We have determined integral and differential elastic
cross sections
for positron scattering with atomic F and F2 molecules
from 0.01 to 1000 eV with different theoretical approaches. Higher
order polarizabilities were successively considered in the scattering
potential, and we observed that the differential and integral cross
sections converge only when the pure dipole second hyperpolarization
level is taken into account, demonstrating the importance of the hyperpolarization
effects on the low energy positron scattering dynamics. Ramsauer structures
were found for both targets, and in the particular case of the F atom,
the effect of its quadrupole moment proved to be relevant around the
position of the Ramsauer minimum, which was determined together with
the scattering length for each of the adopted polarization schemes.
A relation of these quantities with the matching radius between the
correlation and polarization interactions is also discussed. Agreement
between the model potential and ab initio cross sections for the lowest
level of target polarization is found for F2. Since there
is no previous theoretical or experimental determination of cross
sections for these targets, we compared the differential cross sections
of F2 with experimental data available for N2 and O2 and found reasonable agreement.