Fermi-Dirac Gases

Abstract

An atomic nucleus of Helium consists of a gas of 0.18 nucleons in a volume of 1 fm³ (1fm = 10⁻¹³cm). In this system, we can find two kinds of nucleons (protons And neutrons) with spin S=1/2 and their masses, m _n ≈ 1GeV, may be considered equal. Compute the Fermi energy for the system and comment about its nature at the ambient temperature. Assume that the particles are independent with a single particle energy

$$\varepsilon = \frac{{{p^2}}}{{2{m_n}}}$$

where p is the absolute value of the momentum. Also, make use of: h=7×10⁻²⁴GeVS, 10⁻¹⁴cm≈7×10⁻²⁵s, k=8.61×10⁻⁵eV/K