Alpha Decay
Figures for 
Alpha Decay Lab

by
Gerard P. Gilfoyle
Department of Physics
University of Richmond
Richmond, VA 23173
gilfoyle@urvax.urich.edu

Published in:
Mathematica in Education and Research
Vol.4 No.1

Copyright 1995 TELOS/Springer-Verlag

Input, constants, etc.

Constants for the calculation.

Aout = 4.0;        (* The emitted particle mass. *)
Zout = 2.0;        (* The emitted particle charge. *)
hbarc = 197.0;     (* h_bar times c *)
e2 = hbarc/137;    (* electron charge squared *)
$DefaultFont = {"Helvetica",7};

(* Generate the potential here.
   
   Anuc - atomic number of parent nucleus 
   Mout - mass of parent
   Znuc - charge of parent
   R0   - radius of parent
   Rmax - classical turning point of emitted
          particle
   step - width of an individual barrier
   Ve   - array of (radius, potential energy)
   
   *)
   
Ndiv  = 3;
Aout  = 4;
Zout  = 2;
Mout  = Aout 931.5;
Znuc = 84;
Anuc = 212.0;
Eout = 8.78;
R0    = 1.4*(Anuc - 4)^(1/3);
Rmax  = Zout*(Znuc - 2)*e2/Eout;
step  = (Rmax - R0)/Ndiv;
Ve    = Table[{r, Zout*Znuc*e2/r},
              {r, R0, Rmax-step,step}];
Vrec[x_] := Which[x<0,0,
                  0<=x<=1.0,10.0,
                  1<x,0]

Figure 1

p1=Plot[Vrec[x], 
     {x,-0.3,1.3},
     Axes->{True,False},
     PlotRange->{{-0.3,1.3},{-3.0,17.0}},
     Frame->True,
     FrameLabel->{FontForm["x",{"Times-Italic",12}],
                  FontForm["Potential Energy",{"Times-Italic",12}],
                  (* FontForm["Figure 1",{"Times-Italic",12}],*)
                  " "," "},
     FrameTicks->{{{0.0," ",{0.03,0}},
                   {0.5," ",{0.03,0}},
                   {1.0," ",{0.03,0}}},
                  {{0.0," ",{0.03,0}},
                   {5.0," ",{0.03,0}},
                   {10.0," ",{0.03,0},
                   {15.0," ",{0.03,0}}}}}
   ]

Show[{p1,Graphics[Text[FontForm["O",{"Times-Italic",8}],{0.0,-1.0}]  ],
         Graphics[Text[FontForm["a",{"Times-Italic",8}],{1.0,-1.0}]  ],
         Graphics[Text[FontForm["V",{"Times-Italic",8}],{-0.05,10.0}] ],
         Graphics[Text[
                   FontForm["0",{"Times",7}],
                   {-0.03,9.7}] 
                 ],
         Graphics[{Dashing[{0.01,0.01}],
                   AbsoluteThickness[0.5],
                  Line[{{0.0,0.0},
                        {0.0,17.0}}
                      ]}
                 ],
         Graphics[{Dashing[{0.01,0.01}],
                   AbsoluteThickness[0.5],
                  Line[{{1.0,0.0},
                        {1.0,17.0}}
                      ]}
                 ],
         Graphics[Text[FontForm["Region 1",{"Times-Bold",9}],{-0.15,14.0}] ],
         Graphics[Text[FontForm["Region 2",{"Times-Bold",9}],{0.5,14.0}] ],
         Graphics[Text[FontForm["Region 3",{"Times-Bold",9}],{1.15,14.0}] ]
      }
    ]

Figure 2

$DefaultFont={"Helvetica",7};

p2 = Plot[Zout*Znuc*e2/x, 
          {x,R0,40},
          PlotRange->{{0,40},{0,35}},
          Frame->True,
          FrameLabel->{FontForm["x(fm)",{"Times-Italic",12}],
                       FontForm["V(MeV)",{"Times-Italic",12}],
                       " ",
                       " "
                      }
         ]

Show[{p2,
      Graphics[{Dashing[{0.01,0.01}],
               Line[{{0.0,Eout},
                     {40,Eout}}
                   ]}
              ],
      Graphics[Line[{{R0,0},
                     {Ve[[1,1]],Ve[[1,2]]}}
                   ]
              ],
      Graphics[{Dashing[{0.005,0.01,0.02,0.01}],
               Line[{{Ve[[1,1]],Ve[[1,2]]},
                     {Ve[[2,1]],Ve[[1,2]]}}
                   ]}
              ],
      Graphics[{Dashing[{0.005,0.01,0.02,0.01}],
               Line[{{Ve[[2,1]],Ve[[1,2]]},
                     {Ve[[2,1]],Ve[[2,2]]}}
                   ]}
              ],
      Graphics[{Dashing[{0.005,0.01,0.02,0.01}],
               Line[{{Ve[[2,1]],Ve[[2,2]]},
                     {Ve[[3,1]],Ve[[2,2]]}}
                   ]}
              ],
      Graphics[{Dashing[{0.005,0.01,0.02,0.01}],
               Line[{{Ve[[3,1]],Ve[[2,2]]},
                     {Ve[[3,1]],Ve[[3,2]]}}
                   ]}
              ],
      Graphics[{Dashing[{0.005,0.01,0.02,0.01}],
               Line[{{Ve[[3,1]],Ve[[3,2]]},
                     {Rmax,Ve[[3,2]]}}
                   ]}
              ],
      Graphics[{Dashing[{0.005,0.01,0.02,0.01}],
               Line[{{Rmax,Ve[[3,2]]},
                     {Rmax,Eout}}
                   ]}
              ],
      Graphics[{AbsoluteThickness[0.5],
                Line[{{31.5,17},
                      {35,9.2}}
                   ]}
              ],
      Graphics[{Text[FontForm["V",{"Times-Italic",8}],{11.5,31.0},{0,0}],
               Text[FontForm["V",{"Times-Italic",8}],{17.5,18.5},{0,0}],
               Text[FontForm["V",{"Times-Italic",8}],{23.5,13.5},{0,0}]
              }],
      Graphics[{Text[FontForm["1",{"Times-Italic",7}],{12.0,30.5},{0,0}],
               Text[FontForm["2",{"Times-Italic",7}],{18.0,18.0},{0,0}],
               Text[FontForm["3",{"Times-Italic",7}],{24.0,13.0},{0,0}]
              }],
      Graphics[Text[FontForm["a ",{"Symbol",10}],{28.0,18.3}]
              ],
      Graphics[Text[FontForm[" Energy",{"Times-Italic",10}],{32.8,18.2}]
              ]
     }
    ]

Figure 3

Data = { {   2, 4.9 10^-24},
         {   5, 1.28 10^-19},
         {  25, 2.0 10^-17},
         { 125, 5.4 10^-17},
         { 250, 6.1 10^-17},
         { 500, 6.5 10^-17},
         { 900, 6.68 10^-17},
         {  50, 3.73 10^-17},
         {  10, 3.10 10^-18} };

<<Graphics`Graphics`

p3 = 
LogLogListPlot[Data,
   PlotRange->All, (* {{0,3},{10^-24,10^-15}}, *)
   Frame->True,
   FrameLabel->{FontForm["Number of Barriers",{"Times-Italic",10}],
                FontForm["Transmission Coefficient",{"Times-Italic",10}],
                " ",
                " "},
   Prolog->PointSize[0.02]]

p4 = LogLogListPlot[
        {{1.0, 1.83 10^-16},
         {1000.0,1.83 10^-16}},
        PlotJoined->True,
        Frame->True,
   FrameLabel->{FontForm["Number of Barriers",{"Times-Italic",10}],
                FontForm["Transmission Coefficient",{"Times-Italic",10}],
                " ",
                " "},
        PlotRange->All,
        Prolog->PointSize[0.02]]

p5 = Show[{p3,
           p4},
     FrameTicks->{{{0.0,"1",{0.03,0}},
                   {1.0,"10",{0.03,0}},
                   {2.0,"100",{0.03,0}},
                   {3.0,"1000",{0.03,0}},
                   {Log[10,2],"",{0.015,0}},
                   {Log[10,3],"",{0.015,0}},
                   {Log[10,4],"",{0.015,0}},
                   {Log[10,5],"",{0.015,0}},
                   {Log[10,6],"",{0.015,0}},
                   {Log[10,7],"",{0.015,0}},
                   {Log[10,8],"",{0.015,0}},
                   {Log[10,9],"",{0.015,0}},
                   {Log[10,20],"",{0.015,0}},
                   {Log[10,30],"",{0.015,0}},
                   {Log[10,40],"",{0.015,0}},
                   {Log[10,50],"",{0.015,0}},
                   {Log[10,60],"",{0.015,0}},
                   {Log[10,70],"",{0.015,0}},
                   {Log[10,80],"",{0.015,0}},
                   {Log[10,90],"",{0.015,0}},
                   {Log[10,200],"",{0.015,0}},
                   {Log[10,300],"",{0.015,0}},
                   {Log[10,400],"",{0.015,0}},
                   {Log[10,500],"",{0.015,0}},
                   {Log[10,600],"",{0.015,0}},
                   {Log[10,700],"",{0.015,0}},
                   {Log[10,800],"",{0.015,0}},
                   {Log[10,900],"",{0.015,0}}
                 },
                  {{-24,HoldForm[10^-24],{0.03,0}},
                   {-22,HoldForm[10^-22],{0.03,0}},
                   {-20,HoldForm[10^-20],{0.03,0}},
                   {-18,HoldForm[10^-18],{0.03,0}},
                   {-16,HoldForm[10^-16],{0.03,0}},
                   {-23," ",{0.01,0}},
                   {-21," ",{0.01,0}},
                   {-19," ",{0.01,0}},
                   {-17," ",{0.01,0}},
                   {-15," ",{0.01,0}}
                  }
                 },
                 PlotRange->All
     ]