(* Cl- ion Kimball, Ar-center,  16.2.2012 *)
Clear[k1,k2,k3,k4,sig1,sig2,sig3,sig4,c,z,R1,R2,R3,R4,S2,S3];
c = {k1 -> 1.0, k2 -> 1.0, k3 -> 1.0, k4 -> 1.0, sig1 -> 0.3, sig2 -> 0.3, sig3 -> 0.3, sig4 -> 0.3}; z=17.0;

(* He and Neon shell *)
T = 2.25*k1/R1^2+9.0*k2/R2^2 /. c;
ad = Sqrt[3./8.]; 
Vee=3.0*sig1/R1+12.0*sig2/R2+16/(R1+R2)+24*ad/(R1+R2) /. c;
Vne=-3.0*z/R1-8.0*z/(R1+R2);
S2 = R2*4^(1/3);

(* Argon shell, full *)
T = T + 9.0*k3/R3^2 /. c;
Vee = Vee+12.0*sig3/R3+80.0/(S2+R3)+24.0*ad/(S2+R3) /. c;
Vne = Vne-8.35*z/(S2+R3);
S3 = R3*4^(1/3);

func = T + Vee + Vne;

t = FindMinimum[func, {R1,0.08138}, {R2,0.285}, {R3,0.976},{Method -> Automatic},
{MaxIterations -> 500}]

(* Table[N[Vne /. c /. t[[{z-18},2]],10], {z,19,26}]
Table[N[Vee /. c /. t[[{z-18},2]],10], {z,19,26}] *)
N[-(Vee+Vne)/T /. c /. t[[2]],10]
(* Table[N[(S2+R3) /. c /. t[[{z-18},2]],10], {z,19,26}] *)