REAL*8 FUNCTION PFAC(A,Z)
* Precession factor for hierarchy.
* --------------------------------
*
* Maths by Douglas Heggie; function by Rosemary Mardling (11/96).
* @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
*
REAL*8 m,m1,A,Z,C,C1,C2,C3,D1,D2,D3,Z1
*The function is singular for m1=0, but the following holds:
*For 0 < m1 <=1 (m1 never > 1), \infty > PFAC(m1) > 1.6, with P(0.01)=3.6.
*So taking it as 1 isn't too bad for an order of magnitude estimate.
C1 = 0.5*(Z + A**2)
Z1 = 5.0 - Z + 4*A**2
C2 = (Z1 + SQRT(Z1))/6.0
C3 = (Z1 - SQRT(Z1))/6.0
IF (C1.GE.C2) THEN
D1 = C1
D2 = C2
D3 = C3
ELSE IF (C2.GE.C1.AND.C1.GE.C3) THEN
D1 = C2
D2 = C1
D3 = C3
ELSE
D1 = C2
D2 = C3
D3 = C1
END IF
*
C = 1.0/SQRT(D1 - D3)
m = (D2 - D3)/(D1 - D3)
*
* Evaluate elliptic integral by approximate expression.
a0=1.3862944
a1=0.1119723
a2=0.0725296
b0=0.5
b1=0.1213478
b2=0.0288729
m1 = 1.0 - m
m1 = MAX(m1,1.0D-10)
PFAC = (a0+a1*m1+a2*m1**2)+(b0+b1*m1+b2*m1**2)*log(1.0/m1)
*
* Include the square root of (D1 - D3).
PFAC = C*PFAC
END