1/12/06clc

Lifetime of the m meson:

Cosmic rays constantly bombard the earth, and us. Among the energetic particles which reach the surface of the earth, a large fraction are m ⁺ and m ^- mesons, which are generated in collisions of energetic primary cosmic-ray protons with nuclei of air molecules in the upper region of the earth’s atmosphere. They are generated as secondary products: the primary collision produces p mesons via the strong interaction. The charged versions of the p mesons decay via the weak interaction in 26 nsec into m ^{+, -} mesons plus a neutrino. The m mesons in turn decay via a weak interaction into an electron and a neutrino with lifetime of 2.2 msec (for the free

meson) and an energy release of about 50 MeV. Can such a meson live long enough to reach the earth’s surface? If has a large energy, so that it travels nearly at the speed of light, it would take more than 30 msec to traverse the earth’s atmosphere, so the answer is apparently no. But wait! There is time dilation: in the rest frame of the meson, it takes less time for sufficiently energetic mesons than in the earth frame, and so mesons with large gamma can make it.

In this experiment, we measure the mean life of the m mesons which arrive at the earth’s surface. We do this with a very simple procedure. In a large scintillator detector, an energetic charged particle will deposit energy creating a light pulse the intensity of which is proportional to the energy lost in the detector. We seek pulse pairs from the detector: the first is caused when a m mesons enters the detector. The second occurs if the meson stops in the detector and decays there, emitting a fast electron which in turn loses energy and causes a second pulse. The probability that a meson pulse will be accompanied by a decay pulse depends on the scintillator and geometry, but is of the order of 10 ^-2 to 10 ^-3 for your setup. The time separation between these events is the lifetime of the meson. The experiment consists of measuring the distribution of time intervals between the stop and the decay pulses. Of course, you would have to know what causes these pulse pairs in order to be able to interpret the result as a lifetime measurement. Fortunately , we know.

Your apparatus list includes:

• A 10 gallon drum of scintillator fluid, viewed by a photomultiplier tube (PM).
• Electronic modules, including:
1. The photomultiplier preamp (PA).
2. A fast timing-filter amplifier (TFA).
3. A differential constant fraction discriminator (CFD).
4. A time-to-amplitude converter (TAC).
5. A switch-settable delay (DL).
6. A fast amplifier (FA).
7. A scaler (S).
8. A high voltage supply (HV).
9. An oscilloscope (OSC).
10. A mulitichannel analyzer (MCA).
11. Appropriate cables and connectors.

The electronics should be set up roughly as follows:

The purpose of the preamplifier and TFA are to shape and amplify the pulse from the photomultiplier enough to drive the CFD. The purpose of the CFD is to produce a “NIM” (50 ns long, 1 Volt negative) pulse whenever the input pulse exceeds a settable threshold setting. The NIM pulse carries only timing information, no amplitude information. Set the upper and lower thresholds to exclude the lowest pulses and saturated pulses. The purpose of the DL is to delay the NIM pulse. The TAC produces a signal whose amplitude is proportional to the time difference between the start and stop NIM pulses. The range setting gives the time length which will produce a full scale pulse, about 10 volts high. Use a high voltage of + 2000 V. Use the oscilloscope to look at the pulses in and out of each electronics module. Note in your data book how large and how long the pulses into and out of each module are. You will have to terminate the oscilloscope by connecting a 50 ohm resistor to ground in parallel with each cable to avoid reflections. Be sure you understand the function of each module. Set the time constants of the TFA at 100 ns and the gain so that the pulses seldom saturate. Delay the start by about 250 nsec so the TAC will not stop on the same pulse it starts on. You may have to add a fast amplifier (FA) to boost the delayed NIM pulse, since it loses considerable amplitude (and time shape) in the delay box. You can calibrate the time scale by reversing the start and stop and by switching in different values of delay on the DL box. When you are actually doing the experiment, it is good idea to display the TFA output and to trigger the scope on the valid conversion output from the TAC, so you can see what kind of pulse pairs you are analyzing.

Procedure:

It is a good idea to read in Melissinos the section on scintillator detectors and the photomultiplier. The scintillator fluid functions very similarly to a NaI crystal, except that it produces much shorter light flashes at the expense of less light output per flash. You should also read up on the m and p mesons and calculate the energy release of the lepton decay in a Physics 3 text book, such as Tipler and Lewellyn. After satisfying yourself that you understand the principle of the experiment and the functions of all pieces of equipment, use a ⁶⁰ Co source to roughly calibrate the energy scale. This source produces gamma rays near 1 MeV. You will have to replace the TFA by a normal slow amplifier for this step. You will have to keep your wits about you on this exercise and think out each step. You will have to subtract room background and even then you will get a very sloppy looking cutoff with no clear peak. However, you can still do a ballpark calibration. Using this calibration of the MCA, put a pulser into the PA to produce a pulse of about 10 MeV energy, and set the discriminator of the CFD at this level. Now take away the cobalt source and the pulser and find the count rate. It should be around 50 Hz. This procedure is so hard to do accurately that it will probably not give 50 Hz, so in the end you can just set the discriminator to give 50 Hz. The count rate is your best indicator of the correct discriminator setting. The problem is that the intensity of the light flashes is very dependent on where the event occurs in the scintillator and is very non-proportional to the energy deposited in the scintillator.

When you have finished setting the discriminator and verifying that everything looks reasonable on the scope, calibrate the time scale of the MCA. Now take a short run (ten minutes or so). Do a very rough analysis of this data. You will not have enough counts to do a real analysis, but you can estimate the lifetime you will get already. You can use the MCA integration features to integrate the counts over, say, 1 microsecond bins sizes and plot it out in your data book. See if it is in the right ballpark. You will have to run at least overnight, better longer, to get good statistics.

Analysis:

1. Shape of curve: It will eventually take at least overnight to get enough counts to analyze, maybe longer. If there were only a single lifetime present, you would see a curve with the shape Y= A exp(-t/ t) where A is some constant and t is the lifetime.

Q: Why? Derive this in your writeup.

In real life, the curve looks more like Y= A₁ exp (-t/t₁) + A₂ exp (-t/ t₁) + B. The two lifetimes are those of the m ⁺ and m ^- mesons , which have different effective mean lives. The latter has a shortened lifetime because it can be captured by the nucleus of an atom in the scintillator (and surroundings) from which it can decay by interaction with the nucleus. This additional decay mechanism shortens its lifetime by a factor which depends on the material present but which can easily be a factor of two to four. See the supplemental writeups from the Caltech and Harvard experiments for further detail. When you use the differential CFD, the pulse-pair resolution is not sufficient to allow you to see the short time component. This actually simplifies things, although it hides some of the physics. If your instructor is ambitious, he/she may give you a faster CFD which will allow you to see both decay components.

2. Randoms: The B represents random coincidences whereby flashes from different non-associated events start and stop the TAC. You can calculate how large B should be on first principles if you measure the pulse rate of single events using the scaler. Suppose this rate is R (units of counts per time). Then the TAC starts at a rate R and there is a probability R Dt that a second unrelated pulse will stop it during a time interval Dt , giving a randoms rate per channel of R² Dt. Thus if you know what Dt is per channel and how long the experiment has been running, you can figure out what B should be on first principles. Be sure you measure R and the run time so you can calculate this. You can also evaluate B from the flat slope of the data for large time, but you should verify that this value of B agrees with what you expect. Be sure you understand this.

3. You should read out your data and put it into a spreadsheet such as Excel, and fit it using the form given above. If you wish, you may do a least-squares fit. Evaluate the error bar on the lifetime(s) extracted. Be sure your report shows at least one decay curve and the corresponding theoretical fit.

Tips: You can also use a bipolar pulse and the differential zero crossing discriminator. You will then only see the slower decay mode. Adjusting the energy threshold is very difficult. OK also to just adjust it for 50 Hz, eliminating both very large and very small pulses.