  The long-standing paradox of the linear polarization signal of the Na i D1
line was recently resolved by accounting for the atom's hyperfine structure and
the detailed spectral structure of the incident radiation field. That modeling
relied on the simplifying angle-averaged (AA) approximation for partial
frequency redistribution (PRD) in scattering, which potentially neglects
important angle-frequency couplings. This work aims at evaluating the
suitability of a PRD-AA modeling for the D1 and D2 lines through comparisons
with general angle-dependent (AD) PRD calculations, both in the absence and
presence of magnetic fields. We solved the radiative transfer problem for
polarized radiation in a one-dimensional semi-empirical atmospheric model with
microturbulent and isotropic magnetic fields, accounting for PRD effects,
comparing PRD-AA and PRD-AD modelings. The D1 and D2 lines are modeled
separately as two-level atomic system with hyperfine structure. The numerical
results confirm that a spectrally structured radiation field induces linear
polarization in the D1 line. However, the PRD-AA approximation greatly impacts
the Q/I shape, producing an antisymmetric pattern instead of the more symmetric
PRD-AD one, while presenting a similar sensitivity to magnetic fields between
10 and 200 G. Under the PRD-AA approximation, the Q/I profile of the D2 line
presents an artificial dip in its core, which is not found for the PRD-AD case.
We conclude that accounting for PRD-AD effects is essential to suitably model
the scattering polarization of the Na i D lines. These results bring us closer
to exploiting the full diagnostic potential of these lines for the elusive
chromospheric magnetic fields.
