  The hydrogen atoms penetrate the heliosphere from the local interstellar
medium, and while being ionized, they form the population of pickup protons.
The distribution of pickup protons is modified by the adiabatic heating
(cooling) induced by the solar wind plasma compression (expansion). In this
study, we emphasize the importance of the adiabatic energy change in the inner
heliosheath that is usually either neglected or considered improperly. The
effect of this process on the energy and spatial distributions of pickup
protons and energetic neutral atoms (ENAs), which originate in the charge
exchange of pickup protons, has been investigated and quantified using a
kinetic model. The model employs the global distributions of plasma and
hydrogen atoms in the heliosphere from the simulations of a
kinetic-magnetohydrodynamic model of solar wind interaction with the local
interstellar medium. The findings indicate that the adiabatic energy change is
responsible for the broadening of the pickup proton velocity distribution and
the significant enhancement of ENA fluxes (up to $\sim$5 and $\sim$20 times in
the upwind and downwind directions at energies $\sim$1-2 keV for an observer at
1 au). It sheds light on the role of adiabatic energy change in explaining the
discrepancies between the ENA flux observations and the results of numerical
simulations.
