import java.util.Scanner;
class finest {
 public static void main(String[] args) {

          /*  Sommerfeld (= Dirac ) model fine structure     */ 
 
 double c=2.99792e8;     /*  = light speed  m/s   */
 double h=6.626069e-34;   /* =  planck constant  Js      */
 double hbar= 1.05457e-34;  /* =  plank/2pi  Js    */
 double mu=1.256637e-6;      /* = magnetic permeability   */
 double epsi=8.854187e-12;   /* = electric permittivity   */
 double ele=1.602176e-19;    /* = electron charge  Q  */
 double me=9.1093826e-31;     /* = electron mass  kg */
 double pai=3.141592653589793;   /*  = pi      */
  double ah=(epsi*h*h)/(pai*ele*ele*me);    /* = Bohr radius (m)    */
 

 Scanner stdIn=new Scanner(System.in);
 System.out.println("central charge (= Z )�H ");  
 double Z=stdIn.nextDouble();
 System.out.println("energy level ( n = 2, 3 ... )�H ");  
 double n=stdIn.nextDouble();
 System.out.println("Input '1' (= j3/2 - j1/2 ), '2' (= j5/2-j3/2) ...  ");  
 double l=stdIn.nextDouble();    /*  l = angular momentum    */
 double jd=l-0.5; double ju=l+0.5;  /* lower and upper j   */

 double alpha=(ele*ele)/(4.0*pai*epsi*hbar*c);  /* finestructure constant */

 double Ad =n-jd-0.5+Math.sqrt((jd+0.5)*(jd+0.5) - Z*Z*alpha*alpha );
 double Au =n-ju-0.5+Math.sqrt((ju+0.5)*(ju+0.5) - Z*Z*alpha*alpha ); 

                                    /*  Energy in Dirac hydrogen     */
 double Ed = (me*c*c)/(Math.sqrt(1.0+(Z*Z*alpha*alpha)/(Ad*Ad) ));
  double Eu = (me*c*c)/(Math.sqrt(1.0+(Z*Z*alpha*alpha)/(Au*Au) ));
                         
                     /* fine =  fine  structure spilitting by Dirac, sommerfeld  */
 double fine=(Eu-Ed)*6.241509e18;    /*  energy J >> eV       */

                   /*  W = approximate energy form (eV) = Z^4/n^3 form  */
 double chuu=(ele*ele*hbar*hbar)/(4.0*me*me); 
 double W=(2.0* mu * chuu * Z*Z*Z*Z)/(4.0*pai*ah*ah*ah*n*n*n*l*(l+1)) * 6.241509e18;

   System.out.print("\n" );
   System.out.print(" principal quantum number n = "+ (int)n + "\n" );
  
  String upp="3/2"; String low="1/2";
  if ( (int)l ==2 ) { upp="5/2"; low="3/2";  }
  if ( (int)l ==3 ) { upp="7/2"; low="5/2";  }
  if ( (int)l ==4 ) { upp="9/2"; low="7/2";  }
  if ( (int)l ==5 ) { upp="11/2"; low="9/2";  }

  System.out.print("Dirac  energy level, upper j="+ upp + " lower j="+ low + "\n" );
   System.out.printf("                        \n");

  System.out.print(" Sommerfeld upper,  nr=" + (int) (n-ju-0.5) + "  angular ="+ (int)(ju+0.5) + "\n" );
  System.out.print(" Sommerfeld lower,  nr=" + (int) (n-jd-0.5) + "  angular ="+ (int)(jd+0.5) + "\n" );

 
   System.out.printf("                        \n");

   System.out.printf(" finestructure by original equation = %.8f  (eV) \n ", fine);
   System.out.printf(" finestructure by Z^4/n^3 form = %.8f  (eV) \n", W);
   System.out.printf("                        \n");

    double cfine =fine * 8.065544e3;  /* ( eV >> cm-1 ) */
   System.out.printf(" finestructure : %.4f  (cm-1) \n ", cfine);
   
   System.out.printf("                        \n");

 }}