Calculation of scattering amplitude ratio for two different angles

[GAGS]

Hi all, since scattering amplitude is given as:
f(theta) = summation over l(from o to infinity)(2l+1)/k exp(i(phi))sin(phi) P_l(cos theta).But what happen if i want to calculate the ratio of f(theta=0)/f(theta = pi/2).
Can anyone tell me the value of P_l(0).
Thanks

 

[malawi_glenn]

It is a Legendre polynomial, http://mathworld.wolfram.com/LegendrePolynomial.html

For all odd l; the scattering amplitude is 0 for cos(theta) = 0

 

[denian]

The value of Pl(0) is 1. This can be seen from the equation for the scattering amplitude, where Pl(cos theta) is equal to 1 when theta is equal to 0.

To calculate the ratio of f(theta=0)/f(theta = pi/2), you can substitute the value of Pl(0) into the equation and solve for the ratio. This will give you the ratio of the scattering amplitude at theta=0 to the scattering amplitude at theta=pi/2.

It is important to note that this ratio may vary depending on the values of l and k in the equation. Additionally, the scattering amplitude ratio may also depend on the properties of the scattering material and the incident particles. Therefore, it is necessary to carefully consider all parameters when calculating this ratio.