How does the physicist untangle the maze and identify each of the interacting particles? Several analytical techniques have been developed for recognizing specific particles by the pattern of their trails. Some of the techniques are almost as complex as the puzzles they are designed to solve. A few, however, can be grasped by amateurs. One simple technique was devised independently last year by Eric M. Dulberg, who was then a student at Benjamin Franklin Senior High School in New Orleans and now attends the Stevens Institute of Technology in Hoboken, N.J. For this accomplishment he received one of the top awards at the National Science Fair and another award from the Atomic Energy Commission. Dulberg's technique can be used to identify any particle that generates a distinctive trail in a single photograph, as well as some particles that make no trails. The method will not identify the so-called resonance particles, however, because their presence must be established by the statistical analysis of hundreds of photographs.

Dulberg writes: "To identify the particles involved in a nuclear interaction by the technique I use, certain information must be available in addition to that provided by the photograph of the interaction. One must know the kind of particle that initiates the interaction, its kinetic energy, the strength of the magnetic field in which it moves and the target particle with which it reacts by means of the nuclear, or 'strong,' force. This information is always available to those who perform nuclear experiments because known particles such as protons, electrons and mesons are deliberately accelerated to prescribed energies for use as projectiles against known target particles. Typically the target particles are protons, represented by the nuclei of hydrogen atoms. In addition one must be familiar with certain details that distinguish each particle from all others, such as its characteristic mass, electric charge (if any), the 'spin' of the particle and the kinds of particles into which it decays. All these characteristics have been tabulated.

"The analysis of track patterns obviously becomes easier with practice. One learns to recognize the trails of certain particles. As the characteristics of the particles become increasingly familiar the analysis takes on some of the aspects of an art.

"I first examine the photograph of the nuclear event, make a pencil sketch of the significant interaction and, by reference to the known characteristics of the particles, establish a tentative identification. This guess is then checked by comparing the behavior of the assumed particles with that required by the conservation laws that all particles obey. If all the observed particles obey these laws, my tentative identification is accepted as final; otherwise I try again. If all the particles but one appear to obey the laws, and this one would obey them also if it were endowed with certain characteristics, the possibility exists that the exception is an unknown particle. Here the technique can serve to predict the essential characteristics of the unknown particle.

"It is rarely necessary or even possible for the amateur to apply all eight of the known conservation laws to a given interaction. The law of parity conservation, for example, can be applied only if the investigator has access to many different photographs of the interaction. Fortunately most of the analyses for which the technique is appropriate can be confirmed adequately by reference to only a few of the laws. They include the conservation of linear momentum, charge, mass and energy, angular momentum (spin), baryon number, lepton number and strangeness.

"Linear momentum is conserved in a nuclear interaction if the product of the mass and the velocity vector of the impinging particles is equal to the sum of the products of the mass and the velocity vector of each of the product particles that emerge from the interaction. Momentum must be neither gained nor lost as a result of the interaction. Similarly, electric charge must be conserved. When two particles interact, the sum of the charges of the participating particles must remain constant. For example, assume that the symbol Q represents charge in an interaction that involves a particle a that carries a charge of +Q and a particle b with a charge of -Q. If three particles emerge from the interaction, one with a charge of +Q and another with a charge of -Q, the law of conservation of charge requires that the third product particle must be electrically neutral. The total mass and energy of the reacting particles must also equal the total mass and energy of the product particles.

"Spin is found by multiplying the quantity h/2 by a constant, in which is 3.1416 and h is Planck's constant (6.62 x 10^-27 erg second). Depending on the particle, spin can have a value of 1/2, 3/2, 5/2 and so on, or of 0, 1, 2, 3 and so on. Spin is conserved if the total spin of the reacting particles equals that of the product particles.

"Baryons, which are the particles of greatest mass, and leptons, which are the particles of least mass, must also be conserved. Each baryon is assigned the baryon number +1; its antiparticle, -1. Leptons are assigned similar lepton numbers. Baryons and leptons are separately conserved if the sum of their respective baryon and lepton numbers remains unchanged following an interaction.

"The term 'strangeness' came into physics during the past decade as a result of the observation that some particles are formed by interactions that involve the strong nuclear force but decay in processes that involve another force: the 'weak' force. This was a form of behavior then considered strange, and it led to the discovery of a new conservation law. In mathematical terms strangeness is denoted by S and is equal to twice the average charge assigned to a particle minus its baryon number. The average charge of a particle is equal to the charge of the group of particles of which it is a member, divided by the number of particles constituting the group. The nucleons, for example, are a group of two particles: the proton of charge +1 and the neutron of charge 0. The charge of the group is + 1, and the average charge of the proton and neutron is + 1/2. Hence the proton is not strange because its average charge, , equals +1/2 and its baryon number equals +1. Putting these numbers into the formula, one obtains 2(1/2) - (+1) and finds that the proton's strangeness is 0. Strangeness is conserved when the sum of the strangeness values of the reacting particles equals the sum of the strangeness values of the product particles.

"During the course of an analysis the conservation laws can frequently provide clues to the characteristics of a particle that is being sought to explain a trail. The lifetime of an unstable particle-the interval during which it exists before decaying-can also be usefully taken into account during an analysis. In general, particles that have a short lifetime make short trails compared with the trails of particles that have a long lifetime.

"The system of nomenclature I use has now been replaced by a new system that classifies particles by groups. In this discussion, however, the old system will be used and should lead to no confusion. The inventory includes 36 particles. Those of greatest mass include 16 baryons and antibaryons-among them the xi (), sigma () and lambda () particles-and the nucleons. Seven particles of intermediate mass are classed as mesons in two groups, the K particles and pi () particles. The eight leptons, the particles of least mass, include the electron (e), the muons () and the neutrinos (). Finally, there is one massless boson, the photon (). The characteristics of these particles and the product particles into which some of the decay are presented in the accompanying tables [Figures 1 and 2 ].

"The trails of any of these particles may appear in cloud chambers of the kind that amateurs can construct, but practically all of them are made by electrons, protons and pi particles. I experimented with a number of homemade chambers, detecting mostly electrons and alpha particles (helium nuclei) when the source was radium and mostly protons and pi particles when the source was cosmic radiation.

"These tracks are easily identified by inspection. Alpha particles from a radium source make trails about an inch long that occasionally end in a small hook. The trails of electrons are thin and wavy. The trails of some cosmic rays (protons, mesons and electrons) appear as relatively straight lines of intermediate thickness that frequently extend across the chamber. Some, however, may leave wavy or spiraling trails. Their appearance depends somewhat on the angle of view. In a chamber equipped with a viewing window at the top the trails of cosmic rays may be a row of dots if the particles enter the chamber directly from above, or straight lines if they enter obliquely. If the chamber is equipped with an appropriate magnetic field, the velocity and energy of the particles can be computed by the methods discussed in this department for June, 1959.

"The photographs of nuclear interactions that I have analyzed were obtained from the Brookhaven National Laboratory, along with the identity of the impinging particle, its kinetic energy, the strength of the magnetic field and the target particle, which I assume to be a proton at rest. All the trails must lie approximately in the plane of the photographic paper. I first make a drawing of the interaction, as shown in the accompanying illustration [Figure 3]. The path of the incoming particle is labeled with the symbol of the known particle, which in the example illustrated is a ^- meson with a kinetic energy of five billion electron volts. The trails of the product particles are next labeled serially with lowercase letters: a, b, c and so on. In addition I occasionally identify with a capital letter the point at which a trail makes an abrupt angle. Such bends indicate points at which particle decays occur. For example, a particle may decay into another charged particle and an uncharged one that does not make a trail. Such an interaction is indicated at point A in the illustration.

"It is apparent in this example that the entering ^- meson interacted with a proton to yield at least four and possibly five product particles, here labeled a, b, c, d and e. Observe that an extension of the line that bisects the angle made by the diverging trails f₁ and f₂ would intercept the trail of the ^- particle at the point where the interaction occurred. Neither f₁ nor f₂ is curved appreciably, even though each is the trail of a charged particle moving in a relatively strong magnetic field of 17,000 gauss. The fact that the particles make trails proves that they carry charges. The fact that they do not curve much in spite of the magnetic field means that they must be particles of comparatively high mass or energy. It is also apparent that the kinetic energies of the two particles must be approximately equal, because the trails diverge at approximately equal angles from the point of origin. The particles must likewise be equal in mass, because they follow complementary paths. It can be tentatively concluded, therefore, that f_l and f₂ are particles of the same type but of opposite charge, because particles of the same kinetic energy and mass are by definition of the same type. That they are oppositely charged is established by the fact that particle d, which decays into f_l and f₂, has no charge. Thus f_l and f₂ must be oppositely charged to conserve charge.

"The second table [Figure 2] lists only one decay that yields two particles of the same type but of opposite charge: the K_l^O meson. It can be assumed with reasonable confidence that the interaction involved the K_l^O meson because (1) this uncharged particle would have made no trail and (2) charge is conserved in the decay. The assumption can now be made that f₁ is a ⁺ meson and f₂ a ^- meson. The sign of the particles is established by first observing the direction of curvature of any electrons in the photograph. Electrons of low energy characteristically appear as tightly spiraled coils in almost all photographs of nuclear interactions. Those in this photograph spiral in a clockwise direction. The electron carries a negative charge. The particle f₂ also curves in a clockwise direction and so must be the negatively charged meson of the pair.

"Track c curves gently in a counterclockwise direction and accordingly must carry a positive charge. It must also be a fairly massive particle, because its path does not curve appreciably or change direction sharply as might be expected of a particle of low mass and momentum. The photograph shows that particle c decays into a positively charged product and at least one neutral particle, the latter fact being evident in the changed direction of the trail. It is also apparent that the kinetic energy of c must be medium or even low, because it is a relatively heavy particle that manages to curve slightly. The positive particle into which c decays must also be heavy and of low kinetic energy for the same reasons. In addition it is apparent that particle g is stable, because it continues on its way for a considerable distance without decaying. The only known stable particle that carries a positive charge is a proton. Particle g is tentatively so identified. The particle that decayed at point A yielded a proton and an uncharged particle. Only one particle is listed in the table with this mode of decay: the positive sigma particle ⁺. The uncharged particle must therefore be a ⁰ meson.

"At this point a check can be made to ascertain if strangeness has been conserved by the assumed particles. Reference to the table of characteristics shows that the strangeness of the reacting particle ^- is 0. The proton with which it interacted also has a strangeness of 0, so the strangeness of the original event is 0. The sum of the strangeness of the assumed ⁺ and K₁⁰ particles is also 0 (S of ⁺ = - 1, S of K₁⁰ = +1). Strangeness is conserved so far.

"The law of the conservation of baryons can now provide a clue to the identity of the remaining unknown particles. The reaction at this stage can be expressed symbolically: ^- + p

a + b + c + ⁺ + K₁⁰ + e, in which a, b, c and e are the unknowns. Substituting the baryon numbers, as listed in the table, for the tentatively identified particles alters the equation to the form 0 + 1 a + b + c + 1 + 0 + e. The sum of the baryon numbers of a, b, c and e must therefore be 0, because the sum of the reactants is 1 and the sum of the product particles is also 1 without taking a, b, c and e into account. Can any of these be baryons. For the conservation of baryons two of the three particles a, b and c would have to constitute a baryon-antibaryon pair. The particle that made track e cannot be a baryon because the angle between e and the path of the original _^- is so large that momentum could not be conserved if the particle were a baryon. Much the same kind of reasoning leads to the conclusion that a and b cannot be baryons: their energies in this case (the sum of (the individual products of their masses multiplied by their kinetic energy) together with the momentum of the other product particles would exceed that of the reacting particles. Thus they must be mesons, the only other class of particles that participate in the strong interaction.

"Two types of meson are known, and K. Which of these might be the unknowns? K mesons have a strangeness number of +1 and a mass equivalent to approximately 496 million electron volts (mev); mesons have a strangeness of 0 and a mass of approximately 137 mev. The strangeness of the reacting particles is 0. Hence for strangeness and total energy to be conserved the unknown particles must be mesons. The charges of a and e are negative because these unknowns curve in a clockwise direction; b must carry a positive charge because it curves in the opposite direction. The complete interaction can be expressed in the symbolic form ^- + p ^- + ⁺ + ⁺ + K₁⁰ + ^-, followed by the secondary decays ⁺ p + ⁰ and K₁^{0 +} + ^-. The characteristics of the particles can then be written in the same sequence for a check against the conservation laws. Beginning with the charge of the particles the equation for the conservation of charge would be: (-1) + 1 = (-1) + 1 + 1 + 0 + (-1). The equation balances; charge is conserved. When expressed in terms of baryon numbers, the equation also balances: 0 + 1 = 0 + 0+ 1 + 0 + 0. It also does for spin: 0 + (1/2) = 0 + 0 + (1/2) . + 0 + 0. Finally, it also balances for strangeness: 0 + 0 = 0 + 0 + (-1) + 1 + 0. In the case of the decay K₁⁰

⁺ + ^-, the equation takes this form to express conservation of charge: 0 = 1 + (-1); baryons, 0 = 0 + 0; spin, 0 = 0 + 0. K₁⁰ has a strangeness of 1, which means that K₁⁰ is a strange particle. (That is the case with any particle having a strangeness number other than 0.) Strangeness is not conserved in the decay of strange particles. Accordingly the equation for strangeness of the K₁⁰ decay does not balance.

"Useful deductions can be made merely by inspecting the trails of a more complex reaction such as the one depicted by the second accompanying photograph and its associated drawing [Figure 4]. A K^- meson (the antiparticle of K⁺) interacts with a proton in the bubble chamber. The short, straight trail a must have been made by either a massive particle or one of high kinetic energy. Certainly its momentum is much greater than the particle responsible for trail c because the latter particle makes a large angle with respect to the trail of the incoming K meson. Assume that trail a was made by a relatively massive particle. It decays into the particle responsible for trail e that curves in a clockwise direction, indicating negative charge. The conservation of linear momentum for the decay of a would require a neutral particle as a product of the decay. The only heavy, unstable particles that carry negative charge are ^-, ^- and ^-. One of these must be responsible for a.

"Alternatively it can be assumed that the particle responsible for trail a does not decay into d and e but rather into a particle of zero charge j and e. In this event j might be a neutron (or antineutron) because it is not seen to decay. (The lifetime of a neutron is about 1,000 seconds.) The unknown a might then be assumed to be a ^- that would decay into an antineutron and a ^-, or a ^- that would decay into a neutron and a ^-. A simple computation quickly demonstrates that the energy of the reacting particles is not adequate to balance the energy that would be represented by this array of postulated particles. The law of energy conservation would not support the assumption.

"Trail a must have been made by a ^-. This particle decays into a ^- and a ⁰, which in turn decays into a proton and a ^-. The particle that made trail f moved in a clockwise direction and therefore carried a negative charge. Trail g was made by a particle that moved in a counterclockwise direction and so carried a positive charge. The curvature of this trail is substantially less than that of trail f, indicating that the responsible particle is the more massive of the pair. For these reasons the particles that made trails f and g can be tentatively designated as a ^- meson and a proton because these are the decay products of ⁰. The particle that made trail e can now be designated as ^- because this meson is the companion of ⁰ in the ^- decay.

"Still other clues to the identity of particles can be developed by reference to the conservation laws. For example, the table indicates a strangeness of-1 for the anti-K particle and a strangeness of 0 for the proton. Their sum is -1. Similarly, the sum of the baryon products is 1, the baryon number of the reacting particles. The reaction at this point in the analysis can be written symbolically in the form K^- + p ^- + x⁰ + y⁺, in which x⁰ is an unknown particle of zero charge and y⁺ an unknown of positive charge. (It can be demonstrated, as in the case of the assumed ^- previously discussed, that a second particle of zero charge cannot exist in this interaction.) It can be assumed that x⁰ and y⁺ are products of the initial interaction involving K^- and its target proton because other product particles have already accounted nicely for the decay of ^-. In other words, the neutral particle x⁰ must have originated in the initial interaction and decayed into the particles responsible for trails h and i. Trail c must have been made by a positively charged particle of low mass because it curves counterclockwise and makes a large angle with respect to the trail of K^-. In the case of a massive particle this abrupt change in direction would imply more energy than is available in the system, and such a situation would violate the law of the conservation of momentum. Thus the particle is not a baryon, which is heavy. This interaction involved the strong nuclear force, the type of interaction in which leptons do not participate. For this reason x⁰ and y⁺ cannot be leptons. The only remaining particle type is the meson. Assume that x⁰ and y⁺ are mesons, either of the K or types. K is relatively massive, according to the table. Assume that y⁺ is ⁺ since y⁺ has a small mass. The conservation laws are useful for predicting the characteristics of unknown particles and can now be used for developing a clue to the identity of x⁰. Strangeness, for example, must be conserved. The strangeness of the reacting particles is -1 (because that of K^-, the antiparticle, is -1 and that of the proton is 0). The strangeness of ^- is -2. To balance the equation, the sum of the strangeness of the product particles must equal -1. The strangeness of y⁺, if it is indeed ⁺, would be 0. The unknown particle x⁰ must have strangeness of +1 to balance the equation (S of ^-, which is -2, plus S of x⁰). The only meson of zero charge with a strangeness of +1 is the K⁰. K⁰ decays into a ^- and a ⁺, the particles responsible for trails h and i, h being ⁺ and i being ^-. The reader may wish to test these tentative identifications by writing the conservation equations, as in the previous example.

"For those who would like to try their hand at this fascinating form of detective work, the accompanying unidentified photograph and drawing [Figure 5] provide an introductory exercise. The interacting particles of this example will be identified in 'The Amateur Scientist' next month."

Bibliography

FRONTIERS OF NUCLEAR PHYSICS. Walter Scott Houston. Wesleyan University Press, 1963.

THE INTELLIGENT MAN'S GUIDE TO SCIENCE. Isaac Asimov. Basic Books, Inc., Publishers, 1960.

INTRODUCTION TO NUCLEAR SCIENCE. Alvin Glassner. D. Van Nostrand Company, Inc., 1961.

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