  We present the results of 3D particle-in-cell (PIC) simulations that explore
relativistic magnetic reconnection in pair plasma with strong synchrotron
cooling and a small mass fraction of non-radiating ions. Our results
demonstrate that the structure of the current sheet is highly sensitive to the
dynamic efficiency of radiative cooling. Specifically, stronger cooling leads
to more significant compression of the plasma and magnetic field within the
plasmoids. We demonstrate that ions can be efficiently accelerated to energies
exceeding the plasma magnetization parameter, $\gg\sigma$, and form a hard
power-law energy distribution, $f_i\propto \gamma^{-1}$. This conclusion
implies a highly efficient proton acceleration in the magnetospheres of young
pulsars. Conversely, the energies of pairs are limited to either $\sigma$ in
the strong cooling regime or the radiation burnoff limit, $\gamma_{\rm syn}$,
when cooling is weak. We find that the high-energy radiation from pairs above
the synchrotron burnoff limit, $\varepsilon_c \approx 16$ MeV, is only
efficiently produced in the strong cooling regime, $\gamma_{\rm syn} < \sigma$.
In this regime, we find that the spectral cutoff scales as $\varepsilon_{\rm
cut}\approx \varepsilon_c (\sigma/\gamma_{\rm syn})$, and the highest energy
photons are beamed along the direction of the upstream magnetic field,
consistent with the phenomenological models of gamma-ray emission from young
pulsars. Furthermore, our results place constraints on the reconnection-driven
models of gamma-ray flares in the Crab Nebula.
