12 September 2026 AD

The Most Holy Name of Mary

FORTRAN CODE (Double Precision)to compute Coupling Constants (and other constants) from C_-50 to C₊₁₉

PROGRAM ALFA_GENERAL

     

      IMPLICIT NONE

     

      COMPLEX*16 EXPM, ALFA_MINUS_HALF, ALFA_SQUARE

      COMPLEX*16 ALFA_FINAL, C_0, C_87, C_8

      REAL*8 B_1, B_2, B_3

      REAL*8 C_1, C_2

      COMPLEX*16 A, B, C

      COMPLEX*16 ALFA_MINUS_HALF_1, ALFA_MINUS_HALF_3

      REAL *8 ALFA_MINUS_HALF_2

      REAL*8 REAL_PART, ABSOL_VALUE

      COMPLEX*16 IMAG_PART

      COMPLEX*16 THETA, THETA_DEG

     

C      REAL*8 A, B, C

     

      REAL*8 X

     

      INTEGER*8 I, COUNTER

     

      C_0 = 0.9869763503843571923955121936342632741D+00

C PI/E

C      C_87 = 0.3141592653589793238462643383279502797D+01 / 0.27182818284&

C     &59045235360287471352662314D+01

      C_87 = (  0.314159265358979323846D+001 / 0.271828182845904523536D+&

     &001 )

C PI

      C_8 = 0.3141592653589793238462643383279502797D+01

     

     

     

      OPEN(UNIT=11, FILE='C:/FORTRAN/ALFA & THETA GENERAL DOUBLE PRECISI&

     &ON.TXT')

     

     

     

     

     

     

C      COUNTER = 0

C      I = 1

     

      DO 100 I = -50, 19, 1

     

      X = DBLE(I)

     

C      COUNTER = COUNTER + 1

     

C PART A OF EXPM = (A/B)^C

      A =  ((C_0) ** (((I - 8.00D+00) / 8.00D+00)) )

     

     

C PART B OF EXPM = (A/B)^C

C PART B_1 IS EQUAL TO THE CONSTANT C WITH INDEX I

      B_1 = (( C_0 ) * (( C_87 )** (I)))

     

      B_2 =  (( X - 8.00D+00 ) / ( I** 2.00D+00 - 16.00D+00 * I + 80.00D&

     &+00 ) )

    

      B_3 =  (( 11.00D+00 * I - 88.00D+00 ) / 24.00D+00 )

     

C FINAL RESULT FOR B

      B =  (( (B_1) * (B_2) ) ** DCMPLX (B_3) )

     

     

C c PART OF THE EQUATION (A/B) **C

      C_1 = (( C_0 ) * ((C_87 ) ** DCMPLX ( X )))

     

      C_2 =   (( ( I ) - 8.00D+00) / 24.00D+00 )

     

      C =  DCMPLX (( ( C_1)) * ( ( C_2)))

     

C EXPM = (A/B)**C

      EXPM = DCMPLX ((DCMPLX  (A) /  DCMPLX (B)) ** DCMPLX (C))

     

     

COMPUTE ALFA_MINUS_HALF_1 PART = RECIPROCAL OF ALPHA ^ 1/2

      ALFA_MINUS_HALF_1 = DCMPLX ((C_0) * ((C_87) ** (DCMPLX (X + (EXPM)&

     & ) ) ))

    

COMPUTE ALFA_MINUS_HALF_2 PART = RECIPROCAL OF ALPHA ^ 1/2

      ALFA_MINUS_HALF_2 = (( X - 8.00D+00 ) / (( X*X ) - 16.00D+00 *X +8&

     &0.00D+00) )

    

C COMPUTE ALFA_MINUS_HALF_3 PART OF RECIPROCAL OF ALPHA ^ (-1/2)

      ALFA_MINUS_HALF_3 =  ( ((9.00D+00 * X ) - 8.00D+00 ) / ( 8.00D+00 &

     &* EXPM ) )

    

C COMPUTE FINAL ALFA MINUS HALF = (PART18PART2)**PART3

      ALFA_MINUS_HALF =  ((( ( ALFA_MINUS_HALF_1 )) * (( ALFA_MINUS_HALF&

     &_2 )) ) ** (  DCMPLX ( ALFA_MINUS_HALF_3 )) )

    

C ALFA_MINUS_HALF SQUARED = RECIPROCAL OF ALFA

      ALFA_SQUARE =  ( ( ALFA_MINUS_HALF ) ** 2.00D+00 )

    

C FINAL ALFA = 1 / ALFA_SQUARE

      ALFA_FINAL =  ( 1.00D+00 /  ( ALFA_SQUARE ) )

     

C REAL PART OF ALFA

      REAL_PART = DREAL (ALFA_FINAL)

     

C IMAGINARY PART OF ALFA

      IMAG_PART = DIMAG (ALFA_FINAL)

     

C ABSOLUTE VALUE OF ALFA (MODULUS)

      ABSOL_VALUE = ABS  (ALFA_FINAL)

     

C ARCTAN OF THE POLAR FORM = THETA = Y/X

      THETA = ATAN2 ( DIMAG (ALFA_FINAL) , DREAL (ALFA_FINAL ))

     

C ANGLE THETA IN DEGREES

      THETA_DEG = ( THETA * 180.00D+00 ) / C_8

     

     

      WRITE(11,*)'PART A...............................................'

      WRITE(11, *) I, DCMPLX (A)

      WRITE(11,*)'_____________________________________________________'

     

C      WRITE(11,*) I, X

C      WRITE (11,*) C_87

     

C      WRITE (11,200) I, A

     

     

      WRITE(11,*)'PART B...............................................'

      WRITE (11,*) I,  (B_1)

     

      WRITE (11,*) I,  (B_2)

     

      WRITE (11,*) I,  (B_3)

     

      WRITE (11,*) I, (B)

     

      WRITE(11,*)'_____________________________________________________'

     

      WRITE(11,*)'PART C...............................................'

     

      WRITE (11, *) I, DCMPLX (C_1)

      WRITE (11, 200) I, DCMPLX (C_2)

     

      WRITE (11, 200) I, DCMPLX (C)

     

      WRITE(11,*)'_____________________________________________________'

      WRITE(11,*)'EXPONENT MAIN = (A/B)**C.............................'

     

      WRITE(11,*) I, DCMPLX (EXPM)

     

      WRITE(11,*)'_____________________________________________________'

      WRITE(11,*)'ALFA ^ ( -1/2 ) PART.................................'

     

      WRITE(11,*) I, DCMPLX (ALFA_MINUS_HALF_1)

     

      WRITE(11,*) I, DCMPLX (ALFA_MINUS_HALF_2)

     

      WRITE(11,*) I, DCMPLX (ALFA_MINUS_HALF_3)

     

      WRITE(11,*) I, DCMPLX (ALFA_MINUS_HALF)

     

      WRITE (11,*)'ALFA SQUARE_________________________________________'

     

      WRITE(11,*) I,  (ALFA_SQUARE)

     

      WRITE(11,*)'_____________________________________________________'

     

      WRITE(11,*)'ALPHA FINAL = RECIPROCAL OF ALFA MINUS 1_____________'

     

      WRITE(11,*) I, ( ALFA_FINAL )

     

      WRITE(11,*)'_____________________________________________________'

     

      WRITE(11,*)'REAL PART OF ALPHA...................................'

      WRITE(11,*) I, REAL_PART

     

      WRITE(11,*)'IMAGINARY PART OF ALPHA..............................'

      WRITE(11,*) I, IMAG_PART

     

      WRITE(11,*)'_____________________________________________________'

     

      WRITE(11,*)'ABSOLUTE VALUE = MODULUS OF ALFA.....................'

     

      WRITE(11,*) I, ABSOL_VALUE

     

      WRITE(11,*)'ANGLE THETA OF POLAR FORM............................'

     

      WRITE(11,*) (THETA)

     

      WRITE(11,*)'ANGLE THETA IN DEGREES...............................'

     

      WRITE(11,*) THETA_DEG

     

      WRITE(11,*)'_____________________________________________________'

     

     

     

     

     

     

     

     

100   CONTINUE

     

     

      CLOSE(11)

     

      STOP

     

200   FORMAT (I5, (F40.25, E40.25))

300   FORMAT (I5, E40.25)

     

     

      END PROGRAM ALFA_GENERAL