  The energy of a free gas of neutrons and protons is well known to be
approximately isospin parabolic with a negligibly small quartic term of only
$0.45$ MeV at the saturation density of nuclear matter $\rho_0=0.16/\rm{fm}^3$.
Using an isospin-dependent single-nucleon momentum distribution including a
high (low) momentum tail (depletion) with its shape parameters constrained by
recent high-energy electron scattering and medium-energy nuclear
photodisintegration experiments as well as the state-of-the-art calculations of
the deuteron wave function and the equation of state of pure neutron matter
near the unitary limit within several modern microscopic many-body theories, we
show for the first time that the kinetic energy of interacting nucleons in
neutron-rich nucleonic matter has a significant quartic term of
$7.18\pm2.52\,\rm{MeV}$. Such a large quartic term has significant
ramifications in determining the equation of state of neutron-rich nucleonic
matter using both terrestrial and astrophysical observables.
