--%>
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 : Define Ergosphere Ergosphere: The area

    Ergosphere: The area around a rotating black hole, among the event horizon and the static limit, where the rotational energy can be removed from the black hole.

    		•
  • Q : What is Eotvos law of capillarity

    Eotvos law of capillarity (Baron L. von Eotvos; c. 1870): The surface tension gamma of a liquid is associated to its temperature T, the liquid's critical temperature, T*, and its density rho by: gamma ~=

    		•
  • Q : Define Carnots theorem Carnot's theorem

    Carnot's theorem (S. Carnot): The theorem that states that no engine operating between the two temperatures can be more proficient than a reversible engine.

    		•
  • Q : What is Bernoulli's equation

    Bernoulli's equation - In an ir-rotational fluid, the sum of static pressure, the weight of the fluid per unit mass times the height and half of the density times the velocity squared is steady all through the fluid 

    		•
  • Q : What is Boltzmann constant Boltzmann

    Boltzmann constant: k (L. Boltzmann) - The constant that explains the relationship between kinetic energy and temperature for molecules in an ideal gas. This is equivalent to the 1.380 622 x 10-23 J/K.

    		•
  • Q : Define Lenzs law Lenz's law (H.F. Lenz;

    Lenz's law (H.F. Lenz; 1835): The induced electric current always flows in such a direction that it resists the change generating it.

    		•
  • Q : What is basic SI unit of electric

    basic SI unit of electric current is termed as Ampere: A (after A.M. Ampere, 1775-1836) The basic SI unit of electric current, stated as the current that, when going via two infinitely-long parallel conductors of v

    		•
  • Q : Radar gun problem Whenever a radar gun

    Whenever a radar gun states the pitch is 90 miles per hour at what point in the balls travel to home plate is the radar gun evaluating the velocity?

    		•
  • Q : How fireworks turn to shapes similar to

    Briefly illustrate how do fireworks turn to shapes similar to hearts and stars?

    		•
  • Q : Explain Right-hand rule Right-hand

    Right-hand rule: The trick for right-handed coordinate systems to establish which way the cross product of two three-vectors will be directed. There are some forms of this rule, and it can be exerted in many manners. If u and v are two vectors that ar

    		•