Cosmic Ray Decay
On the basis of the information developed in Chapter 14 we may describe the cosmic rays in general terms as cosmic atoms and particles which enter the material environment at the speed of light, at random spatial locations, and with random directions. Here, then, are the contents of the cosmic sector of the universe as they appear, very fleetingly, to our observation. We will now examine what happens to these objects after they arrive.
In the earliest observed stages the cosmic particles are known as the primary cosmic rays. As many observers have pointed out, there is no assurance that these are the original rays, as the decay process may have already begun before the primary rays are observed. The theoretical development indicates that this is, indeed, true, as the primaries contain a considerable percentage of particles that are clearly decay products rather than normal constituents of the origina1 rays. In the subsequent discussion we will follow the general practice, and will refer to the observed incoming particles as the primary rays, but it should be understood that this does not imply that the observed primaries are identical with the particles that originally crossed the boundary into the material sector.
Since the cosmic rays enter the material sector from a region in which the prevailing speeds are greater than unity, these particles make their entry at the speed of light. It is the decrease from a speed greater than unity to a speed less than unity which constitutes entry into the material sector, but the dividing line between the cosmic sector and the material sector is unit speed in all three scalar dimensions. The speed of the primaries therefore remains at or near unity in the observable dimension even after the speed, in total, has decreased to some extent. This accounts for the previously noted fact that the observed speeds of the incoming particles are mainly close to the speed of light.
Inasmuch as these speeds, and the corresponding kinetic energies, are greatly in excess of the normal speeds and energies of the material sector, transfer of the excess kinetic energy to the environment begins immediately on entry. Gravitational and electromagnetic forces, to which the cosmic atom is subject as soon as it crosses the boundary, accomplish part of the energy reduction. Contact with material particles is also an important factor, and a further loss occurs in connection with the reduction of the internal energy that must also take place.
The cosmic atoms of maximum energy content (kinetic equivalent) are those of the most abundant cosmic elements: c-hydrogen and c-helium. The principal constituents of the cosmic rays, the cosmic elements of low atomic number, are therefore not only entering the material frame of reference at speeds which are far too high to be compatible with the material environment, but are also entering in the form of structures whose internal energy (rotational displacement) content is also much too great. These elements must lose rotational energy, as well as kinetic energy, before they can assume forms that will merge with the material phenomena. The required loss of rotational energy from the atomic structures is accomplished by ejection of particles of an appropriate nature. A readjustment of some kind in the atomic motions is required at very short intervals, and the probability principles insure that the direction of the rearrangements is toward greater stability. In the material environment this means a reduction of the excess rotational energy.
At the present stage of the theoretical development it appears that the limitation of the lifetimes of the cosmic elements to extremely short intervals is due to the fact that the rotation in the cosmic structure takes place at a speed greater than unity, and this structure therefore moves inward in time, rather than in space. Consequently, it can exist in a stationary spatial frame of reference for only one unit of time. If it is moving translationally at a speed above unity in all scalar dimensions, as is true of most of the cosmic atoms encountered by chance in our passage through time, it moves away from the line of the time progression of the material sector, and disappears. But this option is not available to cosmic atoms that have dropped below unit speed, and instead, they separate into two or more particles, each of which then has its own appropriate lifetime.
The natural unit of time, in application to macroscopic physical phenomena, was evaluated in Chapter 13 as 1.521×10-16 seconds. Some of the observed particles have lifetimes in this neighborhood, but others range all the way from about 10-16 seconds to about 10-24 seconds. As will be brought out later, the magnitude of the deviation from unit time has been correlated with the dimensions of the spatial motion of the particles, but the exact nature of the modifying factor has not yet been identified, and for the present we will treat it as a modifier of the unit of time, similar to the inter-regional ratio that modifies the unit of space in application to the time region.
The limiting lifetime to which the foregoing comments apply is the limit at zero speed. At higher speeds, the lifetime, as measured by a conventional clock, increases in accordance with the relations expressed in the Lorentz equations, which, as noted earlier, are equally as applicable in the Reciprocal System of theory as in conventional physics. The explanation of this longer life that we deduce from theory is that the particle can remain intact in the spatial reference system as long as it remains in the same unit of time. But an object moving at the speed of light remains in the same unit of time (in the natural system, which is controlling) permanently and such an object can exist indefinitely in any system of reference. The decrease in life at the lower speeds follows the mathematical pattern derived by Lorentz. From the foregoing it is evident that the primary cosmic rays, moving at the speed of light, did not necessarily enter the material sector in our immediate vicinity. The rays that we observe may have entered anywhere in interstellar, or even in intergalactic, space.
In general, as pointed out in the first edition, the successive steps of the decay process which the cosmic atoms undergo after their entry consist of ejections of rotational displacement in the form of massless particles, which continue until the residual cosmic element reaches a status in which it can be transformed into a material structure. Of course, nothing physical can be transformed into something different. Only in the world of magic is that possible. Addition or removal of some constituent can alter a physical entity, but it can be transformed only into some other form of the same thing, as the term itself implies. In the case of the elements the transformation is made possible by the specific relation between the space and time zero points.
As explained in Chapter 12, the difference between a positive speed displacement x and the corresponding negative speed displacement 8-x (or 4-x in the case of two-dimensional motion) is simply a matter of the orientation of the motion with respect to these space and time zero points. The rotational motions of material atoms and particles are all oriented on the basis of the spatial (positive) zero, because, as noted earlier, it is this orientation that enables the rotational combination to remain in a fixed spatial reference system. Similarly, the cosmic atoms and particles are oriented on the basis of the temporal (negative) zero, and are therefore capable of remaining permanently within a fixed temporal reference system, whereas they have only a transient existence in a spatial system. The only difference between a motion with a positive speed displacement x and one with a negative speed displacement 8-x (or 4-x) is in this orientation of the scalar direction. Either can therefore be converted to the other by a directional inversion.
For example, if the negative magnetic displacements of the cosmic helium atoms, (2)-(1)-0, are replaced by the 4-x positive values, this inverts the scalar directions of the rotations without altering the nature or magnitude of either of the rotational components. The product, an atom of the material element argon, 2-3-0 (or 3-2-0 in our usual notation) is therefore the same physical object as the cosmic helium atom. It is merely moving in a different scalar direction. Conversion of cosmic helium into argon is nothing more than a change to another form of the same thing, and thus it is a physical possibility that can be accomplished under the right conditions and by the appropriate processes.
Every atom of either the cosmic or the material type in which the speed displacements do not exceed 3 in either of the magnetic dimensions or 7 in the electric dimension has an equivalent oppositely directed structure. This is illustrated in the following table of equivalents of cosmic and material elements of the inert gas series, the elements with no effective displacement in the electric dimension.
|Cosmic System||Material System|
It does not follow that a direct conversion of an atom of such an element to the equivalent inverse structure is always possible. On the contrary, it is seldom possible. For instance, in order to convert the cosmic helium atom directly to argon the rotations in the two magnetic dimensions would have to be inverted simultaneously, and at the same time the approximately 40 mass units required by the argon atom would have to be obtained from somewhere. The c-helium atom cannot meet these requirements, so at the end of the appropriate unit of time when it must do something, it does what it can do; that is, it ejects a massless particle. This carries away some positive rotational displacement, and moves the residual cosmic atom up the series of elements toward a higher cosmic atomic number, the equivalent of a lower material atomic number.
This process continues until the residual cosmic atom is c-krypton, each rotating system of which is equivalent to a neutron. Here the transformation requirements can be met, as the inversion of each rotation involves only a single effective unit, and no provision for addition of mass is necessary, since the product of the conversion is a massless neutron. The scalar directions of the c-krypton motions therefore invert, and two massless neutrons take their places in the material system. The question as to what then happens to these particles will be discussed in Chapter 17.
The general nature of the cosmic ray decay process, as described in the foregoing paragraphs, was clear from the start of the investigation of the role of the cosmic rays in the theoretical universe of the Reciprocal System. It was therefore evident that the ejections during this decay process must consist of positive rotational displacement in order that the cosmic atoms would be modified in the direction of greater stability in the material environment and ultimately built up to the level where conversion is possible. In the first edition these ejections were discussed in terms of neutrons and neutron equivalents, although it was noted that, in the terrestrial environment at least, they must be massless. Transfer of mass in these events is impossible, as the cosmic atoms have no actual mass. The mass indicated by their behavior in the observed reactions is merely the mass equivalent of the cosmic (inverse) mass that these atoms of the cosmic elements actually do possess. What these atoms must eject is positive magnetic rotational displacement, and this can only take place through the medium of massless particles. The conclusion reached in the earlier study was that in these ejection events the carrier particles must be pairs of neutrinos and positrons (jointly equivalent to neutrons rotationally, but massless) rather than neutrons of the observed type. The more recent finding that the neutron exists in a massless form now resolves this difficulty, as it is now evident that the ejected particles are massless neutrons.
The progress that has been made in both the observational and the theoretical fields has also enabled defining the decay path more accurately and in more detail than was possible in the first edition. Inasmuch as all features of the cosmic sector of the universe are identical with the corresponding features of the material sector, except that space and time are interchanged, the matter accelerated to high speeds by cosmic explosions of astronomical magnitude includes all of the components of cosmic matter: sub-atomic particles and atoms of all of the elements. But in order to be accelerated all the way to unity in three dimensions, a particle must offer a full unit of resistance in all three dimensions. Consequently, the only particles that are able to accelerate up to the escape speeds are the double rotating systems, the atoms. The unit particle in the interchange between the cosmic and material sectors is the atom of unit atomic number, the mass two isotope of hydrogen (deuterium). The mass one isotope of hydrogen does not qualify as a full-sized unit, but it lacks only the equivalent of a cosmic massless neutron, and this can be provided by ejection of a massless neutron of the material type. When subjected to a powerful explosive acceleration the H1 atom therefore ejects such a particle and assumes the H2 status.
The sub-atomic particles are not capable of being accelerated to the escape speed. They are all either inherently massless, or easily separated into massless components, and when they reach their limiting speeds they take the massless forms and thereby terminate the acceleration. The total absence of sub-atomic particles in the cosmic rays that results from this inability to reach the escape speed is not currently recognized because the singly charged particles are mistakenly identified as protons, and the cosmic atoms in the decay sequence—mesons, in the conventional terminology—are accorded a somewhat indefinite kind of a sub-atomic status. But the absence of electrons is a conspicuous and puzzling feature of the cosmic ray phenomenon, and it imposes some severe constraints on theories which try to account for the origin of the rays.
An effect so gross as to exclude completely high-energy electrons from the spectrum at the earth should, it would seem, be accounted for unambiguously by any successful theory for the origin of the cosmic radiation. (T. M. Donahue)65
The unambiguous explanation is now available. No sub-atomic particles are present in the original cosmic rays because these particles are not capable of accelerating to the high inverse speeds necessary for entry into the material sector.
The cosmic property of inverse mass is observed in the material sector as a mass of inverse magnitude. Where a material atom has a mass of Z units on the atomic number scale, the corresponding cosmic atom has an inverse mass of Z units, which is observed in the material sector as if it were a mass of l/Z units. The masses of the particles with which we are now concerned are conventionally expressed in terms of million electron volts (MeV). One atomic mass unit (emu) is equivalent to 931.152 MeV. The atomic number equivalent is twice this amount, or 1862.30 MeV. The primary rotational mass of an element of atomic number Z is then 1862.30 Z MeV, and that of a cosmic element of atomic number Z is 1862.30/Z MeV. Where the atomic mass m is expressed in terms of atomic weight, this becomes 3724.61/m MeV.
As matters now stand, neither the theoretical calculations nor the observations of the masses of the cosmic elements above hydrogen in the cosmic atomic series are sufficiently accurate to justify taking the secondary mass into consideration. The theoretical discussion of the masses of these elements will therefore be confined to the primary mass only, disregarding the small modification due to the secondary mass effect. For the same reasons, both the calculated and observed values in the comparisons that follow will be stated in terms of the nearest whole number of MeV. An exception has been made in the case of hydrogen, because the secondary mass of this element under normal conditions is relatively large, and the probability that it will be altered by changes in environmental conditions is relatively small. Since the mass of a material H² atom is 1.007405 on the atomic number scale, the mass of a cosmic H² atom is the reciprocal of this figure, or 0.99265 units. This is equivalent to 1848.61 MeV.
At this point it will be necessary to recognize that the combinations of motions that constitute the atoms of the elements, both material and cosmic, are capable of acquiring additional motion components of a different kind, each unit of which alters the mass of the atom by one atomic weight unit. It will be convenient to defer the detailed consideration of this new type of motion, which we will call a gravitational charge, until we are ready to discuss the entire class of motions to which it belongs, but for present purposes we need to note that each material element of atomic number Z exists in a number of different forms, or isotopes, each of which has atomic weight 2Z+G, where G is the number of gravitational charges. The normal mass of the corresponding cosmic isotopes is the reciprocal of 2Z+G. but when the cosmic atoms enter the material environment they are able to add gravitational charges of the material (positive) type to the cosmic combinations of motions (including the gravitational charges of the cosmic (negative) type, if any). Each such material type charge adds one atomic weight unit, or 931.15 MeV, to the isotopic mass of the cosmic atom.
In the first edition it was recognized that the incoming cosmic rays would consist primarily of c-hydrogen, but at that time there were no observational indications of any cosmic ray particles in the hydrogen mass range, and the extension of the theoretical development to the questions of scalar motion in two dimensions and the lifetimes of the cosmic atoms had not yet been undertaken. The exact theoretical status of the incoming c-hydrogen atoms was therefore still uncertain. Inasmuch as the “mesons” then known were mainly cosmic elements of the inert gas series, it was concluded that the original c-hydrogen atoms must be stripped of their one-dimensional rotation and reduced to the two-dimensional (inert gas) condition almost immediately on crossing the speed boundary. In the meantime, however, the investigators have been able to extend their observations to earlier portions of the decay path, and they have recently discovered a short-lived particle with a mass that is reported as 3695 MeV.
Identification of this 3695 “psi” particle as a “cosmic deuteron with two material isotopic charges”66 by Ronald W. Satz was the crucial theoretical advance that opened the door to a clarification of the status of cosmic hydrogen. This now enables us to close the gap, and trace the progress of the cosmic atom from its entry into the material sector in the form of cosmic hydrogen (c-H²) all the way to its final transformation into material particles.
For reasons which will be explained in Volume II, the cosmic atom has an effective translational motion in two of the three scalar dimensions at the neutral point where it enters the material half of the universe. The terrestrial environment, into which the observable cosmic atoms enter, is favorable for the acquisition of gravitational charges of the material type. Each of the two dimensions of motion therefore adds such a charge. The two charges acquired by the c-H² atom add 1862.30 MeV to the 1848.61 MeV mass equivalent of the cosmic mass, bringing the total mass of this, the first of the theoretical cosmic ray particles, to 3710.91 MeV. The mass of the newly discovered psi particle is reported as 3695 MeV. In view of the many uncertainties involved in the observations, this can be regarded as consistent with the theoretical value.
As mentioned earlier, the particle lifetimes are correlated with the dimensions of the spatial motions that the particles acquire, the translational motion and the gravitational charges. While the theoretical situation has not yet been clarified, we find empirically that the life of a particle with two dimensions of scalar motion in space and no gravitational charge is about 10-16 seconds, approximately the natural unit of time. Each dimension of motion modifies the unit of time applicable to the particle life by approximately 10-8, while each gravitational charge modifies the unit by about 10-2. On this basis, the following approximate lifetimes are applicable:
|Dimensions||Charges||Life (sec)||Dimensions||Charges||Life (sec)|
The reported lifetime of the 3695 psi particle is in the neighborhood of 10-20 seconds, which agrees with the theoretical determination of the dimensions of motion on which the mass calculation is based.
The general decay pattern defined in the preceding pages indicates that c-H² should undergo an ejection of positive rotational displacement, converting it to c-He³. From the expression 3724.61/m, we obtain 1242 MeV as the rotational mass of c-He³, to which we add the mass of two gravitational charges for a total of 3104 MeV. The observed 3695 particle decays to another psi particle with a reported mass of 3105 MeV, and a life of about 10-20 seconds. This second particle can clearly be identified with the c-He³ atom. Thus the observed masses, the lifetimes, and the decay pattern all confirm the basic identification of the c-hydrogen particle by Satz.
Another decay of the same kind would produce c-He4, and it is probable that some particles of this composition are occasionally formed. Indeed, any cosmic atom between c-hydrogen and c-krypton may appear in the cosmic ray products. But the probabilities favor certain specific cosmic elements, and these are the products that constitute the normal decay sequence we are now examining. The speeds of the cosmic rays and their decay products decrease rapidly in the material environment, and by the time the decay of c-He³ is due the additional energy loss in the decay process is usually sufficient to drop the cosmic residue into the speed range below unity. The consequent elimination of the motion in the second scalar dimension results in a double decay which adds two atomic weight units to the cosmic atom. The product is c-Li5.
Further increases in the inverse mass of the residual cosmic atom by successive additions of single atomic weight units would be possible, but the probabilities favor larger steps as the material equivalent of a cosmic unit increment continues decreasing. The one unit increment in each of the two steps from c-He3 to c-Li-5 is therefore followed by a series of increments that are uniformly one atomic weight unit larger in each successive decay, except for the step between c-N14 and c-Ne20, where the increase over the size of the previous increment is two units.
On this basis, the two l-unit increments that produce c-Li5 are followed by a 2-unit increment to c-Be7, a 3-unit increment to c-B10, a 4-unit increment to c-N14, and a 6-unit increment to c-Ne20. These decay products are not capable of retaining both of the gravitational charges of their precursors, but they keep one of the charges, and all of the cosmic elements identified as members of this section of the decay sequence have masses which include a 931.15 gravitational increment, as well as the basic mass equivalent of the cosmic element, 1862.30/Z MeV. The indicated life of a cosmic atom with one gravitational charge, after dropping into the range of one-dimensional motion, is about l010 seconds. These theoretical masses and lifetimes are in agreement with the observed properties of the class of transient cosmic ray particles known as hyperons, as indicated in the following tabulation:
The masses given are those of the negatively charged particles. Positive electric charges and other variable factors introduce a “fine structure” into the numerical values of the properties of the particles that has not yet been studied in the context of the Reciprocal System.
The observed decay pattern is in agreement with the theory, so far as its general direction is concerned; that is, all of the members of the series decay in such a manner that the eventual result is c-neon. It is still uncertain, however, whether the decay always passes through all of the stages identified with the normal sequence, or whether this sequence is subject to modification, either by omission of one or more of the steps, or by a variation in the size of the ejections of time displacement. The c-Be7 atom, mass 1463 MeV, for instance, is not listed in the tabulation, as its identification with an observed particle of mass 1470 MeV is rather uncertain. This does not preclude its definite identification as a decay product eventually. It may be noted in this connection that the omega particle (c-Li5) was found only as a result of an intensive search stimulated by a theoretical prediction. However, the fact that the last three members of this hyperon series (which were the first to be discovered and are still the best known) are separated by only one decay step, suggests that there is little, if any, deviation from the normal sequence in those cases where the full range of decay from c-He to c-Ne is involved.
When we examine the properties of gravitational charges at a later stage of the theoretical development we will find that the stability of these charges is a function of the atomic number. The mathematical expression of this relation which we will derive from theory indicates that the stability limit for a double gravitational charge in the terrestrial environment falls between the material equivalents of c-He³ and c-Li5. This accounts for the previously mentioned fact that c-Li5 and the elements above it in the cosmic series are incapable of retaining two gravitational charges. But the center of the zone of stability for these elements is closer to the +1 isotope (one gravitational charge) than to the zero isotope (the basic rotation), and for this reason they are all singly (gravitationally) charged, as indicated in the preceding discussion. From c-Si27 upward in the cosmic series, the center of the zone of stability is closer to the zero isotope, and these elements carry no gravitational charges.
Without the gravitational charge, the mass of c-Si27, the decay product resulting from a 7-unit addition to c-Ne20, is 137.95 MeV, and the low speed lifetime is about 10-8 seconds. The corresponding observed particle is the pion, with measured mass 139.57 MeV, and lifetime 2.602×10-8 seconds.
Pions are frequently reported as products of observed cosmic ray events initiated by primaries. As we will see in the next chapter, such production is quite feasible where there is a violent contact of some kind, with the release of a large amount of energy, but direct production of pions in decay is not consistent with the decay pattern as derived from theory. The apparent direct production is, however, understandable when the relative lifetimes of the pion and the earlier decay products are taken into consideration. There is no reason to believe that normal decay in flight will result in any change of direction. Ejection of massless particles will take care of the conservation requirements without the necessity of directional modification. Because the entire decay process up to the production of the pion occupies only a very short time compared to the lifetime of the pion itself, it is unlikely that the usual methods of observation will be able to distinguish between a pion and a cosmic particle undergoing a complete decay to the pion status in flight.
In the kind of a situation mentioned in Chapter 14, for instance, where a pion apparently leaves the scene of an event in a continuation of the direction of motion of the primary, and carries the bulk of the original energy, leading to the conclusion that the primary decayed directly to the pion, there is nothing in the observations that is inconsistent with the theoretical conclusion that during a short interval at the beginning of the motion attributed to the pion, the cosmic particle was actually going through the preceding steps in the decay sequence.
The next event in this decay sequence, the decay of the pion, involves an 8-unit increment to c-Ar35. Again the zero isotope is the stable form. This leads to a mass of 106.42 MeV and a theoretical life equal to that of the pion. The observed particle is the muon, with mass 105.66 MeV, formed by decay of the pion, as required by the theory.
Both the decay to c-Si27 (the pion) and the subsequent decay to c-Ar35 (the muon) continue the same pattern of a uniform one unit increase in the cosmic mass increment in each succeeding event that was followed in the earlier decay steps. But inasmuch as c-argon is equivalent to helium, which, from the material standpoint, is only one step away from the neutron that is the end product of the decay process, the following ejection of positive displacement carries the cosmic atom to the final cosmic structure, c-krypton. Each of the two rotating systems of the c-Kr atom is rotationally equivalent to a neutron, and converts to that particle. Since c-Kr is massless (that is, its observed mass is merely the mass equivalent of the inverse mass of the cosmic sector) the conversion products are massless neutrons, or their equivalents, pairs of neutrinos and positrons. Some of the aspects of this conversion process will be given further consideration in Chapter 17.
Unlike the decay events, which involve changes in the atomic structure, and therefore do not take place until they must, the conversion of the c-krypton rotations to massless neutrons is merely a change in scalar direction to conform with the new environment, and it takes place as soon as it can do so. Consequently, the c-krypton atom, as such, has a zero lifetime. As soon as the particle ejection from c-argon takes place, the conversion to massless neutrons begins. In view of the non-appearance of c-krypton, the apparent lifetime of c-argon, the muon, is the sum of its own proper lifetime and the conversion time. The value reported from observation is 2.20×10-6 seconds. A theoretical explanation of this value is not yet available, but it is probably significant that the difference between this and the life of an uncharged particle moving in one dimension, about 10-8 seconds, is approximately that associated with a gravitational charge.
The absence of the c-krypton atom from the decay process is not due to any abnormal instability of this cosmic atom itself, but to the preference for the alternate scalar direction that prevails in the material environment. In the reverse process, where the directional preference favors the c-krypton atom over the neutron alternate, it plays a prominent part, as we will see in Chapter 16.
In those cases where the incoming cosmic atom is not in the normal decay sequence it ejects enough positive displacement in one or two decay events to reach one of the positions in that sequence, after which it follows the normal path in the same manner as the products of the decay of cosmic hydrogen. However, these heavier elements are beyond the stability limit for two gravitational charges, in a low energy environment, and consequently they do not form structures analogous to the psi particles. This has the effect of increasing the probability that some of the decay products that normally carry one gravitational charge will occasionally be found in the uncharged condition. The one allowable charge would result in an asymmetrical structure during the time that the speed of these particles is in the two-dimensional range, and if they are observed at this stage they are likely to be uncharged (gravitationally). The uncharged lifetime for a particle moving two-dimensionally is approximately one natural unit of time, or about 10-16 seconds. Such a life is the most definite indication that an observed particle is in this early stage of the decay process.
For example, the eta particle, with observed mass 549 MeV and a life of 0.25×10-16 seconds is probably a gravitationally uncharged c-Be7 atom, which theoretically has a mass of 532 MeV. A more questionable identification equates the rho particle with c-Li5. The theoretical mass in this case is 745 MeV, and the observed values range from 750 to 770, the more recent measurements being the higher. The rho lifetime has been reported as about 10-23 seconds, but this is too short to be a decay time. It is evidently a fragmentation time, a concept which will be explained in connection with the discussion of particle production in the accelerators. Both c-Li5 and c-Be7 are in the normal decay sequence, a fact which lends some support to the foregoing identifications. The reported observations of particles that are outside the normal decay sequence will be given some further consideration in the next chapter.
If the incoming cosmic atom is above c-krypton in the cosmic atomic series, so that it cannot enter the normal decay sequence in the manner of the elements of lower atomic number, it must nevertheless separate into parts at the end of the appropriate unit of time, and since it cannot eject massless neutrons as the lighter atoms do, it fragments into smaller units, which then follow the normal decay path.