IntroductionIn this experiment we will explore the particle nature of light. In particular we will see that scattered photons have less energy than unscattered photons in accordance with the same equations that can be used in classical elastic collisions. In general we will show that this collision conserves both energy and momentum.MathTo derive the equation necessary to model Compton scattering we will need to use both conservation of energy and momentum.  Conservation of momentum shows us that the initial momentum of the incoming photon  \(\vec{p_1}\) is equal to the final momentum of the photon  \(\vec{p_2}\) plus the momentum of the electron  \(\vec{p_e}\) .

IntroductionIn this report we will discuss how the Navier-Stokes momentum equation for incompressible flows can be adapted to a numerical solution so that analysis of fluid flow around a fixed object can be made. We will discuss a simplification of the Navier-Stokes equation by a change of variable from velocity to vorticity, the curl of velocity, and the stream function who's spatial derivatives will return the components of our velocity for each section of flow. As well we will examine what boundary conditions are necessary in order to create a flow through our domain and other conditions which will define the boundaries of our object. Finally we will discuss some of the limitations of this examination.MathIn our derivation we began with the incompressible Navier-Stokes equation of the form,

In this experiment we will find that the wavelength of light from a laser can be measured fairly well with the clever use of a ruler. This is a fine way to introduce more advanced forms of error propagation, as well as some introductory statistical analysis tools, to students in an upper division physics lab who are looking to understand the appropriate ways to interpret and report data. The evaluation methods used come directly from John R. Taylor's "An Introduction to Error Analysis" 

OverviewIn this experiment we will try to prove that the gamma rays created from the annihilation of positrons with electrons resulting from the decay of Na22 into Ne22 conserve both energy and momentum.Questions1) Explain what the SCA does for you in this experiment.        In this experiment the single channel analyser will determine if the pulse coming from the amplifier is in the specified range  necessary to have come from an electron-positron annihilation event. This is necessary as the decay products of our sample also include a higher energy gamma ray that is produced when the an excited electron on the Ne22  product falls back to its rest energy.2) Explain how the NaI detector works.        The NaI detector works by advantage of the photo-electric effect. When a photon goes into the crystal an electron is often ejected in the same direction as the motion of the photon. This electron then heads toward our photo-multiplier tube which uses successive dynodes held at a potential relative to each other to further eject electrons. The end result should be a cascade of electrons large enough that we can take a reading of voltage from the capacitor at the end of photo-multiplier tube. 3) Explain why the coincidence detector is so important.        The coincidence detector is important to maintain that any two pulse coming from detector A and B are coming from the same event and not from two random events occurring at the same time.4) Explain how you will count your pulses        For this experiment we were able to count pulses by two methods. First, by a slightly more difficult method, we were able to count gamma rays collected at either detector with a labview program set to count a pulse when the single channel analyser (SCA) detected a pulse within a specified amplitude. Square wave pulses generated by both SCA's were then sent to the coincidence detector in our NIM bin where counts were only made when two pulses were within \(50nm\) of each other. I consider this slightly more difficult than the next method used as it was necessary to use a stop watch and the counter switch to make sure that counts were only made in the 60 second time frame that we specified for the collection of coincidence data. The start button on the labview program as well needed to be pushed when data collection began, which of course required another person and some caution in the timing of all the necessary buttons. In the second method we were able to collect all necessary data through labview with the addition of a coincidence detector and program courtesy of Dr. Professor Chair Extraordinaire Ayars. With this addition we were able to collect single counts from both detectors and coincidences all with a specified time interval and without the need of coordination by multiple people thereby reducing random error.Set-upThis block diagram was taken directly from Positron-Electron lab handout.

IntroductionIn this experiment we will explore whether photons emitted from the decay of positronium, a positron-electron composition, are quantum entangled. When talking about quantum entangled particles it is impossible to fully represent the quantum state of one particle independently of another such that if we know one photon from an entangled pair is horizontally polarized then the other must be vertically polarized. We will use this concept along with knowledge from previous experiments on positron-electron annihilation and Compton scattering to try to determine the truth of this model.ProcedureIn this experiment we used two NaI detectors, photo-multiplier tubes (PMT), pre-amplifiers, and amplifiers. Along with two single channel analyzers, a logic gate, a coincidence detector, a high-voltage supply, and a multi-channel analyzer (MCA) and of course two aluminum targets, a sodium-22 radioactive source, and loads of lead bricks. Our source was encased in the center of our detector configuration such that radiation from the source was focused towards both aluminum targets placed opposite of each other with respect to the source. Both detectors were then stationed so that photons coming from the source were detected after a 90 degree Compton scattering from the target. This ninety degree correlation is necessary for proof of quantum entanglement as we expect no coincidences to occur when both detectors are in the same plane do to quantum pairs anti-correlated polarization causing expected scattering to be related by this ninety degree angle. The picture below shows the basic geometry of this set up.