Measuring Cosmic Ray Muon Momentum using Cherenkov Radiation

Daniel Erickson & Alexander Cina

University of Minnesota

School of Physics

Minneapolis, MN 55455

Abstract:

In this experiment we measured the momentum spectrum of muons generated by cosmic rays striking the earth’s upper atmosphere. In order to do this, we created a muon telescope that measures the Cherenkov radiation produced by the muons passing through a pressurized gas. The pressure of the gas was varied to change the threshold momentum required for the muon to produce the radiation. This process was executed for two different gasses, carbon dioxide and nitrogen. Using the peaks of the Cherenkov radiation, we were able to plot the integral intensity as a function of momentum to create the momentum spectrum for the muons. However, our results indicate that the momentum spectra of these muons was

from the carbon dioxide, while the results from the nitrogen indicate

, where y and x are the integral intensity and muon threshold momentum, respectively. The disparity may be the result of a systematic error found in the experimental set up that went unaccounted for.

Introduction:

When high energy protons strike the molecules of earth’s upper atmosphere, they produce showers of pions, which then decay into muons and muon neutrinos [1]. The muons should decay into electrons and neutrinos before they reach the earth’s surface. However, they are able to be detected at the surface due to relativistic effects from traveling at very near the speed of light [1]. We detected these muons as they travelled through a pressurized tube with a pmt attached to the bottom. In the pressurized gas, the muons are capable of traveling faster than the light can propagate. In this event, the muon exceeds the threshold momentum and creates a shockwave, leading to uv photons that propagate outward [2]. These photons registered as a pulse in the pmt, and the height of that pulse corresponded to a certain momentum above the threshold.

The purpose of this lab was to expand on work done by previous MXP projects, and verify the threshold momentum spectrum for muons traveling through carbon dioxide.

Theory:

The threshold momentum of a muon is the minimal momentum required to produce Cherenkov radiation in a medium. To find the threshold momentum at a particular pressure, we had to find the refraction index of the , n, which can be obtained by solving equation 1.1, when A, the molar refractivity, is determined for atmospheric conditions, then held constant. 1.1 is then solved for n [3].

We are interested in the threshold momentum of a muon at a particular pressure, where the refraction index is a function of pressure, is given by [2]

Where m is the mass of the muon,

, and c is the speed of light. Combining this function with equation 1.2 will give the relation between threshold momentum and pressure

Figure 1 shows the theoretical plot of this function, pth vs. Pressure.

The number photons created by a Cherenkov pulse is found to be [4]

Experimental Setup:

As shown above, the main component of the Muon telescope is a metal tube filled with pressurized gas. This tube is lined with an aluminized mylar light guide to reflect photons to the photomultiplier tube. This is connected to an oscilloscope which is in turn connected to a computer for recording and analyzing the data.

Scintillator paddles are placed at the top and bottom of the metal tube. In order to create a scintillator cross section that matched roughly the size of the metal tube, the paddles were arranged with two at the top and two at the bottom in a crossed arrangement. This was done so that only muons that traveled directly through the tube triggered all four paddles.

When a muon passed through the paddles, it triggered a coincidence detector, which then triggered the recording of the data. A pressurized CO₂ gas cylinder was connected to the metal tube by a pressure regulator. This allowed us to increase and control the pressure within the metal tube from 20 PSI up to 140 PSI. In this way we could vary the refractive index, and thus the threshold momentum for the muons.

Results:

The final plot of the data with the final exponential trend line is shown above. The equation for the trend for CO₂ is . For N₂ the equation is . These equations fit the data with a reduced

of 1.86 for CO₂ and of 1.3 for N₂. The data lines up very well with the reference data [5], however, this may be coincidental as the reference data was collected at a different geomagnetic latitude and at a different time which would change the sea level muon flux.

Conclusions:

While our carbon dioxide trial compares favorably to the Rastin data, it is only useful as a reference for whether our experiment was running correctly, as the muon flux will differ here at the University of Minnesota that the flux at Nottingham in 1983. What we should be seeing here is an agreement between the nitrogen and carbon dioxide trials. While the two trends fall within two standard deviation of each other, (the uncertainty in the prefactors of x in either trend, +- .05 and +-.04 for the carbon dioxide and nitrogen, respectively, lie within 1 standard deviation and 1.25 standard deviations, again, respectively), we should see a closer agreement.

The reason for their differing trends may be a systematic error that hasn’t been accounted for. This would be a reasonable assumption, as the nitrogen data falls consistently below the carbon dioxide, however, due to the time limitations on this course, possible reasons weren’t explored.

In order to try and find agreement in these two trends, future iterations of this experiment should take equivalently long runs for the nitrogen and the carbon dioxide. A data run with a third gas would also help to identify an unaccounted systematic error, as any gas that had similar absorption of radiation between 300 and 600 nm would create a momentum spectrum similar to carbon dioxide or nitrogen.

Acknowledgements:

We would like to thank Dr. Pryke for his extensive knowledge on the subject, Dr. Kurt Wick for his help in setting up our apparatus, and Dr. Rusack for letting us use his Photomultiplier Tube.

Works Cited

[1] K.A. Olive et al. (Particle Data Group), Chinese Physics C38, 090001 (2014).

[2] Jelley, J. V. (1958). Cerenkov Radiation and Its Applications. London: Pergamon Press.

[3] Born, M., \& Wolf, E. (1999). Principles of optics: Electromagnetic theory of propagation, interference and diffraction of light (4th ed.). Cambridge: Cambridge University Press.

[4] Pryke, C., (1996). Instrumentation Development and Experimental Design for a Next Generation of the Highest Energy of Cosmic Rays

[5] Rastin, B.C. ''An accurate measurement of the sea-level muon spectrum within the range 4 to 3000 GeV/c.''Journal of Physics G: Nuclear Physics. 10. (1984): 1609-1628