A Measurement of the Cosmic Ray Muon Momentum Spectrum using Čerenkov Radiation

Cole Kampa & Ryan Quinn

University of Minnesota

Methods of Experimental Physics

Abstract

A nitrogen gas Čerenkov detector has been used to characterize the integral and differential spectra of cosmic ray muons in the 1.8 to 4.0 GeV/c momentum range. The detector was pressurized between 200 and 1000 kPa to produce the desired Čerenkov threshold momenta. The exponent in the power law that relates the rate of integral muon flux to the threshold momentum is determined to be -0.87 ± 0.05, consistent with past experimental results within 0.1 standard deviations. The accuracy of the differential spectrum is limited due to statistical fluctuations. The addition of an auxiliary scintillator paddle used to veto shower events is found to cause effects consistent with expectations and significantly improve the accuracy of this experiment.

Introduction

We seek to determine the integral and differential spectra of cosmic ray muons in the low momentum regime using a Čerenkov gas threshold detector. This is accomplished by measuring the flux of muons that create Čerenkov radiation in gaseous nitrogen at varying pressures. Both spectra are fit to a power law:

Results are compared to fits performed on a dataset provided by I.W. Rogers and M. Tristam [1].

Theory

Charged particles traveling at speeds greater than the speed of light in a medium emit Čerenkov radiation. The speed of light in a gas is given by c/n, where n is the index of refraction. In the limiting case where the speed of the particle equals the speed of light, the particle's momentum is given by:

Using the Lorentz-Lorenz equation [2] to approximate n, the expression for a Čerenkov momentum threshold is:

where R is the gas constant, T is the absolute temperature, A is the molar refractivity, and P is the pressure.

Primary cosmic rays collide with particles at high altitudes, producing relativistic muons which are detectable at ground level. If the momentum of one of these muons is greater than the threshold momentum of a gas, the muon will produce Čerenkov light. Along with the threshold pressure of the gas, the rate at which muons create Čerenkov light can be used to characterize the momentum spectra of cosmic muons.

Methods

Figure 2: Left: Pulse times relative to trigger for the PMT (red) and the veto scintillator (blue). Center: PMT waveforms binned by pulse height at 800 kPa before (red) and after (green) the shower veto cut. Right: PMT waveforms binned by pulse height for three different pressures.

Count rates are produced using the superluminal pulses and the trigger times. Due to inefficiencies with the oscilloscope's data read operation, approximately 17% of all triggers are lost. The missed event momenta distribution is assumed to be similar to the measured distribution, so the measured count rates are multiplied by an appropriate factor.

The corresponding spectra are fit to a power law. Below are the plotted results, with the differential spectrum on the left and the integral spectrum on the right.

Figure 3: Left: The integral spectrum of cosmic muons. Right: The differential spectrum of cosmic muons.

Table 1: Fit parameters for the integral and differential fits as shown in Figure 3.

The steepening of the integral curve due to the shower veto is expected. As the number of muons at higher threshold momenta is less than at lower threshold momenta, the ratio of showers to superluminal muons is higher at higher threshold momenta. Removing these shower events decreases the points at higher momenta less than those at lower momenta, which steepens the curve.

Conclusions

The exponent in the power law describing the integral spectrum of cosmic muons is determined to be -0.87 ± 0.05, consistent with other experimental datasets, though the observed number of counts is less than the other datasets. Candidates for the cause of this discrepancy are scintillator inefficiencies and a lack of proper normalization, but the true cause is still unknown. The differential spectrum is plagued with statistical uncertainties, and the effect of the shower veto on the differential spectrum is not studied.

The shower veto scintillator is observed to cause a significant improvement in the accuracy of the integral spectrum exponent. The steepening of the integral curve due to the veto is also consistent with expectations. These factors signify that the introduction of the auxiliary scintillator into the setup has significantly improved the accuracy of the resulting integral spectrum, and this scintillator should be included in any further iterations of this experiment.

The large amount of small pulses lost to the shower veto requires further investigation. Although the lost events did not directly affect the accuracy of the obtained result, an investigation into this discrepancy is needed in order to fully examine the effectiveness of the veto scintillator. Other possible improvements to this project include placing lead bricks above one pair of scintillators to decrease the probability that an electron could trigger the system, and reproducing the experiment in the basement of a building as another attempt to decrease shower events.

References

[1] Rogers, I.E. and Tristam, M. "The absolute depth-intensity curve for cosmic-ray muons underwater and the integral sea-level momentum spectrum in the range 1-100 GeV/c." J. Phys. G: Nucl. Phys. 10, Great Britain (1984): 983-1001.

[2] Born, Max, and Wolf, Emil. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (7th ed.), section 2.3.3, Cambridge University Press (1999): 92-97.