Introduction

The earth and its inhabitants are being constantly bombarded by dust, elementary particles and atomic nuclei. Some of these elementary particles and atomic nuclei that hit us are called cosmic rays. “Cosmic rays are high energy charged particles, originating in outer space, that travel at nearly the speed of light” (Mewaldt).

________________________________________________________________________________________________________________________________________________

What are cosmic rays?

In General most cosmic rays are the nuclei of atoms, ranging from the lightest to the heaviest elements in the periodic table. These rays include essentially all of the elements in the periodic table; about 89% of the nuclei are hydrogen (protons), 10% helium, and about 1% heavier elements. Most galactic cosmic rays have energies between 100 MeV (corresponding to a velocity for protons of 43% of the speed of light) and 10 GeV (corresponding to 99.6% of the speed of light).

________________________________________________________________________________________________________________________________________________

How high is the energy of these particles?

Since these particles travel at a significant fraction of the speed of light, then Einstein’s theories of relativity come into play. However since that is beyond the scope of this class, I will not go into the details of these laws.

 

Now Einstein’s equation for Total Energy of particles at rest is

            E = gmc²                     where g is the Lorentz factor

However, since cosmic particles are in motion the total energy of a particle with momentum and a velocity relative to the speed of light is

           

Even though the masses of these particles are small, the value of c² compensates for this, thus making the energy of these tiny particles relatively large.

 

Interestingly enough the most energetic proton detected in the cosmic rays coming in from space had a kinetic energy of 3.0 ´ 10²⁰ eV, about 48.1 J. This has "enough energy to warm a teaspoon of water by a few degrees” (Halliday) and can be compared to the energy of a golf ball[1] travelling at about 45.8 m/s (164.8 km/hr).

________________________________________________________________________________________________________________________________________________

Given the energy of these rays, it is no wonder that they can be found throughout the galaxy. Most galactic cosmic rays are believed to derive their energy from supernova explosions light-years away. In a matter of seconds, the core of an old star collapses, releases a large amount of energy and particles into space, and becomes a supernova remnant. Supernova remnants are identified in space by a nebula (cloud) of gas, which remains in the region of the explosion. One example is the Orion Nebula. It is believed that "cosmic rays are accelerated as the shock waves from these explosions travel through the surrounding interstellar gas" (Mewaldt).

Some of these rays make their way to earth where they will possibly collide with other nuclei. See Figure 1.

 

The collisions will result in other particles being formed; some of which will decay quite rapidly. However, since the resulting velocity will still be significantly high, some of these cosmic particles may make their way to ground if they are falling vertically (the ones coming in at an angle will likely decay before they reach earth). See figure 2.

 

 

The premise that these particles make it all the way to the earth's ground after coming from light-years away was the basis of our scientific experiment. We wanted to be able to view, first-hand, these cosmic rays and achieve the objectives below.

 

Objective

•      To identify cosmic rays (specifically muons) through the use of a cloud chamber.

•      To take readings of the occurrence of these rays at different heights.

•      To derive, from the readings, a simplistic rate of decay for muon particles.

________________________________________________________________________________________________________________________________________________

What are muons?

A Muon is an elementary particle in the lepton (particles in which beta decay is the dominant force) family, having a mass 209 times that of the electron, and a negative electric charge. Muons are also a by-product of the interactions between cosmic rays and nuclei in the atmosphere.

 

Cosmic rays will collide (interact) with a nucleus of the air, usually several ten kilometers high. In such collisions, many new particles are usually created and the colliding nuclei evaporate to a large extent. Most of the new particles are pi-mesons (pions). Neutral pions decay very quickly; usually into two gamma-rays. Charged pions also decay but after a longer time. Therefore, some of the pions may collide with another nucleus of the air before decaying, which would form into a muon and a neutrino. The fragments of the incoming nucleus also interact again, also producing new particles. See Figure 3 and Figure 4.

 Figure 3.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4.

 

Mathematically

p = proton,     m =  muon,     v = neutrino,     e⁺ = positron

 

 

The n is dependent on the kinetic energy of the proton and anti-proton

 

 

 

 

 

Apparatus used

•      Cloud Chamber

•      100% isopropyl (rubbing alcohol)

•      1 kg Dry Ice

•      Flashlight

•      Steel disks (about 5-inches thick together)

 

Procedure (See Figure 5a & 5b)

After visually checking the cloud chamber for foreign bodies, soak the felt lining at the top with the 100% isopropyl. The chamber should then be closed and placed on top of a flat piece of dry ice; making sure that the base is in contact as much as possible. At first, only a rain like mist will appear, but after about fifteen to twenty minutes, clouds should begin to form in the chamber, making it ready for the observance of muon rays. Initial readings should be taken at various heights with a flashlight in the dark to make it easier to view the cloud in the chamber. After each experiment, the steel disks should then be placed a few inches above the chamber in order to take environmental readings. These environmental readings should then be subtracted from the initial reading, resulting in a count of muon particles.

Figure 5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

How it works

The room temperature at the top causes the vapor to be released from the alcohol-soaked felt. The vapor will fall downwards and will be super-cooled, allowing it to exist at a temperature the normally could not and thus forming a dense, damp cloud. "When an electrically charged cosmic ray comes along, it ionizes the vapor--that is, tears away the electrons in some of the gas atoms along its path. This leaves these atoms positively charged (since it removed electrons, which have negative charge). Other, nearby atoms are attracted to this ionized atom. This is enough to start the condensation process. So you see little droplets forming along the path the particle took through the chamber " (Foland).

Results

Members of the group claimed to have one unconfirmed muon sighting. The description of this sighting was that a path that ripped into the vapor cloud. The path was described as a short lived one that was straight with a slight turn in the middle. The description seems similar to that of a muon trail as described in other experiments.

Needless to say, the results were very disturbing and thus we began our search for the reasons of our apparent failure. Below, are some of the errors that we agreed on.

Errors Analysis

Low Energy and Incident Rate

The number of particles starts to increase rapidly as the cascade of particles moves downwards in the atmosphere. On their way and in each interaction the particles loose energy, and eventually will not be able to create new particles. After some point called the shower maximum, more particles are stopped (decayed) than created and the number of shower particles declines. Only a small fraction of the particles usually comes down to the ground. How many actually come down depends on the energy and type of the incident cosmic ray and the ground altitude. Actual cosmic ray counts are said to be subject to large fluctuations.

Cosmic Rays in the Solar System

Figure 6

Cosmic rays are deflected by the magnetic fields in interstellar space, and are also affected by the interplanetary magnetic field embedded in the solar wind (the plasma of ions and electrons blowing from the solar corona at about 400 km/sec), and therefore have difficulty reaching the inner solar system. See Figure 6.

"Spacecraft venturing out towards the boundary of the solar system have found that the intensity of galactic comic rays increases with distance from the Sun. As solar activity varies over the 11 year solar cycle the intensity of cosmic rays at Earth also varies, in anti-correlation with the sunspot number" (Mewaldt).

 

At present (Spring-Summer 2000), the sun is quite active, and it would cause the before mentioned problems. In addition, the solar wind causes changes in the intensity of galactic cosmic rays at Earth, which are a major factor governing the electrical conductivity of the atmosphere. Hence, the intensity of the magnetism in the ionosphere is changed, and thus altering the path and count of cosmic rays coming into the Earth’s atmosphere.

 

Figure 7

 

Latitude

Cosmic rays are high energy charged particles and are attracted to the magnetic poles. Only the highest energy cosmic rays will penetrate the magnetic field and the atmosphere to hit the ground at the equator. Many cosmic rays penetrate the magnetic field, but are guided along the Earth’s magnetic field lines towards the polar regions. See Figure 7.

 

Other Errors

The cross-sectional area of the cloud chamber was relatively small (size of a hand palm) and this restricted the likelihood of viewing a muon particle. In addition the height in the chamber (about 8 cm) did not allow a significant temperature difference between the top and the bottom.

For experiments done on the fourth floor of the Technology Center, the lighting was not ideal to clearly see the cloud within the chamber. Also, the building itself may have been a shield against some of the muon rays.

Delano sipping the isopropyl was probably not a good idea. It may have caused delusion, blindness, etc. and could have caused him to miss a few muons.

Conclusion

Even though our results were less than desirable, the knowledge we have gained is tremendous. To actually learn about the intricate relationship between the Earth and the Sun and all these minute particles is simply amazing. Just the thought that particles could be traveling for light-years and then produce other particles that last as short as 2.2 ´ 10^-6, (Halliday 1123) the lifetime of a muon is simply mind-boggling. Hopefully one of these days I will actually get to see, firsthand, a cosmic ray, for myself; particularly a muon.

Reference

“Solar Connections: A Closer Look.” Online. http://umbra.nascom.nasa.gov/solar_ connections/closer_look.html. April 9, 2000.

Crummett, William. “University Physics.” Wm C. Brown Publishers 1994.

Fasso A., & J Poirier. “A Monte Carlo Calculation of Muon Flux at Ground Level.” Online. http://www.slac.stanford.edu/pubs/slacpubs/8000/slac-pub-8148.html. April 9, 2000

Foland Andrew “How to Build a Cloud Chamber.” Online. http://www.lns.cornell.edu/%7eadf4/cloud.html. April 9, 2000.

Halliday, David. Robert Resnick. Jearl Walker. “Fundamentals of Physics Extended.”  Fifth edition 1997.

Houseman, Jan and Alan Fehr “Listening for Cosmic Rays!” Online. http://www.bartol.udel.edu/~neutronm/listen/main.html. April 16, 2000.

Mewaldt R. “Cosmic Rays.” California Institute of Technology. Online. http://www-hfm.mpi-hd.mpg.de/ChLight/Showers.html

Pictures available at

Figure 1& 2 – http://www2.slac.stanford.edu/vvc/cosmic_rays.html

Figure 3 – http://www-hfm.mpi-hd.mpg.de/ChLight/Showers.html

Figure 6 – http://zebu.uoregon.edu/~js/glossary/solar_flares.html

Figure 7 – http://umbra.nascom.nasa.gov/solar_connections/closer_look.html