the other component spins according to right hand rule.

The first type is usually called neutrino represented by symbol 𝜈, the second type is called antineutrino.
 
The spin vector of neutrino points opposite to direction of its motion.

The spin vector of anti neutrino points in the direction of its motion.

Another way of saying this is that the helicity of neutrino is negative and that of anti neutrino is positive or one has right handed helicity and other has left handed helicity.