  The cosmic-ray flux of antiprotons is measured with high precision by the
space-borne particle spectrometers AMS-02.Its interpretation requires a correct
description of the dominant production process for antiprotons in our Galaxy,
namely, the interaction of cosmic-ray proton and helium with the interstellar
medium. In the light of new cross section measurements by the NA61 experiment
of $p + p \rightarrow \bar{p} + X$ and the first ever measurement of $p +
\mathrm{He} \rightarrow \bar{p} + X$ by the LHCb experiment, we update the
parametrization of proton-proton and proton-nucleon cross sections.We find that
the LHCb $p$He data constrain a shape for the cross section at high energies
and show for the first time how well the rescaling from the $pp$ channel
applies to a helium target. By using $pp$, $p$He and $p$C data we estimate the
uncertainty on the Lorentz invariant cross section for $p + \mathrm{He}
\rightarrow \bar{p} + X$. We use these new cross sections to compute the source
term for all the production channels, considering also nuclei heavier than He
both in cosmic rays and the interstellar medium. The uncertainties on the total
source term are at the level of $\pm20$% and slightly increase below antiproton
energies of 5 GeV. This uncertainty is dominated by the $p+p \rightarrow
\bar{p} + X$ cross section, which translates into all channels since we derive
them using the $pp$ cross sections. The cross sections to calculate the source
spectra from all relevant cosmic-ray isotopes are provided in the Supplemental
Material. We finally quantify the necessity of new data on antiproton
production cross sections, and pin down the kinematic parameter space which
should be covered by future data.
