S18_Measuring Cosmic Ray Muon Momentum from Cherenkov Radiation

Measuring the Momentum Distribution of Cosmic Ray Muons from Cherenkov Radiation

Matthew Forsman & Caleb Lindsey

University of Minnesota

Methods of Experimental Physics

Abstract

A technique to measure the rate of muons at Earth's surface was used to obtain the momentum distribution of cosmic ray muons. When relativistic muons passed through a tube filled with a pressurized gas they emitted Cherenkov radiation which was measured using a photomultiplier tube (PMT). The pressure in the tube was varied across six different momentum thresholds for incident muons to generate Cherenkov radiation from 1.43-3.21 GeV/c. The integral flux of muons was plotted for each momentum threshold then fit to a power law equation. After applying a shower veto based on the electronic waveform output of the PMT, the proportionality constant, α, was determined to be (5.7±0.3)×10^-3 while the exponent, β, was found to be -0.99±0.06. These fit parameter values were compared to accepted values in literature such as Rastin [1]. The values differ by four standard deviations which is attributed to calibration errors in the equipment.

Introduction

This experiment utilized a Cherenkov gas threshold detector with a controllable pressure to measure the incidence rate of cosmic ray muons. The pressure was set at six different levels and the total number of muons was recorded over a period of approximately 20 hours. By normalizing the data for solid angle acceptance of the detector and total time recorded, an integral momentum was obtained for each momentum threshold and fit to a power law curve of the following form:

The fit parameters α and ß were compared with values from B.C. Rastin's paper [1].

Theory

Any charged particle that exceeds the phase velocity of light in a medium will emit Cherenkov photons that can be detected by a photomultiplier tube (PMT). The speed of light in a medium is given by the equation:

Cosmic ray muons are relativistic charged particles generated in the upper atmosphere that rain down on Earth's surface. These muons were detected when they exceeded the momentum threshold in the pressurized tube according to the equation above. Any muon over the threshold momentum generated Cherenkov radiation and so each successively lower threshold includes all muons that could have been binned in higher thresholds as well.

Experimental Setup

A metal pressure vessel was filled with pressurized nitrogen gas. The pressure of the gas was controllable, so that the index of refraction inside the vessel could be varied. Superluminal muons passing through the chamber created Cherenkov radiation that was observed by a UV sensitive PMT connected to the bottom of the vessel. Two pairs of crossed scintillators were placed above and below the vessel and guaranteed only vertically traveling muons were observed. A four-fold coincidence of the scintillators signaled an oscilloscope to send a waveform of the PMT connected to the vessel onto a computer, where it was analyzed by a Labview program. Muon shower events, which may have caused unwanted scintillation by colliding with the glass in the PMT, were vetoed by measuring the minimum and maximum voltages of the PMT waveform at each 4-fold coincidence trigger.

Results

Shower events were vetoed based on the maximum and minimum voltage values of the PMT's waveform over a time window around the trigger from the coincidence unit. This technique for veto was chosen because muon showers have a characteristic waveform with significantly larger oscillations than a single superluminal muon. If the voltage saturated the maximum value readable by the oscilloscope then it was considered a shower event. If a trigger from the coincidence unit was received but no obvious voltage maximums or minimums were observed than it was considered a subluminal muon detection and discarded from data. Figure 2 below shows pictures of the different waveforms seen for a single superluminal muon detection verses a muon shower. Figure 3 shows how the veto affected the count rate for a particular momentum threshold.

The total count of muons obtained for each threshold were divided by the solid angle acceptance of the detector and number of total seconds that data was taken over. Then, each data point was graphed and fit to a power law. The shape of the power law curve and fit parameters were compared with accepted values from literature as shown in figure 4 and table 1.

Conclusions

The fit parameters describing the power law for the integral muon momentum spectrum were α = (5.7±0.3)×10^-3 and β = −0.99 ± 0.06. These values were not consistent with the expected values from literature. The correct curve and shape of a power law was observed, but the count rate was low for all pressure thresholds. One likely cause for part of this discrepancy was from scintillator inefficiency. While the experiment factored in scintillator inefficiencies, just a small fluctuation would cause a large effect on the count rate. A correction for this could have improve the data, but the overall reason for the low count rate remained unknown. The method of applying muon shower vetoes by analyzing the maximum and minimum of the PMT's electronic waveform output was shown to make the data worse. After applying the veto, both fit parameters strayed farther from their expected values. It is suspected that some single event muons were incorrectly vetoed as muon showers, due to the voltage threshold for saturation being set too low. If the thresholds were increased, The chance of single event muons being counted as showers would greatly decrease and the data set would improve. Due to the poor results of our modified veto method, it should be avoided if this experiment is repeated in the future.

References

[1] B.C. Rastin, I.C. Appleton, and M.T. Hogue. “A Study of the Muon Momentum Spectrum and Positive-negative Ratio at Sea-level.” Nuclear Physics B 26.2 (1971): 365-389. Print.

[2] Born, Max, and Wolf, Emil. Principles of Optics: Electromagnetic theory of Propagation, Interference and Diffraction of Light (7th ed.), section 2.33, Cambridge University Press (1999): 92-97.