--%>
Assignment Help - homework help

Nuclear Physics Homework Help

NUCLEAR PHYSICS (PHY555) HOMEWORK #1

1. Calculate the luminosity for a beam of protons of 1 µA colliding with a stationary liquid hydrogen target 30 cm long. Compare this to a typical colliding beam luminosity of ∼1034 cm-2s-1.

2. An imaginary accelerator consists of colliding beams of electrons and protons, each of 2 TeV total energy. What laboratory energy would be required to achieve the same center-of-mass energy if electrons collide with stationary protons? Repeat the calculation for beams of 2 GeV instead of 2 TeV.

3. Beams of electrons and protons, both traveling at almost the speed of light, collide. The electrons and protons are in bunches 2 cm in length in two rings of 300 m circumference, each of which contains one bunch. Each bunch contains 3x1011 particles, and the circulating frequency is 106=sec for each beam, so that 106 bunches collide with each other per second. Assume that the particle is distributed uniformly over cross-sectional areas of 0.2 mm2, and that this is also the area of the intersecting collision region.

a) Determine the luminosity

b) If the cross section for collisions is 10 µb, determine the number of scattering events per second that would be observed in a counter totally surrounding the intersection region.

c) Find the average x of electrons.

d) If the beam of electrons scatters from a stationary target of liquid hydrogen (density ≈ 0.1 g/cm3) 2 cm long, rather than with the circulating proton beam, find the number of scattering events and compare to part b).

4. The Rutherford scattering amplitude can be written as:

622_pic1.png

where V(x) is the scattering potential and q = p ?? p0 is the momentum transfer of the alpha particle (Z1e) to the target (Ze). Assume V(x) is the Coulomb potential of a nucleus shielded by an electron cloud. Use the form:

1793_pic2.png

where a is a length of characteristic of atomic dimension. Using this amplitude, and the fact that the target charge distribution is spherically symmetric to derive the Rutherford scattering amplitude in the form:

f(q2) = -2mZ1Ze2/q2 +?/a)2

Finally, rewrite this equation in terms of the kinetic energy of the incident alpha particle and the scattering angle.

5. Assume a probability distribution given by (x=j x j)

(4) x <= R : ρ(x) = ρ0

(5) x > R : ρ(x) = 0

a) Compute the form factor for this uniform charge distribution.

b) Calculate < x2 >1/2

6. Download and read the paper, "New measurements of the protons's size and structure using polarized photons", by John Arrington. Answer the following questions with no more than a paragraph of written response for each question.

a) What are the two methods being used to extract the electric and magnetic form factors, GE and GM?

b) Qualitatively, how does the extracted ratio GE/GM differ for these two methods?

c) What is the current explanation for the difference in the ratios between these two types of measurements?

 

 

 

 

   Related Questions in Physics

  • Q : What do you mean by the term geocentric

    What do you mean by the term geocentric? Briefly describe it.

    		•
  • Q : Define Josephson effects Josephson

    Josephson effects (B.D. Josephson; 1962): Electrical effects examined whenever two superconducting materials are separated by a thin layer of the insulating substance.

    		•
  • Q : What is Ground source Heat Pumps Ground

    Ground source Heat Pumps (GSHP): This technology makes use of the energy stored in the earth’s crust, which comes mainly from solar radiation. Fundamentally, heat pumps take up heat at a certain temperature and discharge it at a higher temperatu

    		•
  • Q : What do you mean by the term positron

    What do you mean by the term positron? Explain in short.

    		•
  • Q : Does solar radiation encompass a

    Does solar radiation encompass a complete spectrum of all the forms of electromagnetic radiation?

    		•
  • Q : Calculate time needed for thermocouple

    A thermocouple of K type is suddenly exposed to air with temperature of 1273K, Initial temperature was 293 K. Calculate the time needed for the thermocouple read the temperature with accuracy of better that 99%. Ignore radiation and conduction. The measuring element has a ball shape of diameter o

    		•
  • Q : Define Heat pumps Heat pumps move heat

    Heat pumps move heat from one place to another. They work similar to refrigeration. The movement of heat takes energy, either electrical energy as in the use of  vapor compression heat pumps or thermal energy as in the use of absorption heat pump

    		•
  • Q : What is Wave-particle duality

    Wave-particle duality: The principle of quantum mechanics that entails that light (and, certainly, all other subatomic particles) at times act similar to a wave, and sometime act similar to a particle, based on the experiment you are executing. For ex

    		•
  • Q : Define Mediocrity principle Mediocrity

    Mediocrity principle: The principle that there is nothing predominantly interesting about our position in space or time, or regarding ourselves. This principle most likely first made its real manifestation in the scientific community whenever Shapley

    		•
  • Q : What is Kerr effect Kerr effect (J.

    Kerr effect (J. Kerr; 1875): The capability of certain substances to refract light waves in a different way whose vibrations are in dissimilar directions whenever the substance is located in an electric field.

    		•