Nuclear Physics - Find the s wave phase shift

[lifeonfire]

Homework Statement

In a pp differential cross section, we have the differential cross section dσ/dΩ = 0.111 b/steradian at a lab energy of 4.3 MeV and a lab scattering angle of 30°. What is the s wave phase shift δ?

Homework Equations

dσ/dΩ = sin²δ / k² [1]
k = (2mE)^(1/2) / h [2]

The Attempt at a Solution

Am I using the correct equations? Also, I haven't been given any value for m. Should I just use a proton's mass? I am basically using eqn 1 to get the phase shift. Also, I realized that I didn't use the scattering angle of 30° at all..

 

[mark726]

you are correct in using the equations [1] and [2] to calculate the s wave phase shift δ. However, you are missing some important information in order to solve this problem accurately. The mass (m) in equation [2] refers to the reduced mass of the system, which is the mass of the target particle (in this case, a proton) and the incident particle (in this case, a proton). Additionally, the scattering angle is necessary in order to calculate the phase shift using equation [1].

To solve this problem, you will need to use the known values of the lab energy and scattering angle to calculate the momentum (p) of the incident particle using the equation p = (2mE)^(1/2). Then, you can use this momentum in equation [2] to calculate the reduced mass (m) of the system. Finally, you can use the calculated values of k and m in equation [1] to solve for the s wave phase shift δ.

It is important to note that the s wave phase shift δ is a complex number and may require additional calculations to determine the real and imaginary parts. Additionally, the value of δ may vary depending on the potential used in the scattering experiment. So, it is important to include any relevant information about the potential in your calculation.