Difference between revisions of "NucPhys I HomeworkProblems"

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Once outside the nucleus, the alpha particle is repelled via Coulombs law
 
Once outside the nucleus, the alpha particle is repelled via Coulombs law
  
: <math>V_{outside} \prop \frac{2(Z-2)e^2}{r} \equiv \frac{A}{r}</math>
+
: <math>V_{outside} \approx \frac{2(Z-2)e^2}{r} \equiv \frac{A}{r}</math>
  
 
The original nucleus had a charge <math>Ze</math> and the alpha particle has a charge <math>2e</math>.
 
The original nucleus had a charge <math>Ze</math> and the alpha particle has a charge <math>2e</math>.
  
Use the WKB approximation to calcualte the transmissivity (T : transmission coefficient) in terms of the alpha particles velocity <math>(v=\sqrt{2E/m})</math> and the dimensionless ratio <math>\sqrt{r_o/r|\equiv cos W</math>.
+
Use the WKB approximation to calcualte the transmissivity (T : transmission coefficient) in terms of the alpha particles velocity <math>(v=\sqrt{2E/m})</math> and the dimensionless ratio <math>\sqrt{r_o/r}\equiv cos W</math>.
  
  
 
[http://www.iac.isu.edu/mediawiki/index.php/Forest_NucPhys_I Go Back]
 
[http://www.iac.isu.edu/mediawiki/index.php/Forest_NucPhys_I Go Back]

Revision as of 17:17, 6 February 2008

Chapter 2

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:

[math]V(x) = \infty \;\; x\lt 0[/math]
[math]V(x) =\left \{ {-V_0 \;\;\;\; 0\lt x \lt a \atop 0 \;\;\;\; x\gt a} \right .[/math]

V_0 > 0 and E>0. Assume particles are incident from [math]x = -\infty[/math], don't try to normalize but do express the wave function in terms of one coefficient.

3.) Given the following barrier potential

[math]V(x) = \infty \;\; x\lt 0[/math]
[math]V(x) =\left \{ {V_o \;\;\;\; 0\lt x \lt a \atop 0 \;\;\;\; x\gt a} \right .[/math]

show that the transmission coefficient is

[math]T = \frac{1}{1+ \frac{V_o^2 \sinh^2(k_2a)}{4E(V_o-E)}}[/math]

when [math]E \lt V_o[/math]

Assume particles are incident from [math]x = -\infty[/math] and [math]k_2^2 = 2m(V_o-E)/\hbar^2[/math].

4.) 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.

V_{bound} =\left \{ {-V_o \;\;\;\; r <r_o \atop \frac{A}{r} \;\;\;\; r>r_o} \right .

Once outside the nucleus, the alpha particle is repelled via Coulombs law

[math]V_{outside} \approx \frac{2(Z-2)e^2}{r} \equiv \frac{A}{r}[/math]

The original nucleus had a charge [math]Ze[/math] and the alpha particle has a charge [math]2e[/math].

Use the WKB approximation to calcualte the transmissivity (T : transmission coefficient) in terms of the alpha particles velocity [math](v=\sqrt{2E/m})[/math] and the dimensionless ratio [math]\sqrt{r_o/r}\equiv cos W[/math].


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