NucPhys I HomeworkProblems
1.) In your own words, describe what the "Standard Model" of physics is using 2 to 5 paragraphs. Your paragraphs should include the concepts of the 4 fundamental forces of physics, QED, and QCD at a minimum. Any sentences in which a string of 5 or more words match a sentence that is found on the internet will be evidence of cheating.
2.) Solve the Schrodinger equation for the following potential:
. Assume particles are incident from , don't try to normalize but do express the wave function in terms of one coefficient.
1.) Given the following barrier potential
show that the transmission coefficient is
Assume particles are incident fromand .
1.) Starting with Shrodinger's time-independent equation, derive the wave functions for a 2-D simple harmonic oscillator. Your derivation should take advantage of separation of variables and you are not required to normalize the wave function.
1.) Show that the mean-square charge radius of a uniformly charged sphere is
2.) Using the definition of the form factorand probably an integral table, calculate when
1.) a.) find the binding energy difference between O-15 and N-15
b.) compute the nuclear radius of O-15 and N-15 assuming the above binding energy is due to the coulomb energy.
2.) Muonic X-rays
a.) Calculate the energies of muonic K-line X-rays from Fe assuming a point nucleus and using a one-electron model..
b.) Calculate the energy correctiondue to the finite nuclear size.
3.) Find the binding energy using the fit equation B(Z,A) from the semi-empirical mass formula for
4.) Find the neutron separation energies for
5.) Find the proton separation energies for
1.) Assume a neutron may be described as a proton with a negative pionin an orbital state.
What would be the orbital magnetic dipole moment of this system?
2.) Assume that the proton magnetic moment is due to the rotational motion of a positive spherical uniform charge distribution of radiusspinning about its axis with angular speed .
a.) Integrate the charge distribution to show that :
b.) show that
using the classical relationship between angular momentum and rotational speed for the spin.
1.) Solving the transcendental equation for the deuteron
a.) Assume the 3-D square well approximates the deuteron system such that the well width is 2.2 fm. Using boundary conditions show that
- : bound state
b.) Rewrite the transcendental equation for the deuteron in the form
and show that
when R = 2 fm.
- Use the reduced mass for the deuteron system.
c.) Solve the transcendental equation forusing an iterative technique.
- I got x = 3.93xxxxxx
5.) Several nuclei decay by the emmission of an alpha particle. An alpha particle (He-4) is a tighlty bound nuclear containing 2 protons and 2 neutrons in which the energy needed to remove one neutron is 20.5 MeV. One model for this decay process views the alpha particle as being bound to the nucleus via a spherical potential well.
Once outside the nucleus, the alpha particle is repelled via Coulombs law
The original nucleus had a chargeand the alpha particle has a charge .
Use the WKB approximation to show that the transmissivity (T : transmission coefficient) is:
- Media:GamowFormula.pdf Gamow's formula
- and and .