If the Fermi energy of a neutron inside a nucleus is 38 MeV,what is the Fermi momentum?

Question

Quizplus · Accepted Answer

The Fermi energy ($E_F$) is related to the Fermi momentum ($p_F$) through the relativistic energy-momentum relation: $E_F^2 = p_F^2c^2 + m^2c^4$, where $m$ is the rest mass of the neutron and $c$ is the speed of light. Given $E_F = 38$ MeV and knowing the rest mass energy of a neutron is approximately 939 MeV, we can solve for $p_F$. However, for high energy particles like a neutron in a nucleus, the kinetic energy ($E_F$) is much smaller than the rest mass energy, so the Fermi momentum can be approximated directly from the Fermi energy without explicitly solving the equation. The correct answer, based on the energy-momentum relation and typical values for neutron mass and energies involved in nuclear physics, is approximately 270 MeV/c.

If the Fermi Energy of a Neutron Inside a Nucleus