Muon Lifetime Alden Deran

Muon Energy Loss in Materials Typical cosmic ray muons experience energy loss in a material almost completely due to electronic stopping power – the ionization of atoms in the material. 1The remaining (approximately 1%) of the energy loss is due to Bremsstrahlung radiation, electron/positron pair production, and photonuclear interraction. However, due to the much lower mass of electrons, they are accelerated much more by atomic nuclei and lose more energy to Bremsstrahlung radiation than muons. The amount of energy loss due to Bremsstrahlung radiation is proportional to 1/m4. This radiation is the dominant form of energy loss for electrons, so some materials will stop muons while having a much smaller effect on electrons. In this experiment, it is hypothesized that books will stop muons but allow electrons to reach the detectors.

DAQ Board Setup Gate width set to 10 microseconds, and changed to 15 microseconds for one experiment. TMC delay set to 48 nanoseconds. Different coincidence settings were tried.

Muon Lifetime Experimental Setup When a muon passes through detector A and then is trapped in the material between the detectors, it will eventually decay into an electron, which may be detected in another one of the detectors (or multiple). The time between these two events will be recorded. If a muon passes through detector a and then is not trapped, it will pass through another detector within a nanosecond, and this event will be ignored.

4

5 Hours Stacked With Books

With Books, stacked, 158 minutes

Without Books, Stacked, 158 minutes

Overnight with Partial Box

Partial Box with 2-Fold Coincidence

Results Data Set Time (minutes) Maximum decays Lifetime (microseconds) Error Comments 1 5 3 Not enough data, gate width set too small 2 Data file was lost 36 6 Still not enough data, though several decays detected 4 120 27 1.921 .307 37 3.145 .608 150 2.401 0.228 First successful overnight test 7 100 1.870 0.139 Second successful overnight test – box configuration. 8 80 2.420 .199 2 fold coincidence 9 155 1.913 .107 2 fold coincidence with partial box 10 30 11 1.853 .384 Without books stacked 13 1.254 .210 With books box configuration 12 158 1.897 .346 With books stacked 39 1.354 .172

Additional Error Calculations Chi-square test can determine how good the curve fit is. Data must be downloaded from quarknet: In the data plot, click “analysis directory.” Then, click “lifetimeOut”. Somehow move the data to an excel file or write an analysis program to parse the data file.

Sources Groom, Donald E. Muon Stopping Power and Range Tables 10 MeV to 100 TeV. http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WBB-45BT4PM-6&_user=4428&_coverDate=07%2F31%2F2001&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000059601&_version=1&_urlVersion=0&_userid=4428&md5=3d7e89088f9c3ffdbe1a22f4459f1f7e