• Support PF! Buy your school textbooks, materials and every day products Here!

Yukawa potential

  • Thread starter raul_l
  • Start date
  • #1
105
0

Homework Statement



I have been given the following assignment:
"The meson moves within the nucleus under the influence of a screened Coulomb potential known as the Yukawa potential. Given that the mass of a meson is about 270 times the mass ot the electron and that the effective extent of the potential is of the order of the size of a nucleus, calculate the energy levels of mesons within a nucleus consisting of 10 protons and 10 neutrons."

Homework Equations



[tex] V(r)=- \frac{Ze^2}{4\pi \epsilon_{0} r} e ^{-\frac{r}{a}} [/tex]

The Attempt at a Solution



I have a very simple question. What exactly is r? The distance from the center of the nucleus? What happens if we get closer and closer to the center of the nucleus? Does the potential reach infinity or does it drop to zero (kinda like gravity which usually increases with 1/r but drops to zero a the center of Earth because of the Gauss law)?

I need to understand these basics things before I can move on.

I've tried searching the web but couldn't find anything useful. :redface:
I'd really appreciate it if anyone could shed some light on this.
 

Answers and Replies

  • #2
39
0
r is just the distance from the centre as in the coulomb potential.
 
  • #3
malawi_glenn
Science Advisor
Homework Helper
4,786
22
This is not a real situation, so don't bother so much about what "really" happens to the meson.

In reallity you have a hard core and so on..

Yes, I think you should think r as radius. The problem is related to the hydrogenic atom I think..
 
  • #4
105
0
Still, how does the meson behave inside the nucleus? Will the potential reach infinity? Or should I just consider the nucleus as a hard core and stay out of it?

In my assignment it says "extent of the potential is of the order of the size of a nucleus". Does this mean that it is practically zero outside the nucleus?

I'm sorry if these questions seem silly but I've never studied particle physics before.
 
  • #5
malawi_glenn
Science Advisor
Homework Helper
4,786
22
yes outside the potential is zero (strong force is short ranged)

Inside, you just treat the system quantum-mechanically.

Do you know how to find the energy levels of the hydrogen atom?

How does the electron behave in the coloumb potential in the hydrogen atom? Recall that.
 
  • #6
105
0
This is a project for the course "computational physics". I have to create a computer program to solve the problem. I have done this before for the hydrogen atom (I'm using the Shooting method).
Basically, all I need is a Schrödinger equation to describe the system. For hydrogen it was in the form [tex] \frac{\hbar^2}{2m}\frac{d^2 \psi}{dr^2}+(V-E)\psi=0 [/tex].
Now I would need something similar for the "meson in a nucleus" system.

I guess I could substitute m (electron mass) with the mass of a meson, but I'm not sure I could just substitute V (hydrogen's potential energy) with [tex] V(r)=- \frac{Ze^2}{4\pi \epsilon_{0} r} e ^{-\frac{r}{a}} [/tex]
 
  • #7
malawi_glenn
Science Advisor
Homework Helper
4,786
22
Why not? I mean, from a physics point of view you do it. But for computational, no idea.
 

Related Threads on Yukawa potential

  • Last Post
Replies
5
Views
325
  • Last Post
Replies
3
Views
5K
  • Last Post
Replies
1
Views
2K
  • Last Post
2
Replies
49
Views
10K
  • Last Post
Replies
7
Views
5K
  • Last Post
Replies
1
Views
815
  • Last Post
Replies
1
Views
3K
Replies
1
Views
1K
  • Last Post
Replies
1
Views
2K
Replies
6
Views
3K
Top