# Elastic reactions, ratio of cross sections

1. Jan 21, 2010

### erwinscat

Hello everybody,

I am having some troubles with this exercise. I have attached the text and the solutions to my post. My problem is, after I have coupled the angular momenta and used the CK coefficients like in ($$|\pi ^{+}p>=|1,1>|1/2, 1/2>=|3/2,3/2>$$) (pag.432) I don't understand what follows..well, I have a problem with :

$$<\frac{3}{2},m_{j}|\hat{H}|\frac{3}{2},m_{i}>=a_{1}$$

$$<\frac{1}{2},m_{j}|\hat{H}|\frac{1}{2},m_{i}>=a_{2}$$

What exactly are coefficient $$a_1$$ and $$a_2$$ ? I assume elements of the $$\hat{H}$$ matrix...Is the matrix $$\hat{H}$$ the transition matrix of the reaction ? How can I calculate it ? This is really my problem, finding the $$\hat{H}$$ matrix. I attach the rest of the exrcise just you know, but my problem is really to understand how to calculate the $$\hat{H}$$ matrix and how to use it properly.

Any help would be very much appreciated!

Erwin

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