  We use the rapid binary stellar evolution code BINARY_C to estimate the rate
of merging neutron stars with numerous combinations of envelope ejection
efficiency and natal kick dispersion. We find a peak in the local rate of
merging neutron stars around $\alpha \approx 0.3$$-$$0.4$, depending on the
metallicity, where $\alpha$ is the efficiency of utilising orbital energy to
unbind the envelope. The peak height decreases with increasing electron-capture
supernova kick dispersion $\sigma_\mathrm{ECSN}$. We explain the peak as a
competition between the total number of systems that survive the
common-envelope phase increasing with $\alpha$ and their separation, which
increases with $\alpha$ as well. Increasing $\alpha$ reduces the fraction of
systems that merge within a time shorter than the age of the Universe and
results in different mass distributions for merging and non-merging double
neutron stars. This offers a possible explanation for the discrepancy between
the Galactic double neutron star mass distribution and the observed massive
merging neutron star event GW190425. Within the
$\alpha$$-$$\sigma_\mathrm{ECSN}$ parameter space that we investigate, the rate
of merging neutron stars spans several orders of magnitude up to more than
$1\times 10^{3} \, \mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$ and can be higher than
the observed upper limit or lower than the observed lower limit inferred thus
far from merging neutron stars detected by gravitational waves. Our results
stress the importance of common-envelope physics for the quantitative
prediction and interpretation of merging binary neutron star events in this new
age of gravitational wave astronomy.
