  Nucleon-nucleon short-range correlations (SRCs) induce a high momentum tail
(HMT) in the single-nucleon momentum distribution function
$n_{\v{k}}^J(\rho,\delta)$ in cold neutron-rich matter. While there are clear
experimental evidences that the SRC/HMT effects are different for neutrons and
protons and their strengths depend strongly on the isospin asymmetry of finite
nuclei mostly based on electron-nucleus scattering experiments, much less is
known experimentally about the SRC/HMT effects in the dense neutron-rich
matter. To facilitate further explorations of SRC/HMT effects in dense
neutron-rich matter especially with heavy-ion reactions involving high-energy
radioactive beams as well as multimessenger observations of neutron stars and
their mergers, by incorporating the SRC-induced HMT in
$n_{\v{k}}^J(\rho,\delta)$ into a Gogny-like energy density functional we study
SRC/HMT effects on the equation of state (EOS) especially its symmetry energy
term and single-nucleon potential in the dense asymmetric nucleonic matter
(ANM). Using a parametrization as a surrogate for the momentum-dependent kernel
in the Gogny-like energy density functional (EDF) we derive analytical
expressions for all components of the ANM EOS and their characteristics (e.g.,
magnitude, slope and curvature as well as nucleon effective mass) at saturation
density $\rho_0$ as well as the momentum-dependent single-nucleon optical
potential in neutron-rich matter using parameters characterizing nuclear
interactions as well as the size, shape and isospin dependence of the HMT at
$\rho_0$. Some consequences of the SRC/HMT effects on properties of neutron
stars are also studied.
