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.
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