Several questions about description of pair_style eam in the doc page

Dear Lammps users,
I want to slightly modify the Au_u3.eam potential file which is in the potential folder of LAMMPS package. But three problems about description of pair_style eam command and Au_u3.eam file confused me. Could you please help me?
(1) The effective charge Z(r) is listed from line 104 to line 203 in Au_u3.eam. According to the doc page, the individual Z(r) values are for r=0, dr, 2*dr,...(Nr-1)*dr. But if I want to calculate the pair potential term by the equation r*phi=27.2*0.529*Zi*Zj, the value of phi at position r=0 will be infinite. It seems no matter how much Z(r=0) is, phi(r=0) is infinite. Could you please tell me how to calculate phi(r=0)?
(2) According to the original paper Foiles etc., PRB 33 (1986) 7983, for pure Au materials, the effective charge is expressed as Z(r) =11*(1+0.1269*r*r)*exp(-1.4475*r), and the pair repulsion potential is given by phi(r)=Z(r)*Z(r)/r. But according to the doc page of pair_style eam command in LAMMPS manual, the pair potential term is calculated via the formula r*phi=27.2 * 0.529 * Zi * Zj, i.e. phi(r)=27.2*0.529*79*79/r for pure Au. I do not know whether these two methods are consistent with each other in calculating phi and why is that?
(3) I thought Nr*dr should equal cutoff. But here in Au_u3.eam, it does not, which obviously can be seen from that 500*1.1212121212121229e-02 does not equal but is greater than 5.5500000000000114e+00. Could you tell me why?
Any help would be much appreciated!

With My Best Regards


Wenqiang Liu