In the Fermi Gas model of the nucleus. protons and neutrons till the available momentum states, up to some maximum "Fermi" momentum. The number of momentum states is Each moment um state can accept 2 nucleons of each species (neutron or proton). Explain why this is true. Assuming V = (4/3)piR3 and R = R0A1/3, for a nucleus with Z = S. the maximum momentum is then P max = h/R0 (9pi/8) For a reasonable value of R0 show that the most energetic nucleon is non relativist (i.e. has Lorentz factor close to 1). (h = 197 MeV/c fin).
Explanation / Answer
(a) According to fermi gas modal, the nucleons having half integral spins (fermions). i.e spin = 1/2 h(bar) they obeay uncertainty principle, hence the momentum space can accept 2 nucleons in each state. (b) the feimi energy Ef = P(max)/ 2M(neutron) = 33 MeV