Particle physics and Ernest Rutherford's alpha particle scattering experiment are the basis of our project. In this experiment, Rutherford aimed a radioactive source, emitting alpha particles, at thin metal foils and recorded the angles at which the particles were deflected. He found that most of the alpha particles traveled directly through the foil, while others were deflected at angles of 90° or more. With this information, Rutherford was able to formulate the theory of the nuclear atom.
We reproduced Rutherford's experiment on the computer in a simulation, and found how many alpha particles were deflected through each integral degree between 0 and 180°. Angles of deflection were found for each set of different numbered events The program ran different numbers of random events, each different number in a set of ten. Each event is a single alpha particle passing by or being deflected by a metal nucleus. Each set of the same number of events were graphed and compared to find how many events are needed to trust an experiment of this type. This process of simulating an experiment on the computer is similar to the methods used by particle physicists to search for new fundamental particles.
In his early 1900's laboratory, Ernest Rutherford is at work on another experiment. He picks up a photographic plate, and a look of annoyance passes over his face. It was fuzzy, again. Something would have to be done to overcome the scattering of the alpha particles and obtain a clear image.
In 1908, the scattering of alpha particles by matter was a troublesome technical obstacle to conquer. But when the experiment was over, Rutherford asked his colleague, Hans Geiger, to look into the anomaly. This mere annoyance soon turned into one of the greatest breakthroughs in particle physics history, the discovery of the nuclear atom.
Our group has chosen particle physics and Rutherford's scattering experiment as the basis of this year's project. The goal was to reproduce Rutherford's experiment on the computer in a FORTRAN program, eventually make this program parallel, and find how many alpha particles were deflected through certain increments of angles. Then, we would find how many events are needed to trust an experiment of this type, and apply the importance of number of events in Rutherford's experiment to particle physics research today.
Our first step was to chose a topic. We had heard about the search for the top quark and other activities at high energy research facilities around the world. This caught our interest, and we selected particle physics as our project foundation. Particle, or high energy, physics is the study of the most fundamental building blocks of all matter, and their interactions with one another. However, this subject was too broad for writing a program, and a more limited topic within the area of particle physics was needed.
At this time, we called information at Iowa State University to look for a specialist in our selected area, and eventually found Dr. Bob Leacock, a theoretician. Dr. Leacock suggested Rutherford's alpha particle scattering experiment and a few different approaches to manipulating the idea on the computer. He indicated what equation to look for and how to set up the experiment in the program. Later in the project, he gave us a correct equation to use after one we had found produced unfeasible results. He was an invaluable resource throughout our project.
During the course of our investigation and as problems arose, Jerry Ferrell, a physics and chemistry teacher at Central Academy in Des Moines, offered outstanding assistance. He helped to troubleshoot our program and answered questions we had on some of the more difficult scientific content. He was also able to supply us with some reading material.
Dr. Dave Turner, a physics Ph.D., helped us parallelize our program and work out bugs in the computations. His assistance was helpful as well.
North Polk Library and Parks Library on the ISU campus served as the source of most of our research material. North Polk provided several books on Rutherford's experiment that were from a historical perspective, and Parks Library furnished scientific matter. The computer and internet were also excellent sources of information. We posted questions on Newton, searched the World Wide Web for current facts on the top quark, used Gopher to access the Iowa State Library Card Catalog and to look up our mentor's e-mail address, communicated with Dr. Turner over e-mail, and delved into Prodigy for information on Rutherford and atom structure.
Another valuable research source was communication received from several high energy physics research facilities located around the world. CERN, Fermilab National Accelerator Laboratory, Brookhaven National Laboratory, and Stanford Linear Accelerator Center responded to our requests by sending letters, pamphlets, e-mail, booklets, and even teachers' guides. On May 22, we traveled to Fermilab, located outside of Chicago, Illinois, after being invited to tour the facility by Liz Buckley, a scientist working on an experiment there. Both the trip and correspondence helped us to get a better understanding of how computers and computer simulation are an integral part of particle physics research and the importance of number of events in experiments.
This is what we found from our multitude of research: In many of Ernest Rutherford's experiments, he used alpha particles as a primary research tool. Alpha particles are one form of radioactivity and are naturally emitted by several radioactive elements. They are composed of two protons and two neutrons, or a helium atom stripped of its electrons. However, one of their drawbacks, at the time, was the fact that they tended to scatter when colliding with matter, as opposed to going straight through. This complication made results much more difficult to interpret by producing a fuzzy image on photographic plates used to make observations.
After the experiments were over, Rutherford asked Hans Geiger, who was later assisted by Ernest Marsden, to look into the anomaly. A radioactive source emitting alpha particles in a narrow beam was aimed at a very thin sheet of metal foil. Metal foil was used because of its malleable properties; it could easily be formed into very thin sheets. When the alpha particles were scattered, the probability of being scattered by more than one atom was greatly decreased by the foil's minute thickness. The gold foil was surrounded by a phosphorescent zinc sulfide screen set in a circle. After the alpha particles had been deflected, they would hit the screen and produce a small flash of light detectable by microscope. All of this was contained in a vacuum, so that gas molecules in the air would not deflect the particles.
The flashes on the zinc sulfide screen were carefully counted, and it was found, as to be expected, that the number of particles deflected at a certain angle decreased rapidly as the angle increased. The amount of scattering increased with an increase in foil thickness and atomic weight of the metal. The thicker the foil, the more times an alpha particle would encounter an atom; the greater the atomic weight, the greater the deviating effect of a single encounter with an atom. And most of the particles went directly through the foil with ease.
But, most importantly, was the fact that a very small number of alpha particles were being deflected through angles of more than 90°. This had not been expected because alpha particles have very high velocities and masses; a very strong charge would be needed to stop them. Furthermore, backwards scattering due to the accumulated effect of many small scatterings was improbable. The chance of an alpha particle being deflected through a large angle because of multiple scatterings was found to be nearly impossible by mathematical calculation. The scattering had to be the consequence of a single encounter with a single atom because as the foil thickness increased, the number of particles coming back increased at first and then became steady.
At the time, the currently accepted model of the atom, J.J. Thomson's model, was composed of a solid, positively charged sphere embedded with electrons. If this model was correct, then it was expected that practically all the alpha particles would go through the metal foil and at most, suffer only a very small degree of deflection from their initial line of motion. This was a reasonable expectation, due to the fact that in the Thomson model there was no large concentration of electric charge to repel such an energetic particle in the direction opposite from which it came. Backwards scattering was an astonishing phenomenon. Rutherford remarked, "It was quite the most incredible event that has ever happened in my life. It was almost as if you had fired a 15-inch shell at a piece of tissue paper and it had come back and hit you."
Rutherford reasoned that for an atomic force to turn back a particle rushing at a speed of 10,000 miles a second, the force would have to be enormous and highly concentrated. To account for this and the fact that many alpha particles were going straight through the foil, he proposed his theory of the nuclear atom in 1911. Rutherford's model consisted of a heavy center, that would later be called the nucleus, of either positive or negative charge. It may seem that the charge of the nucleus would have been obvious because the alpha particle was positively charged and it would need a positive charge to deflect or repel it. But, the deflection of a charged particle is the same for either sign. If the central charge is positive, it repels the positive particle and causes it to go backwards. If it is negative, the positive particle streams past it and is then attracted back and flies away in a hyperbolic orbit. The calculations of each path are the same.
The rest of the atom would be mostly space inhabited by an equal, but opposite charge to that of the nucleus. The great amount of space explained why so many alpha particles passed directly through the atom without deviation from their initial line of motion.
After assuming the atom is composed of a central charge surrounded by electrons, it is possible to calculate the path of an alpha particle that passes by the nucleus. The path depends on how near the alpha particle comes to the nucleus, this distance being the impact parameter. More precisely, the impact parameter is the distance perpendicular to the initial line of motion from the gold nucleus.
The particle has an equal chance of passing the nucleus at any distance. The angle of deflection can be found with the following equation:
where theta is the angle of deflection, D is the distance of closest approach in a head on collision between the alpha particle and the nucleus, and b is the impact parameter. D is found using this equation:
Epsilon is the permittivity constant; Za is the atomic number of the alpha particle, which is two because an alpha particle has two protons; Zn is the atomic number of the nucleus, which varies depending upon what element is used for the metal foil; e is the charge of an electron, Ma is the mass of the alpha particle, which is the mass of a proton times the four particles in the alpha particle; and va is the velocity of the alpha particle.
Our program simulates an alpha particle shooting past a nucleus using the
above equations. Random numbers were needed for the impact parameter since we
wanted to simulate natural conditions, and there is an equal chance of passing
the nucleus at any distance. The impact parameters were generated in a range of
0 to
Due to the fact that FORTRAN works in radians, it was necessary to change theta from radians to degrees. This was done using the following equation:
After this is done, the program takes each event and sorts it into one of 181, 1° bins from 0 to 180°. These bins come from the set up of Rutherford's experiment. We divided the phosphorescent zinc sulfide screen, set in a circle, into the 181, 10 increments.
There are 181 bins because the program uses a NINT(degrees) function which rounds the degrees off to the nearest integer. The range for degrees is 0 to 180, so we needed bins at both ends. Bin 0 will hold all deflections of 0 to 0.5°, and bin 180 will hold deflections of 179.5 to 180°. The other bins hold ranges of a half degree to either side. The number of events that went into each bin were counted using an array, bin(0:180), and written to file "scattering".
Before we made our program parallel, the program sorted the events into eighteen 10° bins from 0 to 180°. Our results below for the smaller numbers of events, 1, 10, 100, ... 100,000 were sorted in this manner.
In order to see how many events are needed to trust an experiment, a set of ten files were generated for each number of events, 1, 10, 100, 1000, ... 1 billion. Different random numbers were used each time a new "scattering" file was created. Each of these was then graphed using Spyglass Plot, and the graphs of the same number of events were compared to see how similar they were.
We also used different metals for the scattering foil and varied the velocity of the alpha particles to investigate the effects of different initial velocities and different target foils on the angular deflection of the alpha particles.
We found that at one event, the results were very random and ranged from bin one to bin six in a eighteen, 10° bin arrangement. However, the event tended to show up in the lower numbered bins. When ten events were used, results were still very random, but a pattern started to emerge where there were often more events in bin one than any other bin. At 100 events, the graphs look even more similar. A rough curve starts to show and there is an obvious tendency toward the first bin. Very few events show up in the last bins. At 1000 events the graphed results look almost identical, and the curve is fairly smooth. At 10,000 the graph is even smoother, but there are still minute differences. At 100,000 the curve is smooth and data from graph to graph is the most similar.
We found that as the atomic number of the foil increased, the amount of scattering increased. We are still working with velocities of the alpha particles.
Our original program used eighteen 10° bins from 0 to 180°. Graphing 100,000 events using this method produced a smooth curve, and at the time, we believed 100,000 events were enough to trust the experiment. However, after we had graphed 340,000 events generated from our parallel program and used a logarithmic scale on the y-axis, the results were not as similar. We are going to continue running our parallel program with the 181 bin system and use a logarithmic scale on the y-axis until we find a better number of events to trust the experiment. We are also planning on using a better method for comparison of the graphs.
During Rutherford's time period, experimental equipment was not widely available, and many scientific endeavors were limited by human capability. Alpha particles falling on the fluorescent zinc sulfide screen had to be counted one at a time, using a microscope, by whomever was running the experiment. Because of this, events were nonabundant. In the experiment run by Marsden and Geiger, only 1 in 8000 alpha particles were deflected by platinum greater than 90°. Rutherford had to rely on the events that he had to make scientific reasonings and postulate his theory of the atom.
Today, even though scientific technology has greatly increased, particle physicists are still hindered by the number of events available in experiments. To prove the top quark's existence, only eighteen candidate events were available. Before the announcement, twelve candidate events were available, six more than would have been expected if the top quark had not been present. The odds of having that many extra events occurring by chance rather than top quark decay is 400 to 1. These may sound like very good odds, but particle physicists want better odds before they claim to have discovered a new particle. As a result, they were not able to say for sure that the top quark existed.
Scientists must accumulate enough evidence before they can prove or disprove a theory. Without enough events, false scientific theories would be accepted. This applies not only to particle physics, but to all divisions of science.
Anderade, E.N. and C. Rutherford and the Nature of the Atom. Garden City, New York: Doubleday Inc., 1964.
Birks, J. B. Rutherford at Manchester. New York, New York: W. A. Benjamin Inc., 1963.
Blin-Stoyle, R.J. Nuclear and Particle Physics. New York, New York: Chapman and Hall, 1991, pp. 4, 5-7, 75-77, 81-85.
Burcham, W.E. Nuclear Physics: an Introduction (1st and 2nd Editions). San Francisco, California: McGraw-Hill Book Company, 1963, pp. 36-39, 88-97, 138-149, 692-693.
Close, Frank, Michael Marten and Christine Sutton. The Particle Explosion. New York, New York: Oxford University Press, 1987.
Ferbel, Thomas. Experimental Techniques in High Energy Physics. Menlo Park, California : Addison-Wesley Publishing Company, Inc., 1986, pp. 627-633.
Giancli, Douglas C. Physics for Scientists and Engineers. Englewood Cliffs, New Jersey : Prentice Hall, 1989, pp. 202-203, 878.
Harvey, Bernard G. Introduction to Nuclear Physics and Chemistry. Englewood Cliffs, New Jersey: Prentice Hall Inc., 1962, pp. 2-5.
Valentine, L. Subatomic Physics: Nuclei and Particles. Amsterdam, Holland: North-Holland Publishing, 1981, pp. 8-13.
Wilson, David. Rutherford: Simple Genius. Cambridge, Massachusetts: The MIT Press, 1983.
Boslough, John. "Worlds Within the Atom." National Geographic May 1985: pp. 634, 638, 640-642, 649, 650, 653-656, 658-663.
Breuker, Horst, et al. "Tracking and Imaging Elementary Particles." Scientific American August 1991: pp. 58, 60-63.
Folger, Tim. "The Top Quark at Last (Maybe)" Discovery January 1995: pp. 45-47.
Peterson, I. "Particle physics: Stanford wins a B Factory." Science News October 16, 1993 Vol. 144 No. 16: 246.
Pope, Gregory T. "The Trouble With Antimatter." Popular Mechanics June 1994: pp. 112-113.
Teresi, Dick. "The Last Great Experiment of the 20th Century." Omni January 1994: pp. 39-40, 42, 44, 46, 47, 82, 85, 86, 88-89.
Yam, Philip. "You're the Top..." Scientific American July 1994: pp. 24, 26.
Erich, Robert Paul. "Rutherford, Sir Ernest." Academic Encyclopedia (1994), 16, 387.
Ankenbrandt, Chuck. Personal interview at Fermilab. May 22, 1995.
Buckley, Liz. Personal interview at Fermilab. May 22,1995.
Ferrell, Jerry. Personal interview. Five different occasions.
Gillies, James. Letter from CERN European Organization for Nuclear Research to Ms. Kellan Brumback on February 2, 1995.
Lanning, Nancy. Letter from Fermilab to Ms. Brumback. January 25, 1995; January 26, 1995; April 5, 1995.
Leacock, Dr. Bob. Personal interview. Three different occasions.
Leonhardt, Nina A. Letters from Brookhaven National Laboratory to Ms. Kellan Brumback. February 9, 1995; April 5, 1995.
Newburg, Heidi. Personal interview at Fermilab. May 22, 1995.
Turner, Dr. Dave. Helped parallelize program. May, 1995.
Rutherford Scattering of Alpha Particles. Princeton, New Jersey: Films for the Humanities and other Sciences, 1987.
Stanford Linear Accelerator Center. Letter, brochure, document from Nina Stolar to Ms. Kellan Brumback. February 7, 1995.
This is the parallel version of our program.
program p22
*********************************************************
* by Kellan Brumback, Jessica Greubel, Anna Keyte, *
* and Angel Sheriff *
* Function Random and Function GetSeed written by *
* John Gustafson and modified by Dave Turner. *
* May 20, 1995 *
*********************************************************
* Program p22 reads an impact parameter, b, in *
* meters, and calculates the angle the alpha *
* particle is deflected by the gold nucleus. *
* The angles of deflection are then sorted into 181 *
* 1 degree bins from 0 to 180 degrees. The results *
* are written to file "scattering". *
* bin(0:180) are the bins in which the alpha *
* particles enter and are recorded. *
* i and j are loop counting variables. *
* b is the impact parameter, a random number *
* between 0 and 4.9d-12 meters. *
* theta is the angle of deflection. *
* e is the charge of an electron in Coloumbs. *
* Zalpha is the number of protons in an alpha *
* particle. *
* Malpha is the mass of an alpha particle in *
* kilograms. *
* Zmetal is the Atomic number of the metal foil. *
* Velocity is the velocity of the alpha particle. *
* The range for the velocity is 1.4d7 to 2.0d7 in *
* meters/second. *
* epsilon is the permittivity constant. *
*********************************************************
real*8 b,theta,seed,GetSeed,Random,e,Malpha,velocity,
cepsilon,pi,C1
integer i,j,k,bin(0:180),process,host,dim,Zalpha,Zmetal
common/save/ seed
* Open file 'constants' and read
open(unit=15, file ='constants',status='old')
read(15,*)epsilon,Zalpha,Zmetal,e,Malpha,velocity,pi
close(unit=15)
* Calculate one constant and pull out of loop for efficiency
C1=0.5*(1/(4*pi*epsilon))*(Zalpha*Zmetal*e*e)/(0.5*
cMalpha*velocity**2)
* Set the i/o mode to local and get node information
call nlocal()
call whoami(mynode,process,host,dim)
numnodes=2**dim
if( mynode .eq. 0) then
write(6,*)'Program p22 started on ',numnodes,' nodes'
endif
* Clear out bins
do 5 i = 0, 180
bin(i) = 0
5 continue
* Pull conversion constant out of the loop to speed it up
degperrad=360.0d0/3.1415926d0
* Get the starting seed for my node to guarantee no overlap of the
* random number sequence between nodes.
k=mynode
seed=GetSeed(k)
* Loop through a large number of random events on mynode
do 30 i=1,10000
b=Random(4.9d-12)
* The next line calculates angle of deflection.
theta=degperrad*atan(C1/b)
j=DINT(theta)
bin(j)=bin(j)+1
30 continue
* Collect the results from all the nodes by summing all of the
* bin(0:180) arrays together
write(6,*)'Node ',mynode,' bin(7)=',bin(7)
call nisumn(bin(0),181,-1,1,-1)
* Dump out the results
open(unit=13, file='scattering',status='unknown')
do 40 i=0,180
write(13,*)bin(i)
40 continue
close(unit=13)
stop
end
*****************************************************************
* Random returns a random number and updates the seed *
* Written by John Gustafson - Ames Laboratory *
* Modified by Dave Turner - Ames Laboratory *
*****************************************************************
REAL*8 FUNCTION Random(range)
INTEGER*8 i8, j8, k8
REAL*8 r46, seed, range
PARAMETER (k8 = 1220703125, j8 = 70368744177663)
PARAMETER (r46 = 1.D0 / 70368744177664.D0)
common/save/ seed
i8 = seed
i8 = ((i8 * k8) .AND. j8)
seed= DBLE (i8)
Random =(r46 * seed)*range
END
***********************************************************************
*GetSeed gives node k the correct random number seed for its subsequence
* Written by John Gustafson - Ames Laboratory
* Modified by Dave Turner - Ames Laboratory
************************************************************************
REAL*8 FUNCTION GetSeed (k)
INTEGER*4 i, j, k, m
INTEGER*8 i8, j8, k8, m8
PARAMETER (j8 = 70368744177663)
k=k*2**25
k8 = 271828183
m8 = 1220703125
m = 0
j = 1
1 IF (j .LE. k) THEN
m = m + 1
j = j + j
GO TO 1
END IF
DO 2 i = 1, m
j = k / 2
IF (j + j .NE. k) k8 = k8 * m8
m8 = m8 * m8
k = j
2 CONTINUE
GetSeed = DBLE (k8 .AND. j8)
END
EXERCISES
1. What is the investigative question answered in this project?
2. How was this topic selected?
3. What kind of research was done for this project?
4. What information was included in the background section of the paper and how does it contribute to your understanding of the project?
5. Are there any sections of the project report that you do not understand? Explain.
6. What is the most significant accomplishment of this project?