EP0099946A1 - Procédé et appareil pour provoquer la décroissance nucléaire bêta - Google Patents

Procédé et appareil pour provoquer la décroissance nucléaire bêta Download PDF

Info

Publication number
EP0099946A1
EP0099946A1 EP82303910A EP82303910A EP0099946A1 EP 0099946 A1 EP0099946 A1 EP 0099946A1 EP 82303910 A EP82303910 A EP 82303910A EP 82303910 A EP82303910 A EP 82303910A EP 0099946 A1 EP0099946 A1 EP 0099946A1
Authority
EP
European Patent Office
Prior art keywords
beta decay
beta
decay
nuclear
field
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
EP82303910A
Other languages
German (de)
English (en)
Other versions
EP0099946B1 (fr
Inventor
Howard R. Reiss
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
University Patents Inc
Original Assignee
University Patents Inc
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by University Patents Inc filed Critical University Patents Inc
Priority to EP19820303910 priority Critical patent/EP0099946B1/fr
Priority to DE8282303910T priority patent/DE3273860D1/de
Publication of EP0099946A1 publication Critical patent/EP0099946A1/fr
Application granted granted Critical
Publication of EP0099946B1 publication Critical patent/EP0099946B1/fr
Expired legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G21—NUCLEAR PHYSICS; NUCLEAR ENGINEERING
    • G21G—CONVERSION OF CHEMICAL ELEMENTS; RADIOACTIVE SOURCES
    • G21G1/00—Arrangements for converting chemical elements by electromagnetic radiation, corpuscular radiation or particle bombardment, e.g. producing radioactive isotopes
    • G21G1/04—Arrangements for converting chemical elements by electromagnetic radiation, corpuscular radiation or particle bombardment, e.g. producing radioactive isotopes outside nuclear reactors or particle accelerators
    • G21G1/10—Arrangements for converting chemical elements by electromagnetic radiation, corpuscular radiation or particle bombardment, e.g. producing radioactive isotopes outside nuclear reactors or particle accelerators by bombardment with electrically charged particles

Definitions

  • This invention relates to a method and apparatus for inducing nuclear beta decay transitions that are normally inhibited by angular momentum or parity considerations.
  • a method of inducing nuclear beta decay transitions comprises providing a medium which includes atomic nuclei that have forbidden beta decay transitions in which the initial and final nuclear states do not have the same intrinsic pairty or have total angular momenta which differ by more than one quantum unit of angular momentum, and applying to the medium an electromagnetic field which has an intensity sufficient to provide the angular momentum or intrinsic parity necessary to overcome the forbiddenness of the beta decay transitions of the atomic nuclei, thereby to induce the beta decay transitions.
  • an apparatus for inducing beta decay transitions comprises a medium which includes atomic nuclei that have forbidden beta decay transitions in which the initial and final nuclear states do not have the same intrinsic parity or have total angular momenta which differ by more than one quantum unit of angular momentum, field producing means for producing an electromagnetic field in the medium and means for energising the field producing means to establish the field at an intensity sufficient to provide the angular momentum or intrinsic parity necessary to overcome the forbiddenness of the beta decay transitions of the atomic nuclei.
  • the energy released in these induced nuclear transitions is useful for the controlled production of power.
  • the induced beta decay transitions are also useful to reduce the halflives of long-lived fission product wastes from conventional nuclear fission power plants.
  • the present invention involves induced emission from a certain type of metastable nuclear state.
  • the 2s state of the hydrogen atom is metastable; but it can be induced to decay to the Is ground state by a nonresonant electromagnetic field.
  • the emission occurs with at least one photon of inducing field type, plus another photon carrying the remaining energy of the 2s-ls energy level difference.
  • the theory for this process was given by Zernik 3/ for a first order process in the inducing field.
  • the theory of arbitrarily high order processes involving a low frequency inducing field has also been developed.
  • the present invention relates to the production of nuclear energy by the process of induced beta radioactivity.
  • the word “stimulated” is suggestive of laser physics, where the stimulating radiation is resonant with an atomic or molecular transition, so that the stimulated radiation and stimulating radiation are of the same type.
  • the word “accelerated” might be more acceptable, although it seems inappropriate in those cases where the nuclear species in question exhibits no radioactivity at all when not subjected to inducing radiation.
  • the term “forbidden” is used in beta decay physics, not as an absolute term, but to indicate that the transition is strongly inhibited.
  • Such species therefore have very long halflives. It is the basic purpose and objective of the present invention to induce the beta decay of such species so as to materially reduce their halflives. With nuclides which normally exhibit beta decay, this would lead to an increased rate of release of energy. In like fashion, those nuclides which only have a potential beta decay can be induced to release that energy. In either case, these species would be useful fuel for the controlled production of power. In addition, since certain radioactive by-products or wastes of nuclear fission power plants have long halflives because of their property of beta decay forbiddenness, the present invention, when applied to these materials, would afford the advantage of rapidly converting such wastes to nonradioactive species. At the same time, useful energy could be extracted therefrom.
  • beta decay transitions are unimpeded when the initial and final nuclear states have the same intrinsic parity and have total angular momenta which are either the same or differ by one quantum unit of angular momentum. These beta decays are categorized as "allowed.” On the other hand, beta decay transitions are inhibited when the initial and final nuclear states either do not have the same intrinsic parity, or have total angular momenta which differ by more than one quantum unit of angular momentum. These beta decays are categorized as "forbidden.” Forbiddenness has a very strong influence on the observed halflife.
  • strontium-90 one of the wastes of nuclear fission power plants
  • strontium-92 beta decays with a halflife of only 2.7 hours.
  • the two nuclei have very similar nuclear parameters for beta decay, the primary difference being that an allowed decay exists for strontium-92, but not for strontium-90.
  • the degree of forbiddenness varies for different nuclides. Whereas strontium-90 represents a type of "first forbidden" decay, calcium-48 is an example of a "fourth forbidden" decay.
  • forbidden beta decay transitions are rendered allowed. This result is accomplished by employing an externally applied electromagnetic field to serve as a reservoir of angular momentum and parity to remove forbiddenness from the beta decay.
  • the necessity for having an electromagnetic interaction in the beta decay in addition to the usual beta decay interaction invokes a penalty in the halflife expected. That is, the halflife for a beta decay induced by an electromagnetic field can never be as short as the halflife for an otherwise comparable allowed transition. Nevertheless, the halflife shortening possible through the intercession of an electromagnetic field in a forbidden decay can be very striking.
  • a photon is the basic elementary particle of the electromagnetic field.
  • the fields considered here are coherent fields involving a superposition of different types of photons, so a photon representation is not suitable for practical calculation. Nevertheless, the photon provides a simple conceptual notion of how forbiddenness is removed.
  • Each photon of the electromagnetic field carries one quantum unit of angular momentum, and has negative intrinsic parity.
  • the photon is a pseudovector particle.
  • the angular momentum and parity of a photon are independent of the energy carried by the photon, and since there are no critical energy or momentum conservation conditions which the photon must satisfy, the choice of the frequency of the applied electromagnetic field is largely determined by practical considerations about the best way to achieve certain values of an interaction strength parameter to be discussed below.
  • the superscript on 90 Sr and on its daughter nucleus 90 Y indicate the total number of nucleons in the nucleus.
  • the left subscript shows the number of protons, and the right subscript gives the number of neutrons.
  • the beta decay of 90 Sr to 90 Y involves the conversion of one of the neutrons in 90 Sr into a proton, thus causing a transmutation from strontium to yttrium.
  • the horizontal lines show the energy levels of the nuclei.
  • the O + at the left of the line means that this ground-state energy level of 90 Sr has zero angular momentum and positive parity.
  • the 2 - shown for 90 Y signifies two units of angular momentum, and negative parity.
  • the opposite parities of the states, and the need for a change in angular momentum of two units, accounts for the 28 .6-year halflife of 90 Sr.
  • the initial state ( 90 Sr) or final state ( 90 Y) can be thought of as emitting or absorbing a photon, with a resulting change in angular momentum and parity.
  • the ground state of 90 Sr in the electromagnetic field would have a 1 component, so that the beta decay could proceed with a change of only one unit of angular momentum and no parity change, which is an allowed beta transition.
  • An energy level diagram for this is where the straight diagonal lines represent beta transitions, and the wavy lines represent photon absorption or emission. The amount of energy represented by the photon is greatly exaggerated in this diagram.
  • a photon of the applied field contributes essentially zero energy.
  • the result of this interaction with the electromagnetic field is to enhance the transition rate due to removal of forbiddenness from the beta decay, while accepting some penalty in the total transition rate due to the introduction of an interaction with the electromagnetic field.
  • a significant overall increase in the transition rate achieved by application of the electromagnetic field in accordance with the present invention has practical importance from at least two points of view. One is achieving useful power production from the beta decay of materials which are long-lived when not induced to decay; and the other is achieving relief from a major aspect of.the problem of disposal of radioactive wastes arising from nuclear fission power.
  • nuclear species most useful in the practice of the present invention will now be considered, and these will be discussed under two principal headings: those nuclides, found in Nature, most promising for power production; and the beta-active fission products which present the major burden of radioactive waste disposal, and which could also contribute to power production.
  • the nuclear species relevant to this category are 40 K (potassium-4 0 ), 48 Ca (calcium- 48 ), 50 v (vanadium-50), 87 Rb (rubidium- 87 ), 96 Zr (zirconium-96), 113 Cd (cadmium- 113 ), and 115 In (indium-115).
  • (Other beta decay species found in Nature-- 123 Te , 138 La 176 Lu 180 Ta 197 Re-- will not be mentioned further, because of small abundance and/or low decay energy).
  • a striking feature common to all these nuclides is their very long halflives. The shortest lifetime in the list is possessed by 40 K , whose 1.277 x 10 9 -year 8/ halflife is about 1/4 the age of the Earth.
  • the halflife of 87 Rb, 4 . 80 x 10 10 years, 9/ is more than ten times the age of the Earth.
  • the other nuclei bracket the threshold of detectability.
  • 115 In is listed at 4. 41 x 10 14 years. 10/
  • the decay of 113 Cd ( halfl i fe 9 . 3 x 10 15 years 11/ ) was detected for the first time only recently. 12/ 48 Ca, 50 V and 96 Zr have never been observed to decay, even though it is possible in principle, and nuclear data compilations give only a lower limit for their halflives.
  • a feature of those materials which decay in a single stage of beta emission is related to the safety of power reactors with such fuels.
  • the enhanced beta activity of the fuel requires the establishment of precisely the correct conditions within the reactor. If the reactor malfunctions, the beta decay enhancement is interrupted, and the fuel immediately reverts to the near-zero radioactivity of its normal state. There is no possibility of a runaway reaction. Furthermore, there is neither induced nor residual radioactivity to deal with upon shutdown. Even if some mechanical accident should breach the integrity of the reactor, any fuel or waste products which might escape are as innocuous as the original charge of fuel. The situation is not quite as straightforward with 48Ca and 96 Z r which experience a spontaneous beta decay following the induced decay. However, since the spontaneous decays have halflives of the order of one or two days, do not induce further activity, and emit nothing gaseous, hazards associated with an accident are minimal. Several weeks delay after an accident would be necessary to permit the activity to disappear.
  • Some of the nuclides considered here experience only beta decay, with no.associated gamma emission.
  • a feature of such a pure beta decay energy source is the prospect of direct generation of electrical energy. Essentially all of the energy in a pure beta decay appears in the charged beta particle, and in a neutral neutrino or antineutrino (with a trivial amount appearing in nuclear recoil). The neutrino energy is irretrievably lost, but if the kinetic energy of the beta particle is used to carry it to a collector separate from the fuel, the consequence is a separation of charge. This separation of charge creates an electric potential difference which can cause electrical current to flow.
  • beta decay properties of 40 K will now be discussed.
  • the natural decay of 40 K exhibits all the types of beta activity. Its beta decay can be represented by the following energy level diagram, adapted from Endt and Van der Leun. 8/
  • the horizontal line for 40 K is the ground state, with a spin and parity of 4 .
  • the line slanting down to the right signifies a ⁇ - decay to the 0 + ground state of 40 Ca (calcium-40). This decay arises from the conversion of one of the neutrons in 40 K into a proton, which is the reaction
  • the three emergent particles from the reaction are the proton, electron (or ⁇ - particle) and the antineutrino, ⁇ .
  • the antineutrino has such infinitesimally small probability of interaction with anything, that its primary importance in practical application is that it carries away, and thus "wastes," about half of the energy released in the beta decay.
  • the 1.312 MeV of kinetic energy shown in the diagram for the ⁇ - decay thus over states, by a factor of about two, the average energy retrievable from the process.
  • the 4 to 0 + transition is called "unique third forbidden.”
  • the line in the 40 K level diagram slanting down to the left represents the capture of an atomic electron by the nucleus, leading to the first excited state of 40 Ar (argon-40).
  • This EC electron capture is equivalent to the conversion of one of the protons in 40K into a neutron, or
  • the reaction is placed in quotation marks to emphasize the fact that such a reaction is energetically impossible with free protons and electrons, but can become possible within an appropriate nucleus.
  • the symbols on the right hand side is a neutrino, the antiparticle of the antineutrino of ⁇ - decay.
  • the 4 to 2 + transition, "unique first forbidden,” would be the dominant decay mode of 40 K since it is so much less forbidden than 4 to 0 + , were it not for the very small transition energy involved in the EC decay--only 44 keV as compared to 1312 keV for These opposite trends give the result that 89.33% of the natural decays occur by ⁇ - and 10.67% by EC. Since the EC process leads to an excited state of 40 A r, it is followed quickly by the emission of a 1.46 MeV gamma ray as the newly-formed argon goes into its ground state.
  • the line in the diagram showing ⁇ + decay has a vertical portion followed by a slanted part.
  • the vertical line is an indicator of an energy equal to the combined rest mass energies of an electron and a positron (totaling 1.022 MeV) which enters into the energy balance for ⁇ + decay.
  • the energy available to the positron and neutrino amounts to 1505 keV less 1022 keV, or only 483 keV. This accounts for the fact that a ⁇ + transition to the first excited state of 40 Ar is not possible. It is also most of the reason why the ⁇ + decay of 40 K is so strongly dominated by the ⁇ - decay, even though both are 4 to 0 + transitions. (There are other reasons having to do with details of nuclear structure.)
  • Rubidium-87 9/ is interesting because of its comparatively large isotopic abundance (27.85%), and its relatively great importance in terms of energy resources.
  • Zirconium-96 15/ is very similar in nature to 48 Ca.
  • 96 Zr is apparently non-radioactive, with the beta-active 96 Nb (niobium-96) as its daughter nucleus if decay is induced.
  • 96 Nb decays to excited states of g6 Mo (molybedenum-96).
  • the nearly stable nuclide 113 Cd 11/ has a higher degree of forbiddenness than 87 R b, and slightly more available transition energy.
  • the isotopic abundance of 113 Cd is 12.26%, but it is less widely distributed in Nature than 87 Rb.
  • 115 In 10/ has the same forbiddenness in its beta decay as 113 Cd, a more energetic ⁇ decay, but nearly as long a lifetime.
  • Natural indium is largely 115 In (95.7%).
  • the second group of nuclides to be examined is the fission products which arise from the breakup of the fissionable fuel in nuclear reactors. A great many different fission products occur, but they all share the property of being neutron-rich when they are created, and so they exhibit decay.
  • beta decay nuclei By far the most important beta decay nuclei from the standpoint of fission reactor waste disposal are 90 Sr (strontium-90) and 137 Cs (cesium-137). For the first 700 years or so of natural decay, 90 Sr and 137 Cs comprise virtually the entire burden of fission waste radioactivity. 16/ The reason for this arises only in part from the fact that they are among the most likely in occurrence in the probability distribution of fission products. More important is that their beta decays have a moderate degree of forbiddenness. The nuclei with allowed beta transitions decay with sufficient rapidity that their radioactivity is significantly depleted during the first year or so of waiting time after spent fuel rods are removed from the reactor.
  • Nuclei with highly forbidden beta transitions decay so slowly as to moderate the level of radioactivity they present, although their persistence is thereby increased.
  • 90 Sr and 137 Cs both have "unique first forbidden” beta decays (angular momentum change of two, and change of parity) which give them halflives of the order of thirty years. This makes temporary storage of little use, and yet the levels of activity are high. It is also a particularly obnoxious halflife in terms of health hazards, since thirty years is the order of magnitude of a human lifetime.
  • 90 Sr in particular becomes incorporated in bone when ingested, where it continues to damage the host organism.
  • the biological halflife (i.e. , the halflife for retention in humans) of 90 Sr is 49 years in bone and 36 years on a whole body basis. 17/
  • the decay of 90 Sr is to 90 Y (yttrium-90), which, in turn, has a first-forbidden, but more energetic decay to the stable 90 Zr nucleus. 7/ Application of an appropriate external field would accelerate both 90 Sr and 90 Y decays, but the 90 Sr decay always remains the controlling factor.
  • the beta decay nuclides are evaluated in terms of the sum of half the beta decay energy plus all the gamma decay energy emitted in the progress of the decay to the final state.
  • the abundance data used 20/ are atom abundances (atoms per 100 silicon atoms) of the elements as they occur in the igneous rocks of the Earth's crust.
  • Beta energy resources are about one half of DT fusion energy resources, and they are about three hundred times greater than 235 U fission energy resources. This second comparison signifies that beta energy resources exceed the resources available in total from uranium, with breeding included. Furthermore, assessments based on igneous rock understate beta energy resources since calcium, for example, is much more abundant in sedimentary rock. An energy resource comparison of 235 U with 48 Ca in limestone favors 48 Ca by a factor of the order of I0 4 .
  • beta energy resources occur extensively in seawater, so the resources in the Earth's hydrosphere should be considered in addition to the resources of the lithosphere listed above.
  • Seawater is not a significant source of either lithium or uranium, so a direct comparison as just done for igneous rock is not available. Instead, an index of resource assessment introduced by Hubbert 21/ can be employed. He compared DD fusion resources with fossil fuels, based on the extraction of 1% of the deuterium from the oceans. With the same 1% extraction assumed for the beta energy fuels, and with the composition of seawater as given by Rankama and Sahama 22/ , the resource figures in the following table are arrived at.
  • beta energy resources are seen to be very large indeed.
  • the energy of 48 Ca is twenty thousand times as large, and 40 K and 87 R b are also impressively larger in magnitude than the energy resources of petroleum.
  • Hubbert has estimated that DT fusion energy resources are of the same order of magnitude as total fossil fuel energy, a comparison between beta energy resources in the hydrosphere and in the lithosphere can be made.
  • resources from the oceans are much greater than from the rocks; 50 V is similar in importance from either source; while 113 Cd and 115 In are available only from the lithosphere.
  • the primary intent of stimulating forbidden beta transitions in fission products is to reduce the burden of radioactive wastes, or to achieve useful energy therefrom, an assessment of the size of the power source thus available is appropriate. If nuclear fission power capacity reaches a level of 900,000 megawatts, then the long lived beta active fission products generated per year by this nuclear industry would have an energy content of the order of 2000 megawatt years. That is, if it should be possible to consume these fission products on a steady-state basis as they are produced, the total power available from the fission products is about 2000 MW, or about 800 MW of electricity if thermal losses are considered. Of this total, 90 Sr and 137 Cs taken together represent about 80% , and 135 Cs and 99 Tc together represent another 10% or so.
  • forbidden beta decays can have their forbiddenness removed by the intervention of the angular momentum and parity contained in an applied electromagnetic field.
  • nuclear species whose beta decays are so highly forbidden by angular momentum and parity selection rules that their halflives are of the order of, or greater than, the age of the solar system.
  • Other nuclides have such long halflives that no beta decay activity has ever been observed in them, even though it is possible in principle.
  • Such quasi-stable nuclear species are thus still to be found among the mineral resources of the Earth.
  • Other nuclides with forbidden beta decays are generated as byproducts of nuclear fission reactions.
  • Both natural and manmade forbidden beta species contain potential energy resources which can be released for practical use when their beta decays are induced to occur by an applied field. Independently of (or conjointly with) any utilization of energy therefrom, the induced beta decay of fission products serves to reduce a major radioactive waste disposal problem.
  • the theory of induced beta decay is developed by first deducing the quantum mechanical dynamical equations for the relevant internal nuclear coordinates in the presence of an external field. This both specifies the equation of motion which must be solved, and serves to exhibit the effective charge with which the beta active portion of the nucleus is coupled to the external field.
  • a formalism is developed which is the extension of the usual beta decay theory to the case where the nuclear states and beta particle experience interaction with the applied field. Specific calculational examples are given to demonstrate the formalism in computing a final result.
  • the nature of the applied field is examined in its context as input to the nuclear calculation.
  • the electromagnetic field experienced by a nucleus is a superposition of the externally applied field and the internal fields in the medium contributed by the atom or solid in which the nucleus is embedded.
  • electromagnetic field potentials in Coulomb gauge, it is shown that it is the vector potential which is unaffected by fields internal to the medium, and it is the vector potential which is effective in causing induced beta decay.
  • an electromagnetic field source to induce beta decay is a coaxial transmission line operating in TEM (transverse electromagnetic) mode.
  • the fuel is incorporated as the dielectric medium between the inner and outer conductors of the coaxial line.
  • the power transmitted along the line is dumped into an absorptive load which is cooled by the same coolant employed to remove energy from the fuel.
  • the electromagnetic field in the simplest TEM mode in a coaxial transmission line has just the form presumed in the theoretical treatment developed here. An example of the application of this system is given.
  • Another electromagnetic field source is a resonant coaxial cavity. This is similar to the coaxial transmission line, except that the line is terminated by reflectors at a cavity length equal to an integer number of half wavelengths of the cavity field (in simplest TEM mode). Other cavity lengths are possible, depending on the design of the input circuit, and how the termination is loaded. An example is given.
  • transmission lines other than coaxial can be used, such as two-wire, four-wire, coaxial cage, strip line, etc.
  • circuit elements carrying alternating current will possess in their vicinity electromagnetic fields, a fractional amplitude of which corresponds to the TEM mode of a propagating plane wave as considered in the theoretical development.
  • An in-between case with certain advantages is a hollow conducting torus.
  • the fuel is placed in those regions near the conductors where the field configuration and intensity are most advantageous. This would be, for example, in a cylinder coaxial with the long conducting cylinder, or a torus enveloping the hollow conducting torus.
  • the nucleus is considered to consist of two parts: a "core” and a "fragment.”
  • the core is a stable sub-nucleus of zero total angular momentum; and the fragment contains the nucleon (or nucleons) which is a candidate for beta decay, plus any other nucleons which are angular momentum coupled to it in initial or final states.
  • the equation of motion is then separated into center-of-mass (CM) and relative coordinate equations giving, respectively, the dynamical equations for the motion of the center of mass of the entire nucleus and the relative motion of the fragment with respect to the core. It is this latter equation which must be solved.
  • CM center-of-mass
  • the theory of induced beta decay involves a coupling of the nuclear fragment both to the external electromagnetic field and to the weak (beta decay) interaction.
  • the coupling constant of the weak interaction is very small.
  • the coupling constant to the electromagnetic field is very much larger, particularly in view of the relatively large intensity of the applied field.
  • the field can be regarded as being on for a time approaching infinity before and after the beta decay occurs. Therefore, the weak interaction is treated as a perturbation which causes a transition of the nucleus-plus-field system from one state to another.
  • the combined nuclear-electromagnetic field system is explicitly time dependent, so the standard derivation of the perturbation formalism of beta decay (based on stationary nuclear states) is not appropriate. However, a derivation which is applicable in the presence of explicit time dependence gives a result which has the standard form.
  • the perturbation theory just described requires a knowledge of the state vector for the nuclear fragment in the presence of the field.
  • the interacting nuclear wave function employed is the momentum translation approximation.
  • the electron emitted in the beta decay does not appear until the decay has occurred, and so its interaction with the field might be thought to be of little consequence.
  • the field intensity parameter associated with induced beta decay is so large (and the mass of the electron sufficiently small) that the onset of effective interaction of the electron with the field occurs on a shorter time scale than the Heisenberg uncertainty time of the beta decay interaction.
  • the onset of field-electron interaction is also much faster than the transit time of the newly created beta particle across the nucleus.
  • the electron is therefore represented by a Volkov wave function, which is an exact solution for a free charged particle in the presence of an electromagnetic field.
  • a general expression for the transition probability for induced beta decay contains matrix elements for Fermi and Gamow-Teller transitions which are generalizations of those which occur in ordinary beta decay. Coupling of the electromagnetic field to the beta particle causes the transition probability to split into three parts corresponding to: direct interaction of the field with the electron charge, interaction of the field with the spin of the electron, and an interference between the direct and spin terms.
  • the direct term and the spin terms are of approximately equal importance for the more energetic beta decays, although the direct term dominates for low energy decays.
  • the initial nucleus in the cases of interest here, one can consider the initial nucleus to consist of a stable, relatively tightly-bound "core,” plus a “fragment” of one or several nucleons outside the core.
  • This fragment contains the nucleon which is a candidate for beta decay, plus any other nucleons which couple with it to provide the observed total angular momentum and parity of the nucleus.
  • the "core” will always be such as to 90 have spin and parity O + .
  • 88 Sr is particularly stable since the neutron number of 50 is a magic number, and the proton number of 38 corresponds to completed p 3/2 and f5/2 shells beyond the magic number of 28.
  • the "fragment" constituents of two neutrons in 90 Sr outside the 88 Sr core are both d 5/2 neutrons, coupled together to give an overall O + state.
  • One of these two neutrons will decay to a p 1/2 proton, which will couple with the remaining d 5/2 neutron to form a 2 state in the daughter 90 Y nucleus.
  • Eq. (4) The implication of the reduced charge expression, Eq. (4), is that the fragment behaves as if it has a positive charge when there is a preponderance of protons in the fragment, a negative charge when neutrons predominate, and a near-zero charge when equal numbers of protons and neutrons exist in the nuclear fragment.
  • the beta decay transition probability When the beta decay transition probability is induced by an applied electromagnetic field, it is appropriate to view the asymptotic states as states which contain the full influence of the applied field, and the transition-causing "perturbation" will be the beta decay interaction. This means that the asymptotic states are explicitly time dependent, and not the stationary states normally employed. This is not a "textbook” situation, but a derivation of the appropriate S-matrix element (or transition amplitude) gives the result
  • ⁇ i and ⁇ f are the initial and final nuclear states
  • ⁇ (e) and ⁇ ( ⁇ ) are the electron and neutrino states, all in the presence of the applied field
  • G is the weak interaction coupling constant
  • ⁇ is the ratio of axial vector to vector couplings for nuclear beta decay
  • the ⁇ ⁇ , y 5 are D i ra c matrices.
  • the calculational procedure developed above for induced beta emission is to substitute wave functions including the effects of the applied electromagnetic field.
  • the formalism is otherwise the standard beta decay calculation.
  • the nuclear wave function to be used must represent the effects of the applied field to an order of interaction which is at least as large as the order of forbiddenness of the natural beta decay. It must also be valid: in the presence of electromagnetic fields of such intensity that the convergence of conventional perturbation theory is suspect.
  • a technique ideally suited to the present problem is the momentum translation approximation 5/ .
  • Equation (8) states essentially that the ratio of the nuclear radius to the wavelength of the applied field is very small, which is amply satisfied for all fields of possible interest.
  • the reduced charges, ⁇ i and ⁇ f are the appropriate forms of Eq. (4); and ⁇ i ( r ), ⁇ f ( r ) are stationary state nuclear wave functions with no field present.
  • the leptons emitted in ⁇ - decay are an electron and an antineutrino 25/ .
  • the antineutrino is uncharged, and possesses no coupling to the electromagnetic field.
  • the antineutrino is therefore described by an ordinary free-particle wave function.
  • the emitted antineutrino is treated as a neutrino in the initial state with reversed four-momentum, i.e.,
  • k ( ⁇ ) is the four-momentum with time part E( ⁇ )
  • u ( ⁇ ) is a spinor
  • s ( ⁇ ) is the spin parameter
  • V is the normalization volume.
  • the electron emitted in beta decay is a charged particle whose coupling to the electromagnetic field is very significant when the field intensity is high.
  • the electron is treated as a free particle, although Coulomb corrections are sometimes introduced.
  • the free particle electron solution is replaced by the V olkov solution 26/ , which is an exact wave function for a free, charged particle in the presence of a plane wave electromagnetic field.
  • the electromagnetic field is specified as whereP is a phase shift reflecting the fact that the beta decay cannot be expected to occur in phase with the field.
  • One intensity parameter can be associated with the interaction of the nuclear particles with the electromagnetic field. It is given by where a is the amplitude of the vector potential of the field as given in Eq. (12), and R is the nuclear radius. This quantity is typical of intensity parameters which arise in bound-state intense-field problems. 27,28/ The other intensity parameter is associated with the interaction of free electrons with the electromagnetic field. 27,28/ It is
  • the two parameters are related by
  • the transition probability per unit time, W is of the form where is a spectral integral consisting of three parts arising from the direct, spin, and interaction terms; and where the squared nuclear matrix element is
  • the form (18) corresponds to- the standard form for allowed beta decay, where with and, when Coulomb corrections are neglected, as they are in the present work, the spectral integral is
  • ⁇ e is a dimensionless electron energy
  • ⁇ o is a dimensionless nuclear energy change
  • p e is a dimensionless electron momentum defined by
  • Table 1 gives the information required to apply the foregoing formalism to computation of nuclear matrix elements involved in induced beta decay.
  • the first seven nuclides listed are materials found in Nature, and the last two are the principal fission fragment waste products.
  • Nuclear spin and parity assignments are from "Nuclear Data Sheets" (except for 40 K, which is from P. M. Endt and C. Van der Leun, Nucl. Phys. A310, 1 (1978)).
  • Angular momentum assignments for nucleons in the "fragments” are standard shell model assignments. 29/ The reduced charge for the fragment comes from Eq. (4).
  • 113 Cd has a single nucleon fragment.
  • the core nucleus, 112 48 Cd 64 is a stable nuclide in Nature with spin and parity of O + .
  • This means that this "even-even" nuclide has the spins of all of its protons and of all of its neutrons anti-aligned in pairs to give pairwise and overall zero angular momentum.
  • the odd neutron in 113 Cd has a shell model assignment of s 1/2 , which should then determine the entire nuclear spin and parity to be which is the case.
  • beta decay the unpaired s 1/2 neutron becomes an unpaired g 9/2 proton, which then contributes the entire observed spin and parity of the final 113 49 In 64 nucleus.
  • An example of a two nucleon fragment is provided by 90 38 Sr 52 .
  • the core nucleus, 88 38 Sr 50 is the principal stable isotope of strontium.
  • 87 37 Rb 50 is an example of a nuclide where the fragment must consist of three nucleons.
  • the odd proton in 87 R b must be part of the fragment because initially this p 3/2 particle accounts for the entire 87 Rb spin and parity of 2
  • the beta decay itself involves a neutron, not the odd proton, and since the beta decay neutron is initially paired with another to give O + , then both of these neutrons must also be assigned to the fragment.
  • the g 9/2 neutron which beta decays to a p 3/2 proton will couple to O + with the initial odd proton, while the remaining g 9/2 neutron finds itself unpaired in the final state, and so accounts for the spin and parity of the 87 Sr daughter nucleus. 2
  • the contrast between the spins and parities of these states suggests something unusual.
  • 137 Ba has 81 neutrons and 137 Cs has 82 neutrons--a magic number. The last two neutron shells to be filled before the magic number is reached are the d 3/2 and h 11/2 shells. Between neutron numbers 67 and 79, there is alternation in the filling of these two levels.
  • Equation (20) is expressed as the sum of four terms.
  • the first pair of terms arises from the vector part of the beta decay interactioh, and corresponds to the usual Fermi matrix element of beta decay theory.
  • the second pair of terms comes from the axial vector part of the beta decay interaction, and corresponds to the usual Gamow-Teller matrix element of beta decay theory.
  • a simplification can be introduced from isospin considerations, which have not been placed in evidence in the above work.
  • the terms in the square bracket in Eq. (21) are squared nuclear transition matrix elements, with the f and i subscripts referring to final and initial nuclear states.
  • the coordinate r which occurs in the matrix elements refers to the position vector r of the nuclear fragment with respect to the nuclear core. In practical calculation of the nuclear matrix elements, one needs the coordinates of the separate nucleons contained in the fragment.
  • the vector r gives the location of the CM of the fragment. Since each nucleon in the fragment can be taken to have the same mass M, then the position vector of the jth nucleon in the fragment ( r j ) is related to r by where q is the total number of nucleons in the fragment.
  • Equation (21) can be stated in more detail as where
  • u j is the dimensionless radial coordinate j i is the total angular momentum of the initial state, so that (2j i +1) -1 times the sum over m i is an average over orientations of initial angular momentum; and the sum over m f is a sum over orientations of the final angular momentum.
  • Eq. (22) only one of the two terms in Eq. (22) will be nonzero.
  • Low-intensity behavior is proportional to z 7/2 .
  • Equations (26) and (27) apply again to this result.
  • the intensity parameter which maximizes Eq. (29) is which is a substantially greater intensity than the maximum for 113 Cd given in E q. (28).
  • the squared induced transition matrix element in this case is which has a maximum at
  • the halflife for beta decay is related to the transition probability per unit time by
  • Equation (25) when evaluated at the intensity stated in Eq. (28), gives
  • 2 3.08 x 10 .
  • the negative value for f 3 means that interference between direct and spin terms is a partially destructive interference.-
  • the total induced spectral integral is
  • Power density in an induced beta decay fuel can be expressed as where E is the decay energy involved in the beta decay of a single nucleus, Wind is the total induced transition probability as found from Eq. (18), and P is the number of active nuclei per unit volume. If E is expressed in MeV, W ind in sec 1 , p in nuclei per cubic meter, and power density in watts per cubic meter, then Eq. (42) becomes
  • This expression can be used inversely to find the density of active nuclei needed to achieve a given power density. For example, assuming the lower limit of power density of practical interest is of the order of 10 watts per m 3 , Eq. (43) leads to a minimum density of active nuclei of the order of 10 14 /EW ind .
  • Equation (22) shows that contributions arising from an Lth order interaction of the nucleus with the field is diminished by z f 1/2, a free electron interaction parameter coming from the beta particle.
  • the parameter z has been spoken of as a field intensity parameter; but, as is evident from Eq. (44), it is identified also as the coupling strength of the field-nucleus interaction.
  • An alternative way to write z is as
  • a o is the fine structure constant, which is conventionally taken in quantum electrodynamics to be the measure of the strength of coupling between the electromagnetic field and an elementary particle of charge e.
  • the electromagnetic field is a Bose field, and the more photons there are in a given mode of the field, the more the interaction probability involving that mode is increased. This enhancement is measured by the photon density p.
  • the factors ⁇ R o 2 in Eq. (45) define an effective interaction volume, so that p ⁇ R o 2 is a measure of the number of photons which are in interaction with the charged nuclear system.
  • the interaction volume can be viewed as a box whose cross-sectional area is defined by the area of the nucleus, and whose length is the wavelength of the field.
  • a way to avoid possible confusion about gauge invariance of z is to express it directly in physical quantities.
  • One way is to write the intensity parameter for the plane wave in terms of the electric field as or in terms of the magnetic induction as where E and B o are the amplitudes of the E and B fields and ⁇ r is the dielectric constant of the material in which the wave propagates.
  • E and B are given in Mks units (as volts per meter and teslas, respectively)
  • R is taken to be 5x10 -15 meters
  • Equation (48) can be used inversely to find field parameters necessary to achieve a given intensity parameter. For example, assuming the lowest z of practical interest is of the order of 10 -3 , then the magnetic induction needed to achieve this at the frequency v is of the order of where B is in teslas and v is in Hz.
  • the intensity parameter z must be roughly of the order of unity for induced beta decay to be important. A value for the intensity parameter of the order of unity is difficult to achieve. Some possibilities will be reviewed here. First, the energy flux of the applied field will be expressed in terms of z. If the energy flux is stated in units of watts per square centimeter (W/cm 2 ), and all other quantities are in Gaussian units, the connection is
  • the factor 10 -7 is for conversion from ergs to joules.
  • the factor ⁇ c/ ⁇ R o 2 is the energy flux associated with the passage of a single photon through the interaction volume, and the factor z/ ⁇ o converts this into the overall energy flux. If z is set to unity, and R is replaced approximately by X c /80, then the applied field must supply where ⁇ is in centimeters and P in W/cm 2 .
  • a central fact is the inverse square dependence on wavelength, strongly favoring long wavelength sources, other things being equal. "Other things," however, are not equal, since the technological capability for producing large radiated power is very non-uniform across the electromagnetic spectrum.
  • the energy fluxes listed above are very large.
  • the figure given for the Nd-glass laser is beyond present capabilities.
  • the C0 2 laser might reach the required intensity, but only in a very small volume with a short pulse.
  • the energy input would greatly exceed output.
  • the microwave requirement is also unreasonably large, even in a high-Q cavity. At long wavelengths, however, practical systems become possible.
  • the applied electric field at the position of a nucleus will largely be cancelled by counter-fields generated within the solid of which the nucleus is a part.
  • the applied magnetic field will be essentially unaffected. It is very important to note that the internal fields which accomplish cancellation of the applied electric field are entirely quasistatic (i.e., oscillating
  • Eq. (50) The p,z coordinates which appear in Eq. (50) are macroscopic coordinates.
  • the integral which appears in Eq. (49) is over nuclear, or microscopic coordinates.
  • Such a scalar interaction term is of no consequence for induced beta decay.
  • a scalar potential of this type gives the result where a is the vector amplitude of the trigonometric term in A.
  • the vector potential A through the perturbing term -A ⁇ (i ⁇ ) gives the result
  • a field source based on a low-frequency standing wave in a resonant coaxial cavity was employed.
  • the field in the cavity can be regarded as the superposition of two plane waves of equal amplitude traveling in opposite directions. Because the transverse dimensions of the coaxial line are very small as compared to a wavelength, only the TEM (transverse electromagnetic) or plane-wave-like mode can exist.
  • the coaxial cavity had an air dielectric, with physically very small radioactive sources attached to the central conductor at a location where the fields are such that
  • c
  • the cavity was operated as a three-quarter-wavelength stub 11, off a coaxial transmission line 20 as shown schematically in Fig. la.
  • the power supply 4 was a 4.1 MHz radio transmitter sending an unmodulated 40 kW signal down the transmission line into a water-cooled non-reflecting resistive load 3.
  • Two sources10 wereemplaced at the
  • c
  • One source was approximately 15 ⁇ Ci of 137 Cs, and the other was about 100 ⁇ Ci of 7 Be.
  • the 137 Cs is the "active" source whose first forbidden beta decays to the first excited state of 137 Ba give rise to 661.64 keV gamma rays. It is this source which should show the effects of the electromagnetic field.
  • 7 Be is a "normalizing" source whose electron capture transition to 7 Li is superallowed, and thus is expected to show little or no effects from the applied field. A 477.57 keV gamma ray is emitted following electron capture.
  • Radioactive decay of the sources was monitored by detection of the gamma rays emitted following the decay. These gamma rays easily penetrate the outer conductor of the coaxial cavity, and were detected by a Ge(Li) (lithium-drifted germanium) crystal outside the cavity. As a way of increasing field intensity at the location of the sources, they were emplaced in a specially constructed test section of very small diameter. In the test section, the inner conductor diameter was 6 mm, and the outer conductor diameter was 14 mm. The test section and detection crystal were both encased in a special low-radiation background shield.
  • Output from the detector was processed by a 8192 channel analyzer, which provided background subtraction routines to permit determination of the net gamma-ray count from each of the two sources.
  • a schematic diagram of the nuclear detection apparatus is given in Fig. lb, which shows the sources 11 attached to the inner conductor 2, of the coaxial line.
  • the gamma ray detection crystal13 is located outside the outer conductor 14 of the coaxial line 11.
  • the experiment was conducted by alternating equal periods of time with the rf power on and with the power off. Each power-on and power-off part of the cycle was divided into four equal periods of length determined by presetting "live time" on the multichannel analyzer to 135 seconds. This corresponded to about 2.5 minutes of clock time.
  • the reason for this choice is that the 137 Cs decay leads to an isomeric state in 137 Ba which has a 2.55 minute halflife for decay to the ground state. There is no corresponding delay in emission of the gamma ray following 7 Be decay.
  • the isomerism in 137 Ba gives a characteristic buildup and decay pattern to the Cs/Be count ratios through the successive power-on and power-off cycles.
  • the desired result to be obtained from the experiments is a knowledge of the change in beta decay transition probability in 137 Cs caused by the field.
  • the experiment measures the gamma rays emitted from 137 Ba as a consequence of beta decay from 137 Cs .
  • state a is the initial 137 Cs state
  • state b is the first excited state in 137 Ba
  • state c is the ground state of 137 Ba
  • N a ⁇ is the initial population of state a
  • W a is the transition probability for the beta decay from state a to state b
  • W is the transition probability for the gamma transition from state b to state c
  • the transition probability for a ⁇ b is modified from 4 a to ⁇ , where A is the incremental transition probability caused by the field.
  • the experiment is conducted by alternating power-off and power-on cycles of duration T.
  • the integration constant ⁇ is evaluated anew by taking the final condition from each cycle as the initial condition for the following cycle.
  • the results are expressible as where ⁇ refers to power-off cycles and ⁇ refers to power-on cycles.
  • the inequality V b >> W a is used, and the origin of time t starts anew at every switch between on and off cycles.
  • the rate of gamma-ray emission is so the number of gamma-ray emissions in time T is ⁇ o T dt r(t). This is measured experimentally.
  • emission rates are identified as coming from power-on or power-off cycles by up or down arrows as above, then the quantity can be determined directly from the experiment.
  • the relative change in beta decay transition probability is given by
  • each of the quantities in Eq. (51) is divided by a decay-corrected count of gamma emissions from 7 Be decay within the same on and off cycles as the 137 Cs counts.
  • these 7 Be counts are time-independent, and so do not affect the analysis leading up to Eq. (53).
  • the number given after the ⁇ sign in Eq. (54) is the "standard error", which is the standard deviation divided by the square root of the number of separate determinations of ⁇ /w a - 200 in this case.
  • the first a number in Eq. (54) is the measured mean value for A /w a .
  • One embodiment of this invention employs the electromagnetic field propagated in lowest TEM mode along a coaxial transmission line of circular cylinder configuration.
  • the fuel constitutes the dielectric medium that lies in the cylindrical annulus between the inner and outer conductors of the transmission line.
  • the nuclear radiations emitted by the fuel are converted to thermal energy by being stopped within the fuel and/or surrounding materials. This thermal energy is then converted in the conventional manner to drive rotating machinery, or it can be further converted to electrical energy in conventional fashion.
  • the coaxial transmission line operating in the simplest TEM mode represents a straightforward application of the theory of induced beta decay, since apart from a radial decrease of the amplitude of the fields, the fields are of pure plane wave type.
  • the fuel should be in the form of a non-conducting material.
  • a solid material of high melting point e.g., K2Si205, CaC0 3 , CdF 2 , SrSi0 3
  • Coolant can be passed through channels within the fuel annulus, and/or at the outer periphery of the outer conductor, and/or within the inner conductor.
  • Another strategy is to have the fuel in the form of an aggregate of geometrical shapes over which a gaseous or liquid coolant flows.
  • Another approach is to use a fuel with low melting point (but preferably a high boiling point), so that the fuel is a dielectric liquid at normal operating temperatures.
  • the fuel itself can then be used as the heat transfer medium, circulating between the region of the fuel annulus and an external heat exchanger.
  • An advantage of this technique is that the circulating fuel can be continuously purged of decay products and replenished with fresh fuel to maintain a steady fuel concentration.
  • Figure 2 shows a system based on a coaxial transmission line, consisting of an outer conductor 1 and an inner conductor 2, terminating in an absorptive load 3, represented schematically by a resistor.
  • a power supply 4 transmits power of appropriate frequency along the line.
  • the resulting electromagnetic field in the insulating fuel medium 5, which comprises the dielectric separating inner and outer conductors of the coaxial transmission line, causes beta decays to be induced in the fuel.
  • the energy generated within the fuel 5, and the energy transmitted to the absorptive load 3, are transferred to a coolant fluid 6, which runs a conventional system of turbines 7, and generators 8, to produce the electric power output.
  • a heat dump 9 is provided in the working fluid system in order to complete the thermal cycle. If the generators 8 are omitted, the power plant can be used to provide mechanical energy rather than electrical energy.
  • Fig. 2 shows two such assemblies.
  • the transmission line in Fig. 2 is shown with a larger diameter-to-length ratio than is likely to be used in practice. Also for ease of representation, the transmission line is shown straight, whereas in practice it may be employed in a coiled configuration with coils one or more layers deep, with axis of coiling horizontal, vertical, or at any other orientation. Other space-saving configurations other than coiling may also be used.
  • An alternative configuration would have the transmission line consist of a grid of conductors embedded in a natural mineral deposit containing the fuel material, where this natural deposit is protected, by nature or by design, from developing inadvertent conductivity paths.
  • a circular cylinder transmission line operating in the simplest TEM mode has electric and magnetic fields given by expressed in p, ⁇ ,z cylindrical coordinates, and with permittivity ⁇ and permeability u relating to the dielectric material contained between the inner and outer conductors.
  • the amplitude factor C contained in Eqs. (55) and (56) can be related to the intensity parameter z. It is convenient to use a mean intensity parameter z , where the mean is obtained by averaging over the volume of the dielectric in the transmission line. From Eqs. (46) or (47), z is proportional to 1/p 2 , and where P 0 and P i are, respectively, the inner radius of the outer conductor and the outer radius of the inner conductor. The end result is that z is or
  • the transmission line is presumed to terminate in a non-reflecting absorptive load. This means that the simple propagating plane wave character of the fields is unaffected. It also means that the power transmitted along the line can be converted to thermal power, which adds to that arising from induced beta decay. Thus, a portion of the power employed to operate the device can be recovered.
  • the transmission lines considered will not be long enough for attenuation along the line to be an important factor.
  • Output power from the coaxial system is just average power density times fuel volume, or, from Eq. (43),
  • E is the usable energy released per beta decay nucleus expressed in joules (not in MeV as in Eq. (43))
  • p without subscript is the density of beta decay nuclei
  • & is the length of the transmission line. Equations (59) and (60) make clear that input and output powers have the same dependence on the radius of the transmission line, but output power is proportional to the length of the line. This suggests the use of long lines, which may be coiled into compact arrays. Total power output of a single plant need not come from a single transmission line, but could be the summed contributions of a number of long, coiled lines.
  • Another embodiment of this invention employs the electromagnetic field existing in a resonant coaxial cavity excited in lowest TEM mode.
  • the cavity is just like the coaxial transmission line treated above, except that it is terminated by reflectors at a length equal to an integer number of half wavelengths.
  • the fuel constitutes the dielectric medium contained between the inner and outer conductors of the coaxial cavity.
  • the nuclear radiations emitted by the fuel are converted to thermal energy by being stopped within the fuel and/or surrounding materials. This thermal energy is then converted to mechanical and/or electrical energy in the conventional manner.
  • Figure 3 shows a system based on a coaxial resonant cavity consisting of an outer conductor 1 and an inner conductor 2.
  • a power supply 4 provides the power necessary to sustain an electromagnetic field which is resonant in the cavity. This electromagnetic field induces beta decays to occur in the insulating fuel medium 5, which comprises the dielectric separating the inner and outer conductors of the coaxial cavity.
  • the energy generated within the fuel medium, as well as the energy occurring as wall losses in the cavity, are transferred to a coolant fluid 6, which runs a conventional system of turbines 7, and generators 8, to produce the electric power output.
  • a heat dump 9 is provided in the working fluid system in order to complete the thermal cycle. Direct mechanical output can be provided in place of electrical output if the generators 8 are omitted.
  • Fig. 3 shows two such assemblies.
  • the resonant cavity in Fig. 3 is shown with a larger diameter-to-length ratio than is likely to be used in practice. Also for ease of representation, the cavity is shown straight, whereas in practice it may be employed in a coiled configuration with coils one or more layers deep, with axis of coiling horizontal, vertical, or at any other orientation. Other space-saving configurations other than coiling may also be used.
  • resonant cavity consist of a grid of conductors embedded in a natural mineral deposit containing the fuel material, where this natural deposit is protected, by nature or by design, from developing inadvertent conductivity paths.
  • the coaxial cavity considered here is taken to be the same as the coaxial transmission line treated above, but with the length specified to be an integer multiple of half a wavelength, and with both ends closed by reflectors. Equations (55) and (56) are replaced by
  • the length of the cavity is given in terms of field frequency v by where n is the number of half wavelengths within the cavity.
  • k is defined by
  • the intensity parameter can be averaged radially as it was in the transmission line, but an axial averaging is also appropriate.
  • This axial averaging is complicated by the fact that induced beta decay occurs under plane-wave-like conditions where
  • c
  • axial averaging is done in a cavity under the premise that the governing field amplitude is always the smaller of the local values of
  • Eq. (66) and (67) are the skin depth, given by where ⁇ is the conductivity of the cavity wall material. If this material is copper, then Eq. (68) is
  • Equation (64) takes into consideration the spatially periodic decline to zero of the fields within the cavity.
  • transmission lines represent a very convenient way to provide plane-wave-like electromagnetic fields of large enough intensity to induce beta decay
  • other field-producing configurations can also be used.
  • the fields in such cases will not be strictly simple TEM such as provided by plane waves and transmission lines, but nevertheless some proportion of the total fields produced can be of that nature.
  • the fields in close proximity to a long cylinder carrying an alternating current, or the fields inside a large-diameter solenoid carrying alternating current, or the fields in close proximity to a large, hollow torus carrying alternating current in the azimuthal direction will all possess components that can be employed to induce beta decay.

Landscapes

  • Chemical & Material Sciences (AREA)
  • Chemical Kinetics & Catalysis (AREA)
  • General Chemical & Material Sciences (AREA)
  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • General Engineering & Computer Science (AREA)
  • High Energy & Nuclear Physics (AREA)
  • Particle Accelerators (AREA)
  • Measurement Of Radiation (AREA)
EP19820303910 1982-07-23 1982-07-23 Procédé et appareil pour provoquer la décroissance nucléaire bêta Expired EP0099946B1 (fr)

Priority Applications (2)

Application Number Priority Date Filing Date Title
EP19820303910 EP0099946B1 (fr) 1982-07-23 1982-07-23 Procédé et appareil pour provoquer la décroissance nucléaire bêta
DE8282303910T DE3273860D1 (en) 1982-07-23 1982-07-23 Method and apparatus for induced nuclear beta decay

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
EP19820303910 EP0099946B1 (fr) 1982-07-23 1982-07-23 Procédé et appareil pour provoquer la décroissance nucléaire bêta

Publications (2)

Publication Number Publication Date
EP0099946A1 true EP0099946A1 (fr) 1984-02-08
EP0099946B1 EP0099946B1 (fr) 1986-10-15

Family

ID=8189724

Family Applications (1)

Application Number Title Priority Date Filing Date
EP19820303910 Expired EP0099946B1 (fr) 1982-07-23 1982-07-23 Procédé et appareil pour provoquer la décroissance nucléaire bêta

Country Status (2)

Country Link
EP (1) EP0099946B1 (fr)
DE (1) DE3273860D1 (fr)

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO1991015857A1 (fr) * 1990-04-03 1991-10-17 Teleki Peter Procede d'utilisation de la technique de capture k au moyen d'electrons de haute energie
FR2680613A1 (fr) * 1991-08-19 1993-02-26 Meyer Michel Activateur pour mutation isotopique.
WO1996016414A1 (fr) * 1994-11-18 1996-05-30 Jury Alexeevich Baurov Procede de regulation des interactions faibles de particules elementaires de matiere
WO2001073474A2 (fr) * 2000-03-30 2001-10-04 Zakrytoe Aktsionernoe Obschestvo 'nek-Eltrans' Procede de transmutation d'isotopes radioactifs a vie longue en isotopes a vie courte
WO2008068466A2 (fr) * 2006-12-04 2008-06-12 Alan Charles Sturt Procédé et appareil destinés à réduire la radioactivité d'une particule
RU2569095C1 (ru) * 2014-07-04 2015-11-20 Федеральное Государственное Автономное Образовательное Учреждение Высшего Профессионального Образования "Дальневосточный Федеральный Университет" (Двфу) Способ дезактивации радиоактивных отходов

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE10032886A1 (de) * 2000-07-06 2002-01-17 Kent O Doering Verfahren und Vorrichtung zum Reduzieren von Radioaktivität
DE10354251A1 (de) * 2003-11-20 2005-06-23 Viaceslav Gorodezki Vorrichtung für eine beschleunigte Entaktivierung von radioaktiven Stoffen

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB802971A (en) * 1956-01-27 1958-10-15 Louis Verschraeghen Process for the destruction of radio-active residues
GB1147585A (en) * 1967-07-18 1969-04-02 Atomic Energy Commission Method and apparatus for removing impurity gas particles from a particle beam
DE2249429A1 (de) * 1972-10-09 1974-04-18 Kernforschung Gmbh Ges Fuer Verfahren zur umwandlung von langlebigen spaltprodukten oder radionukliden mit langer halbwertszeit

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB802971A (en) * 1956-01-27 1958-10-15 Louis Verschraeghen Process for the destruction of radio-active residues
GB1147585A (en) * 1967-07-18 1969-04-02 Atomic Energy Commission Method and apparatus for removing impurity gas particles from a particle beam
DE2249429A1 (de) * 1972-10-09 1974-04-18 Kernforschung Gmbh Ges Fuer Verfahren zur umwandlung von langlebigen spaltprodukten oder radionukliden mit langer halbwertszeit

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
NUCLEAR INSTRUMENTS AND METHODS, vol. 141, no. 3, 15th March 1977, pages 429-432, North-Holland Publishing Co.; *

Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO1991015857A1 (fr) * 1990-04-03 1991-10-17 Teleki Peter Procede d'utilisation de la technique de capture k au moyen d'electrons de haute energie
FR2680613A1 (fr) * 1991-08-19 1993-02-26 Meyer Michel Activateur pour mutation isotopique.
WO1996016414A1 (fr) * 1994-11-18 1996-05-30 Jury Alexeevich Baurov Procede de regulation des interactions faibles de particules elementaires de matiere
WO2001073474A2 (fr) * 2000-03-30 2001-10-04 Zakrytoe Aktsionernoe Obschestvo 'nek-Eltrans' Procede de transmutation d'isotopes radioactifs a vie longue en isotopes a vie courte
WO2001073474A3 (fr) * 2000-03-30 2001-12-27 Zakrytoe Aktsionernoe Obschest Procede de transmutation d'isotopes radioactifs a vie longue en isotopes a vie courte
WO2008068466A2 (fr) * 2006-12-04 2008-06-12 Alan Charles Sturt Procédé et appareil destinés à réduire la radioactivité d'une particule
WO2008068466A3 (fr) * 2006-12-04 2008-08-14 Alan Charles Sturt Procédé et appareil destinés à réduire la radioactivité d'une particule
RU2569095C1 (ru) * 2014-07-04 2015-11-20 Федеральное Государственное Автономное Образовательное Учреждение Высшего Профессионального Образования "Дальневосточный Федеральный Университет" (Двфу) Способ дезактивации радиоактивных отходов

Also Published As

Publication number Publication date
EP0099946B1 (fr) 1986-10-15
DE3273860D1 (en) 1986-11-20

Similar Documents

Publication Publication Date Title
Meredith et al. Fundamental physics of radiology
Cameron Nuclear fission reactors
Joyce Nuclear engineering: a conceptual introduction to nuclear power
Smith A primer in applied radiation physics
US3117912A (en) Method of producing neutrons
US20170263337A1 (en) Methods and apparatus for enhanced nuclear reactions
EP0099946B1 (fr) Procédé et appareil pour provoquer la décroissance nucléaire bêta
JP3145555B2 (ja) 核融合を利用した放射性廃棄物の消滅処理方法
US4961880A (en) Electrostatic voltage excitation process and apparatus
RU2003191C1 (ru) Способ трансмутации изотопов
KR20020043456A (ko) 소모된 원자핵 폐기물의 핵 분열로부터의 전력
CA1209282A (fr) Desintegration beta nucleaire induite
US20030058980A1 (en) Method and apparatus for the transmutation of nuclear waste with tandem production of tritium
Reiss Induced nuclear beta decay
Reiss Method and apparatus for induced nuclear beta decay
JPS5956200A (ja) 物質から有用なエネルギ−を得る方法およびその装置
Bakır et al. Medical Radioisotope Production in a Power‐Flattened ADS Fuelled with Uranium and Plutonium Dioxides
Shultis et al. Fundamentals of Nuclear Science and Engineering Third Edition
Zaider et al. Radiation science for physicians and public health workers
Tandon et al. Basics of Radiation Physics
Longmena et al. CALCULATION OF PROTON INDUCED REACTION CROSS SECTIONS OF LONG-LIVED FISSION PRODUCTS USING EMPIRE CODE
Tanabe Sources of Energetic Quanta (EQ)(Radiation Sources)
Cardarelli et al. Nuclear Materials
RU2200353C1 (ru) Способ дезактивации радиоактивных отходов
McNally Jr Cold fusion and graser prospects

Legal Events

Date Code Title Description
PUAI Public reference made under article 153(3) epc to a published international application that has entered the european phase

Free format text: ORIGINAL CODE: 0009012

AK Designated contracting states

Designated state(s): BE CH DE FR GB IT LI NL SE

17P Request for examination filed

Effective date: 19840717

GRAA (expected) grant

Free format text: ORIGINAL CODE: 0009210

AK Designated contracting states

Kind code of ref document: B1

Designated state(s): BE CH DE FR GB IT LI NL SE

PG25 Lapsed in a contracting state [announced via postgrant information from national office to epo]

Ref country code: NL

Effective date: 19861015

Ref country code: IT

Free format text: LAPSE BECAUSE OF FAILURE TO SUBMIT A TRANSLATION OF THE DESCRIPTION OR TO PAY THE FEE WITHIN THE PRESCRIBED TIME-LIMIT;WARNING: LAPSES OF ITALIAN PATENTS WITH EFFECTIVE DATE BEFORE 2007 MAY HAVE OCCURRED AT ANY TIME BEFORE 2007. THE CORRECT EFFECTIVE DATE MAY BE DIFFERENT FROM THE ONE RECORDED.

Effective date: 19861015

PG25 Lapsed in a contracting state [announced via postgrant information from national office to epo]

Ref country code: SE

Effective date: 19861031

REF Corresponds to:

Ref document number: 3273860

Country of ref document: DE

Date of ref document: 19861120

ET Fr: translation filed
NLV1 Nl: lapsed or annulled due to failure to fulfill the requirements of art. 29p and 29m of the patents act
PLBE No opposition filed within time limit

Free format text: ORIGINAL CODE: 0009261

STAA Information on the status of an ep patent application or granted ep patent

Free format text: STATUS: NO OPPOSITION FILED WITHIN TIME LIMIT

26N No opposition filed
PGFP Annual fee paid to national office [announced via postgrant information from national office to epo]

Ref country code: DE

Payment date: 19910830

Year of fee payment: 10

PG25 Lapsed in a contracting state [announced via postgrant information from national office to epo]

Ref country code: DE

Effective date: 19930401

PGFP Annual fee paid to national office [announced via postgrant information from national office to epo]

Ref country code: FR

Payment date: 19960709

Year of fee payment: 15

PGFP Annual fee paid to national office [announced via postgrant information from national office to epo]

Ref country code: GB

Payment date: 19960715

Year of fee payment: 15

PGFP Annual fee paid to national office [announced via postgrant information from national office to epo]

Ref country code: CH

Payment date: 19960805

Year of fee payment: 15

PGFP Annual fee paid to national office [announced via postgrant information from national office to epo]

Ref country code: BE

Payment date: 19960911

Year of fee payment: 15

PG25 Lapsed in a contracting state [announced via postgrant information from national office to epo]

Ref country code: GB

Free format text: LAPSE BECAUSE OF NON-PAYMENT OF DUE FEES

Effective date: 19970723

PG25 Lapsed in a contracting state [announced via postgrant information from national office to epo]

Ref country code: LI

Free format text: LAPSE BECAUSE OF NON-PAYMENT OF DUE FEES

Effective date: 19970731

Ref country code: CH

Free format text: LAPSE BECAUSE OF NON-PAYMENT OF DUE FEES

Effective date: 19970731

Ref country code: BE

Free format text: LAPSE BECAUSE OF NON-PAYMENT OF DUE FEES

Effective date: 19970731

BERE Be: lapsed

Owner name: UNIVERSITY PATENTS INC.

Effective date: 19970731

REG Reference to a national code

Ref country code: CH

Ref legal event code: PL

GBPC Gb: european patent ceased through non-payment of renewal fee

Effective date: 19970723

PG25 Lapsed in a contracting state [announced via postgrant information from national office to epo]

Ref country code: FR

Free format text: LAPSE BECAUSE OF NON-PAYMENT OF DUE FEES

Effective date: 19980331

REG Reference to a national code

Ref country code: FR

Ref legal event code: ST