  The process of $\nu \bar{\nu}$ radiation due to interaction of electrons with
phonons in the crust of a cooling neutron star is studied with the consistent
account of an electromagnetic coupling between electrons in the medium. The
wavelength of radiated neutrinos and antineutrinos is typically much larger
than the electron Debye screening distance in the medium, and therefore plasma
polarization substantially modifies the effective weak current of the electron.
Is shown, that under above conditions plasma polarization screens totally a
vector weak interaction of the electron with a neutrino field. As a result, the
$\nu \bar{\nu}$ emissivity is less in approximately 2.23 times than previously
estimated.
