Mean momentum of a nucleon as a function of mass number A

[nunuhoyv]

Homework Statement

How to determine variation of mean momentum of a nucleon with the mass number A of nucleus?

Homework Equations

R=R_0A^(1/3)

The Attempt at a Solution

Can't find a solution with elementary approach.

 

[mfb]

The mean momentum has to be zero, otherwise the nucleon escapes. But you can find the mean variance of motion, variance of the kinetic energy or similar things.

What do you know about the energy of things confined to a space of limited size?

 

[nunuhoyv]

deBroglie relation gives momentum p = h/lambda, and lambda can't be greater than size of nucleus~R-0*A*(1/3). So momentum varies as A*(-1/3). This gives the minimum momentum, not the mean, doesn't it? Also how good is the assumption about lambda and size of nucleus?

 

[mfb]

Also how good is the assumption about lambda and size of nucleus?

That is good.

This gives the minimum momentum, not the mean, doesn't it?

Right. What is the distribution for other allowed momenta? Focusing on one dimension is fine for now.