# Homework Help: Scattering problem

1. Nov 29, 2007

### ercagpince

Hi , I got stuck on a point of griffiths' scattering problem on "the introduction to elementary particles"
1. The problem statement, all variables and given/known data
Consider the case of elastic scattering , A+B-->A+B , in the lab frame (B initially at rest) assuming the target is so heavy (mbc2 >> Ea) that its recoil is negligible . Use (6.34) to determine the differential scattering cross section .

2. Relevant equations
Equation (6.34) :
$$\frac{d\sigma}{d\Omega}$$=M$$^{2}$$$$\frac{$$\frac{\hbar}{2}$$S}{4\sqrt{\left(p_{1}\bullet p_{2}\right)^{2}-\left(m_{1}m_{2}c^{2}\right)^{2}}$$$$\left[\left(\frac{cd^{3}p_{3}}{$$\left(2\Pi^{3}$$$$\right)$$2E_{3}}$$$$\right)$$\left(\frac{cd^{3}p_{4}}{$$\left(2\Pi^{3}$$$$\right)$$2E_{4}}[/tex]$$\right)$$\bullet\bullet\bullet\left(\frac{cd^{3}p_{n}}{$$\left(2\Pi^{3}$$$$\right)$$2E_{n}}[/tex]$$\right)$$$$\right]$$$$\times$$$$\left(2\Pi^{4}$$$$\right)$$$$\delta^{4}\left(P_{1}+P_{2}-P_{3}-P_{4}\bullet\bullet\bullet-P_{n}\right)$$

3. The attempt at a solution

$$\frac{d\sigma}{d\Omega}$$=M$$^{2}$$$$\frac{$$\frac{\hbar}{2}$$S}{16\left(2\Pi\right)^{2}\left|P_{1}\right|m_{2}c}\frac{\rho*d\rho}{\left(\rho^{2}+P_{1}^{2}-2\rho\left|P_{1}\right|cos\theta\right)^{1/2}}\delta\left(\frac{E_{1}+E_{2}}{c}-\rho-\left|P_{4}\right|\right)$$

I got this formula so far , however , I cannot cancel out the delta function . It seems that it is impossible for me to separate rho and p1 as independent variables when p4 is involved in the delta function .

Last edited: Nov 29, 2007
2. Nov 29, 2007