Experiment VI-7

Binding Energy

missing isotope mass suggests nuclear structure


As described in Experiment VI-5, Enrico Fermi proposed to his research group in Rome that neutrons, lacking any electric charge, should provide an ideal tool for causing nuclear transformations.  Unlike α particles which are repelled as they approach a nucleus, even slow neutrons might approach a nucleus without repulsion, be absorbed, and create a heavier radioactive isotope.  Early results in 1934 found silver gained more radioactivity when absorbing neutrons on a wood table than on a marble table.  Fermi suspected that neutrons slowed by rebounding off the hydrocarbons in wood were absorbed more readily.  The team confirmed the hypothesis by repeating the experiment in the decorative pool of water in front of their building.  Soon several European teams were attempting to use neutrons to create an element heavier than Uranium, the largest atom then known.

While neutrons were absorbed creating a radioactive isotope, all teams encountered difficulty chemically identifying the new element produced.  In Berlin the chemist, Fritz Strassmann, part of a project started by Lise Meitner and led by Otto Hahn, chemically separated and attempted to identify the new product of

1on + 23892U ⇒ 23993X + o-1β.

MeitnerMeitner, (photo at left) born a Jew, had just narrowly escaped arrest by the Nazis and fled to Stockholm.  Just before Christmas 1938, Hahn wrote that when Strassmann used procedures used to collect elements in the Radium family, he isolated a product with the properties of Barium.  Hahn asked Meitner to consider the possibility the product was a Barium isotope heavier than Uranium.  Walking outside in the snow, Meitner discussed the problem with her nephew, Otto Robert Frisch who had been working with Niels Bohr in Copenhagen.  Considering Bohr's liquid drop model of the nucleus, Meitner calculated on a scrap of paper that probably the intermediate nucleus had fissioned producing two radioactive isotopes which could actually include Barium.

To understand Meitner's proposal it might be helpful to recall the relationship between forces, fields, and energy:

These three descriptions provide different but equivalent perspectives on the same physical effect.  Force between objects is easiest for describing the force between two point-like objects.  Fields allow people to deal with more complicated situations where a great many objects are located at different distances.  Potential energy is most useful for situations where it is too complicated to keep track of all the fields.

Albert Einstein (1879-1955) connected mass with energy by finding the equation E = mc2.

Chemists such as Antoine Lavoisier experimentally found that mass is always conserved so that the total mass never measurably changes during chemical reactions.  However measurable amounts of energy are released in exothermic reactions, seeming to contradict Einstein's equation.  Calculation using E = mc2 of expected mass change reveals that it was simply too small for chemists to measure.  Because an electron's electric charge is tiny, electrical attraction of electrons to atomic nuclei involves small amounts of potential energy.

But accurate measurements of isotope masses revealed that atoms have significant missing mass compared to the sum of masses for constituent protons, neutrons, and electrons.  The mass deficit is the equivalent of an object being in a deep hole, held there by gravity unless sufficient potential energy is supplied to hoist the object out of the hole.  The mass deficit is a measure of the nuclear binding energy holding the atom together.  The nuclear force holding the nucleus together is orders of magnitude greater than the electrical force holding the atom's electrons.  Most interesting is a graph of the missing mass per nuclear particle:

binding energy

Hydrogen, 1H, is composed of a single proton in the nucleus, precluding any nuclear forces.  Inside atoms with several nuclear particles, there could be attractions to every other particle as calculated in the table:

nucleons 1 2 3 4 5 6 ...
# of bonds 0 1 3 6 10 15 ...
bonds/nucleon 0 .5 1.0 1.5 2.0 2.5 ...

If that were true, the graph should be a straight line with a rising slope of 0.5 bond/nuclide2.  But the actual graph of missing mass is not a straight line but peaks with iron, Fe, then gradually declines.  This suggests that attractive nuclear forces occur at only short range and become marginal at greater distances.

Because of the short range of the nuclear force, larger atoms are less stable than medium sized atoms.  Thus is was plausible to Meitner and Frisch that a nucleus larger than Uranium might actually oscillate like a shimmering liquid drop then break into two pieces.  As noted on the graph, the pieces roughly half as large would have MORE missing energy than Uranium, an amount of energy just matching that Meitner calculated the repelling pieces would generate.  It was this agreement between missing mass and the potential energy available due to electrical repulsion that convinced Meitner.  After Christmas, Frisch returned to Copenhagen and told Bohr about fission.  Bohr then took the news across the Atlantic to an international meeting in New York.  Almost immediately physicists realized that the roughly 200 MeV of energy released might be used for making an atomic bomb if enough neutrons were released to carry on a chain reaction.  Enrico Fermi, who had used the occasion of receiving the 1938 Nobel Prize to emigrated to America to escape Mussolini, did experiments which confirmed the possibility of a chain reaction.  By August 1939 Leo Szilard had drafted a letter (read a copy of the letter) which Albert Einstein signed and sent to U.S. President Roosevelt recommending support for further research.

fermi & wifeMoving to the University of Chicago, Enrico Fermi (shown with wife, Laura) headed construction of a graphite pile to demonstrate that neutrons emitted from fissioning Uranium could be slowed by collisions, then subsequently absorbed, producing controlled chain fission.  That demonstrated, Fermi supervised the design and construction of large nuclear fission reactors at Hanford, Washington.  (Download and listen to many of the original scientists discuss the discovery of fission. 36 minutes from American Institute of Physics)

Not all attempts to make atoms heavier than Uranium had failed.  Efforts by Edwin McMillan and Glenn Seaborg at the University of California, Berkeley, to use Ernest Lawrence's cyclotron to collide slow neutrons and later deuterons with an Uranium target produced submicroscopic amounts of elements 93 and 94, named Neptunium and Plutonium after the recently discovered planets.

The Hanford nuclear reactors Fermi's team designed were optimized to make large amounts of the artificial element Plutonium.  The Plutonium was then used to construct one of two atomic bombs which, when exploded in Japan, ended World War II.  Today nuclear reactors around the world are instead design optimized to produce a significant fraction of the world's electricity.  While intensely radioactive (β emitting) wastes are produced, these compact wastes can be readily contained compared to vast amounts of CO2 (a greenhouse gas) released by production of electricity using carbon fuels.

The rapid rise of the graph of missing mass for the first few elements suggested that a fusion reaction combining light elements to make heavier ones would be extremely exothermic.  A number of physicists, knowing that stars are composed mostly of Hydrogen and Helium, speculated that energy of starlight is likely the result of Hydrogen fusing to Helium.  After World War II, the United States developed a Hydrogen bomb powered by fusion which is much more powerful than an atomic bomb.

Efforts to find other elements heavier that Uranium in the debris from atomic and Hydrogen bombs found several additional new elements.  But as predicted by the drop model of the nucleus, larger nuclei were less tightly bound together, were unstable with briefer existences called half lives (defined as the median period of existence, the time elapsed until half decayed).

peninsula of stabilityBut a three dimensional graphs of the missing mass per nucleon plotted verses an isotope's number of protons (Z) and neutrons (N) revealed periodic ridges and peaks suggesting that nuclei have a quantized shell structure similar to that of electrons in atoms.  Certain magic numbers of electrons filled quantum energy levels of atoms resulting in inert elements and stable ions.  It appeared that similar magic numbers of protons and neutrons make nuclei more stable.  The question arose in the early sixties whether quantum shell effects in nuclei much heavier than Uranium could cause them to be stabilized enough that they might still occur in trace amounts in nature, or could be synthesized.  A configuration with two magic numbers, similar to 20882Pb (with 82 protons & 126 neutrons), was anticipated for the isotope 298114X (with 114 protons & 184 neutrons).  Calculations in 1966 predicted an island of stability in this region.  GSI was founded in Germany in 1969 to build a UNiversal heavy Ion Linear ACcelerator (UNILAC) to systematically investigate all nuclear reactions that could conceivably produce superheavy elements.

Efforts they call cold fusion collide stable ions and atoms typically producing a new atom and a single neutron.  More recent efforts using hot fusion collide stable ions with radioactive superheavy elements producing a new atom and four or five neutrons.  While only a single atom is produced at a time (at rates of only a few a day), teams at GSI have developed methods of investigating the chemical properties of the atom and its compounds during its brief existence.


identifying radiation using bubble chamber tracks

Donald GlaserIn 1952 Donald Arthur Glaser (b. 1926, Cleveland), replaced the saturated air in cloud chambers with a liquid on the verge of boiling, improving the resolution of the tracks made visible.  In such a bubble chamber, the formation of bubbles would scatter light much like the droplets in a cloud chamber.  If extremely cold liquid Hydrogen was used, occasionally the radiation collided with the Hydrogen, revealing clues about the interactions between the elementary particles which constitute matter.  They also provide evidence about the properties of elementary particles and their decays.  Bubble chamber photographs have been used to make many important discoveries and measurements.

A single high energy particle may interact with matter in several ways:  Passing close by, a portion of its energy and momentum may be transferred to particles in the target.  Newly ejected particles leave diverging forked tracks except that any particle without electric charge leaves no track at all.  If energy is great enough, interaction may transform energy into a pair of particle and its anti-particle (E = mc2) which in the presence of perpendicular magnetic fields curl in opposite directions.  Or the radiation might pass through the matter without any interaction.  Thus an uncharged particle that rarely interacts with matter could be extremely hard to discover.

While cloud chambers of condensing vapor and bubble chambers of boiling liquids have been retired and replaced by faster detectors, archived photographs from such chambers still provide visual insights into the nature of high energy particles and the procedures we still used to learn about the particles' properties and interactions.  Today such tracks are electronically detected then presented on computer screens looking much like the older photographs.  So understanding the imaging processes and studying the particle tracks can help us understand the nature of matter.

To understand some of the behaviors of elementary particles it might be helpful to review what was learned earlier about electromagnetic force:  Electric force bonds electrons to atoms.  Adding energy to those atoms can create quantized excited states which decay releasing photons of the spectra for that atom.  Various rules must be followed, but typically such exited states decay rapidly in 10-16 seconds or so.  (Removed from the energy in a flame, atoms immediately stop glowing!)  Similar events were observed to occur with particles such as protons that experience the nuclear force which make atomic nuclei stable.  These particles called baryons can be excited to various quantized excited states which decay more rapidly in only about 10-23 seconds.  This is consistent with a stronger force being able to act more quickly.  It was also clear that electrons are not bound by the stronger nuclear force (electrons are not baryons) but are involved in slower β decays.  Therefore there is likely a weaker force. which requires a longer 10-10 seconds to decay.  The tracks in cloud chambers and bubble chambers provided evidence that the strong force causes changes so rapidly that particles have little change to move, while the particles often leave tracks of considerable length waiting for a weak decay to occur.

But in 1947 cloud chamber photographs below lead struck by cosmic rays revealed forked tracks not caused by later secondary collisions but recording delayed decay of baryons.  Expected to rapidly decay while still inside the lead, these baryons travelled much further than expected before decaying.  In 1953 Murray Gell-Mann in the United States and Kazuhiko Nishijima in Japan independently proposed that these baryons had a strange quantum property which was conserved by the strong force (thus precluding the strong force from acting with its characteristic quickness), but could be changed by the weak force.  Thus the strong force could rapidly create (in collision with lead) a strange particle and another with opposite strangeness (so total strangeness =0), but once parted, each strange particle could only be decayed using the slower weak force.  Later, other quantum properties were also discovered.


This experiment involves a few photographs taken at the 2 meter bubble chamber at CERN near Geneva.  The pictures were recorded in a bubble chamber filled with liquid hydrogen exposed to a "beam" of negative kaon particles (K-) each with the same momentum.  Each picture shows a small region of the chamber (about 20 cm in length) so the distance on the screen is roughly the actual distance in the chamber.  The paths of fast moving charged particles in the chamber leave a trail of bubbles which appear as small dots on the photograph.

The superheated liquid in the bubble chamber is prepared by starting with the very cold liquid under pressure (about 5 atmospheres and 3K) and then, just before the particle beam arrives, the pressure is reduced suddenly by expanding the volume by about 1% by means of a piston.  After the particles have passed through the liquid, the bubbles expand until they are a few tenths of a millimeter across before being photographed by flash illumination.  To enable the reconstruction of the event in three dimensions, photographs from different perspectives are taken using several cameras.  The relativistic particles cross the few meters of liquid in a few nanoseconds (1ns = 10-9s); the necessary growth time of the bubbles is about a million times longer, about 10ms.  Once the multiple view photographs are taken, the bubbles are collapsed by recompressing the liquid to prepare the bubble chamber for another shower of particles.  This process requires a few seconds limiting the speed of the research.  The analysis of photographs is labor intensive thus requiring much additional time and funding.  The detectors that now replace cloud chambers and bubble chambers can be recycled much more rapidly and their output is computer analyzed allowing searches for much rarer events.

The kaons shower is made by beam of protons from the CERN accelerator collided with appropriate energy into a target.  After other particles are removed from the beam, the Kaons typically pass through the mainly empty spaces within each hydrogen atom in the bubble chamber without much interaction.  The beam particles are a mixture of neutral and negatively charged.  The negative particles curve slightly in the magnetic field of 1.78 Tesla and leave bubble trails.  Because they all have the same initial direction and momentum and are travelling in a uniform magnetic field, their track curvature and direction should be the same.  Neutral particles do not generate strong magnetic fields which transfer energy needed to create bubbles.  So neutral particles do not leave a visible trail.  But their presence may be surmised if they decay to charged particles within the bubble chamber or if the visible particles' total of energy and momentum is short.  Most uncharged Kaons pass invisibly through the chamber.  Occasional cosmic rays or other particles produced outside the bubble chamber also pass through the chamber but typically not parallel to the shower of beam particles.

When a beam particle of just sufficient energy collides with a proton, the kinetic energy of the center of mass can be converted into additional mass (if E = mc2) producing extra particles equal the energy.  The number and type of particles produced must be consistent with the conservation laws of the strong force.  These include momentum, energy, charge, strangeness, baryon number and lepton number conservation.  As the beam (K-) particle is strange (so assigned strangeness =-1) and the proton his not strange (strangeness =0), the produced particles must also have a total strangeness of -1.  Because the target proton is a baryon (i.e., baryon number =+1) and the beam K- is a meson (not a baryon, so baryon number =0), the produced particles must have a total baryon number of +1.

The electron and it antiparticle called positron have a much smaller mass than other particles.  When they experience electromagnetic forces they are accelerated more than more massive particles leading to a more rapid loss in their energy by radiation of photons.  This rapid loss of energy results in the characteristic tight decreasing spiral of an electron (or positron) track.

It is often difficult to use the track properties to distinguish between different particles.  However the large mass of the proton means it can sometimes be clearly identified by the density of bubbles (or darkness) of the track.  The number of bubbles per centimeter is inversely proportional to the square of the particle velocity.  Where two particles have similar momentum then the velocity of a particle will be inversely proportional to its mass.  As the proton is the heaviest stable particle and is around seven times heavier than the pion its bubble density will be around fifty times larger than a pion.  Consequently the darkest tracks are typically caused by protons.

The walls of the chamber are marked with "X"s to facilitate three-dimensional reconstruction of a collision using simultaneous pictures from several perspectives.  The photographs selected for our use were selected because the recorded events which lie is primarily the plane perpendicular to the camera so that only a single two-dimensional camera view is needed for our analysis.

This experiment has been deliberately structured into two different tasks.  After a short introduction to common features of the photographs you are asked to examine the main features of each photograph and identify the types of particle interactions and decays that occur.

Later some pictures are revisited so you can extract even more information using advanced concepts.  Some particles only exist for 10-23 seconds so they do not leave a measurable track in the bubble chamber even when travelling a speed equal that of light.  They can only travel a distance equal to the diameter of a proton before decaying.  Yet with advanced concepts their presence can be detected and their properties measured.


First Bubble Chamber Photograph

Use this link to open the first photograph.
  1. Notice that most tracks (the beam shower) travel nearly horizontal.  Since they occasionally strike protons or electrons or make particle pairs increasing the number of particles moving their general direction, the beam must be travelling in the direction towards the forked trails they produce.  So which direction is the beam travelling?
  2. Recalling that the visible beam is composed of negatively charged K-, use the right hand rule to determine the direction of the magnetic field.
  3. Recalling the tight spiral paths of electrons, which red letter is near where a K- collision created an electron?
  4. The ionization energy for hydrogen's electrons is rather low enabling uncharged photons (light) to occasionally be absorbed away from beam tracks emitting low energy electrons in small spirals.  Identify a red letter near one such ionized electron.
  5. Occasionally a neutral particle such as a neutron or a neutral kaon (Ko) will decay producing two particles of opposite charge (track curvature).  Identify red letters near several such pair productions.

Interpretations from first photograph:

  1. The beam is moving from left to right.
  2. Pointing your right thumb in the direction of the beam (right) and your palm opposite the direction of curvature (up since the negative particles curve down), your outstretched fingers point in the direction of the magnetic field.  The magnetic field must point into the photograph.
  3. An electron is recoiling at a from collision with beam (K-).
  4. An electron near b is recoiling from collision with a photon.
  5. At d a neutral kaon (Ko) decays into two oppositely charged pions (π- and π+).  At i a neutral particle (Ko) decays into two oppositely charged pions (π+ and π-).  At c there was an interaction between K- and a proton producing two visible oppositely charged particles.  At e of a neutral particle (neutron) interacted with a proton producing two positive and one negative particles.  f. Decay of a pion (π+) into a muon (μ+) and subsequent decay to a positron (e+).  g. Interaction of a neutral particle (neutron) with a proton.  The recoiling proton leaves the dark track.

Second Bubble Chamber Photograph

Use this link to open the second photograph.
  1. Look at the interaction at h.  Is there a K- track coming in from left to right?  What particle did it probably collided with in the liquid Hydrogen?  From the curvatures of each track, what were their charges of the particles produced?
  2. What happened at j?
  3. Look at the interaction at k.  Is there a K- track coming in from left to right?  So what likely was the cause of this forked track?  What particle did it probably collided with in the liquid Hydrogen?  From the curvatures of each track, what were their charges of the particles produced?

Interpretations from second photograph:

  1. h. Interactions of a beam (K-) with a proton producing two oppositely charged particles.
  2. j. Electron recoiling from collision with a beam particle.
  3. k. Interactions of a beam (Ko) with a proton producing two visible oppositely charged particles.

Third Bubble Chamber Photograph

Use this link to open the third photograph.
  1. Look at the interaction at l.  Is there a K- track coming in from left to right?  So what likely was the cause of this forked track?  What particle did it probably collided with in the liquid Hydrogen?  From the curvatures of each track, what were their charges of the particles produced?
  2. Look at the interaction at k.  Is there a K- track coming in from left to right?  So what likely was the cause of this forked track?  What particle did it probably collided with in the liquid Hydrogen?  From the curvatures of each track, what were their charges of the particles produced?  What is indicated by both tracks heading upwards?
  3. Look at the interaction at m.  Is there a K- track coming in from left to right?  So what likely was the cause of this forked track?  What particle did it probably collided with in the liquid Hydrogen?  From the curvatures of each track, what were their charges of the particles produced?
  4. What happened at o?

Interpretations from third photograph:

  1. l. Decay of a neutral particle (Ko) into two oppositely charged pions (π+ and π-).
  2. k. Decay of a neutral particle (K-) into two oppositely charged pions (π+ and π-).  But the angle at which they leave suggest some neutral particle was also produced leaving in a somewhat downward direction.
  3. m. Interaction of a beam (K-) with a proton producing two positive and two negative particles.
  4. o. Electron recoiling from collision with a beam (K-).

Fourth Bubble Chamber Photograph

Use this link to open the last photograph.
  1. Look at the interaction at u.  Presume there is a K- track coming in from left to right.  Don't be confused by the K- track barely above that crosses the photograph without interaction.  So what likely was the cause of this forked track?  What particle did it probably collided with in the liquid Hydrogen?  From the curvatures of each track, what were their charges of the particles produced?
  2. Look at the interaction at v.  Is there a K- track coming in from left to right?   From the curvatures of each track, what were their charges of the particles produced?  So what likely was the cause of this forked track?
  3. What happened atw?
  4. Look at the interaction at x.  Is there a K- track coming in from left to right?  So what particle likely was the cause of this forked track?  What particle did it probably collided with in the liquid Hydrogen?  Notice the darkness of the track moving upwards.  What likely was this particle?  From the curvatures of each track, what were their charges of the particles produced?  What probably happened at x?

Interpretations from fourth photograph:

  1. u. Interaction between a beam (K-) and a proton producing one negative and one positive particle.
  2. v. The decay of a neutral particle into a positive and negative particle.
  3. w. Electron recoiling from collision with a beam (K-).
  4. x. Interaction between a beam (K-) and a proton producing one negative and one positive particle. The dark track is positive and shows the path followed by a proton that stops in the chamber and so the collision is probably an example of elastic scattering.

Advanced Task for first photograph

If necessary, use this link to open the first photograph.
  1. Why does the radius of the spiral get smaller?
  2. By considering the momentum of the particles before and after the collision say why there must be at least one other particle produced at c. What can you say about the charge of this particle?
  3. For the two particles produced in the decay at d use the radius of curvature to determine which has the largest momentum. Use your knowledge of momentum conservation to estimate the original direction of the neutral particle that decays at d.
  4. Consider the two particles that move to the left from e. How can you tell that they have approximately the same momentum? The lower track is much denser than the other one. What does this tell us about the relative mass of the two particles?

Advanced INTERPRETATIONS for first photograph

  1. The electron experiences an electric force due to nearby atoms when it passes through the hydrogen. As its mass is much smaller than the proton the acceleration produced by this force is very large. Any accelerated charge loses energy by emitting photons and this means the electron loses energy and momentum rapidly which leads to a smaller radius of curvature because
    B q v = m v2/r
    r = m v/B q = p/B q (where p is momentum)
  2. Momentum conservation requires that at least one additional neutral particle must be produced and emitted to the left of the observed particles. The additional particle must be neutral as it leaves no track.
  3. The particle moving to the right has the highest momentum. The direction of the neutral particle can be estimated if it decays to the two observed particles and no additional neutral particle. The momentum of each of the two decays products is proportional to their radius of curvature. The momentum of the parent is the vector sum of the two decay particle momenta. The line of flight will always be between the decay products and in this case will lie closer to the line of the higher momentum negative track which is on the right. This means that the neutral particle is probably produced at the nearby kaon proton interaction labelled c.
  4. They have approximately the same curvature. The number of bubbles/cm is inversely proportional to v2 where v is the velocity of the particle. Where two particles have similar momentum e.g. the two nearby particles in this interaction then the velocity of the particle will be inversely proportional to its mass. The proton is the heaviest stable charged particle and has a mass around seven times that of a pion and so the bubble density will be around fifty times larger for the proton. This means that very dark tracks are usually protons. There are a few exceptions e.g. where a track is travelling towards or away from the camera but these can be eliminated when using photographs from three different cameras.

Advanced Task for second photograph

If necessary, use this link to open the second photograph.

The negatively charged beam kaon interacts with the positively charged proton at h to produce positive, negative and a neutral particle.
  1. The magnetic field is into the paper.  Which of the particles produced at h is positively charged?
  2. Which particle has the highest momentum?
  3. Assume that all the particles in the interaction travel at approximately the speed of light and that the picture is full scale.  Estimate the lifetime of the neutral particle produced at h which decays at i.
  4. Does this time indicate that the decay proceeds by the weak or strong force?
  5. How could you check if any neutral particles were produced at interaction h?
  6. If a single neutral particle were produced and this did not decay in the bubble chamber, how could its mass be estimated?
  7. How can the direction of the neutral particle which decays at i be estimated?
  8. How can the mass of this neutral particle be calculated?

Advanced INTERPRETATIONS for second photograph

  1. The particle moving to the left is positive. Notice that it is the direction of curvature, not the direction of its motion, that depends on the charge.
  2. The particle with larger radius of curvature has the higher momentum.
  3. The neutral particle travels about 3.5 cm in the chamber before it decays.  If it travelled at the speed of light then the time for it to decay is
    t = 0.035 / 3 x 108 = 1.2 x 10-10 seconds
  4. The neutral particle is a Ko which is the lightest strange particle.  Because strangeness is conserved by the strong force this decay can only proceed using a different force.  Decays via the strong force occur extremely rapidly in typically 10-23 seconds but this decay which is able to change strangeness takes much longer and is therefore called the weak force.  The Ko decays to two pions, neither of which are strange (having no known slow decay modes).
  5. In beginning Physics SI units are always used. But particle physicists find it much more convenient to use the units which have the speed of light (c) equal unity.  These have been introduced to avoid the need to have to repeatedly multiply or divide by the speed of light (c) in all the equations.  The commonly used energy (E) unit is GeV which is 109 electron volts. The units used for momentum (P) and mass (M) are GeV/c and GeV/c2 respectively,  So with these units the relativistic equation can be written as
    E2 = P2 + M2

    Although this seems confusing it means that with these units that energy, momentum and mass always have the same dimensions.
    One could check whether energy and momentum conservation is consistent with the observed particles. The momentum (PK) and rest mass (MK) of the incident kaon is known and so the kaon energy (EK) can be calculated using
    EK2 = PK2 + MK2

    The target proton has zero momentum and mass MP and so has energy EP = MP and so the total initial energy E and momentum P can be computed using
    E = EK + EP
    P = PK

    The momentum P1 and P2 of each of the two charged outgoing particles can be measured from their radius of curvature using P = Bqr.  Note the magnitude of the vector momentum, in the plane of the photograph, is obtained from this equation and then we need to measure the angle of the trajectory at the interaction point to convert to a vector momentum.  We would need to use the photograph from all three cameras to measure these angles in three dimensions.  If we could identify the outgoing particle types from the bubble density or other characteristics then we could use E2 = p2 + m2 to obtain the energy of each track.  We can then compare the initial and final energy and momentum sums for the event to see if they are consistent allowing for the experimental errors on the measurements.  Missing energy and momentum suggests a missed invisible particle.
  6. If a single neutral particle is produced then its energy and momentum can be deduced from the shortage.  The mass can be evaluated using
    M2 = E2 - P2
  7. In this neutral decay the two charged decay tracks originate from one point and cross at a separate point in the chamber. Momentum conservation means that the neutral particle flight path follows the line joining these two crossing points.  In this case it is clear that the neutral particle is produced at the interaction labelled h.
  8. If the neutral particle decays into the two observed charged particles then its mass can be estimated by the following method. If the identity of the two decay particles are known and their momenta measured then we can use energy and momentum conservation in the decay to evaluate the energy and momentum of the decaying neutral particle. Then its mass can be evaluated using
    M2 = E2 - P2


Glaser was awarded the 1960 Nobel Prize for Physics:


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created 18 October 2003
revised 31 March 2007
by D Trapp
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