Li2_Na2.nb

(* singly charged ions from Be+ to Na+ 10.09.2012 *)
c1={k1 -> 1.0, k2 -> 1.0, s1 -> 0.3, s2 -> 0.3};
Z = 4.0;
T=2.25*k1/P^2+1.125*k2/Q^2;
Vne=-3*Z/P-Z/(P+Q);
Vee=2/(P+Q)+3*s1/P;
func=T+Vne+Vee;
func = func /. c1;
N[t=FindMinimum[func, {P,0.55},{Q,3.1}],10]
u = t[[2]];
(* Vne *)
N[Vne /. u /. c1, 10]
(* Vee *)
N[Vee /. u /.c1, 10]
(* Virial ratio *)
N[-(Vne+Vee)/T /. u /. c1, 10]

plot1=Graphics[{
Circle[{0,0},P],
Circle[{P+Q,0},Q],
Disk[{0,0},0.1]}] /. u;

Show[plot1,{AspectRatio->Automatic, Frame -> True, Axes -> True, GridLines -> Automatic,
PlotRange -> {{-4,4},{-4,4}}}]

[Graphics:Images/Li2_Na2_gr_5.gif]

Z = 5.0;
T=2.25*k1/P^2+2.25*k2/Q^2;
Vne=-3*Z/P-2*Z/(P+Q);
Vee=4/(P+Q)+3*s1/P+0.5/(P+Q);
func=T+Vne+Vee;
func = func /. c1;
N[t=FindMinimum[func, {P,0.40},{Q,1.9}],10]
u = t[[2]];
(* Vne *)
N[Vne /. u /. c1, 10]
(* Vee *)
N[Vee /. u /.c1, 10]
(* Virial ratio *)
N[-(Vne+Vee)/T /. u /. c1, 10]

plot1=Graphics[{
Circle[{0,0},P],
Circle[{P+Q,0},Q],Circle[{-P-Q,0},Q],
Disk[{0,0},0.1]}] /. u;

Show[plot1,{AspectRatio->Automatic, Frame -> True, Axes -> True, GridLines -> Automatic,
PlotRange -> {{-4,4},{-4,4}}}]

[Graphics:Images/Li2_Na2_gr_11.gif]

Z = 6.0;
T=2.25*k1/P^2+3*1.125*k2/Q^2;
Vne=-3*Z/P-3*Z/(P+Q);
Vee=6/(P+Q)+3*s1/P+3/(Sqrt[3]*(P+Q));
func=T+Vne+Vee;
func = func /. c1;
N[t=FindMinimum[func, {P,0.31},{Q,1.39}],10]
u = t[[2]];
(* Vne *)
N[Vne /. u /. c1, 10]
(* Vee *)
N[Vee /. u /.c1, 10]
(* Virial ratio *)
N[-(Vne+Vee)/T /. u /. c1, 10]

plot1=Graphics[{
Circle[{0,0},P],
Circle[{P+Q,0},Q],Circle[{-0.5*(P+Q),0.866*(P+Q)},Q],
Circle[{-0.5*(P+Q),-0.866*(P+Q)},Q],Disk[{0,0},0.1]}] /. u;

Show[plot1,{AspectRatio->Automatic, Frame -> True, Axes -> True, GridLines -> Automatic,
PlotRange -> {{-4,4},{-4,4}}}]

[Graphics:Images/Li2_Na2_gr_17.gif]

Z = 7.0;
T=2.25*k1/P^2+4*1.125*k2/Q^2;
Vne=-3*Z/P-4*Z/(P+Q);
Vee=8/(P+Q)+3*s1/P+6/(4*(P+Q)/Sqrt[6]);
func=T+Vne+Vee;
func = func /. c1;
N[t=FindMinimum[func, {P,0.26},{Q,1.39}],10]
u = t[[2]];
(* Vne *)
N[Vne /. u /. c1, 10]
(* Vee *)
N[Vee /. u /.c1, 10]
(* Virial ratio *)
N[-(Vne+Vee)/T /. u /. c1, 10]

plot1=Graphics[{
Circle[{0,0},P],
Circle[{P+Q,0},Q],Circle[{-0.333*(P+Q),0.943*(P+Q)},Q],{Dashing[{0.02,0.02}],
Circle[{-0.3333*(P+Q),-0.471*(P+Q)},Q]},Disk[{0,0},0.1]}] /. u;

Show[plot1,{AspectRatio->Automatic, Frame -> True, Axes -> True, GridLines -> Automatic,
PlotRange -> {{-4,4},{-4,4}}}]

[Graphics:Images/Li2_Na2_gr_23.gif]

Z = 8.0;
T=2.25*k1/P^2+5*1.125*k2/Q^2;
Vne=-3*Z/P-5*Z/(P+Q);
Vee=10/(P+Q)+3*s1/P+3*s2/Q+9/(4*(P+Q)/Sqrt[6]);
func=T+Vne+Vee;
func = func /. c1;
N[t=FindMinimum[func, {P,0.22},{Q,0.9}],10]
u = t[[2]];
(* Vne *)
N[Vne /. u /. c1, 10]
(* Vee *)
N[Vee /. u /.c1, 10]
(* Virial ratio *)
N[-(Vne+Vee)/T /. u /. c1, 10]

plot1=Graphics[{
{GrayLevel[0.6],Disk[{P+Q,0},Q]},Circle[{P+Q,0},Q],Circle[{0,0},P],
Circle[{-0.333*(P+Q),0.943*(P+Q)},Q],{Dashing[{0.02,0.02}],
Circle[{-0.3333*(P+Q),-0.471*(P+Q)},Q]},Disk[{0,0},0.1]}] /. u;

Show[plot1,{AspectRatio->Automatic, Frame -> True, Axes -> True, GridLines -> Automatic,
PlotRange -> {{-4,4},{-4,4}}}]

[Graphics:Images/Li2_Na2_gr_29.gif]

Z = 9.0;
T=2.25*k1/P^2+6*1.125*k2/Q^2;
Vne=-3*Z/P-6*Z/(P+Q);
Vee=12/(P+Q)+3*s1/P+2*3*s2/Q+13/(4*(P+Q)/Sqrt[6]);
func=T+Vne+Vee;func = func /. c1;
N[t=FindMinimum[func, {P,0.19},{Q,0.8}],10]
u = t[[2]];
(* Vne *)
N[Vne /. u /. c1, 10]
(* Vee *)
N[Vee /. u /.c1, 10]
(* Virial ratio *)
N[-(Vne+Vee)/T /. u /. c1, 10]

plot1=Graphics[{
{GrayLevel[0.6],Disk[{P+Q,0},Q],Disk[{-0.333*(P+Q),0.943*(P+Q)},Q]},
Circle[{0,0},P],
{Dashing[{0.02,0.02}],
Circle[{-0.3333*(P+Q),-0.471*(P+Q)},Q]},Circle[{-0.333*(P+Q),0.943*(P+Q)},Q],Circle[{P+Q,0},Q],Disk[{0,0},0.1]}] /. u;

Show[plot1,{AspectRatio->Automatic, Frame -> True, Axes -> True, GridLines -> Automatic,
PlotRange -> {{-4,4},{-4,4}}}]

[Graphics:Images/Li2_Na2_gr_35.gif]

plot2=Graphics[{
{GrayLevel[0.6],Disk[{0,0.943*(P+Q)},Q],Disk[{0,0},Q]},
Circle[{0,0.943*(P+Q)},Q],Circle[{0,0},P],Circle[{-0.82*(P+Q),-0.471*(P+Q)},Q],
Circle[{0.82*(P+Q),-0.471*(P+Q)},Q],{Dashing[{0.02,0.02}],Circle[{0,0},Q]},Disk[{0,0},0.1]}] /. u;

Show[plot2,{AspectRatio->Automatic, Frame -> True, Axes -> True, GridLines -> Automatic,
PlotRange -> {{-4,4},{-4,4}}}]

[Graphics:Images/Li2_Na2_gr_37.gif]

Z = 10.0;
T=2.25*k1/P^2+7*1.125*k2/Q^2;
Vne=-3*Z/P-7*Z/(P+Q);
Vee=14/(P+Q)+3*s1/P+3*3*s2/Q+18/(4*(P+Q)/Sqrt[6]);
func=T+Vne+Vee;func = func /. c1;
N[t=FindMinimum[func, {P,0.16},{Q,0.7}],10]
u = t[[2]];
(* Vne *)
N[Vne /. u /. c1, 10]
(* Vee *)
N[Vee /. u /.c1, 10]
(* Virial ratio *)
N[-(Vne+Vee)/T /. u /. c1, 10]

plot1=Graphics[{
{GrayLevel[0.6],Disk[{-0.333*(P+Q),0.943*(P+Q)},Q],
Disk[{-0.3333*(P+Q),-0.471*(P+Q)},Q]},Circle[{0,0},P],
{Dashing[{0.02,0.02}],
Circle[{-0.3333*(P+Q),-0.471*(P+Q)},Q]},Circle[{-0.333*(P+Q),0.943*(P+Q)},Q],Circle[{P+Q,0},Q],Disk[{0,0},0.1]}] /. u;

Show[plot1,{AspectRatio->Automatic, Frame -> True, Axes -> True, GridLines -> Automatic,
PlotRange -> {{-4,4},{-4,4}}}]

[Graphics:Images/Li2_Na2_gr_43.gif]

Z = 11.0;
T=2.25*k1/P^2+4*2.25*k2/Q^2;
Vne=-3*Z/P-8*Z/(P+Q);
Vee=16/(P+Q)+3*s1/P+3*4*s2/Q+6*4/(4*(P+Q)/Sqrt[6]);
func=T+Vne+Vee;func = func /. c1;
N[t=FindMinimum[func, {P,0.14},{Q,0.62}],10]
u = t[[2]];
(* Vne *)
N[Vne /. u /. c1, 10]
(* Vee *)
N[Vee /. u /.c1, 10]
(* Virial ratio *)
N[-(Vne+Vee)/T /. u /. c1, 10]

plot1=Graphics[{{GrayLevel[0.6],
Disk[{P+Q,0},Q],Disk[{-0.333*(P+Q),0.943*(P+Q)},Q],{Dashing[{0.02,0.02}],
Disk[{-0.3333*(P+Q),-0.471*(P+Q)},Q]}},
Circle[{0,0},P],
Circle[{P+Q,0},Q],Circle[{-0.333*(P+Q),0.943*(P+Q)},Q],{Dashing[{0.02,0.02}],
Circle[{-0.3333*(P+Q),-0.471*(P+Q)},Q]},Disk[{0,0},0.1]}] /. u;

Show[plot1,{AspectRatio->Automatic, Frame -> True, Axes -> True, GridLines -> Automatic,
PlotRange -> {{-4,4},{-4,4}}}]

[Graphics:Images/Li2_Na2_gr_49.gif]

Converted by Mathematica September 10, 2012