- #1
vintagelover007
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- Homework Statement
- This is a homework assignment for my Modern Physics Class, I cannot find where to start in my textbook or class notes.
- Relevant Equations
- R = r0A^1/3
r_0=1.25*10^-15m
Stable nuclei have radii that are approximately given by the formula:
R = r0_A^1/3 Where r0 = 1.25 × 10−15m and A is the atomic mass number.
In many experiments of interest to modern particle physics, beams of neutrinos scatter from nucleons within the nucleus. Even though the nucleus is at rest, the nucleons inside it cannot be, because of the Heisenberg uncertainty principle.
The “Fermi momentum” they must carry has to be accounted for when modeling the scattering interaction. Approximating that the wave function of a given nucleon inside the nucleus has a 3D Gaussian wave function with σ = R:
a) Show that the mean momentum is: |pˆ|| = 4√ 2π σx/h bar integral dpp^3 exp [-2 p^2 R^2/h bar^2]
b) Evaluate this integral and calculate the mean momentum of the nucleons in a nucleus of 12^C.
R = r0_A^1/3 Where r0 = 1.25 × 10−15m and A is the atomic mass number.
In many experiments of interest to modern particle physics, beams of neutrinos scatter from nucleons within the nucleus. Even though the nucleus is at rest, the nucleons inside it cannot be, because of the Heisenberg uncertainty principle.
The “Fermi momentum” they must carry has to be accounted for when modeling the scattering interaction. Approximating that the wave function of a given nucleon inside the nucleus has a 3D Gaussian wave function with σ = R:
a) Show that the mean momentum is: |pˆ|| = 4√ 2π σx/h bar integral dpp^3 exp [-2 p^2 R^2/h bar^2]
b) Evaluate this integral and calculate the mean momentum of the nucleons in a nucleus of 12^C.
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