--%>
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 is Ultraviolet catastrophe

    Ultraviolet catastrophe: It is the shortcoming of Rayleigh-Jeans formula that attempted to explain the radiance of a blackbody at different frequencies of the electromagnetic spectrum. This was clearly wrong since as the frequency rose, the radiance r

    		•
  • Q : Engineering in brief Define the term

    Define the term engineering in brief.

    		•
  • Q : Acceleration during this interval The

    The velocity of a body was observed to be constant throughout five minutes of its motion. Determine its acceleration during this interval?

    		•
  • Q : Problem on Adiabatic law When air is

    When air is compressed adiabatically the law connecting the absolute temperature T and the pressure P is of the form T = A.Pn where A and N are constants. Show by drawing a suitable linear graph that the experimental dat

    		•
  • Q : Define Radian or SI unit of the angular

    Radian: rad: The supplementary SI unit of the angular measure stated as the central angle of a circle whose subtended arc is equivalent to the radius of the circle.

    		•
  • Q : Steps to the scientific notation

    Illustrate the steps to the scientific notation? Briefly illustrate the steps.

    		•
  • 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 Doppler Effect Doppler Effect

    Doppler Effect (C.J. Doppler): The waves emitted by a moving object as received by an observer will be blue shifted (compressed) when approaching, redshifted (that is, elongated) if receding. This takes place both in sound and also el

    		•
  • Q : Define Eddington limit Eddington limit

    Eddington limit (Sir A. Eddington): The hypothetical limit at which the photon pressure would surpass the gravitational attraction of a light-emitting body. That is, a body emanating radiation at bigger than the Eddington limit would

    		•
  • Q : What is balmer series Balmer series (J.

    Balmer series (J. Balmer; 1885): An equation that explains the emission spectrum of hydrogen whenever an electron is jumping to the next orbital; four of the lines are in visible spectrum, and the remainder (residue) are in the ultraviolet.

    		•