Question

For a two-nucleon system in spin singlet state, the spin is represented through the Pauli matrices \( \sigma_1, \sigma_2 \) for particles 1 and 2, respectively. The value of \( \sigma_1 \cdot \sigma_2 \) (in integer) is \(\underline{\hspace{2cm}}\).

Hint:

For a two-nucleon system in a singlet state, the spin-spin interaction is represented by \( \sigma_1 \cdot \sigma_2 = -3 \).

Answer 1

Correct Answer: -3

In the spin singlet state, the total spin of the system is zero, and the spin operators \( \sigma_1 \) and \( \sigma_2 \) for the two particles are related by: \[ \sigma_1 \cdot \sigma_2 = -1. \] Thus, the value of \( \sigma_1 \cdot \sigma_2 \) is \( -3 \).