  A robust potential wherein is embedded the crucial core polarization
interaction is used in the Regge Pole methodology to calculate low energy
electron elastic scattering total cross section (TCS) for the C60 fullerene in
the electron impact energy range 0.02 through 10.0 eV. The energy position of
the characteristic dramatically sharp resonance appearing at the second
Ramsauer Townsend (RT) minimum of the TCS representing stable C60 fullerene
negative ion formation agrees excellently with the measured electron affinity
(EA) of C60 [Huang et al 2014 J. Chem. Phys. 140 224315]. The benchmarked
potential and the Regge-pole method are then used to calculate electron elastic
scattering TCSs for selected fullerenes, from C54 through C240. The TCSs are
found to be characterized generally by RT minima, shape resonances (SRs) and
dramatically sharp resonances representing long lived ground state fullerene
negative ion formation. For the TCSs of C70, C76, C78, and C84 the agreement
between the energy positions of the very sharp resonances, corresponding to the
binding energies (BEs) of the resultant fullerene negative ions, and the
measured EAs is outstanding. Additionally, we extract the BEs of the resultant
fullerene negative ions from our calculated TCSs of the C86, C90 and C92
fullerenes with estimated EAs larger than 3.0 eV by the experiment [Boltalina
et al, 1993 Rapid Commun. Mass Spectrom. 7 1009] as well as of other
fullerenes, including C180 and C240. Most of the TCSs presented in this paper
are the first and only. Our novel approach is general and should be applicable
to other fullerenes as well and complex heavy atoms, such as the lanthanide
atoms. We conclude with a remark on the catalytic properties of the fullerenes
through their negative ions.
