# WE theorem to evaluate matrix elements

1. Dec 3, 2008

### pollo

Hi!

In my work I use the WE theorem to evaluate matrix elements. F being the total spin and m the projection onto the z-axis, I am using:

<JIFm|r_(-q)|J'IF'm'>=(-1)^(F'+m'-m)<Fm1q|F'm'>sqrt(2F+1)sixj(F, F', 1:J',J,I)<J'||r||J>

I have a problem with the (-1)^ part which I suspect to be wrong, but have not been able to find a formula to compare a check. Am quite sure the rest is right. Could somebody help and tell what should be in the exponent?

2. Dec 4, 2008

### DeShark

Re: Wigner-Eckart

I have the theorem as:

$$<\tau J M|T_q^{(k)}|\tau' J' M'> = {1 \over {\sqrt{2J+1}}}<\tau J ||T^{(k)}||\tau' J'><J' k M' q| J M>$$

where $$<\tau J ||T^{(k)}||\tau' J'>$$ is the reduced matrix element.

Unfortunately I couldn't make head nor tail of the function you're trying to use. Maybe I'll've been of some help. Either way, this has been here for a couple of days with no reply, so maybe this will help the discussion.