# Difference between revisions of "NucPhys I HomeworkProblems"

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# Chapter 2

## Set 1

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.

## Set 2

1.) Given the following barrier potential

show that the transmission coefficient is

when

Assume particles are incident from and .

## Set 3

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.

## Set 4

1.) Show that the mean-square charge radius of a uniformly charged sphere is

2.) Using the definition of the form factor and probably an integral table, calculate when

a.):

b.)

c.)

## Set 5

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 correction due to the finite nuclear size.

3.) Find the binding energy using the fit equation B(Z,A) from the semi-empirical mass formula for

a.) Ne-21

b.) Fe-57

c.) Bi-209

d.) Fm-256

4.) Find the neutron separation energies for

a.) Li-7

b.) Zr-91

c.) U-236

5.) Find the proton separation energies for

a.) Ne-20

b.) Mn-55

c.) Au-197

## Set 6

1.) Assume a neutron may be described as a proton with a negative pion in 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 radius spinning about its axis with angular speed .

a.) Integrate the charge distribution to show that :

(hint: )

b.) show that

using the classical relationship between angular momentum and rotational speed for the spin.

## Set 7

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

where

and

: 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 for using an iterative technique.

I got x = 3.93xxxxxx

## Set 500

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 charge and the alpha particle has a charge .

Use the WKB approximation to show that the transmissivity (T : transmission coefficient) is:

Gamow's formula Media:GamowFormula.pdf

where

and and .