// ( 3/2 J2 J3 )
// ( M1 M2 M3 )
private static double ThreeJ_ThreeHalvesJ(SpinState s1, SpinState s2, SpinState s3)
{
Debug.Assert(s1.TwoJ == 3);
if (s1.TwoM < 0)
{
// m1 is negative; invert the m's
double r = ThreeJ_ThreeHalvesJ(s1.Invert(), s2.Invert(), s3.Invert());
// fix sign!
return(r);
}
else if (s1.TwoM == 1)
{
// m1 = 1/2
if (s3.TwoJ == (s2.TwoJ + 1))
{
// j3 = j2 + 1/2
double r = (s2.JMinusM - s2.TwoM) * Math.Sqrt(1.0 * (s2.JPlusM + 1) / s2.TwoJ / (s2.TwoJ + 1) / (s2.TwoJ + 2) / (s2.TwoJ + 3));
if (s2.JMinusM % 2 != 0)
{
r = -r;
}
return(r);
}
else
{
// j3 = j2 + 3/2
double r = Math.Sqrt(3.0 * (s2.JPlusM + 1) * (s2.JPlusM + 2) * (s2.JMinusM + 1) / (s2.TwoJ + 1) / (s2.TwoJ + 2) / (s2.TwoJ + 3) / (s2.TwoJ + 4));
if (s2.JMinusM % 2 != 0)
{
r = -r;
}
return(r);
}
}
else
{
// m1 = 3/2
if (s3.TwoJ == (s2.TwoJ + 1))
{
// j3 = j2 + 1/2
double r = -Math.Sqrt(3.0 * (s2.JPlusM + 1) * (s2.JPlusM + 2) * (s2.JMinusM) / s2.TwoJ / (s2.TwoJ + 1) / (s2.TwoJ + 2) / (s2.TwoJ + 3));
if (s2.JMinusM % 2 != 0)
{
r = -r;
}
return(r);
}
else
{
// j3 = j2 + 3/2
double r = -Math.Sqrt(1.0 * (s2.JPlusM + 1) * (s2.JPlusM + 2) * (s2.JPlusM + 3) / (s2.TwoJ + 1) / (s2.TwoJ + 2) / (s2.TwoJ + 3) / (s2.TwoJ + 4));
if (s2.JMinusM % 2 != 0)
{
r = -r;
}
return(r);
}
}
}
// ( 1/2 J2 J+1/2 )
// ( M1 M2 -M1-M2 )
private static double ThreeJ_HalfJ(SpinState s1, SpinState s2)
{
Debug.Assert(s1.TwoJ == 1);
if (s1.TwoM < 0)
{
// m1 = -1/2
// invert to turn into m1 = +1/2 case
double r = ThreeJ_HalfJ(s1.Invert(), s2.Invert());
if (s2.TwoJ % 2 == 0)
{
r = -r;
}
return(r);
}
else
{
// m1 = +1/2
double r = -Math.Sqrt((s2.JPlusM + 1.0) / (s2.TwoJ + 1.0) / (s2.TwoJ + 2.0));
if (s2.JMinusM % 2 != 0)
{
r = -r;
}
return(r);
}
}
// ( J1 J2 M1 M2 | J M ) =
// (-1)^{J1-J2+M} * Sqrt(2J+1) *
// ( J1 J2 J )
// ( M1 M1 -M )
/// <summary>
/// Computes a Clebsch-Gordon coefficient.
/// </summary>
/// <param name="s1">The first spin state.</param>
/// <param name="s2">The second spin state.</param>
/// <param name="s">The total spin state.</param>
/// <returns>The Clebsch-Gordon coefficient measuring the contribution of the given first and
/// second spin states to the given total spin state.</returns>
public static double ClebschGodron(SpinState s1, SpinState s2, SpinState s)
{
double f = Math.Sqrt(s.TwoJ + 1);
if (s1.JPlusM % 2 != 0)
{
f = -f;
}
if (s2.JMinusM % 2 != 0)
{
f = -f;
}
return(f * ThreeJ(s1, s2, s.Invert()));
}
// ( 1 J2 J3 )
// ( M1 M2 M3 )
private static double ThreeJ_OneJ(SpinState s1, SpinState s2, SpinState s3)
{
Debug.Assert(s1.TwoJ == 2);
if (s1.TwoM < 0)
{
// m1 = -1
double r = ThreeJ_OneJ(s1.Invert(), s2.Invert(), s3.Invert());
if ((s1.TwoJ + s2.TwoJ + s3.TwoJ) / 2 % 2 != 0)
{
r = -r;
}
return(r);
}
else if (s1.TwoM == 0)
{
// m1 = 0
if (s3.TwoJ == s2.TwoJ)
{
// j3 = j2
double r = s2.TwoM / Math.Sqrt(s2.TwoJ * (s2.TwoJ + 1) * (s2.TwoJ + 2));
if ((s2.JMinusM % 2) != 0)
{
r = -r;
}
return(r);
}
else
{
// j3 = j2 + 1
double r = -Math.Sqrt(2.0 * (s2.JPlusM + 1) * (s2.JMinusM + 1) / (s2.TwoJ + 1) / (s2.TwoJ + 2) / (s2.TwoJ + 3));
if ((s2.JMinusM % 2) != 0)
{
r = -r;
}
return(r);
}
}
else
{
// m1 = 1
if (s3.TwoJ == s2.TwoJ)
{
// j3 = j2
double r = Math.Sqrt(2.0 * s2.JMinusM * (s2.JPlusM + 1) / s2.TwoJ / (s2.TwoJ + 1) / (s2.TwoJ + 2));
if ((s2.JMinusM % 2) != 0)
{
r = -r;
}
return(r);
}
else
{
// j3 = j2 + 1
double r = Math.Sqrt(1.0 * (s2.JPlusM + 1) * (s2.JPlusM + 2) / (s2.TwoJ + 1) / (s2.TwoJ + 2) / (s2.TwoJ + 3));
if ((s2.JMinusM % 2) != 0)
{
r = -r;
}
return(r);
}
}
}