ENERGY/MATTER CONVERSION METHODS AND STRUCTURES

Abstract: Methods and structures of energy/matter conversion according to the present invention provides applications including the generation of power according to controlled relatively low temperature nuclear fusion by selective annihilation of the coulombic forces present in the fusion material atoms. The selective annihilation of electron orbital energies is provided according to a novel model of the atom described herein, which further provides the composition of superconductor materials by selective combination of matter to provide the conditions necessary to provide superconductivity. Furthermore, the present invention provides selective energy absorption, as illustrated by photon absorption and the creation of additional material according to the novel model of the atom described herein, which overcomes limitations of prior models and is consistent with basic principles, such as Maxwell's equations.

Description: ENERGY/MATTER CONVERSION METHODS AND STRUCTURES Field of the Invention This invention relates to methods and apparatus for energy/matter conversion according to a novel atomic model and the applications derived therefrom including controlled nuclear fusion and the formation of materials such as superconductors. BACKGROUND Toward the end of the I9th century, many physicists believed that all of the principles of physics had been discovered. The laws then discussed and accepted, now called "classical physics," included laws relating to Newton's mechanics, Gibb's thermodynamics, LaGrange and Hamilton's elasticity and hydrodynamics, Maxwell-Boltzmann molecular statistics, and Maxwell's equations. However, a discrepancy between nature and the understanding provided by prevailing laws was discovered in the case of black body radiation, wherein classical physics predicted the intensity to go to infinity as a function of temperature while experimentally it goes to zero. In 1900, Planck made the revolutionary assumption that energy levels were quantized which resulted in a model which was consistent with experimentation. Models of the atom were developed by Bohr based on the concept of quantized energy levels. Bohr's model was in agreement with the observed hydrogen spectrum; however, it failed with the helium spectrum and could not account for chemical bonds in molecules. It was reasoned that Bohr's model failed because it was based on the application of Newtonian mechanics to a discrete particle, and its limited applicability was due to the unwarranted condition that the energy levels be quantized. Quantization occurs in wave motion; hence, in 1923 de Broglie suggested that electrons have a wave aspect analogous to light with λ - h/p, where λ is the wavelength, h is Planck's constant, and p is the momentum. - ■ • In 1927, Davisson and Germer experimentally confirmed de Brogue's hypothesis by observing diff_action ir e!fe6ts by reflecting' electrons from metals. Schrodinger reasoned further that if electrons have wave properties, then there must be a wave equation that governs their motion. In 1926, Schrodinger proposed that the Schrodinger equation, HΨ = EΨ, was the law which governs the motion of electrons (where Ψ is a wave function, H is a wave operator and E is the energy of the wave). This equation and its associated postulates provides the basis for the field of quantum mechanics. Quantum mechanics requires that physics on an atomic scale are quite different from that on a macroscopic scale. However, it entails postulates which are not proven, but are assumed to be absolute laws of nature. Central to quantum mechanics is that it is statistical in nature. Knowing the state, a position measurement cannot be predicted with certainty, and only the probabilities of various possible results can be predicted as reflected in the Heisenberg Uncertainty Principle: σp σx > tϊ which is fundamental to the prevailing view of quantum mechanics and establishes the lower bound for the uncertainty of two observables. The Heinsberg Uncertainty Principle states that the product of the uncertainty in position and the uncertainty in momentum of an electron must be greater than fi where tl is Planck's constant divided by 2π. Prevailing understanding of quantum mechanics does not provide that an electron is distributed over a larger region of space as a wave is distributed. Rather, it is believed that the probability patterns (wave functions) used to describe the electron's motion behave like waves and satisfy a wave equation ψ(x). Max Born interpreted ψ * (x)ψ(x)dx to be the probability that the electron is located between x and x + dx, where ψ * is the complex conjugate of ψ(x), and this interpretation is generally accepted. However, Bom's view results in intangible concepts which conflict with known physical laws. For example, it results in overlap of negative probability density in molecules, the possibility of an electron instantaneously traveling from the nucleus to infinity and back which violates conservation of energy; radial kinetic energy which violates conservation of energy and angular momentum, and acceleration of a charged particle without radiation which violates Maxwell's equations. Schrodinger had a different interpretation of ψ(x) as a charge density function, but his interpretation also produces radiation which is contrary to experimentation as described in Appendix III. With respect to the interpretations of Born and Schrodinger, problems have arisen concerning the realization of kinetic energy, spin, and angular momentum of the electron. For instance, there is no time dependence of the stationary state wave equation; furthermore, the hypothesized electron-electron repulsions in multiple electron atoms violates the law of conservation of energy. Moreover, the Schrodinger equation provides no 5 rational basis for the phenomenon of spin, the Paul Exclusion Principle, or Hund's Rule. Also, bonding requires exchange of electrons between atoms which would result in violation of conservation of energy and angular momentum. As a result of the forgoing assumptions and incomplete or erroneous 1 0 models and theories, the numerous resulting conflicting models prevent the development of useful or functional systems and structures requiring an accurate understanding of atomic structure and energy transfer. The Schrodinger equation, for example, does not explain the high transition- temperature superconductors or "cold" nuclear fusion which comprise the 1 5 present invention. Thus, advances in materials and energy/matter conversion is largely limited to laboratory discoveries having limited or sub-optimal commercial application. SUMMARY OF THE INVENTION The methods and structures according to the present invention provide 20 unique applications of energy/matter conversion according to a novel mathematical model of the atom consistent with Maxwell's equations and principles of conservation of energy and angular momentum. According to the present invention, methods and apparatus for the useful generation of energy are provided wherein fusionable material is selected from a wide 25 range of possible elements wherein the orbital energies of the fusionable material are determined. The energy of the electrons is selectively depleted by an energy hole provided by one or more selective materials placed in close proximity to the fusionable material. Fusion is permitted * to occur at a rate determined by the relative equality of the orbital 30 energies and the energy hole. According to one embodiment, the rate of * fusion is adjusted by the external control of energies transferred into or out of the vicinity of the fusionable material and the energy hole to selectively adjust the equivalence of the energies. The energy produced by the resulting fusion of the nuclei of the fusionable material is received in 35 a surrounding material which serves to energize or propel apparatus for the generation of power, such as electric power or steam. A further product according to the present invention is the selective production of matter, including byproducts of the above described fusion, and matter having special characteristics, such as superconductor material. Furthermore, the atomic structure and energy of existing matter is selectively adjustable according to the present invention, such as by selectively reducing or increasing the electron orbitals by depletion of energy as described above or selection absorption, such as resonant photon absorption described according to the present invention. Time and spherical harmonic angular charge density functions and their energies and angular momenta which describe the electron before and after a transition are consistent with the laws of conservation of energy and angular momentum. The radial component of the charge density waves of the novel atomic model provides that the entire charge density function of three dimensional space and time does not radiate. The condition for zero radiation is the absence of Fourier components of the space time transform that are synchronous with waves traveling at the speed of light as described in Appendix I and Appendix II. The boundary condition of the radial function which forces the charge density function to be nonradiative and the result that the moment of inertia of each said function is a function of quantum numbers naturally give rise to the wavelike nature of the electron. The wavelength is identical to the de Broglie wavelength, λ = h/p, for all these functions that describe the electron and its energy in space-time and are hereafter referred to as Mills orbitals possessing energy, hereafter referred to as the Mills energy.- To distinguish the basis of the present invention from the prior art, the mechanics of the present novel atomic model is hereinafter referred to as Mills mechanics. The electron orbitals according to the novel atomic model, referred to as Mills orbitals, are spherically symmetric charge density functions hich are the product of a radial delta function, two angular spherical harmonic functions, and a time harmonic function. Each orbital is the sum of a constant Mills orbital which rotates with a quantized angular velocity and a Mills orbital ' charge density modulation function- which also rotates with a quantized angular velocity to result in a traveling wave of charge density on the surface of the sphere. The time harmonic motion of the former gives rise to the phenomenon of magnetic spin of one Bohr magneton for the electron. The latter time harmonic traveling naturally gives rise to orbital angular momentum. The interaction of the independent time harmonic motions gives rise to spin-orbital coupling, and the predicted spin, orbital angular momentum, and the associated 5 energies are in exact agreement with experimentation. The energy of an electron is stored in its electric and magnetic fields. Orbital energies are approximately equal to ionization energies. The orbital energies of several one- and two-electron atoms juxtaposed with their experimentally determined ionization energies appear in Table I and 1 0 Table II. Photon absorption by an electron with a transition to a higher energy Mills orbital arises naturally where a standing traveling wave of the photon is formed inside of the Mills orbital. This photon wave is a solution of Laplace's equation in spherical coordinates; thus, it is a spherical 1 5 harmonic. The photon wave rotates in both directions simultaneously, or it rotates in the opposite direction of the spin or angular momentum of the Mills orbital to change the spin or angular momentum by one quantum which is carried by the photon, thus, the selection rules ΔM; ΔS = O.± 1 for transitions arise naturally from conservation of angular momentum. 20 The electric field of an electron of a Mills orbital in the ground state is zero inside the orbital and is the field of a point charge at the origin outside of the orbital; thus, electron-electron repulsions are naturally eliminated in multi-electron atoms. The radii of orbitals in atoms are calculated in turn by setting the 25 centripetal force equal to the sum of the coulombic and magnetic forces. Thus, the result that isolated Mills orbitals are stable where the coulombic attractive force does not cause the electron to collapse into the nucleus arises naturally. For all atoms and ions, there exists a central *"» coulombic force acting on each orbital that is proportional to the net 30 charge (that is the charge not cancelled by other electrons). A positive central magnetic spin pairing force exists between two unpaired electrons which results in pairing in the same shell with spins opposed. Thus, the Pauli ' Exclusion Principle arises naturally. A diamagnetic repulsive central force exists between paired electrons of an inner shell and an unpaired 35 electron of an outer shell. A four body problem does not arise because the change in the centripetal force Of the inner shell electrons affected by the outer electron is exactly balanced by the Lorentzian force provided by the magnetic field of the outer shell electron; thus, it is possible to calculate the exact radius and exact energy of the Mills orbital of any electron of any atom. Illustrative examples appear in Table 1 and Table 2. The electric field of a Mills orbital is zero inside the shell, and this feature naturally gives rise to the chemical bond. Bonding between atoms occurs because the overlap of Mills orbitals of two atoms reduces the total energy stored in the electric fields of the participating atoms. The bond distance of the H2 molecule is determined in accordance with the present invention and shown Appendix V to be the experimentally confirmed value of .748A. Mills orbitals are spherical, and the radius increases with the absorption of electromagnetic energy. When the electron is ionized the radius of the Mills orbital goes to infinity, and the electron is a plane wave with the de Broglie wavelength. The plane wave nature of an electron is consistent with the results of prior double slit experiments. Furthermore, coupling of two such plane waves which are 180° out of phase as a zero phonon event provides Cooper pair formation and provides the basis of a model which provides for superconductors of high transition temperature which is the present invention. These materials comprise one or two dimensional lattices that contain atoms whose electrons can be ionized by an applied electric or magnetic field. Moreover, the lattice is of low symmetry so that the existence of symmetric phonons is improbable. Interactions of said phonons and Cooper's pairs causes the pairs to break. A representative two-dimensional unit cell is M is a metal and A, B, C, and D are different atoms or different oxidation states of the same atom or atoms. Mills orbitals can resonantly absorb an energy hole, and, as a consequence, the radius decreases. With sufficient decrease in radius the electron can annihilate a proton to form a neutron. Thus, K capture arises naturally from r this phenomenon. ■ . . .• - .. > - Furthermore, otrtside of the outermost Mills orbital of a neutral atom, the electric field of the nucleus is zero; thus, as the radii of atoms resonantly decrease, atoms can approach more closely before nuclear coulombic repulsive forces occur. And, with sufficient decrease, the nuclei of atoms, such as deuterium atoms in deuterium molecules, can approach sufficiently for fusion to occur at relatively low temperature. This process of providing low temperature fusion according to the present invention is hereafter referred to as Coulombic Annihilation Fusion (CAF). For deuterium, CAF requires a source of energy holes of slightly greater energy than 27 eV (n/2 27.21 eV; n = 2,3,4,...) to cause a resonant radius reduction of a Mills orbital of the deuterium atom. An illustration of such an energy hole system is Pd^+ and Li+ which catalytically removes a quantum of energy during each cycle of a reaction where the oxidation states increase and decrease by one, respectively, and are regenerated by the reverse redox reaction. Also, the present invention provides for many more such energy hole systems. BRIEF DESCRIPTION QFTHE DRAWINGS The present invention is further described with respect to the drawings having the following solely exemplary figures, wherein: Figure 1 is a pictorial illustration of Mills orbitals of the novel atomic model; Figure 2 is a pictorial illustration of the magnetic field lines of an electron in a Mills orbital in an un-ionized state; Figure 3 is a pictorial illustration of two approaching hydrogen atoms; Figure 4 is a pictorial illustration of the two hydrogen molecules as their Mills orbitals spatially overlap; Figure 5 is a pictorial illustration of the electric field vectors when the Mills orbitals of two hydrogen atoms penetrate; and Figure 6 is a block diagram of a fusion reactor according to one embodiment of the present invention. DETAILED DESCRIPTION OF THE INVFNTION Principle? Conservation of mass-energy, conservation of linear and angular momentum, Maxwell's equations, and Newtonian mechanics for sublight speeds are absolute laws of nature. Thus, a body in equilibrium which is not acting on or being acted on by another body possesses constant mass- energy, constant angular momentum, force balance, and is not radiating. And, a body not at equilibrium exchanges mass-energy and angular momentum in a conservative manner until the body is again at equilibrium. An isolated atom or molecule qualifies as such a body, and a novel model of the atom and molecules hereafter referred to as Mills mechanics is derived based solely on these principles, and the charge/mass density functions which describe the electron are Mills orbitals. Mills Orbitals Consider the body of an isolated hydrogen atom at rest in three- dimensional space. All forces are central and the coordinate system is spherical. The mass-energy and angular momentum are constant which necessitates that the equation of motion of the electron of the atom be a time harmonic. Conservation of angular momentum further necessitates that the electron space-time angular mass density function must be a solution of a wave equation given in general form as follows: Spherical harmonics are general solutions of this equation. Conservation of momentum and energy in the absence of external forces or energy exchange determine that the angular functions must be separable. The electron has a charge of 1.6 X 10 ~1 9 C and possesses an angular space-time mass density function which is a spherical and time harmonic. Charge is conserved and obeys superposition; thus, the mass density function of an electron is equivalent to its charge density function which depending on the form of its separable radial function will radiate due to the time harmonic angular acceleration of charge. The condition for radiation by moving charge is derived from Maxwell's equations in Appendix I. To radiate, the space-time Fourier transform of the charge density function must possess components synchronous with waves traveling at the speed of light. Thus, the product of two spherical harmonic functions, a time harmonic function, and a radial function must not possess space-time Fourier components that are synchronous with waves traveling at the speed of light. The solution of this boundary value problem Is the radial function given as follows: f( 0 = δ(r-r 0 ) The boundary condition for the .product of the said four functions which results in the absence of radiation is given in Appendix IL For an angular • frequency of ω = ωo, the space-time Fourier transform is zero when 2πr = nλ. This function, with the boundary condition 2πr = nλ is a Mills orbital. The boundary condition requires that the electron possess a wavelength λ. The wavelength of an electron is the de Broglie wavelength, xΛ P The exact forms of the angular and time harmonic functions can now be solved from the wave equation in spherical coordinates. The form of the wave equation for the angular and time harmonic functions is as follows: ( V2 + ^H) A(θ. φ, t) - 0 ( _τ- ΪM (Sinθ( M> r ' Φ + .2^ _ " _f> r ' θ + ^&) A(θ ' ♦■ *> " ° The energy, E, of a rotating body is given as follows: E = 1/2 lω 2 , 1 0 where I is the body's moment of inertia and ω is its angular velocity. The angular velocity ω is related to the frequency υ as follows: ω = 2πυ And, the wavelength, λ, can be expressed in terms of the frequency υ and velocity v as follows: 1 5 υλ = v Substitution of these relationships into the wave equation gives the result, Γ ς β (sinθ( n > + s*e <S )] A(θ ' ♦• " = E A(θ ' ♦• l) The time harmonic function K(t) =eiω 0 is separable and is cancelled 20 yielding the following equation: r [ ._iέ (siπθ( έ ) + ϋ 5 1Y(θ φ) = EY(θ ' φ) < 6 - 46 > If we multiply Eq. 6-46 by sin 2 θ and let <* _ we find the partial differential equation ' δ δY λ δ Y 2.5 . sinθ — ( sinθ — ) + ^-2- + β sin2θ Y « 0 (6-48) To solve this partial .differential equation, we use the method of separation of variables and let Y(θ, φ) - g(θ) h(φ) (6-49) If we substitute Eq. 6-49 into Eq. 6-48 and then divide by Θ(θ)Φ(φ), we find sinθ d / dg \ n 1 d 2 h Because θ and φ are independent variables, we must have that + 0 sιπ2 θ - m2 (6 - 51 > and where m 2 is a constant. Note that Eqs. 6-51 and 6-52 add up to Eq. 6-50. Equation 6-52 is relatively easy to solve, and its solutions are h(φ) = A m e im and h(φ) = A. m e- im Φ (6-53) The requirement that h(φ) be continuous is that h(φ + 2π) = h(φ) (6-54) By substituting Eq. 6-53 into Eq. 6-54, we see that A me i (φ+2π) = A m e'mφ (6-55 ) and that A- m e- im (Φ +2π ) = A- m e-' m Φ (6-56) Equations 6-55 and 6-56 together imply that e ±i2πm = 1 (6-57) In terms of sines and cosines, Eq. 6-57 is cos(2πm) ± i sin (2πm) = 1 which implies that m = 0, ±1 , ±2,..., because cos 2πm = 1 and sin 2πm = 0 for m = 0, ±1 , +2,... Thus Eq. 6-53 can be written as one equation hm(Φ) = A m e'mφ m - 0, ±1 , ±2,... (6-58) We can find Am by requiring that the hm(Φ) be normalized. The normalization condition is that 2π Using Eq. 6-58 for the h m (φ), we have 2π |A m |2 j dφ = 1 0 or |A m |2 2π = 1 or Am = ( π)-l/2 Thus, the normalized version of Eq . 6-58 is _\_ h m(Φ) - (/2.π)M " /2 eimφ m = 0, ±1 , ±2,.. (6-59) The solution to Eq. 6-51 is obtained by the power series method. We shall not present all the details for the solution to Eq. 6-51 , but when one does solve Eq. 6-51 , it turns out naturally that β in Eq. 6-47 must obey the condition β = 1(1+ 1 ) 1 = 0, 1 , 2,... (6-60) Using the definition of β, Eq. 6-60 is equivalent to E| - ^ l(l+ 1 ) 1 = 0,1 ,2,... (6-61 ) A set of discrete energy levels are obtained. The charge density functions of Mills orbitals are given by the solutions to Eq. 6-46. To solve Eq. 6-46, we assumed separation of variables and wrote Y(θ,φ) = g(θ) h(φ) (Eq. 6-49) . The resulting differential equation for h(φ) (Eq. 6-52) is relatively easy to solve, and we showed that its solutions are (Eq. 6-59). The differential equation for g(θ), (Eq. 6-51), is not easy to solve. It is convenient to let x = cos θ and g(θ) = P(x) in Eq. 6-51. Because 0 < θ < π, the range of x is -1 < x < +1. Under the change of variable, x = cos θ, Eq. 6-51 becomes (l ■ χ2)d α5 " " 2x d^ + t |( ' +1) " ^ P(x) = ° (6"69) In Eq. 6-69 we have used the fact that β = l(l + l)(Cf. Eq. 6-60). Equation 6- 69 for P(x) is called Legendre's equation and is a well-known equation in classical physics. It occurs in a variety of problems that are formulated in spherical coordinates. When the power series method of solution is applied to Eq. 6-69, the series must be truncated in order that the solutions be finite at x ■ ±1. It is this truncation that yields Eq. 6-60. The solutions to Eq. 6-69 when m = 0 are called Legendre polynomials and are denoted by P|(x). Legendre polynomials arise in a number of physical problems. The first few Legendre polynomials are given in Table 6-1. Table 6-1 The First Few Legendre Polynomials, Which Are the Solutions to Eq. 6-69 with m = 0. The Subscript Indexing the Legendre Polynomials Is the Value of I in Eq. 6-69. Pθ (x) = 1 P1 (x) = x P2 (x) - 1/2 (3x -1 ) P3 (x) = 1/2 (5 χ 3-3x) P4 (x) = 1/8 (35x 4 -30x +3) Notice from Table 6-1 that P|(x) is an even function if I is even and an odd function if I is odd. The factors in front of the Pi (x) are chosen such that P j (1) - 1. In addition, although we shall not prove it, it can be shown generally that the P-| (x) in Table 6-1 are orthogonal or that 1 Keep in mind here that the limits on x correspond to the natural, physical limits on θ(0 to π) in spherical coordinates because x - cosθ. The Legendre polynomials are normalized by the general relation, which we simply present: 1 Equation 6-71 shows that the normalization constant of R (x) is [(21 +1 )/2]1/ 2 . Although the Legendre polynomials arise only in the case m = 0, they are customarily studied first because the solutions for the m *= Ocase, called associated Legendre functions, are defined in terms of the ordinary Legendre functions. If we denote the associated Legendre polynomials by iml P j (x) , then their defining relation is Iml nm Pj '(x) - (1-χ2)|m|/2 — p t(x ) ( 6 .72) Note that only the magnitude of m is relevant here because the defining differential equation, Eq. 6-69, depends on only m 2 . The first few associated Legendre functions are given in Table 6-2. Before we go on to discuss a few of the properties of the associated Legendre polynomials, let us be sure to realize that it is θ and not x that is the variable of physical interest. Table 6-2 also lists the associated Legendre polynomials in terms of cos θ and sin θ. Note that the factors (1 - x 2 )! 2 in Table 6-2 become sin θ when the associated Legendre functions are expressed in the variable θ. Because x = cos θ, Eqs. 6-70 and 6-71 are 1 " ^n P | (x)P n (χ)dx = dθ sinθ P | (cosθ)Pn(cosθ) = 2Ϊ+ ( 6 " 73 ) - 1 0 Because the differential volume element in spherical coordinates is dτ = r 2 sin θ dr dθ dφ, we see that the factor sin θ dθ, in Eq. 6-73, is the "θ part" of dτ in spherical coordinates. Table 6-2 m The First Few Associated Legendre Functions P | (x) P_j (x) _ x __ COSΘ P (x) - 1/2(3x2 - 1) = 1/2(3 cos2 θ - 1) P 2 (χ) = 3X/1 - x 2 = 3 cosθ sinθ P 2 (x) - 3(1 - x 2 ) = 3 sin θ P°(x) = 1/2(5x3 - 3x) = 1/2(5 cos3 θ - 3 cos θ) P^(x) = 3/2(5χ2 - 1)(1 - χ2)l/2 = 3/2(5 cos2 θ - 1)sin θ p fw = 15x(1 - χ2) = 15 cos θ sin2 θ P,(x) - 15(1 - χ2)3/2 = 15 S j n 3 θ The associated Legendre functions satisfy the relation 1 '(x) = dθ sin θ P | (cos θ) P „ (cos θ) 2 (l-t- l l)l (21 + 1)(l - |m|)nn (6-74) Equation 6-74 can be used to show that the normalization constant of the associated Legendre functions is • r(2l _ ■ 1)(l - |ml)! l 1/2 ' "im e t 2 (1 + |m|)|J (6"75) Returning to the original problem now, Eq. 6-46, the Mills orbitals I m I functions are P | (cos θ)hm(Φ). By referring to Eqs. 6-59 and 6-75, we see that the functions Yr(e, . ) = μ^ {f^ ] p! m| (cose) e imΦ ,6-76) 4π (I + | m | ) . are solutions to Eq. 6-46. The Y, (θ, φ) form an orthonormal set ,δ mk (6-77) Note that the Y j (θ, φ) are orthonormal with respect to sinθ dθ dφ and do not just dθ dφ. The factor sinθ dθ dφ has a simple physical interpretation. The differential volume element in spherical coordinates is r 2 sinθ dr dθ dφ If r is a constant, as it is in the case of a radial delta function, and set equal to unity for convenience, then the spherical coordinate volume element becomes a surface element, dA = sinθ dθ dφ. If this surface element is integrated over θ and φ, we obtain 4π, the surface area of a sphere of unit radius. Thus, sinθ dθ dφ is an area element on the surface of a sphere of unit radius. According to Eq. 6-77, the Y ( (θ, φ) are orthonormal over a spherical surface and so are called spherical harmonics. The first few spherical harmonics are given in Table 6-3. Table 6-3 The First Few Spherical Harmonics Y 0° = (4π) 1/2 ,0 (— ) COS θ 1 .3.1/2. iφ Y 1 - <£? sιn θ e -1 ,3 1/2 -iφ Y 1 = (— ) cos θ e 1 /151/2. iφ γ 2 " ζr " s,n θ cos θ e The angular functions of Mills orbitals are spherical harmonics, and the angular kinetic energy is given as Ek = f[l(l + 1) 1 -0, 1,2, ... The angular kinetic energy E| is related to the angular momentum, L, by the following relationship: L2 E k = 2Ϊ Thus, L* Vi(l + 1) I - 0, 1, 2, ... Mills orbitals are the product of the angular, radial, and time functions which are given as follows: M(r, θ, φ, t) = Y(θ, φ) δ(r - r 0 ) e'ω 0 t Y(θ,φ) is a function of e im Φ for I * 0. The product e' m Φe' ω ot = e'(mφ + ω 0 t) is a traveling wave with angular frequency ω 0 . The angular frequency can be derived from the angular momentum energy as follows: G)2 = ^- |(| + 1 ) |2 ω - yVl(l + 1 ) In addition to the spherical harmonics of Table 6-3, Y^ and γ " _, Λ , , with 1 = 1/2 is also a solution to equation 6-46. A Mills orbital of one of these functions is a time harmonic spinning charge density function, and it can be shown that this Mills orbital always possesses a magnetic moment of one Bohr magneton, β, given as follows: en β = ^ ~ F 2μ where e is the charge and μ is the mass of the electron and ft is Planck's constant divided by 2π. The angular momentum of these functions is distinguished from that of the former solutions by assigning it the variable S, the spin angular momentum of the electron which is given as follows: S = ft Vs(s + 1 ) S = 1/2 m s = ±1/2 And, the angular momentum, L, is defined as orbital angular momentum. A sum of independent solutions to Eq. 6-46 is a solution, and the same condition applies to the boundary condition for nonradiation. Thus, the Mills orbital of the electron is given as the sum of the following functions: M(r, θ, φ, t) = Y^ (θ, φ) δ(r - r 0 ) e'ω, t + Y^Θ, φ) δ(r - r 0 ) e'c^ I s where ft ω 1 = T T l T+ ) I = 0, 1, 2,. Thus, it is apparent that a Mills orbital is a spherical shell of charge/mass density of zero width where the charge/mass is a base function defined by Y » to which is added a component of modulation of s mass/charge density given by Y ' where the total charge is e, the charge of an electron, and the total mas 's is μ, the mass of the electron. (Diagrams of several representative Mills orbitals are given in Figurel .) The two components are independent time harmonics which rotate in the same or opposite directions. The interaction of the two independent components gives rise to spin-orbital coupling. It can be demonstrated that the moment of inertia of the orbital angular momentum and spin angular momentum are given respectively as follows: l spin = μr 2 I( _ iT 'angular = ^ \(\ + 1 ) where μ is the mass of the electron and r is the radius of the Mills orbital. Substitution of this result into the angular frequency relationships gives: The linear velocity is obtained from the angular velocity by the following equation: v = r ω Thus, the linear velocity of the spin and orbital Mills orbitals is given as follows: ft v = — μr To prove this result is consistent with the boundary condition for nonradiation, the wavelength is derived from this result and the boundary condition, 2πr = nλ; n =1 ,2,3,... as follows: 2π _ ω ft λ ~ v ~ μι-2v 1 _ h λ ~ 2πr2πrμv 1 h λ λμv Position an -d E5nergies of Mills Orbitals The radius of each Mills orbital can be calculated by equating the centripetal force with the other central forces. The forces are as follows: 1.) coulombic attractive force of the positively charged nucleus for the negatively charged Mills orbital; 2.) an attractive magnetic spin pairing force between two unpaired electrons which causes them to be at the force balance at the same radius with vectorially opposed spins; thus, the magnetic moments cancel; 3.) a repulsive diamagnetic force between two paired electrons and an unpaired electron where the radius of the former is unaffected by this force. Only the coulombic force is involved in the one electron atom. The coulombic and the spin-pairing forces are involved in two electron atoms, and the coulombic and diamagnetic forces are involved in calculating the radius of the third electron of a three electron atom, where the previously calculated radius of the inner shell comprising two spin-paired electrons is used in the calculation. The orbital energy of any electron can be calculated from the calculated radius as the energy stored in its electric and magnetic fields. (The magnetic field of an electron and the energy stored in the magnetic field of two electrons is given in Appendix IV. A magnetic field diagram of an electron is given in Figure 2.) Examples of one-, two-, and three-electron atoms are given below which demonstrate the said forces. And, it is further demonstrated, in the case of lithium, that the sum of the orbital energy and the change in orbital energies of the two remaining inner shell electrons following ionization is equal to the experimentally determined first ionization energy of lithium. The One-Electron Atom μv centripetal force = — — * • * i i * _ * • * (+Ze)(-e) -Ze 2 centripetal electrostatic force = — ; — LΛ~ _τ J - = . « 4πε 0 r 2 4πε 0 r 2 (obtained by taking the gradient of the electrostatic potential) We can solve for the radius of the electron shell by balancing these forces. μv 2 _ Ze r ~ 4πε 0 r 2 The boundary condition is 2πr = nλ which gives ω = — 2 ; v = rω ; thus, v = ft2 — . When an electron in the ground state absorbs a photon of sufficient energy to take it to a new non-radiative state, n = 2, 3, 4, .... force balance must be maintained. This is possible only if we let Z e ff = ~ and, therefore, μ n 2 Z eff e2 r_ ~ 4π . 0 r n 2 The reduction of the charge from Ze to Ze/n is caused by trapping a photon in the orbitsphere cavity — a spherical cavity. Therefore, 4πε 0 nft 2 na Q The energy stored in the electric field of the orbitsphere, E e)e ,is E eie - (j) ε r 2 sin θdrdθdφ where the electric field.E, is E = °' r < a ° : E = 4^ ' r - a ° nap oo E ele β - § 3-589) eV (2) Equations (1) and (2) can be used for any one-electron atom. The energies for several one-electron atoms are shown in Table 1. Table 1 Calculated energies (non-relativistic) and calculated ionization energies for some one-electron atoms (without realtivistic correction). Atom Energy (eV) a Ionization Energy (eV) H -13.589 13.595 He+ -54.35 54.587 ϋ 2 + -122.28 122.45 Be3+ -217.40 217.71 B4+ -339.68 340.22 C5+ 489.14 489.98 Nδ+ 665.77 667.03 07+ 869.58 871 .39 a from equation (2) The Two-Electron Atom μv centripetal force = centripetal electrostatic force centripetal magnetic force = - (obtained by taking the gradient of the angular momentum energy) Consider two indistinguishable electrons where each is subject to an effective nuclear charge of Z-1 due to cancellation of one nuclear charge by the other electron. Each electron has a positive spin pairing force for the other. The balance of force equations is as follows: For n - 1 , v2 « -~ μr2 μv< _ft2_ (Z - 1 )e2 1 ft2 μr 3 4πε 0 r Z μr 3 VS(S + 1 ) and, The magnetic energy is 2πμ 0 e2ft2 E(magnetιc) = — (5) μ r (The energy stored in the magnetic field of an electron is derived in Appendix IV.) Table II The calculated electrostatic and magnetic energies for some two-electron atoms (without relativistic corrections). Atom Atomic R(a 0 ) a Electrostatic Magnetic Total Experimental Number Energy 0 Energy 0 Energy Ionization (eV) (eV) (eV) Energy (eV) He 2 0.567 -23.96 -0.63 -24.59 24.587 Li 3 0.356 -76.41 -2.54 -78.95 75.638 Be 4 0.261 -156.08 -6.42 -162.50 153.893 B 5 0.207 -262.94 -12.96 -275.90 259.368 C 6 0.171 -396.98 -22.83 -419.81 392.077 N 7 0.146 -558.20 -36.74 -594.93 552.057 0 8 0.127 -746.59 -55.35 -801.95 739.315 F 9 0.113 -962.17 -79.37 -1 ,041.54 953.886 a from equation (3) bfrom equation (4) c from equation (5) Three-Electron Atom (First Ionization Energy of Lithium) From the Li 2+ (see Table 2), it was determined that there are two oppositely spin-paired electrons in a shell with the radius The next electron is added to form a new shell. This is a consequence of a repulsive force that exists between the two spin-paired electrons and the spin unpaired electron. This repulsive magnetic force arises from the phenomenon of diamagnetism involving the magnetic field produced by the outer electron and the two paired electrons of the inner shell. (The following calculation is given by Edward Purcell in Electricity and Magnetism, p. 370-389. The diamagnetic force of the two paired inner shell electrons acting on the outer shell electrons is given as -mvpAv Δ\ _ eB eB _ft_ r r = 2μ = 4μ V ° = μr 0 where r, is the radial distance of the first shell from the origin. ft eB n μ The magnetic flux is that supplied by the constant field inside the shell of the outer electron and is given by: μoβft B = ' — g- ; therefore, e 2 μ 0 μr = Vs(s + 1 ) F - - 4, μ ft r 2 2 rι . Vs (s + 1 ) ' The radius of the orbital for the outer electron of lithium is calculated by equating the centripetal force to the sum of the coulombic and diamagnetic forces as follows: μv 2 e ft2 ~ r = 4 A πε r . 0 r 2 - ~ 4 Λ μr 2 n S ( v S + 1 ) ' VT thus, The energy stored in the electric field is calculated as follows: e _ e 2 8πε 0 r " 8πε 0 2.56a 0 ~ The field due to the outer shell electron changes the angular velocities of the inner shell electron; however, the magnetic field of the outer electron provides a central Lorentzian force which exactly balances the change in centripetal force due to the change in angular velocity. Thus, the radius of the inner shell is unchanged. Consequently, the electric energy of the inner shell is unchanged upon ionization. However, the outer field changes the magnetic moments of the inner shell electrons. The change per electron is given by Purcell as follows: where τ _ is the radius of the inner shell and r2 is the radius of the outer shell. e 2 rι 2 μoeft = s (s + 1 ) μr 2 2 r 2 : s(s + 1 ) Multiply the result by two because there are two electrons. = 0.0167 We add one and square to get the fractional change in the magnetic energy of the inner shell. (because the energy stored in the magnetic field is proportional to the magnetic field strength squared). (1 .0167)2 = 1.0338 Thus, the change in magnetic energy of the inner shell is 3.382% which is given by: 2.543 eV (0.3382) = .0860 eV (Where the magnetic energy of lithium* appears in Table II.) Eionization - -0860 eV + 5.318 eV = 5.4038 eV The calculated ionization energy without relativistic correction is 5.40 eV. The experimental ionization energy is 5.392 eV. Energy due to Spin Nuclear Interactions If the magnetic quantum number of the nucleus is greater than 0, the nucleus has a magnetic moment and the magnetic field of the electron can interact with the nuclear moment. This interaction is an important parameter for structural determinations by electron paramagnetic resonance spectroscopy and Mossbauer spectroscopy. The energy of interaction is given as follows: E = n. B, where μn is ! the nuclear moment and B is the magnetic flux. In the case of an electron, it can be seen from Figure 2 that the flux of an electron at the nucleus is uniform and is given in Appendix IV as follows: μoβft * Λ B = — g- (ir cos θ - ι σ sin θ) The magnetic moment of a proton is given as follows: eft where, mp is the mass of the proton. When the nuclear moment is aligned with the electron's field θ = 0 and the energy is given as follows: eft μoeft 2mp μr 3 These energies are small. For example the energy of spin-nuclear interactions for hydrogen are 1.98 * 10 * 5 eV. The Nature of the Chemical Bond The driving force of molecular bonding is the decrease in the energy stored in the electric fields of the participating atoms as a consequence of overlap of their Mills orbitals. (The magnetic stored energy is involved but is dominated by the electric stored energy.) Consider two isolated hydrogen atoms that approach each other along the internuclear axis as shown in Figure 3. The electric field of each atom is zero for radial distance greater than ao, the radius of the Mills orbital of the electron. As the Mills orbitals from one atom penetrates the space of the other, the electric field components add vectorially. The components parallel to the internuclear axis cancel, and the perpendicular components add positively. The latter components have a positive tangential projection onto the angular vectors of the Mills orbitals in the region of overlap. The energy stored in the electric fields of the atoms decreases as the internuclear distance decreases; however, it reaches a minimum then increases rapidly as a function of the internuclear distance. The trajectory produces the classic potential well, and the internuclear distance is given the geometric calculation in Appendix V as V ~ 2 ao = .748A which is the exact experimental value. Thus, molecular bonding is demonstrated to result from interactions of the electric fields of atoms which minimizes the energy. Starting with the case of the hydrogen molecule of Appendix ' V, consider reducing the total charge ' of one of the Mills orbitals. The internuclear distance increases as the charge decreases. In the limit of no charge, the internuclear distance is 2ao. This is apparent from the following argument, the addition of an infinitesimal amount of charge to the Mills orbital of zero charge produces an infinitesimal overlap due to an infinitesimal lowering of the total energy. Thus, the internuclear distance before the infinitesimal addition was 2ao which is the exact experimentally measured distance for the H2+ molecule. Furthermore, it can be shown that the diatomic molecule can be approximated by a harmonic oscillator with quantized energy levels given as follows: Evib - (n + 1/2)hυ 0 n = 0, 1 , 2,... where μ is the reduced mass of the atoms, and k is the spring constant which is proportional to the bond strength; therefore, k is proportional to the gradient of the function of the bond energy as the internuclear distance changes. It can also be shown that the rotational energies of a diatomic molecule are given as follows E ro t = hcB(J + 1) J = 0, 1 , 2,... Selection Rules The electrons which are described by Mills orbitals can absorb energy and achieve an excited state, and they can lose or emit energy and achieve a lower energy state. In the case electromagnetic radiation, energy flow is governed by Poynting's theorem V • S = -jωμH ■ H + jωεE • E - J • E where the parameters are as follows: S. is the power; the first term is th§ rate of change in the stored magnetic energy, . the second term is the rate of change in the stored electric energy, and the , third term is the . dissipated power. For electromagnetic radiation, the ground state is the lowest energy state. The ground state is given by the balance of the centripetal and coulombic forces. For the hydrogen atom, the radius an,d energy appear .In- able 2 as ao and 13.6 eV, respectively. The boundary condition for Mills orbitals was given in the Mills Orbital Section as 2πr = nλ where r = ao for n = 1. Thus, the absorption or emission of a photon by a hydrogen atom causes the radius to change by an integer multiple of ao- The energy of the photon is the difference in energy of the initial and final orbitals where the equation for the energies of the orbitals is given in the One Electron Atom Section. Photon absorption by an electron creates a standing wave of the photon's electric and magnetic fields inside of the Mills orbital. These fields are solutions to Laplace's equations in three dimensions which are spherical harmonic equations. The photon field exists as a standing wave where surface currents of the Mills orbital are generated by the said wave and are boundary conditions for its existence. The angular momentum and spin angular momentum of all Mills orbitals are given by E| - t l(l + 1 ) and E s = t s(s + 1) , respectively. The angular momentum is a vector; thus, it is apparent that the angular momentum can change by zero or ±1 during a photon absorption or emission event, a transition. Angular momentum must be conserved; therefore, the quantum of angular momentum is provided by the photon which carries the exact opposite quantum of angular momentum as that imparted to the Mills orbital. The standing wave of the photon is a traveling standing wave where the Mills orbital surface currents, induced by the wave, provide one quantum of angular momentum to the Mills orbital in the opposite direction to the angular direction of the traveling wave. Furthermore, angular momentum is also conserved if the wave does not travel. In this case, the photon wave can be considered as the superposition of two traveling waves rotating in opposite directions with the same angular velocity and is analogous to plane polarized light. Thus, the selection rules for a photon induced transition of Δm. Δs ■ 0, ±1 arise naturally (Δm is the change in angular momentum, and Δs is the change in spin angular momentum) where a change of zero is the nontraveling wave case and a change of 1 is the traveling wave case. This is totally consistent with experimentation which demonstrates these rules to be correct where the photon carries one or zero quantum of angular momentum. Consistently, a transition has a rise time and, consequently, a line width, as is the case in electrodynamics. The standing photon wave has a nonzero electric field at the Mills orbital which has a radial component which combined with the induced surface currents provided by its tangential electric field cause the centripetal and central coulombic forces to be balanced at an integer multiple of ao- Thus, the standing wave has an effective charge given by , 0 ε?r which reduces the coulombic attraction of the nucleus. Because a photon can only reduce the coulombic attraction, the ground state, which contains no photon field, is the smallest radius possible for photon transitions. It will be shown in the Coulombic Annihilation Fusion Section that the resonant absorption of energy holes can shrink the radius by quantized fractions of ao- Effects of External Fields External magnetic fields align magnetic moments (Bohr magnetons) of atoms for those with unpaired electrons, or external magnetic fields effect diamagnetic phenomenon in those materials that do not have unpaired electrons. Neither phenomenon affects the boundary conditions for nonradiation. External electric fields cause a redistribution of the charge density of the Mills orbitals, the charge density functions, to create a dipole moment in the atom or molecule. This phenomenon is polarization. The orbital condition 2πr = nλ is not violated, so no radiation occurs. Electrons can absorb photons from magnetic or electric fields to become ionized. This occurs readily in a conductor or superconductor. Mills orbitals of electrons are spherically symmetric. As photons are absorbed the radius expands from the ground state with radius ri to nri where n = 2, 3,... . As n goes to infinity the radius r goes to infinity and the Mills orbital becomes a plane wave. The boundary condition for a Mills orbital 2πr = nλ still applies; therefore, λ = — he plane wave nature of the ionized electron is confirmed by double slit experiments that demonstrate that the , resulting interference pattern is consistent with the electron traveling through both slits simultaneously and possessing a wavelength Metals have electrons as Mills orbitals which individually absorb energy in the form of a photon from applied magnetic or electric fields to become ionized to produce individual plane waves which are scattered by phonons. There exists many electrons which can absorb the electric or magnetic energy to become ionized and propagate as plane waves through the material. In the case of superconductors, two electrons are ionized simultaneously and pair 180° out of phase as a zero phonon event to form Cooper pairs which have a low probability of being scattered as they propagate. Superconductors are described in detail in the Superconductor Section. Superconductors The Mills orbital of an electron is a spherical shell. The shell annihilates photons during absorption to trap them as standing waves inside the Mills orbital. The radius of the Mills orbital increases as the energy stored in the field of the photonic wave increases. Because the Mills orbital is a sphere, the orbital approaches a plane wave of charge density as the radius goes to infinity. Thus, an electron becomes a plane wave carrying a plane photon wave when it is ionized. Two electrons can be ionized simultaneously to create two traveling waves. If they are initially oppositely paired in terms of spin and angular momentum, then the two electrons with their accompanying photonic waves may add destructively. (180° out of phase, as plane waves when they are simultaneously ionized). This event occurs with no excitation of a phonon (lattice vibration). That is it must be a zero phonon event because phonons change the relative phases of the plane waves and exchange energy with the photonic fields. These paired Mills orbital plane waves, which are 180° out of phase, carry the supercurrent in superconductors, and are known as Cooper pairs. They possess a low phonon interaction cross section for dephasing and breaking in the superconductor. Breaking the pairs requires the simultaneous absorption by the pair of anti-symmetric phonons. This is the boundary condition because Cooper pair creation was a zero phonon event; thus, anti-symmetric phonons must simultaneously be absorbed to break the Cooper pairs to conserve angular and linear momentum of the entire system-Cooper pair plus phonons (lattice distortions). Thus, It is apparent that a superconductor with a high transition temperature is a material with the following properties: 1.) a large population of atoms with electrons which can readily absorb energy from an electric or magnetic field to become ionized in such a fashion that they can participate in Cooper pair formation 2.) a low population of phonons at high temperatures 3.) a low population of phonons of sufficient energy to break Cooper pairs at high temperatures 4.) a low population or low probability ofopposite symmetry phonons of energy sufficient to break Cooper pairs. Materials that contain atoms of transition elements satisfy condition 1. Materials which contain one of two dimensional lattices with strong bond energies satisfy conditions 2 and 3. Ceramics are materials of condition 2. Materials which contain one or two dimensional lattices with mixed valency or all different atoms in the unit well satisfy condition 4. The ideal unit cell is where M is a transition metal and A, B, C, and D are different atoms or different oxidation states of the same or different atoms. Perovskite superconductors such as (Ba, Sr, Y) x La2-χ Cuθ4 are examples of materials which contain all of the said parameters. Coulombic Annihilation Fusion It was demonstrated in the Selection Rules Section that resonant photon absorption can only increase the radius of a Mills orbital. For resonant photon absorption, the ground state has the smallest radius possible. For the hydrogen, atom the radius of the ground state Mills orbital is given in Table 1 as ao- This orbital contains no photonic waves, and the outward centripetal force and the inward coulombic force of the electron exactly balance. The relationship is as follows: μ V 2 e 2 • u ft — - = where v = — ao 4πεoap μap It is apparent from this relationship that the radius would decrease if the velocity were somehow decreased. To decrease the velocity, energy must be removed which is equivalent to the absorption of an energy hole by the electron. When energy is removed the Mills orbital will decrease to another allowed state where the boundary condition, 2πr - nλ, and the force balance is met. Thus, it can be demonstrated, as appears in Appendix VI, that the absorption of an energy hole with concomitant shrinkage of the radius of the Mills orbital is a resonant process with quantum numbers. The resonance "shrinkage" energy given in Appendix VI for the hydrogen atom is n 2 27.21 eV where n » 2, 3,..., and the radius shrinkage is ao( ~ - ~ — ) where ni is the quantum integer of the initial orbital and n2 is the quantum integer of the final orbital of a radius shrinkage transition. The electrons in deuterium atoms are described by Mills orbitals which satisfy the boundary condition 2πr = nλ, and possess no space-time Fourier components synchronous with waves traveling at the speed of light; thus, they do not radiate. The electric field of the Mills orbital of a deuterium atom is that of a point charge at the origin for radial distances greater than the orbital radius. For these distances, the field of the Mills orbital exactly cancels the field of the proton which is also that of a point charge at the origin. The electric field of a Mills orbital is zero inside the orbital; thus, the electric field inside the orbital of the deuterium atom is the point charge field of the proton. It was demonstrated in the Nature of the Chemical Bond Section that chemical bonding was due to this feature of electric fields of Mills orbitals where the total energy of the electric fields of the participating atoms was minimized when the internuclear distance is >/2 times the radius of the Mills orbital. And, this feature together with resonant shrinkage of the Mills orbitals is the basis of "cold fusion" of deuterium, Coulombic Annihilation Fusion, the present invention. Coulombic repulsions of the nuclei prevent them from approaching sufficiently for the strong nuclear force to dominate and for fusion to occur. However, outside of the Mills orbital of a deuterium atom there is no electric field; thus, for each of two deuterium atoms, when the Mills orbital is sufficiently decreased by the resonant absorption by energy holes, the internuclear distance of two deuterium atoms becomes the distance at which the attractive strong nuclear force dominates the repulsive coulombic force, and fusion of deuterium to helium and tritium occurs with the release of 931 MeV/amu. The mass change for fusion of deuterium is 0.03 amu; therefore 28 MeV/atom of energy is released. It Is demonstrated in Appendix VI that the radius of the Mills orbital of the deuterium atom will decrease by ao ( ~ - ~ ) when an energy hole of energy equal to n/2 27.21 eV; n = 2, 3, 4 is resonantly absorbed. With continued resonance shrinkage-absorption of energy holes-by the atom, the Mills orbital shrinks to small dimensions, and when approximately 100 KeV of energy holes have been absorbed the radius is sufficiently small that the deuterium atom will fuse with another atom of deuterium with a similar dimension of its Mills orbital. A catalystic system to produce energy holes of 27.21 eV is a preferred embodiment of the present invention. For such a system the population of energy holes is not exhausted because they are regenerated. Palladium 2 + and lithium+ is such a system. The catalytic cycle which affects the quantized decrease in the radius of the Mills orbital of the deuterium atom is as follows: 27.54 eV + Li + + Pd 2+ + + l) 2 - n 2 ] x 13.6 eV Li + Pd3+ = i+ + Pd 2+ + 27.54 eV Overall reaction 2H R ] → 2H fe ϊ ] + p + D 2 -p 2] x l3.6 eV where p - 1 , 2, 3 The Palladium lithium system involves three species. The rate of the resonance shrinkage can be increased by reducing the number of species to two. Titanium, rubidium, or argon are effective catalysts. The catalytic reactions are as follows: 27.491 eV + Ti 2 + + 2 H[^] → Ti 3 + + e ~ + 2 H[(T^[) ] + [(p + l) 2 - p 2 ] x 13.6 eV Ti + + e ~ → Ti 2+ + 27.491 eV (8.8) And, the overall reaction is 2H [?] → 2H [φ ϊ)] + KP + D -p 2 ] x l3.6 eV where the ionization energy, Ejon. for Ti 2+ is 27.491 eV; p is a integer 27.491 eV+ Rb + + + [(p + l) 2 - p 2 ] x 13.6 eV Rb 2+ + e ~ → Rb+ + 27.28 eV Overall reaction where the ionization energy, Ejon. for Rb+ is 27.28 eV 27.63 eV+ Ar + + 2 H[^ ] → Ar + + er + 2 ^J f_ ] + Kp + V 2 - P 2 1 x 1.6 eV Ar 2+ +e ~ → Ar+ + 27.63 eV Overall reaction ^] → 2H [φ Ϊ)] + [(P + D 2 -P 2 3xl3.6eV where the ionization energy, Ejon . for Ar+ is 27.629 eV. The present invention comprises a source of energy holes of approximately 27 eV to resonantly shrink the Mills orbitals of deuterium atoms, including a source of said holes produced by further electrochemical reactions or chemical, photochemical, thermal, free radical, sonic, or nuclear reactions or inelastic particles, or photon scattering reactions. The closer the energy of the hole is to the quantum of 27.21 eV or the quanta of j 27.21 eV; n = 2, 3, 4 the greater the rate of reaction because phonons ortranslational or rotational modes do not have to be simultaneously excited to match the resonant shrinkage energy. Table 3 is a table of ionization energies as given in Chemical Structure and Bonding, Rodger L DeKock and Harry P. Gray, the Benjamim Cummings Publishing Company, Menlo Park, CA, (1980), pp. 76-77 which is incorporated by reference. Electrochemical couples with ionization energy differences of approximately 27 eV can catalyze the removal of energy from the electrons of deuterium and/or tritium atoms and molecules and catalyze cold fusion of deuterium and/or tritium. > I . Representative electrochemical couples which generate energy holes of approximately 27 eV appear in Table 4, and some catalytic couples comprising single elements which are cations, neutral, or anions and single molecules which are cations, anions, or neutral or combinations of the said species-reactants are also found in Table 4. For n = 2, the resonance energy is 27.21 ; for n = 16 the resonance energy is 217.68 eV; for n = 54, the resonance energy is 734.67 eV. •ϊ l ' K Table 4. Representative Electrochemical couples that catalytically produce energy holes of 27 eV to shrink deuterium atoms. Electrochemical lonizatior i Energy Hole Couple Enerςjv Lu3+ 45.19 27.768 F+ 17.422 Pb 2 + 32.93 27.538 Li+ 5.392 Ni 2 + 35.17 27.3 Fe+ 7.46 Ag 2 + 34.83 27.37 Rh+ 7.46 Zr3+ 34.34 27.241 Mo+ 7.099 Nb3+ 38.3 27.863 Hg+ 10.437 Cu 2 + 36.83 27.605 Au+ 9.225 Pb 2 + 31.937 27.596 K+ 4.341 Ge 2 + 34.22 27.34 Nb+ 6.88 Many others exist and are given in the above referenced Table 3 of ionization energies. Table 4. Some representative single-ions capable of producing (con't) energy holes for shrinking deuterium atoms. The number following the atomic symbol, (n), is the nth ionization energy of the atom. That is for example, Ti 2+ + 27.49 eV = Ti3+ + e". /tic Ion n nth Ionization Energy Al 2+ 3 28.45 Ar 1 + 2 27.63 Ti 2+ 3 27.49 As 2+ 3 28.35 Rb 1 + 2 27.28 Mo 2+ 3 27.16 Ru 2+ 3 28.47 In 2+ 3 28.03 Te 2+ 3 27.96 Table 4. Some representative two-ion couples capable of (con't) producing energy holes for shrinking deuterium atoms. The number following the ion, (n), is the nth ionization energy of the atom. That is for example, Pd 2+ + 32.93 eV = Pd 3 + + e" and Li+ + e" = Li + 5.39 eV. Atom n nth Ion¬ Atom n nth Ion¬ Energy Oxidiz¬ ization Reduced ization Hole ed Energy Energy (eV) (eV) (eV) Ne 1 + 2 40.96 H 1 + 13.60 27.36 Ar 2 + 3 40.74 H 1 + 13.60 27.14 Sn 3 + 4 40.73 H 1 + 13.60 27.14 Pm 3 + 4 41.10 H 1 + 13.60 27.50 Sm 3 + 4 41 .40 H 1 + 13.60 27.80 Dy 3 + 4 41 .50 H 1 + 13.60 27.90 Kr 3 + 4 52.50 He 1 + 24.59 27.91 Rb 3 + 4 52.60 He 1 + 24.59 28.01 K 4 + 5 82.66 He 2 + 2 54.42 28.24 Zn 4 + 5 82.60 He 2 + 2 54.42 28.18 Se 5 + 6 81 .70 He 2 + 2 54.42 27.28 He 1 + 2 54.42 Rb 2 + 2 27.28 27.14 Zr4 + 5 81.50 He 2 + 2 54.42 27.08 He1 + 2 54.42 Mo 3 + 3 27.16 27.26 Si 2 + 3 33.49 Li 1 + 5.39 28.10 Mn 2 + 3 33.67 Li 1 + 5.39 28.27 Co 2 + 3 33.50 Li 1 + 5.39 28.11 Pd2 + 3 32.93 Li 1 + 5.39 27.54 I 2 + 3 33.00 Li 1 + 5.39 27.61 Hf 3 + 4 33.33 Li 1 + 5.39 27.94 Li 1 + 2 75.64 C 3 + 3 47.89 27.75 Li 1 + 2 75.64 N 3 + 3 47.45 28.19 Li 1 + 2 75.64 Na2 + 2 47.29 28.35 Li 1 + 2 75.64 S 4 + 4 47.30 28.34 Cu5 + 6 103.00 Li 2 + 2 75.64 27.36 Li 1 + 2 75.64 Br4 + 4 47.30 28.34 Br 6 + 7 103.00 Li 2 + 2 75.64 27.36 V 6 + 7 150.17 Li 3 + 3 122.45 27.72 Li 2 + 3 122.45 Mn6 + 6 95.00 27.45 Cu2 + 3 36.83 Be1 + 9.32 27.51 Kr2 + 3 36.95 Be1 + 9.32 27.63 Cd2 + 3 37.48 Be 1 + 9.32 28.16 Te3 + 4 37.41 Be1 + 9.32 28.09 Ce3 + 4 36.76 Be1 + 9.32 27.44 K 2 + 3 45.72 Be 2 + 2 18.21 27.51 V 3 + 4 46.71 Be2 + 2 18.21 28.50 Ge3 + 4 45.71 Be2 + 2 18.21 27.50 Mo3 + 4 46.40 Be2 + 2 18.21 28.19 Bi 3 + 4 45.30 Be2 + 2 18.21 27.09 Be2 + 3 153.89 Ne5 + 5 126.21 27.68 Be2 + 3 153.89 Kr8 + 8 126.00 27.89 Be2 + 3 153.89 Mo7 + 7 126.80 27.09 Be3 + 4 217.71 AI.6 + 6 190.47 27.24 Br 2 + 3 36.00 B 1 + 1 8.30 27.70 Ce3 + 4 36.76 B.1 + 1 8.30 28.46 CI3 + 4 53.46 B 2 + 2 25.15 28.31 Kr3 + 4 52.50 B 2 + 2 25.15 27.35 Rb3 + 4 52.60 B 2 + 2 25.15 27.45 B 2 + 3 37.93 P 1 + 1 10.49 27.44 P 4 + 5 65.02 B 3 + 3 37.93 27.09 B 2 + 3 37.93 S 1 + 1 10.36 27.57 V 4 + 5 65.23 B 3 + 3 37.93 27.30 B 2 + 3 37.93 As 1 + 1 9.81 28.12 B 2 + 3 37.93 Se1 + 1 9.75 28.18 B 2 + 3 37.93 I 1 + 1 10.45 27.48 B 2 + 3 37.93 Ba2 + 2 10.00 27.93 B 2 + 3 37.93 Ce2 + 2 10.85 27.08 B 2 + 3 37.93 Pr 2 + 2 10.55 27.38 B 2 + 3 37.93 Nd2 + 2 10.73 27.20 B 2 + 3 37.93 Pm 2 + 2 10.90 27.03 B 2 + 3 37.93 Hg1 + 1 10.44 27.49 B 2 + 3 37.93 Rn1 + 1 10.75 27.18 B 2 + 3 37.93 Ra2 + 2 10.15 27.78 CI2 + 3 39.61 C 1 + 1 11.26 28.35 Zn2 + 3 39.72 C 1 + 1 11.26 28.46 Nb3 + 4 38.30 C 1 + 1 11.26 27.04 Pr3 + 4 38.98 C 1 + 1 11.26 27.72 Kr3 + 4 52.50 C 2 + 2 24.38 28.12 Rb3 + 4 52.60 C 2 + 2 24.38 28.22 C 2 + 3 47.89 P 2 + 2 19.73 28.16 Ar 4 + 5 75.02 C 3 + 3 47.89 27.13 Fe4 + 5 75.00 C 3 + 3 47.89 27.11 Ni4 + 5 75.50 C 3 + 3 47.89 27.61 C 2 + 3 47.89 Cu2 + 2 20.29 27.60 C 2 + 3 47.89 Ga2 + 2 20.51 27.38 C 2 + 3 47.89 Y 3 + 3 20.52 27.37 C 2 + 3 rt 47.89 Pd2 + 2 19.43 28.46 C 2 + 3 47.89 Ce3 + 3 20.20 27.69 C 2 + 3 47.89 Gd3 + 3 20.63 27.26 C 2 + 3 47.89 Au 2 + 2 20.50 27.39 C 2 + 3 47.89 Tl 2 + 2 20.43 27.46 Sc4 + 5 91.66 C 4 + 4 64.49 27.17 C 3 + 4 64.49 Cu3 + 3 36.83 27.66 C 3 + 4 64.49 Br3 + 3 36.00 28.49 C 3 + 4 64.49 Kr3 + 3 36.95 27.54 C 3 + 4 64.49 Cd3 + 3 37.48 27.01 C 3 + 4 64.49 Te4 + 4 37.41 27.08 C 3 + 4 64.49 Ce4 + 4 36.76 27.73 Se3 + 4 42.94 N 1 + 14.53 28.41 Eu3 + 4 42.60 N 1 + 14.53 28.07 Ho3 + 4 42.50 N 1 + 14.53 27.97 Er3 + 4 42.60 N 1 + 14.53 28.07 Tm 3 + 4 42.70 N 1 + 14.53 28.17 Pb3 + 4 42.32 N 1 + 14.53 27.79 Sr3 + 4 57.00 N 2 + 2 29.60 27.40 N 2 + 3 47.45 P 2 + 2 19.73 27.72 Ar 4 + 5 75.02 N 3 + 3 47.45 27.57 Fe4 + 5 75.00 N 3 + 3 47.45 27.55 Ni 4 + 5 75.50 N 3 + 3 47.45 28.05 N 2 + 3 47.45 Cu2 + 2 20.29 27.16 N 2 + 3 47.45 Pd2 + 2 19.43 28.02 N 2 + 3 47.45 I 2 + 2 19.13 28.32 N 2 + 3 47.45 La 3 + 3 19.18 28.27 N 2 + 3 47.45 Ce3 + 3 20.20 27.25 N 2 + 3 47.45 Tl 2 + 2 20.43 27.02 N 3 + 4 77.47 Cr4 + 4 49.10 28.37 N 3 + 4 77.47 As 4 + 4 50.13 27.34 N 3 + 4 77.47 La 4 + 4 49.95 27.52 Ne4 + 5 126.21 N 5 + 5 97.89 28.32 Fe6 + 7 125.00 N 5 + 5 97.89 27.11 Kr7 + 8 126.00 N 5 + 5 97.89 28.11 Nb6 + 7 125.00 N 5 + 5 97.89 27.11 N 4 + 5 97.89 Te6 + 6 70.70 27.19 Ne1 + 2 40.96 0 1 + 13.62 27.34 Ar 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Ar 3 + 4 59.81 Xe3 + 3 32.10 27.71 Ar 3 + 4 59.81 Pb3 + 3 31.94 27.87 Bi 5 + 6 88.30 Ar 4 + 4 59.81 28.49 Ar4 + 5 75.02 V 4 + 4 46.71 28.31 Cu5 + 6 103.00 Ar 5 + 5 75.02 27.98 Ar4 + 5 75.02 Br 4 + 4 47.30 27.72 Br6 + 7 103.00 Ar5 + 5 75.02 27.98 Nb5 + 6 102.60 Ar 5 + 5 75.02 27.58 Ti 5 + 6 1 9.36 Ar 6 + 6 91.01 28.35 Mn6 + 7 119.27 Ar 6 + 6 91.01 28.26 Ar 5 + 6 91.01 Ga4 + 4 64.00 27.01 Ar 5 + 6 91.01 As 5 + 5 63.63 27.38 Ar7 + 8 143.46 Y 7 + 7 116.00 27.46 K 1 + 2 31.63 K 1 + 1 4.34 27.28 Xe2 + 3 .32,10 K 1 + 1 4.34 27.76 Pb2 + 3 31.94 K 1 + 1 4.34 27.60 K 1 + 2 '31.'63 K 1 + 1 -4.34 27.28 Zn3 + 4 59.40 K 2 + 2 31.63 27.78 Br4 + 5 59.70 K 2 + 2 31.63 28.08 K 1 + 2 31.63 Rb1 + 1 4.18 27.45 Te4 + 5 58.75 K 2 + 2 31.63 27.13 K 1 + 2 31.63 Cs1 + 1 3.89 27.73 Sc3 + 4 73.47 K 3 + 3 45.72 27.75 K 2 + 3 45.72 Ni2 + 2 18.17 27.55 K 2 + 3 45.72 Zn 2 + 2 17.96 27.76 K 2 + 3 45.72 As 2 + 2 18.63 27.09 K 2 + 3 45.72 Rh2 + 2 18.08 27.64 K 2 + 3 45.72 Te2 + 2 18.60 27.12 K 2 + 3 45.72 Pt2 + 2 18.56 27.16 K 3 + 4 60.91 Mn3 + 3 33.67 27.24 K 3 + 4 60.91 Co 3 + 3 33.50 27.41 Br5 + 6 88.60 K 4 + 4 60.91 27.69 K 3 + 4 60.91 Pd3 + 3 32.93 27.98 K 3 + 4 60.91 l 3 + 3 33.00 27.91 K 3 + 4 60.91 Hf 4 + 4 33.33 27.58 Bi 5 + 6 88.30 K 4 + 4 60.91 27.39 Sc5 + 6 111.10 K 5 + 5 82.66 28.44 K 4 + 5 82.66 Fe4 + 4 54.80 27.86 K 4 + 5 82.66 Ni4 + 4 54.90 27.76 K 4 + 5 82.66 Cu4 + 4 55.20 27.46 Kr6 + 7 111.00 K 5 + 5 82.66 28.34 Ca6 + 7 127.70 K 6 + 6 100.00 27.70 V 5 + 6 128.12 K 6 + 6 100.00 28.12 K 5 + 6 100.00 Mn5 + 5 72.40 27.60 As 5 + 6 127.60 K 6 + 6 100.00 27.60 K 5 + 6 100.00 Sr5 + 5 71.60 28.40 K 5 + 6 100.00 Sn5 + 5 72.28 27.72 K 7 + 8 154.86 Ca7 + 7 127.70 27.16 K 7 + 8 154.86 As 6 + 6 127.60 27.26 K 7 + 8 154.86 Mo 7 + 7 126.80 28.06 Mn2 + 3 33.67 Ca1 + 6.11 27.55 Co 2 3 33.50 Ca1 + 6.11 27.39 Ge2 + 3 34.22 Ca1 + 6.11 28.11 Zr3 + 4 34.34 Ca1 + 6.11 28.23 Hf + 4 33.33 Ga1 + 6.11 27.22 Hg2 + 3 34.20 Ca1 + 6.11 28.09 Zn2 + 3 39.72 Ca2 + 2 11.87 27.85 Rb2 + 3 40.00 Ca2 + 2 11.87 28.13 Pr3 + 4 38.98 Ca2 + 2 11.87 27.11 Tb3 + 4 39.80 Ca2 + 2 11.87 27.93 Kr5 + 6 78.50 Ca3 + 3 50.91 27.59 Ca2 + 3 50.91 Zr3 + 3 22.99 27.92 Ca2 + 3 50.91 Sm3 + 3 23.40 27.51 Ca2 + 3 50.91 Dy3 + 3 22.80 28.11 Ca2 + 3 50.91 Ho 3 + 3 22.84 28.07 Ca2 + 3 50.91 Er3 + 3 22.74 28.17 Ca2 + 3 50.91 Tm 3 + 3 23.68 27.23 Ca2 + 3 50.91 Hf 3 + 3 23.30 27.61 Mn 5 + 6 95.00 Ca4 + 4 67.10 27.90 Ca3 + 4 67.10 Zn3 + 3 39.72 27.38 Ca3 + 4 67.10 Rb3 + 3 40.00 27.10 Ca3 + 4 67.10 Pr4 + 4 38.98 28.12 Ca3 + 4 67.10 Tb4 + 4 39.80 27.30 Ca4 + 5 84.41 Sr4 + 4 57.00 27.41 Ca4 + 5 84.41 Sb5 + 5 56.00 28.41 Ca4 + 5 84.41 Bi5 + 5 56.00 28.41 Ca5 + 6 108.78 Se6 + 6 81.70 27.08 Rb7 + 8 136.00 Ca6 + 6 108.78 27.22 Ca5 + 6 108.78 Zr5 + 5 81.50 27.28 Te6 + 7 137.00 Ca6 + 6 108.78 28.22 Ca6 + 7 1-27.70 Ti 5 + 5 99.22 28.48 Se6 + 7 155.40 Ca7 + 7 127.70 27.70 Ca7 + 8 147.24 Ti 6 + 6 119.36 27.88 Ca7 + 8 147.24 Mn7 + 7 119.27 27.97 Mn2 + 3 33.67 Sc 1 + 6.54 27.13 Ge2 + 3 34.22 Sc1 + 6.54 27.68 Zr3 + 4 34.34 Sc1 + 6.54 27.80 Ag2 + 3 34.83 Sc1 + 6.54 28.29 Hg2 + 3 34.20 Sc1 + 6.54 27.66 Rb2 + 3 40.00 Sc2 + 2 12.80 27.20 Sn3 + 4 40.73 Sc2 + 2 12.80 27.93 Nd3 + 4 40.41 Sc2 + 2 12.80 27.61 Pm 3 + 4 41.10 Sc2 + 2 12.80 28.30 Kr3 + 4 52.50 Sc3 + 3 24.76 27.74 Rb3 + 4 52.60 Sc3 + 3 24.76 27.84 Sc3 + 4 73.47 Ge4 + 4 45.71 27.76 Sc3 + 4 73.47 Mo 4 + 4 46.40 27.07 Sc3 + 4 73.47 Lu4 + 4 45.19 28.28 Sc3 + 4 73.47 Bi 4 + 4 45.30 28.17 Ti 5 + 6 119.36 Sc5 + 5 91.66 27.70 Mn 6 + 7 119.27 Sc5 + 5 91.66 27.61 Sc4 + 5 91.66 Ga4 + 4 64.00 27.66 Sc4 + 5 91.66 As 5 + 5 63.63 28.03 Cu6 + 7 139.00 Sc6 + 6 111.10 27.90 Cu7 + 8 166.00 Sc7 + 7 138.00 28.00 Ni2 + 3 35.17 Ti 1 + 6.82 28.35 Ge2 + 3 34.22 Ti 1 + 6.82 27.40 Zr3 + 4 34.34 Ti 1 + 6.82 27.52 Ag2 + 3 34.83 Ti 1 + 6.82 28.01 Hg2 + 3 34.20 Ti 1 + 6.82 27.38 Sn3 + 4 40.73 Ti 2 + 2 13.58 27.15 Pm 3 + 4 41.10 Ti 2 + 2 13.58 27.52 Sm 3 + 4 41.40 Ti 2 + 2 13.58 27.82 Dy3 + 4 41.50 Ti 2 + 2 13.58 27.92 Fe3 + 4 54.80 Ti 3 + 3 27.49 27.31 Ni3 + 4 54.90 Ti 3 + 3 27.49 27.41 Cu3 + 4 55.20 Ti 3 + 3 27.49 27.71 Ti 3 + 4 43.27 Mn2 + 2 15.64 27.63 Ti 3 + 4 43.27 Fe2 + 2 16.18 27.09 Ti 3 + 4 43.27 Ge2 + 2 15.93 27.33 Rb4 + 5 71.00 Ti 4 + 4 43.27 27.73 Sr4 + 5 71.60 Ti 4 + 4 43.27 28.33 Ti-3 + 4 43.27 Mo 2 + 2 16.15 27.12 Ti 3 + 4 43.27 Tc2 + 2 15.26 28.01 Ter5>+ 6 70.70 Ti + 4 43_27 27.43 Ti 3 + 4 43.27 H 2 + 2 14.90 28.37 Ti 3 + 4 43.27 Pb2 + 2 15.03 28.23 As 5 + 6 127.60 Ti 5 + 5 99.22 28.38 Ti 4 + 5 99.22 Rb5 + 5 71.00 28.22 Ti 4 + 5 99.22 Sr5 + 5 71.60 27.62 Mo 6 + 7 126.80 Ti 5 + 5 99.22 27.58 Ti7 + 8 168.50 Ti 7 + 7 140.80 27.70 Ti 7 + 8 168.50 Ti 7 + 7 140.80 27.70 Mn7 + 8 196.46 Tl 8 + 8 168.50 27.96 Ni2 + 3 35.17 V 1 + 6.74 28.43 Ge2 + 3 34.22 V 1 + 6.74 27.48 Zr3 + 4 34.34 V 1 + 6.74 27.60 Ag2 + 3 34.83 V 1 + 6.74 28.09 Hg2 + 3 34.20 V 1 + 6.74 27.46 Se3 + 4 42.94 V 2 + 2 14.65 28.29 Eu3 + 4 42.60 V 2 + 2 14.65 27.95 Ho 3 + 4 42.50 V 2 + 2 14.65 27.85 Er3 + 4 42.60 V 2 + 2 14.65 27.95 Tm 3 + 4 42.70 V 2 + 2 14.65 28.05 Pb3 + 4 42.32 V 2 + 2 14.65 27.67 Sr3 + 4 57.00 V 3 + 3 29.31 27.69 Fe4 + 5 75.00 V 4 + 4 46.71 28.29 V 3 + 4 46.71 As 2 + 2 18.63 28.07 V 3 + 4 46.71 Pd2 + 2 19.43 27.28 V 3 + 4 46.71 In 2 + 2 18.87 27.84 V 3 + 4 46.71 Te2 + 2 18.60 28.11 V 3 + 4 46.71 I 2 + 2 19.13 27.58 V 3 + 4 46.71 La 3 + 3 19.18 27.53 V 3 + 4 46.71 Pt2 + 2 18.56 28.14 V 3 + 4 46.71 Hg2 + 2 18.76 27.95 V 4 + 5 65.23 CU3 + 3 36.83 28.40 Ge4 + 5 93.50 V 5 + 5 65.23 28.27 V 4 + 5 65.23 Kr3 + 3 36.95 28.28 Y 5 + 6 93.00 V 5 + 5 65.23 27.77 V 4 + 5 65.23 Cd3 + 3 37.48 27.75 V 4 + 5 65.23 Te4 + 4 37.41 27.82 V 4 + 5 65.23 Ce4 + 4 36.76 28.47 Se6 + 7 155.40 V 6 + 6 128÷12 27.28 V 6 + 7 150.17 Sr8 + 8 122.30 27.87 Ni2 + 3 35.17 Cr 1 + 6.77 28.40 Ge2 + 3 34.22 Cr1 + 6.77 27.45 Zr3 + 4 34.34 Cr 1 + 6.77 27.57 Ag2 + 3 34.83 Cr 1 + 6.77 28.06 Hg2 + 3 34.20 Cr 1 + 6.77 27.43 Sr2 + 3 43.60 Cr2 + 2 16.50 27.10 Sb3 + 4 44.20 Cr2 + 2 16.50 27.70 Gd3 + 4 44.00 Cr2 + 2 16.50 27.50 Yb3 + 4 43.70 Cr2 + 2 16.50 27.20 Zn3 + 4 59.40 Cr3 + 3 30.96 28.44 Te4 + 5 58.75 Cr3 + 3 30.96 27.79 Cr2 + 3 30.96 Cs1 + 1 3.89 27.07 Cr3 + 4 49.10 Se2 + 2 21.19 27.91 Cr3 + 4 49.10 Br 2 + 2 21.80 27.30 Y 4 + 5 77.00 Cr4 + 4 49.10 27.90 Cr3 + 4 49.10 Ag2 + 2 21.49 27.61 Cr3 + 4 49.10 Xe2 + 2 21.21 27.89 Cr3 + 4 49.10 Pr3 + 3 21.62 27.48 Cr3 + 4 49.10 Gd3 + 3 20.63 28.47 Cr3 + 4 49.10 Tb3 + 3 21.91 27.19 Cr3 + 4 49.10 Lu 3 + 3 20.96 28.14 Cr4 + 5 69.30 Pm4 + 4 41.10 28.20 Cr4 + 5 69.30 Sm 4 + 4 41.40 27.90 Cr4 + 5 69.30 Dy4 + 4 41.50 27.80 Cr6 + 7 161.10 Ni7 + 7 133.00 28.10 Cr6 + 7 161.10 Zn7 + 7 134.00 27.10 Cr7 + 8 184.70 Co 8 + 8 157.00 27.70 Ni2 + 3 35.17 Mn1 + 1 7.43 27.73 Ag2 + 3 34.83 Mn 1 + 1 7.43 27.40 Se3 + 4 42.94 Mn2 + 2 15.64 27.30 Sr2 + 3 43.60 Mn2 + 2 15.64 27.96 Gd3 + 4 44.00 Mn 2 + 2 15.64 28.36 Tm3 + 4 42.70 Mn2 + 2 15.64 27.06 Yb3 + 4 43.70 Mn2 + 2 15.64 28.06 Mn2 + 3 33.67 Ga1 + 1 6.00 27.67 Mn2 + 3 33.67 Sr 1 + 1 5.70 27.97 Mn2 + 3 33.67 Y 1 + 1 6.38 27.29 Y 3 + 4 61.80 Mn3+ . 3 33.67 28.13 Mo 4 + 5 61.20 Mn3+ , 3 33.67 27.53 Mn2 + 3 33.67 In 1 + 1 5.79 27.88 Mn2 + 3 33.67 Ba1 + 1 5.21 28.45 Mn2 + 3 33.67 La1 + 1 5.58 28.09 Mn2 + 3 33.67 Ce1 + 1 5.47 28.20 Mn2 + 3 33.67 Pr 1 + 1 5.42 28.24 Mn2 + 3 33.67 Nd1 + 1 5.49 28.18 Mn2 + 3 33.67 Pm 1 + 1 5.55 28.11 Mn2 + 3 33.67 Sm 1 + 1 5.63 28.04 Mn2 + 3 33.67 Eu1 + 1 5.67 28.00 Mn2 + 3 33.67 Gd1 + 1 6.14 27.53 Mn2 + 3 33.67 Tb1 + I 5.85 27.82 Mn2 + 3 33.67 Dy 1 + I 5.93 27.74 Mn2 + 3 33.67 Ho1 + I 6.02 27.65 Mn2 + 3 33.67 Er1 + I 6.10 27.57 Mn2 + 3 33.67 Tm 1 + ■ I 6.18 27.48 Mn2 + 3 33.67 Yb1 + I 6.25 27.41 Mn2 + 3 33.67 Lu 1 + ' I 5.43 28.24 Mn2 + 3 33.67 Hf 1 + I 6.60 27.07 Mn 2 + 3 33.67 Tl 1 + ■ I 6.11 27.56 Mn2 + 3 33.67 Ra1 + " I 5.28 28.39 Mn2 + 3 33.67 Ac1 + ' I 5.20 28.47 Mn2 + 3 33.67 Th1 + ' I 6.10 27.57 Mn2 + 3 33.67 Pa1 + 5.90 27.77 Mn2 + 3 33.67 U 1 + 1 6.05 27.62 Mn2 + 3 33.67 Np1 + 1 6.20 27.47 Mn2 + 3 33.67 Pu1 + 1 6.06 27.61 Mn2 + 3 33.67 Am 1 + 1 5.99 27.68 Mn2 + 3 33.67 Cm 1 + 1 6.02 27.65 Mn2 + 3 33.67 Bk1 + 1 6.23 27.44 Mn2 + 3 33.67 Cf 1 + 1 "6.30 27.37 Mn2 + 3 33.67 Es1 + 1 6.42 27.25 Co 4 + 5 79.50 Mn4+ ^ \ 51.20 28.30 Kr5 + 6 78.50 Mn4+ i \ 51.20 27.30 Mn3 + 4 51.20 Zr3 + 3 22.99 28.21 Mn 3 + 4 51.20 Sm3 + 3 23.40 27.80 Mn3 + 4 51.20 Dy3 + 3 22.80 28.40 Mn3 + 4 51.20 Ho 3 + 3 22.84 28.36 Mn3 + 4 51.20 Er3 + 3 22.74 28.46 Mn3 + 4 51.20 Tm 3 + 3 23.68 27.52 Mn3 + 4 51.20 Hf 3 + 3 23.30 27.90 Mn 4 + 5 72.40 Sb4 + 4 44.20 28.20 Mn4 + 5 72.40 Gd4 + 4 44.00 28.40 Mn4 + 5 72.40 Lu4 + 4 45.19 27.21 Mn4 + 5 72.40 Bi 4 + 4 45.30 27.10 Sr7 + 8 122.30 Mn6 + 6 95.00 27.30 Mn 6 + 7 119.27 Sr6 + 6 90.80 28.47 Ni2 + 3 35.17 Fe1 + 1 7.87 27.30 Br2 + 3 36.00 Fe1 + 1 7.87 28.13 Sr 2 + 3 43.60 Fe2 + 2 16.18 27.42 Sb3 + 4 44.20 Fe2 + 2 16.18 28.02 Gd3 + 4 44.00 Fe2 + 2 16.18 27.82 Yb3 + 4 43.70 Fe2 + 2 16.18 27.52 Te4 + 5 58.75 Fe3 + 3 30.65 28.10 Zn4 + 5 82.60 Fe4 + 4 54.80 27.80 Fe3 + 4 54.80 Rb2 + 2 27.28 27.52 Fe3 + 4 54.80 Mo 3 + 3 27.16 27.64 Cu5 + 6 103.00 Fe5 + 5 75.00 28.00 Fe4 + 5 75.00 Br4 + 4 47,30 27.70 Br 6 + 7 103.00 Fe5 + 5 75.00 28;00 Nb5 + 6 102.60 Fe5 + 5 75.00 27.60 Fe5 + 6 99.00 Rb5 + 5 71.00 28.00 Fe5 + 6 99.00 Sr 5 + 5 71.60 27.40 Mo 6 + 7 126.80 Fe6 + 6 99.00 27.80 Fe5 + 6 99.00 Te 6 + 6 70.70 = 28.30 Mo 7 + 8 153.00 Fe7 + 7 125:00 28.00 Ni2 + 3 35.17 Co 1 + 1 7.86 27.31 Br.2 + 3 36.00 Co1 + 1 7.86 28.14 Sb3 + 4 44.20 Co 2 + 2 17.06 27.14 Lu3 + 4 45.19 Co 2 + 2 17.06 28.13 Bi 3 + 4 45.30 Co 2+ 2 17.06 28.24 Co 2 + 3 33.50 Ga1 + 1 6.00 27.50 Co 2 + 3 33.50 Sr 1 + 1 5.70 27.81 Co 2 + 3 33.50 Y 1+ 1 6.38 27.12 Y 3 + 4 61.80 Co 3+ 3 33.50 28.30 Mo 4 + 5 61.20 Co 3+ 3 33.50 27.70 Co 2 + 3 33.50 In 1 + 1 5.79 27.71 Co 2 + 3 33.50 Ba1 + 1 5.21 28.29 Co 2 + 3 33.50 La1 + « I 5.58 27.92 Co 2 + 3 33.50 Ce1 + " I 5.47 28.03 Co 2 + 3 33.50 Pr 1 + - 5.42 28.08 Co 2 + 3 33.50 Nd1 + " 5.49 28.01 Co 2 + 3 33.50 Pm 1 + ' 5.55 27.95 Co 2 + 3 33.50 Sm 1 + ' 5.63 27.87 Co 2 + 3 33.50 Eu1 + " I 5.67 27.83 Co 2 + 3 33.50 Gd1 + ■ I 6.14 27.36 Co 2 + 3 33.50 Tb1 + ■ I 5.85 27.65 Co 2 + 3 33.50 Dy1 + • I 5.93 27.57 Co 2 + 3 33.50 Ho1+ • I 6.02 27.48 Co 2 + 3 33.50 Er1 + - I 6.10 27.40 Co 2 + 3 33.50 Tm 1 + • I 6.18 27.32 Co 2 + 3 33.50 Yb1 + I 6.25 27.25 Co 2 + 3 33.50 Lu 1 + I 5.43 28.07 Co 2 + 3 33.50 Tl 1 + I 6.11 27.39 Co 2 + 3 33.50 Ra1 + I 5.28 28.22 Co 2 + 3 33.50 Ac 1 + 1 5.20 28.30 Co 2 + 3 33.50 Th 1 + 1 6.10 27.40 Co 2 + 3 33.50 Pa1 + I 5.90 27.60 Co 2 + 3 33.50 U 1 + I 6.05 27.45 Co 2 + 3 33.50 Np1 + I 6.20 27.30 Co 2 + 3 33.50 Pu1 + I 6.06 27.44 Co 2 + 3 33.50 Am 1 + I 5.99 27.51 Qo-2 +, 3 33.50 Cm 1 + I 6.02 2748 Co 2 + 3 33.50 Bk1 + I 6.23 27.27 Co 2 + 3 33.50 Cf l + 1 6.30 27.20 Co 2 + 3 33.50 Es1 + 1 6.42 27.08 Co 4 + 5 79.50 Co 4 + 4 51.30 28.20 Kr5 + 6 78.50 Co 4 + 4 51.30 27.20 Co 3 + 4 51.30 Zr3 + 3 22.99 28.31 Co 3 + 4 51.30 Sm 3 + 3 23.40 27.90 Co 3 + 4 51.30 Ho 3 + 3 22.84 28.46 Co 3 + 4 51.30 Tm 3 + 3 23.68 27.62 Co 3 + 4 51.30 Hf 3 + 3 23.30 28.00 Co 4 + 5 79.50 Co 4 + 4 51.30 28.20 Co 7 + 8 157.00 Co 7 + 7 129.00 28.00 Co 7 + 8 157.00 Co 7 + 7 129.00 28.00 Co 7 + 8 157.00 Y 8 + 8 129.00 28.00 Ni2 + 3 35.17 Ni 1 + 1 7.64 27.53 Br2 + 3 36.00 Ni 1 + 1 7.64 28.36 Ag2 + 3 34.83 Ni 1 + 1 7.64 27.20 Ge3 + 4 45.71 Ni 2 + 2 18.17 27.54 Mo 3 + 4 46.40 Ni 2 + 2 18.17 28.23 Lu3 + 4 45.19 Ni2 + 2 18.17 27.02 Bi 3 + 4 45.30 Ni 2 + 2 18.17 27.13 Ni2 + 3 35.17 Ni 1 + 7.64 27.53 Ni2 + 3 35.17 Cu1 + 7.73 27.44 Ni2 + 3 35.17 Ge1 + 7.90 27.27 As 4 + 5 63.63 Ni3 + 3 35.17 28.46 Ni2 + 3 35.17 Zr 1 + 6.84 28.33 Ni2 + 3 35.17 Nb1 + 6.88 28.29 Ni2 + 3 35.17 Mo1 + 7.10 28.07 Ni2 + 3 35.17 Tc 1 + 7.28 27.89 Ni2 + 3 35.17 Ru 1 + 7.37 27.80 Ni2 + 3 35.17 Rh1 + 7.46 27.71 Ni2 + 3 35.17 Ag 1 + 7.58 27.59 Ni2 + 3 35.17 Sn 1 + . 7.34 27.83 Ni2 + 3 35.17 Ta1 + 7.89 27.28 Ni2 + 3 35.17 W 1 + 7.98 27.19 Ni2 + 3 35.17 Re1 + 7.88 27.-29 Ni2 + 3 35.17 Pbl + 7.42 27.75 Ni2 + 3 35.17 Bi 1 + 7.29 27.88 Zn4 + 5 82.60 Ni4 + 4 54.90 27.70 Ni3 + 4 54.90 Rb2 + 2 27.28 27.62 Ni 3 4 54.90 Mo 3 + 3 27.16 27.74 Cu5 + 6 103.00 Ni5 + 5 75.50 27.50 Ni4 + 5 75.50 Br 4 + 4 47.30 28.20 Br6 + 7 103.00 Ni5 + 5 75.50 27.50 Nb5 + 6 102.60 Ni5 + 5 75.50 27.10 Ni5 + 6 108.00 Cu5 + 5 79.90 28.10 Rb7 + 8 136.00 Ni6 + 6 108.00 28.00 Ni7 + 8 162.00 Zn7 + 7 134.00 28.00 Br2 + 3 36.00 Cu1 + 7.73 28.27 Ag2 + 3 34.83 Cu1 + 7.73 27.10 Br3 + 4 47.30 Cu2 + 2 20.29 27.01 Cu2 + 3 36.83 Zn1 + 9.39 27.44 Ga3 + 4 64.00 Cu3 + 3 36.83 27.17 Cu2 + 3 36.83 As 1 + 9.81 27.02 Cu2 + 3 36.83 Se1 + 9.75 27.08 Kr4 + 5 64.70 Cu3 + 3 36.83 27.87 Cu2 + 3 36.83 Pd1 + 8.34 28.49 Cu2 + 3 36.83 Cd1 + 8.99 27.84 Cu2 + 3 36.83 Sb1 + 8.64 28.19 Cu2 + 3 36.83 Te 1 + 9.01 27.82 Cu2 + 3 36.83 Os1 + 8.70 28.13 Cu2 + 3 36.83 Ir 1 + 9.10 27.73 Cu2 + 3 36.83 Pt 1 + 9.00 27.83 Gu2 + 3 36.83 Au 1 + 9.23 27.61 Cu2 + 3 36.83 Po1 + 8.42 28.41 Zn4 + 5 * 82.60 Cu4 + 4 55.20 27.40 Cu3 + 4 . 55.20 Rb2 + 2 27.28 27.92 Cu3 + 4 - 55.20 Mo 3 + 3 27.16 28.04 Cu3 + 4 55.20 In 3 + 3 28.03 27.17 Cu3 + 4 , 55.20 Te3 + 3 27.96 27.24 Zn5 + 6 108.00 Cu5 + 5 79.90 28.10 Cu + 5 79.90 Kr4 + 4 52.50 27.40 Cu4 + 5 79.90 Rb4 + 4 52.60 27.30 Sb5 + 6 108.00 Cu5 + 5 79.90 28.10 Cu6 + 7 139.00 Kr7 + 7 111.00 28.00 Kr2 + 3 36.95 Zn 1 + 1 9.39 27.56 Cd2 + 3 37.48 Zn 1 + 1 9.39 28.09 Te3 + 4 37.41 Zn 1 + 1 9.39 28.02 Ce3 + 4 36.76 Zn 1 + 1 9.39 27.36 Ge3 + 4 45.71 Zn2 + 2 17.96 27.75 Mo 3 + 4 46.40 Zn2 + 2 17.96 28.44 Lu3 + 4 45.19 Zn2 + 2 17.96 27.23 Bi 3 + 4 45.30 Zn2 + 2 17.96 27.34 Zn2 + 3 39.72 Br 1 + 1 11.81 27.91 Zn2 + 3 39.72 Y 2 + 2 12.24 27.48 Mo 5 + 6 68.00 Zn3 + 3 39.72 28.28 Zn2 + 3 39.72 Xe1 + 1 12.13 27.59 Zn2 + 3 39.72 Eu2 + 2 11.24 28.48 Zn2 + 3 39.72 Gd2 + 2 12.09 27.63 Zn2 + 3 39.72 Tb2 + 2 11.52 28.20 Zn2 + 3 39.72 Dy 2 + 2 11.67 28.05 Zn2 + 3 39.72 Ho 2 + 2 11.80 27.92 Zn2 + 3 39.72 Er2 + 2 11.93 27.79 Zn2 + 3 39.72 Tm 2 + 2 12.05 27.67 Zn2 + 3 39.72 Yb2 + 2 12.18 27.54 Zn3 + 4 59.40 Rh3 + 3 31.06 28.34 Zn 3 + 4 59.40 Xe3 + 3 32.10 27.30 Zn3 + 4 59.40 Pb3 + 3 31.94 27.46 Kr 6 + 7 111.00 Zn5 + 5 82.60 28.40 Rb7 + 8 136.00 Zn6 + 6 108.00 28.00 Zn6 + 7 134.00 Sr7 + 7 106.00 28.00 Ge2 + 3 34.22 Ga1 + 6.00 28.22 Zr3 + 4 34.34 Ga1 + 6.00 28.34 I 2 + 3 33.00 Ga1 + 6.00 27.00 Hf 3 + 4 33.33 Ga1 + 6.00 27.33 Hg2 + 3 34.20 Ga1 + 6.00 28.20 Te4 + 5 58.75 Ga3 + 3 30.71 28.04 Ga3 + 4 64.00 Br3 + 3 36.00 28.00 Ga3 + 4 64.00 Kr3 + 3 36.95 27.05 Ga3 + 4 64.00 Ce4 + 4 36.76 27.24 Br2 + 3 36.00 Ge1 + 1 7.90 28.10 Se3 + 4 42.94 Ge2 + 2 15.93 27.01 Sr 2 + 3 43.60 Ge2 + 2 15.93 27.67 Sb3 + 4 44.20 Ge2 + 2 15.93 28.27 Gd3 + 4 44.00 Ge2 + 2 15.93 28.07 Yb3 + 4 43.70 Ge2 + 2 15.93 27.77 Ge2 + 3 34.22 Y 1 + 1 6.38 27.84 Y 3 + 4 61.80 Ge3 + 3 34.22 27.58 Ge2 + 3 34.22 Zr1 + 6.84 27.38 Ge2 + 3 34.22 Nb1 + 6.88 27.34 Ge2 + 3 34.22 Mo1 + 7.10 27.12 Ge2 + 3 34.22 In 1 + 5.79 28.43 Ge2 + 3 34.22 Gd1 + 6.14 28.08 Ge2 + 3 34.22 Tb1 + 5.85 28.37 Ge2 + 3 34.22 Dy1 + 5.93 28.29 Ge2 + 3 34.22 Ho1 + 6.02 28.20 Ge2 + 3 34.22 Er1 + 6.10 28.12 Ge2 + 3 34.22 Tm 1 + 6.18 28.04 Ge2 + 3 34.22 Yb1 + 6.25 27.97 Ge2 + 3 34.22 Hf 1 + 6.60 27.62 Ge2 + 3 34.22 Tl 1 + 6.11 28.11 Ge2 + 3 34.22 Th 1 + 6.10 28.12 Ge2 + 3 34.22 Pa1 + 5.90 28.32 Ge2 + 3 34.22 U 1 + 6.05 28.17 Ge2 + 3 34.22 Np1 + 6.20 28.02 Ge2 + 3 34.22 Pu1 + 6.06 28.16 Ge2 + 3 34.22 Am 1 + 5.99 28.23 Ge2 + 3 34.22 Cm 1 + 6.02 28.20 Ge2 + 3 34.22 Bk1 + 6.23 27.99 Ge2 + 3 34.22 Cf 1 + 6.30 27.92 Ge2 + 3 34.22 Es1 + 6.42 27.80 Ge3 + 4 45.71 As 2 + 2 18.63 27.08 Ge3 + 4 45.71 Rh2 + 2 18.08 27.63 Ge3 + 4 45.71 Te2 + 2 18.60 27.11 Ge3 + 4 45.71 Pt2 + 2 18.56 27.15 Kr2 + 3 36.95 As 1 + 1 9.81 27.14 Nb3 + 4 38.30 As 1 + 1 9.81 28.49 67 Cd2 + 3 37.48 As 1 + 1 9.81 27.67 Te3 + 4 37.41 As 1 + 1 9.81 27.60 Mo 3 + 4 46.40 As 2 + 2 18.63 27.77 Sb4 + 5 56.00 As 3 + 3 28.35 27.65 Bi 4 + 5 56.00 As 3 + 3 28.35 27.65 As 3 + 4 50.13 Br2 + 2 21.80 28.33 Kr5 + 6 78.50 As 4 + 4 50.13 28.37 As 3 + 4 50.13 Zr3 + 3 22.99 27.14 As 3 + 4 50.13 Nd3 + 3 22.10 28.03 As 3 + 4 50.13 Pm3 + 3 22.30 27.83 As 3 + 4 50.13 Tb3 + 3 21.91 28.22 As 3 + 4 50.13 Dy3 + 3 22.80 27.33 As 3 + 4 50.13 Ho 3 + 3 22.84 27.29 As 3 + 4 50.13 Er3 + 3 22.74 27.39 As 4 + 5 63.63 Br3 + 3 36.00 27.63 Sr 5 + 6 90.80 As 5 + 5 63.63 27.17 Se6 + 7 155.40 As 6 + 6 127.60 27.80 As 5 + 6 127.60 Rb7 + 7 99.20 28.40 Kr2 + 3 36.95 Se1 + 1 9.75 27.20 Cd2 + 3 37.48 Se1 + 1 9.75 27.73 Te3 + 4 37.41 Se1 + 1 9.75 27.66 Ce3 + 4 36.76 Se1 + 1 9.75 27.01 Te4 + 5 58.75 Se3 + 3 30.82 27.93 Rb4 + 5 71.00 Se4 + 4 42.94 28.06 Se3 + 4 42.94 Tc2 + 2 15.26 27.68 Se3 + 4 42.94 Sn2 + 2 14.63 28.31 Te5 + 6 70.70 Se4 + 4 42.94 27.76 Se3 + 4 42.94 Hf2 + 2 14.90 28.04 Se3 + 4 42.94 Pb2 + 2 15.03 27.91 Se4 + 5 68.30 Rb3 + 3 40.00 28.30 Se4 + 5 68.30 Sn4 + 4 40.73 27.57 Se4 + 5 68.30 Nd4 + 4 40.41 27.89 Se4 + 5 68.30 Pm 4 + 4 41:10 27.20 Se5 + 6 81.70 In 4 + 4 54.00 27.70 Rb2 + 3 40.00 Br 1 + 1 11.81 28.19 Pr3 + 4 38.98 Br 1 + 1 11.81 27.17 Tb3 + 4 39.80 Br 1 + 1 11.81 27.99 La 3 + 4 49.95 Br2 + 2 21.80 28.15 Br2 + 3 36.00 Pd1 + 8.34 27.66 Br2 + 3 36.00 Ag1 + 7.58 28.42 Br2 + 3 36.00 Cd1 + 8.99 27.01 Br2 + 3 36.00 Sb1 + 8.64 27.36 Br2 + 3 36.00 Ta1 + 7.89 28.11 Br 2 + 3 36.00 W 1 + 7.98 28.02 Br2 + 3 36.00 Re1 + 7.88 28.12 Br2 + 3 36.00 Os1 + 8.70 27.30 Br2 + 3 36.00 Po1 + 8.42 27.58 Br3 + 4 47.30 Pd2 + 2 19.43 27.87 Br3 + 4 47.30 In 2 + 2 18.87 28.43 Br 3 + 4 47.30 I 2 + 2 19.13 28.17 Br3 + 4 47.30 La 3 + 3 19.18 28.12 Br3 + 4 47.30 Ce3 + 3 20.20 27.10 Br4 + 5 59.70 Xe3 + 3 32.10 27.60 Br4 + 5 59.70 Pb3 + 3 31.94 27.76 Y 6 + 7 116.00 Br6 + 6 88.60 27.40 Br5 + 6 88.60 Mo 5 + 5 61.20 27.40 Pm3 + 4 41.10 Kr 1 + 1 14.00 27.10 Sm3 + 4 41.40 Kr 1 + 1 14.00 27.40 Dy3 + 4 41.50 Kr 1 + 1 14.00 27.50 Pb3 + 4 42.32 Kr 1 + 1 14.00 28.32 Kr3 + 4 52.50 Kr2 + 2 24.36 28.14 Rb3 + 4 52.60 Kr2 + 2 24.36 28.24 Kr4 + 5 64.70 Kr3 + 3 36.95 27.75 Kr2 + 3 36.95 Cd1 + 8.99 27.96 Kr2 + 3 36.95 Sb1 + 8.64 28.31 Kr2 + 3 36.95 Te1 + 9.01 27.94 Kr2 + 3 36.95 Os1 + 8.70 28.25 Kr2 + 3 36.95 Ir 1 + 9.10 27.85 Kr2 + 3 36.95 Pt 1 + 9.00 27.95 Kr2 + 3 36.95 Au 1 + 9.23 27.73 Kr3 + 4 52.50 Kr2 + 2 24.36 28.14 Kr3 + 4 52.50 Nb3 + 3 25.04 27.46 Kr3 + 4 52.50 Sb3 + 3 25.30 27.20 Kr3 + 4 52.50 Cs2 + 2 25.10 27.40 Kr3 + 4 52.50 Eu3 + 3 24.90 27.60 Kr3 + 4 52.50 Yb3 + 3 25.03 27.47 Kr4 + 5 64.70 Kr3 + 3 36.95 27.75 Y 5 + 6 93.00 Kr5 + 5 64.70 28.30 Kr4 + 5 64.70 Cd3 + 3 37.48 27.22 Kr4 + 5 64.70 Te4 + 4 37.41 27.29 Kr4 + 5 64.70 Ce4 + 4 36.76 27.94 Sr6 + 7 106.00 Kr6 + 6 78.50 27.50 Kr5 + 6 78.50 Nb5 + 5 50.55 27.95 Xe2 + 3 32.10 Rb1 + 1 4.18 27.92 Pb2 + 3 31.94 Rb1 + 1 4.18 27.76 Rb2 + 3 40.00 Y 2 + 2 12.24 27.76 Mo 5 + 6 68.00 Rb3 + 3 40.00 28.00 Rb2 + 3 40.00 Xe1 + 1 12.13 27.87 Rb2 + 3 40.00 Gd2 + 2 12.09 27.91 Rb2 + 3 40.00 Tb2 + 2 11.52 28.48 Rb2 + 3 40.00 Dy2 + 2 11.67 28.33 Rb2 + 3 40.00 Ho 2 + 2 11.80 28.20 Rb2 + 3 40.00 Er2 + 2 11.93 28.07 Rb2 + 3 40.00 Tm 2 + 2 12.05 27.95 Rb2 + 3 40.00 Yb2 + 2 12.18 27.82 Rb3 + 4 52.60 Nb3 + 3 25.04 27.56 Rb3 + 4 52.60 Sb3 + 3 25.30 27.30 Rb3 + 4 52.60 Cs2 + 2 25.10 27.50 Rb3 + 4 52.60 Eu3 + 3 24.90 27.70 Rb3 + 4 52.60 Yb3 + 3 25.03 27.57 Rb3 + 4 52.60 Bi 3 + 3 25.56 27.04 Rb6 + 7 99.20 Rb5 + 5 71.00 28.20 Rb4 + 5 71.00 Sr3 + 3 43.60 27.40 Rb4 + 5 71.00 Eu4 + 4 42.60 28.40 ;R + 5 71.00 Er4 + 4 42.60 28.40 Rb4 + 5 71.00 Tm 4 + 4 42.70 28.30 Rb4 + 5 71.00 Yb4 + 4 43.70 27.30 Rb5 + 6 84.40 Sr4 + 4 57.00 27.40 Rb5 + 6 84.40 Sb5 + 5 56.00 28.40 Rb5 + 6 84.40 Bi 5 + 5 56.00 28.40 Rb6 + 7 99.20 Rb5 + 5 71.00 28.20 Rb6 + 7 99.20 Sr5 + 5 71.60 27.60 Mo 6 + 7 126.80 Rb7 + 7 99.20 27.60 Rb7 + 8 136.00 Sb6 + 6 108.00 28.00 Pd2 + 3 32.93 Sr 1 + 1 5.70 27.24 I 2 + 3 33.00 Sr 1 + 1 5.70 27.31 Hf 3 + 4 33.33 Sr 1 + 1 5.70 27.64 Nb3 + 4 38.30 Sr2 + 2 11.03 27.27 Pr3 + 4 38.98 Sr2 + 2 11.03 27.95 Sr4 + 5 71.60 Sr3 + 3 43.60 28.00 Sr2 + 3 43.60 Mo 2 + 2 16.15 27.45 Sr2 + 3 43.60 Tc2 + 2 15.26 28.34 Sr2 + 3 43.60 Sb2 + 2 16.53 27.07 Te5 + 6 70.70 Sr 3 + 3 43.60 27.10 Sr3 + 4 57.00 Tc3 + 3 29.54 27.46 Sr3 + 4 57.00 Tl 3 + 3 29.83 27.17 Sr4 + 5 71.60 Sr3 + 3 43.60 28.00 Sr4 + 5 71.60 Sb4 + 4 44.20 27.40 Sr4 + 5 71.60 Gd4 + 4 44.00 27.60 Sr4 + 5 71.60 Yb4 + 4 43.70 27.90 Zr3 + 4 34.34 Y 1 + 1 6.38 27.96 Ag2 + 3 34.83 Y 1 + 1 6.38 28.45 Hg2 + 3 34.20 Y 1 + 1 6.38 27.82 Sn3 + 4 40.73 Y 2 + 2 12.24 28.49 Nd3 + 4 40.41 Y 2 + 2 12.24 28.17 Tb3 + 4 39.80 Y 2 + 2 12.24 27.56 Y 3 + 4 61.80 Zr4 + 4 34.34 27.46 Y 3 + 4 61.80 Hf 4 + 4 33.33 28.47 Y 3 + 4 61.80 Hg3 + 3 34.20 27.60 Y 4 + 5 77.00 La 4 + 4 49.95 27.05 Y6 + 7 116,00 Bi 6 + 6 88.-30 27.70 Zr3 + 4 34.34 Zr1 + 1 6.84 27.50 Ag 2 + 3 34.83 Zr1 + 1 6.84 27.99 Hg2 + 3 34.20 Zr1 + 1 6.84 27.36 Sn3 + 4 40.73 Zr2 + 2 13.13 27.60 Nd3 + 4 40.41 Zr2 + 2 13.13 27.28 Pm3 + 4 41.10 Zr2 + 2 13.13 27.97 Sm3 + 4 41.40 Zr2 + 2 13.13 28.27 Dy3 + 4 41.50 Zr2 + 2 13.13 28.37 Nb4 + 5 50.55 Zr3 + 3 22.99 27.56 Zr3 + 4 34.34 Zr1 + 1 6.84 27.50 Zr3 + 4 34.34 Nb1 + 1 6.88 27.46 Zr3 + 4 34.34 Mo1 + 1 7.10 27.24 Zr3 + 4 34.34 Tc 1 + 1 7.28 27.06 Zr3 + 4 34.34 Gd1 + 1 6.14 28.20 Zr3 + 4 34.34 Tb1 + 1 5.85 28.49 Zr3 + 4 34.34 Dy1 + 1 5.93 28.41 Zr3 + 4 34.34 Ho1 + 1 6.02 28.32 Zr3 + 4 34.34 Er 1 + 1 6.10 28.24 Zr3 + 4 34.34 Tm 1 + 1 6.18 28.16 Zr3 + 4 34.34 Yb1 + 1 6.25 28.09 Zr3 + 4 34.34 Hf 1 + 1 6.60 27.74 Zr3 + 4 34.34 Tl 1 + 1 6.11 28.23 Zr3 + 4 34.34 Bi 1 + I 7.29 27.05 Zr3 + 4 34.34 Th 1 + I 6.10 28.24 Zr3 + 4 34.34 Pa1 + • I 5.90 28.44 Zr3 + 4 34.34 U 1 + 1 6.05 28.29 Zr3 + 4 34.34 Np1 + 1 6.20 28.14 Zr3 + 4 34.34 Pu 1 + 1 6.06 28.28 Zr3 + 4 34.34 Am 1 + 1 5.99 28.35 Zr3 + 4 34.34 Cm 1 + 1 6.02 28.32 Zr3 + 4 34.34 Bk1 + 1 6.23 28.11 Zr3 + 4 34.34 Cf 1 + 1 6.30 28.04 Zr3 + 4 34.34 Es1 + 1 6.42 27.92 Zr4 + 5 81.50 In 4+ A 54.00 27.50 Ag2 + 3 34.83 Nb1 + 1 6.88 27.95 Hg2 + 3 34,20 Nb1 + 1 6.88 27.32 Sm3 + 4 41.40 Nb 2+ 2 14.32 27.08 Eu3 + 4 42.60 Nb2+ 2 14.32 28.28 Dy3 + 4 41.50 Nb2+ 2 14.32 27.18 Ho 3 + 4 42.50 Nb2 + 2 14.32 28.18 Er3 + 4 42.60 Nb2 + 2 14.32 28.28 Tm 3 + 4 42.70 Nb2 + 2 14.32 28.38 Pb3 + 4 42.32 Nb2 + 2 14.32 28.00 Nb3 + 4 38.30 I 1 + 1 10.45 27.85 Nb3 + 4 38.30 Ba2 + 2 10.00 28.30 Nb3 + 4 38.30 La 2 + 2 11.06 27.24 Nb3 + 4 38.30 Ce2 + 2 10.85 27.45 Nb3 + 4 38.30 Pr 2 + 2 10.55 27.75 Nb3 + 4 38.30 Nd2 + 2 10.73 27.57 Nb3 + 4 38.30 Pm 2 + 2 10.90 27.40 Nb3 + 4 38.30 Sm2 + 2 11.07 27.23 Nb3 + 4 38.30 Eu2 + 2 11.24 27.06 Nb3 + 4 38.30 Hg1 + 1 10.44 27.86 Nb3 + 4 38.30 Rn 1 + 1 10.75 27.55 Nb3 + 4 38.30 Ra2 + 2 10.15 28.15 Nb4 + 5 50.55 Nd3 + 3 22.10 28.45 Nb4 + 5 50.55 Pm 3 + 3 22.30 28.25 Nb4 + 5 50.55 Sm 3 + 3 23.40 27.15 Nb4 + 5 50.55 Dy3 + 3 22.80 27.75 Nb4 + 5 50.55 Ho 3 + 3 22.84 27.71 Nb4 + 5 50.55 Er3 + 3 22.74 27.81 Nb4 + 5 50.55 Hf 3 + 3 23.30 27.25 Mo 7 + 8 153.00 Nb7 + 7 125.00 28.00 Ag2 + 3 34.83 Mo 1 + 1 7.10 27.73 Hg2 + 3 34.20 Mo1 + 1 7.10 27.10 Sb3 + 4 44.20 Mo 2 + 2 16.15 28.05 Gd3 + 4 44.00 Mo 2 + 2 16.15 27.85 Yb3 + 4 43.70 Mo 2 + 2 16.15 27.55 Mo.3 + 4 46.40 Rh2 + 2 18.08 28.32 Mo 3 + 4 46.40 In 2 + 2 18.87 27.53 Mo 3 + 4 46.40 Te2 + 2 18.60 27.80 Mo 3 + 4 46.40 I 2 + 2 19.13 27.27 Mo 3 + 4 46.40 La 3 + 3 19.18 ' 27.22 Mo 3 + 4 46.40 Pt2 + 2 18.56 27.84 Mo 3 + 4 46.40 Hg2 + 2 18.76 27.64 73 Mo 4 + 5 61.20 Pd3 + 3 32.93 28.27 Mo 4 + 5 61.20 I 3 + 3 33.00 28.20 Mo 4 + 5 61.20 Hf4 + 4 33.33 27.87 Bi 5 + 6 88.30 Mo 5 + 5 61.20 27.10 Mo 5 + 6 68.00 Sn4 + 4 40.73 27.27 Mo 5 + 6 68.00 Nd4 + 4 40.41 27.59 Mo 5 + 6 68.00 Tb4 + 4 39.80 28.20 Ag2 + 3 34.83 Tc 1 + 1 7.28 27.55 Eu3 + 4 42.60 Tc2 + 2 15.26 27.34 Ho 3 + 4 42.50 Tc2 + 2 15.26 27.24 Er3 + 4 42.60 Tc2 + 2 15.26 27.34 Tm 3 + 4 42.70 Tc2 + 2 15.26 27.44 Yb3 + 4 43.70 Tc2 + 2 15.26 28.44 Pb3 + 4 42.32 Tc2 + 2 15.26 27.06 Ag2 + 3 34.83 Ru1 + 1 7.37 27.46 Sb3 + 4 44.20 Ru2 + 2 16.76 27.44 Gd3 + 4 44.00 Ru2 + 2 16.76 27.24 Lu3 + 4 45.19 Ru2 + 2 16.76 28.43 Sb4 + 5 56.00 Ru3 + 3 28.47 27.53 Bi 4 + 5 56.00 Ru3 + 3 28.47 27.53 Ag2 + 3 34.83 Rh1 + 1 7.46 27.37 Lu3 + 4 45.19 Rh2 + 2 18.08 27.11 Bi 3 + 4 45.30 Rh2 + 2 18.08 27.22 Te4 + 5 58.75 Rh3 + 3 31.06 27.69 Rh2 + 3 31.06 Cs 1 + 3.89 27.17 Ce3 + 4 36.76 Pd1 + 8.34 28.42 Pd2 + 3 32.93 In i + 5.79 27.14 Pd2 + 3 32.93 Ba1 + 5.21 27.72 Pd2 + 3 32.93 La 1 + 5.58 27.35 Pd2 + 3 32.93 Ce1 + 5.47 27.46 Pd ' 2 + 3 32.93 Pr 1 + 5.42 27.51 Pd2 + 3 32.93 Nd1 + 5.49 27.44 Pd2 + 3 32.93 Pm 1 + 5.55 27.38 Pd2 + 3 32.93 Sm 1 + 5.63 27.30 Pd2 + 3 32.93 Eu1 + 5.67 27.26 Pd2 + 3 32.93 Tb1 + 5.85 27.08 Pd2 + 3 32.93 Dy 1 + 5.93 27.00 Pd2 + 3 32.93 Lu 1 + 5.43 27.50 Pd2 + 3 32.93 Ra1 + 5.28 27.65 Pd2 + 3 32.93 Ac 1 + 5.20 27.73 Pd2 + 3 32.93 Pa1 + 5.90 27.03 Ag2 + 3 34.83 Ag 1 + 7.58 27.25 La 3 + 4 49.95 Ag2 + 2 21.49 28.46 Ag2 + 3 34.83 Ag 1 + 7.58 27.25 Ag2 + 3 34.83 Sn 1 + 7.34 27.49 Ag2 + 3 34.83 Hf 1 + 6.60 28.23 Ag2 + 3 34.83 Pb1 + 7.42 27.41 Ag2 + 3 34.83 Bi 1 + 7.29 27.54 Ag2 + 3 34.83 Es1 + 6.42 28.41 Cd2 + 3 37.48 Cd1 + 8.99 28.49 Te3 + 4 37.41 Cd1 + 8.99 28.42 Ce3 + 4 36.76 Cd1 + 8.99 27.76 Sb3 + 4 44.20 Cd2 + 2 16.91 27.29 Gd3 + 4 44.00 Cd2 + 2 16.91 27.09 Lu 3 + 4 45.19 Cd2 + 2 16.91 28.28 Bi 3 + 4 45.30 Cd2 + 2 16.91 28.39 Cd2 + 3 37.48 Cd1 + 8.99 28.49 Cd2 + 3 37.48 Te1 + 9.01 28.47 Cd2 + 3 37.48 I 1 + 10.45 27.03 Cd2 + 3 37.48 Ba2 + 2 10.00 27.48 Cd2 + 3 37.48 Ir 1 + 9.10 28.38 Cd2 + 3 37.48 Pt 1 + 9.00 28.48 Cd2 + 3 37.48 Au 1 + 9.23 28.25 Cd2 + 3 37.48 Hg1 + 10.44 27.04 Cd2 + 3 37.48 Ra2 + 10.15 27.33 I 2 + 3 33.00 In 1 + 5.79 27.21 Hf 3 + 4 33.33 In 1 + 5.79 27.54 Hg2 + 3 34.20 In 1 + 5.79 28.41 Sb4 + 5 56.00 In 3 + 3 28.03 27.97 BI4 + 5 56.00 In 3 + 3 28.03 27.97 In 3 + 4 54.00 Bi 3 + 3 25.56 28.44 Eu3 + 4 42.60 Sn2 + 2 14.63 27.97 Ho 3 + 4 42.50 Sn 2 + 2 14.63 27.87 Er3 + 4 42.60 Sn2 + 2 14.63 27.97 Tm 3 + 4 42.70 Sn2 + 2 14.63 28.07 Pb3 + 4 42.32 Sn2 + 2 14.63 27.69 Te4 + 5 58.75 Sn3 + 3 30.50 28.25 Pb4 + 5 68.80 Sn4 + 4 40.73 28.07 Sn4 + 5 72.28 Sb4 + 4 44.20 28.08 Sn4 + 5 72.28 Gd4 + 4 44.00 28.28 Sn4 + 5 72.28 Lu4 + 4 45.19 27.09 Ce3 + 4 36.76 Sb1 + 1 8.64 28.12 Sb3 + 4 44.20 Sb2 + 2 16.53 27.67 Gd3 + 4 44.00 Sb2 + 2 16.53 27.47 Yb3 + 4 43.70 Sb2 + 2 16.53 27.17 Sb3 + 4 44.20 Sb2 + 2 16.53 27.67 Sb3 + 4 44.20 Bi 2 + 2 16.69 27.51 Sb4 + 5 56.00 Te3 + 3 27.96 28.04 Te3 + 4 37.41 Te1 + 1 9.01 28.40 Ce3 + 4 36.76 Te 1 + 1 9.01 27.75 Bi 4 + 5 56.00 Te3 + 3 27.96 28.04 Te3 + 4 37.41 Te1 + 1 9.01 28.40 Te3 + 4 37.41 Ba2 + 2 10.00 27.41 Te3 + 4 37.41 Ir 1 + 1 9.10 28.31 Te3 + 4 37.41 Pt 1 + 1 9.00 28.41 Te3 + 4 37.41 Au 1 + 1 9.23 28.18 TΘ.3 + 4 37.41 Ra2 + 2 10.15 27.26 Te 5 + 6 70.70 Eu4 + 4 42.60 28.10 Te5 + 6 70.70 Ho 4 + 4 42.50 28.20 Te5 + 6 70.70 Er4 + 4 42.60 28.10 Te5 + 6 70.70 Tm 4 + 4 42.70 28.00 Te 5 + 6 70.70 Pb4 + 4 42.32 28.38 I 2 + 3 33.00. Bal + 5.21 27.79 I 2 + 3 33.00 La1 + 5.58 27.42 I 2 + 3 33,00 Ce1 + 5.47 27.53 I ,2 + 3 33.00 Pr 1 + 5.42 27.58 I 2 + 3 33.00 Nd1 + 5.49 27.51 I 2 + 3 33.00 Pm 1 + 5.55 27.45 I 2 + 3 33.00 Sm 1 + I 5.63 27.37 I 2 + 3 33.00 Eu1 + 5.67 27.33 I 2 + 3 33.00 Tb1 + 5.85 27.15 I 2 + 3 33.00 Dy1 + 5.93 27.07 I 2 + 3 33.00 Lu 1 + 5.43 27.57 I 2 + 3 33.00 Ra1 + 5.28 27.72 I 2 + 3 33.00 Ac 1 + 5.20 27.80 I 2 + 3 33.00 Pa1 + 5.90 27.10 I 2 + 3 33.00 Am 1 + 5.99 27.01 Nd3 + 4 40.41 Xe1 + 12.13 28.28 Tb3 + 4 39.80 Xe1 + 12.13 27.67 Xe2 + 3 32.10 Cs 1 + 3.89 28.21 Pb2 + 3 31.94 Cs1 + 3.89 28.04 Hf 3 + 4 33.33 Ba 1 + 5.21 28.12 Hf 3 + 4 33.33 La1 + 5.58 27.75 Pr3 + 4 38.98 La 2 + 2 11.06 27.92 La 3 + 4 49.95 Pr3 + 3 21.62 28.33 La 3 + 4 49.95 Nd3 + 3 22.10 27.85 La 3 + 4 49.95 Pm3 + 3 22.30 27.65 La 3 + 4 49.95 Tb3 + 3 21.91 28.04 La 3 + 4 49.95 Dy3 + 3 22.80 27.15 La 3 + 4 49.95 Ho 3 + 3 22.84 27.11 La 3 + 4 49.95 Er3 + 3 22.74 27.21 Hf 3 + 4 33.33 Ce1 + 1 5.47 27.86 Pr3 + 4 38.98 Ce2 + 2 10.85 28.13 Ce3 + 4 36.76- Os1 + 8.70 28.06 Ce3 + 4 36.76 lr 1 + 9.10 27.66 Ce3 + 4 36.76. Pt1 + 9.00 27.76 Ce3 + 4 36.76 Au 1 + 9.23 27.53 Ce3 + 4. 36.7 Po1 + 8.42 ' 28.34 Hf 3 + 4 33.33- Pr 1 + 5.42 27.91 Pr3 + 4 38.98 Pr2 + 2 10.55 28.43 Pr3 + 4 38.98 Pr2+ . 2 10.55 28.43 Pr3 + 4 38.98 Nd2 + 2 10.73 28.25 Pr3 + 4 38.98 Pm2 + 2 10.90 28.08 Pr3 + 4 38.98 Sm2 + 2 11.07 27.91 77 Pr 3 + 4 38.98 Eu2 + 2 11.24 27.74 Pr 3 + 4 38.98 Tb2 + 2 11.52 27.46 Pr 3 + 4 38.98 Dy2 + 2 11.67 27.31 Pr 3 + 4 38.98 Ho 2 + 2 11.80 27.18 Pr 3 + 4 38.98 Er2 + 2 11.93 27.05 Pr3 + 4 38.98 Rn1 + 1 10.75 28.23 Hf 3 + 4 33.33 Nd1 + 1 5.49 27.84 Nd3 + 4 40.41 Gd2 + 2 12.09 28.32 Nd3 + 4 40.41 Er2 + 2 11.93 28.48 Nd3 + 4 40.41 Tm2 + 2 12.05 28.36 Nd3 + 4 40.41 Yb2 + 2 12.18 28.23 Pb4 + 5 68.80 Nd4 + 4 40.41 28.39 Hf 3 + 4 33.33 Pm 1 + 1 5.55 27.78 Pm3 + 4 41.10 Lu2 + 2 13.90 27.20 Pb4 + 5 68.80 Pm4 + 4 41.10 27.70 Hf 3 + 4 33.33 Sm 1 + 1 5.63 27.70 Sm 3 + 4 41.40 Lu2 + 2 13.90 27.50 Pb4 + 5 68.80 Sm4 + 4 41.40 27.40 Hf 3 + 4 33.33 Eu1 + 1 5.67 27.66 Eu3 + 4 42.60 Hf 2 + 2 14.90 27.70 Eu3 + 4 42.60 Pb2 + 2 15.03 27.57 Hf 3 + 4 33.33 Gd1 + 1 6.14 27.19 Hg2 + 3 34.20 Gd1 + 1 6.14 28.06 Tb3 + 4 39.80 Gd2 + 2 12.09 27:71 Gd3 + 4 44.00 Bi 2'+ 2 16.69 ' 27.31 Hf 3 + 4 33.33 Tb1 + 1 5.85 27.48 Hg2 + 3 34.20 Tb1 + 1 5.85 28.35 Tb3 + 4 39.80 Tb2 + 2 11.52 28.28 Tb3 + 4 39.80 Tb2 + 2 11.52 28.28 T 3 + 4 39.80 • • Dy2 + 2 11.67 28.13 T 3 + 4 39_80 Ho ' 2 + 2 11.80 28.00 Tb3 + 4 39.80 Er2 + 2 11.93 27.87 Tb3 + 4 39,80 Tm 2 + 2 12.05 27.75 T 3 + 4 39.80 Yb2 + 2 12.18 27.62 Hf 3 + 4 33.33 Dy 1 + 1 5.93 27.40 Hg2 + 3 34.20 Dy 1 + 1 5.93 28.27 Dy3 + 4 41.50 Lu2 + 2 13.90 27.60 Pb4 + 5 68.80 Dy4 + 4 41.50 27.30 Hf3 + 4 33.33 Ho1 + 1 6.02 27.31 Hg2 + 3 34.20 Ho1 + 1 6.02 28.18 Ho 3 + 4 42.50 Hf 2 + 2 14.90 27.60 Ho 3 + 4 42.50 Pb2 + 2 15.03 27.47 Hf 3 + 4 33.33 Er1 + 1 6.10 27.23 Hg2 + 3 34.20 Er1 + 1 6.10 28.10 Er3 + 4 , 42.60 Hf 2 + 2 14.90 27.70 Er3 + 4 42.60 Pb2 + 2 15.03 27.57 Hf 3 + 4 33.33 Tm 1 + 1 6.18 27.15 Hg2 + 3 34.20 Tm 1 + 1 6.18 28.02 Tm 3 + 4 42.70 Hf 2 + 2 14.90 27.80 Tm 3 + 4 42.70 Pb2 + 2 15.03 27.67 Hf 3 + 4 33.33 Yb1 + 1 6.25 27.08 Hg2 + 3 34.20 Yb1 + 1 6.25 27.95 Yb3 + 4 43.70 Bi 2 + 2 16.69 27.01 Hf 3 + 4 33.33 Lu 1 + 1 5.43 27.90 Pb3 + 4 42.32 Lu 2 + 2 13.90 28.42 Lu3 + 4 45.19 Bi 2 + 2 16.69 28.50 Hg2 + 3 - 34.20 Hf 1 + 1 6.60 27.60 Pb3 + 4 42.32 Hf 2 + 2 14.90 27.42 Hf3 + 4 33.33 Tl 1 + 1 6.11 27.22 Hf 3 + 4 33.33 Ra1 + 1 5.28 28.05 Hf3 + 4 33.33 Ac1 + 1 5.20 28.13 Hf3 + 4 33.33 Th 1 + 1 6.10 27.23 Hf 3 + 4 33.33 Pa1 + 1 5.90 27.43 Hf3 + 4 33.33 U 1 + 1 6.05 27.28 Ηf3 + 4 33.33 Np1 + 1 6.20 27.13 Hf3 + 4 33.33 Pu1 + 1 6.06 27.27 Hf3 + 4 33.33 Am 1 + 1 5.99 27.34 Hf 3 + 4 33.33 Cm 1 + 1 6.02 27.31 Hf3 + 4 33.33 B 1 + 1 6.23 27.10 Hf3 + 4 . 33.33 Cf 1 + 1 6.30 27.03 Hg2 + 3 34.20 Tl 1 + 1 6.11 28.09 Hg2 + 3 34.20 Th 1 + 1 6.10 28.10 Hg2 + 3 34.20 Pa1 + I 5.90 28.30 Hg2 + 3 34.20 U 1 + ■ I 6.05 28.15 Hg2 + 3 34.20 Np1 + I 6.20 28.00 Hg2 + 3 34.20 Pu1 + I 6.06 28.14 Hg2 + 3 34.20 Am 1 + I 5.99 28.21 Hg2 + 3 34.20 Cm1 + ■ I 6.02 28.18 Hg2 + 3 34.20 Bk1 + I 6.23 27.97 Hg2 + 3 34.20 Cf 1 + 1 6.30 27.90 Hg2 + 3 34.20 Es1 + 1 6.42 27.78 Pb3 + 4 42.32 Pb2+ . I 15.03 27.29 Pb3 + 4 42.32 Pb2+ I 2 15.03 27.29 n n = 16 (resonance shrinkage energy is given by 27.21 e V; with n = 16, the resonance shrinkage energy is 217.68) Atom n nth Ion¬ Atom n nth Ion¬ Energy Oxidiz¬ ization Reduced ization Hole ed Energy Energy (eV) (eV) (eV) Ne7 + 8 239.09 He1 + 1 24.59 214.50 AI6 + 7 241.43 He1 + 1 24.59 216.84 Mg6 + 7 224.94 Li 1 + 1 5.39 219.55 P 5 + 6 220.43 Li 1 + 1 5.39 215.04 B 4 + 5 340.22 Li 3 + 3 122.45 217.77 Mg6 + 7 224.94 Be1 + 1 9.32 215.62 Ne7 + 8 239.09 Be 2 + 2 18.21 220.88 Mg6 + 7 224.94 B 1 + 1 8.30 216.64 Al 6 + 7 241.43 B 2 + 2 25.15 216.28 B 3 + 4 259.37 Ne2 + 2 40.96 218.41 B 3 + 4 259.37 Si 4 + 4 45.14 214.23 B 3 + 4 259.37 CI3 + 3 39.61 219.76 B.3 + 4 259.37 Ar3 + 3 40.74 218.6.3 B 3 + 4 259.37 Ti 4 + 4 43.27 216.10 B 3 + 4 259.37 Zn3 + 3 39.72 219.65 B 3 + 4 259.37 Se4 + 4 42.94 216.42 B 3 + 4 259.37 Rb3 + 3 40.00 219.37 B 3 + 4 259.37 Sr3 + 3 43.60 215.77 B 3 + 4 259.37 Sn4 + 4 40.73 218.63 B 3 + 4 259.37 Sb4 + 4 44.20 215.17 B 3 + 4 259.37 Pr4 + 4 38.98 220.39 B 3 + 4 259.37 Nd4 + 4 40.41 218.96 B 3 + 4 259.37 Pm4 + 4 41.10 218.27 B 3 + 4 259.37 Sm4 + 4 41.40 217.97 B 3 + 4 259.37 Eu4 + 4 42.60 216.77 B 3 + 4 259.37 Gd4 + 4 44.00 215.37 B 3 + 4 259.37 Tb4 + 4 39.80 219.57 B 3 + 4 259.37 Dy4 + 4 41.50 217.87 B 3 + 4 259.37 Ho 4 + 4 42.50 216.87 B 3 + 4 259.37 Er4 + 4 42.60 216.77 B 3 + 4 259.37 Tm 4 + 4 42.70 216.67 B 3 + 4 259.37 Yb4 + 4 43.70 215.67 B 3 + 4 259.37 Lu4 + 4 45.19 214.18 B 3 + 4 259.37 Pb4 + 4 42.32 217.05 B 3 + 4 259.37 Bi 4 + 4 45.30 214.07 B 4 + 5 340.22 Ne5 + 5 126.21 214.01 B 4 + 5 340.22 Al 4 + 4 119.99 220.23 B 4 + 5 340.22 Ar7 + 7 124.32 215.90 B 4 + 5 340.22 Ti 6 + 6 119.36 220.86 B 4 + 5 340.22 Mn7 + 7 119.27 220.95 B 4 + 5 340.22 Fe7 + 7 125.00 215.22 B 4 + 5 340.22 Kr8 + 8 126.00 214.22 B 4 + 5 340.22 Sr8 + 8 122.3:0 217.92 B 4 + 5 340.22 Nb7 + 7 125.00 215.22 Ne7 + 8 239.09 C 2 + 2 24.38 214.71 Al 6 + 7 241.43 C 2 + 2 24.38 217.05 Na7 + 8 264.18 C 3 + 3 47.89 216.29 Mg7 + 8 265.90 C 3 + 3 47.89 218.01 P 6.+ 7 263.22 C 3 + 3 47.89 215.33 Al 7 + 8 284.59 C 4 + 4 64.49 220.10 S 6 + 7 280.93 C 4 + 4 64.49 216.44 C 4 + 5 392.08 Na6 + 6 172.15 219.93 C 4 + 5 392.08 V 8 + 8 173.70 218.38 C 4 + 5 392.08 Zn8 + 8 174.00 218.08 Si 6 + 7 246.52 N 2 + 2 29.60 216.92 Na7 + 8 264.18 N 3 + 3 47.45 216.73 Mg7 + 8 265.90 N 3 + 3 47.45 218.45 P 6 + 7 263.22 N 3 + 3 47.45 215.77 S 7 + 8 328.23 O 5 + 5 113.90 214.33 F 7 + 8 953.89 0 7 + 7 739.32 214.57 S 6 + 7 280.93 F 3 + 3 62.71 218.22 Si 7 + 8 303.17 F 4 + 4 87.14 216.03 Ne7 + 8 239.09 Ne1 + 1 21.56 217.53 Al 6 + 7 241.43 Ne1 + 1 21.56 219.87 S 6 + 7 280.93 Ne3 + 3 63.45 217.48 Ne7 + 8 239.09 Ne1 + 1 21.56 217.53 Ne7 + 8 239.09 Al 2 + 2 18.83 220.26 Ne7 + 8 239.09 P 2 + 2 19.73 219.36 Ne7 + 8 239.09 S 2 + 2 23.33 215.76 Ne7 + 8 239.09 Cl 2 + 2 23.81 215.28 Ne7 + 8 239.09 Sc3 + 3 24.76 214.33 Ne7 + 8 239.09 Ni2 + 2 18.17 220.92 Ne7 + 8 239.09 Cu 2 + 2 20.29 218.80 Ne7 + 8 239.09 Ga2 + 2 20.51 218.58 Ne7 + 8 239.09 As 2 + 2 18.63 220.46 Ne7 + 8 239.09 Se2 + 2 21.19 217.90 Ne7 + 8 239.09 Br2 + 2 21.80 217.29 Ne7 + 8 239.09 Kr2 + 2 24.36 214.73 Ne7 + 8 239.09 Y 3 + 3 20.52 218.57 Ne7 + 8 239.09 Zr3 + 3 22.99 216.10 Ne7 + 8 239.09 Nb3 + 3 25.04 214.05 Ne7 + 8 239.09 Pd2 + 2 19.43 219.66 Ne7 + 8 239.09 . Ag 2 + 2 21.49 217.60 Ne7 + 8 239.09 In ' 2 + 2 18.87 220.22 Ne7 + 8 239.09 Te2 + 2 18.60 220.49 Ne7 + 8 239.09 I 2 + 2 19.13 219.96 Ne7 + 8 239.09 Xe2 + 2 21.21 217.88 Ne7 + 8 239.09 La 3 + 3 19.18 . 219.91 Ne7 + 8 239.09 Ce3 + 3 20.20 218.89 Ne7 + 8 239.09 Pr3 + 3 21.62 217.47 Ne7 + 8 239.09 Nd3 + 3 22.10 216.99 Ne7 + 8 239.09 Pm 3 + 3 22.30 216.79 Ne7 + 8 239.09 Sm3 + 3 23.40 215.69 Ne7 + 8 239.09 Eu3 + 3 24.90 214.19 Ne7 + 8 239.09 Gd3 + 3 20.63 218.46 Ne7 + 8 239.09 Tb3 + 3 21.91 217.18 Ne7 + 8 239.09 Dy3 + 3 22.80 216.29 Ne7 + 8 239.09 Ho 3 + 3 22.84 216.25 Ne7 + 8 239.09 Er3 + 3 22.74 216.35 Ne7 + 8 239.09 Tm 3 + 3 23.68 215.41 Ne7 + 8 239.09 Yb3 + 3 25.03 214.06 Ne7 + 8 239.09 Lu3 + 3 20.96 218.13 Ne7 + 8 239.09 Hf 3 + 3 23.30 215.79 Ne7 + 8 239.09 Pt2 + 2 18.56 220.53 Ne7 + 8 239.09 Au 2 + 2 20.50 218.59 Ne7 + 8 239.09 Hg2 + 2 18.76 220.33 Ne7 + 8 239.09 Tl 2 + 2 20.43 218.66 Mg 6 + 7 224.94 Na1 + 1 5.14 219.80 P 5 + 6 220.43 Na1 + 1 5.14 215.29 Na7 + 8 264.18 Na2 + 2 47.29 216.89 Mg7 + 8 265.90 Na2 + 2 47.29 218.61 P 6 + 7 263.22 Na2 + 2 47.29 215.93 Na7 + 8 264.18 Na2 + 2 47.29 216.89 Na7 + 8 264.18 Si 4 + 4 45.14 219.04 Na7 + 8 264.18 S 4 + 4 47.30 216.88 Na7 + 8 264.18 K 3 + 3 45.72 218.46 Na7 + 8 264.18 Ti4 + 4 43.27 220.91 Na7 + 8 264.18 V 4 + 4 46.71 217.47 Na7 + 8 264.18 . Cr4 + 4 49.10 215.08 Na7 + 8 264.18 Ge4 + 4 45.71 218.47 Na7 + 8 • 264.18 As 4 + 4 50.13 214.05 Na7 + 8 264.18 Br 4 + 4 47.30 216.88 Na7 + 8 264.18 Sr3 + 3 43.60 220.58 Na7 + 8 264.18 Mo 4 + 4 46.40 217.78 Na7 + 8 264.18 Sb4 + 4 44.20 219.98 Na7 + 8 264.18 La 4 + 4 49.95 214.23 Na7 + 8 264.18 Gd4+ 4 44.00 220.18 Na7 + 8 264.18 Yb4+ 4 43.70 220.48 Na7 + 8 264.18 Lu4+ 4 45.19 218.99 Na7 + 8 264.18 Bi 4 + 4 45.30 218.88 Mg 6 + 7 224.94 Mg1 + 1 7.65 217.29 S 7 + 8 328.23 Mg4+ 4 109.24 218.99 Mg6 + 7 224.94 Mg 1 + 1 7.65 217.29 Mg6 + 7 224.94 Al 1 + 1 5.99 218.95 Mg6 + 7 224.94 Si 1 + ' 8.15 216.79 Mg 6 + 7 224.94 P 1 + I 10.49 214.45 Mg6 + 7 224.94 S 1 + ■ 10.36 214.58 Mg6 + 7 224.94 K 1 + ■ 4.34 220.60 Mg 6 + 7 224.94 Ca1 + " 6.11 218.83 Mg6 + 7 224.94 Sc1 + ■ I 6.54 218.40 Mg6 + 7 224.94 Ti 1 + " I 6.82 218.12 Mg 6 + 7 224.94 V 1 + I 6.74 218.20 Mg6 + 7 224.94 Cr 1 + ■ I 6.77 218.17 Mg 6 + 7 224.94 Mn1 + I 7.43 217.51 Mg 6 + 7 224.94 Fe 1 + I 7.87 217.07 Mg 6 + 7 224.94 Co1 + I 7.86 217.08 Mg 6 + 7 224.94 Ni 1 + I 7.64 217.31 Mg6 + 7 224.94 Cu1 + I 7.73 217.21 Mg 6 + 7 224.94 Zn1 + 1 9.39 215.55 Mg 6 + 7 224.94 Ga1 + 1 6.00 218.94 Mg6 + 7 224.94 Ge1 + 1 7.90 217.04 Mg 6 + 7 224.94 As 1 + 1 9.81 215.13 Mg6 + 7 224.94 Se1 + I 9.75 215.19 Mg6 + 7 224.94 Rb1 + I 4.18 220.76 Mg6 + 7 224.94 Sr 1 + 1 5.70 219.24 Mg6 + 7 224.94 Y 1 + 1 6.38 218.56 Mg6 + 7 224.94 Zr 1 + 1 6.84 218.10 Mg6 + 7 224.94 Nb1 + 1 6.88 218.06 Mg6 + 7 224.94 Mo1 + 1 7.10 217.84 Mg6 + 7 224.94 Tc1 + 1 7.28 . 217.66 Mg6 + 7 224.94 Ru1 + 1 7.37 217.57 Mg6 + 7 224.94 Rh1 + 1 7.46 217.48 Mg 6 + 7 224.94 Pd1 + 1 8.34 216.60 Mg6 + 7 224.94 Ag1 + 1 7.58 217.36 Mg6 + 7 224.94 Cd1 + 1 8.99 215.95 Mg6 + 7 224.94 In 1 + 5.79 219.15 Mg6 + 7 224.94 Sn1 + * 7.34 217.60 Mg6+ ' 7 224.94 Sb1 + 1 I 8.64 216.30 Mg6 + 7 224.94 Te1 + ' I 9.01 215.93 Mg6 + 7 224.94 1 1 + 10.45 214.49 Mg6 + 7 224.94 Ba1 + J I 5.21 219.73 Mg6 + 7 224.94 Ba2+ . I 10.00 214.94 Mg6 + 7 224.94 La1 + " I 5.58 219.36 Mg 6 + 7 224.94 Ce1 + " I 5.47 219.47 Mg 6 + 7 224.94 Ce2+ ' I 10.85 214.09 Mg6 + 7 224.94 Pr 1 + I 5.42 219.52 Mg 6 + 7 224.94 Pr 2+ J I 10.55 214.39 Mg6 + 7 224.94 Nd1 + I 5.49 219.45 Mg6 + 7 224.94 Nd2+ I 10.73 214.21 Mg 6 + 7 224.94 Pm 1 + I 5.55 219.39 Mg6 + 7 224.94 Pm 2 + J I 10.90 214.04 Mg6 + 7 224.94 Sm 1 + I 5.63 219.31 Mg6 + 7 224.94 Eu1 + l 5.67 219.27 Mg6 + 7 224.94 Gd1 + 1 6.14 218.80 Mg6 + 7 224.94 Tb1 + I 5.85 219.09 Mg 6 + 7 224.94 Dy 1 + 1 5.93 219.01 Mg6 + 7 224.94 Ho1 + 1 6.02 218.92 Mg6 + 7 224.94 Er1 + 1 6.10 218.84 Mg6 + 7 224.94 Tm 1 + 1 6.18 218.76 Mg6 + 7 224.94 Yb1 + 1 6.25 218.69 Mg6 + 7 224.94 Lu 1 + 1 5.43 219.51 Mg6 + 7 224.94 Hf 1 + 1 6.60 218.34 Mg6 + 7 224.94 Ta1 + 1 7.89 217.05 Mg6 + 7 224.94 W 1 + 1 7.98 216.96 Mg6 + 7 224.94 Re1 + 1 7.88 217.06 Mg6 + 7 224.94 Os1 + 1 8.70 . 216.24 Mg6 + 7 224.94 Ir 1 + 1 9.10 215.84 Mg 6 + 7 224.94 Pt 1 + 1 9.00 215.94 Mg 6 + 7 224.94 Au 1 + 9.23 215.71 Mg 6 + 7 224.94 Hg1 + 10.44 214.50 Mg 6 + 7 224.94 Tl 1 + 6.11 218.83 Mg6 + 7 224.94 Pb1 + 7.42 217.52 Mg6 + 7 224.94 Bi 1 + 7.29 217.65 Mg 6 + 7 224.94 Po 1 + 8.42 216.52 Mg6 + 7 224.94 Rn 1 + 10.75 214.19 Mg 6 + 7 224.94 Ra1 + 5.28 219.66 Mg 6 + 7 224.94 Ra2 + 2 10.15 214.79 Mg6 + 7 224.94 Ac 1 + 5.20 219.74 Mg 6 + 7 224.94 Th 1 + 6.10 218.84 Mg6 + 7 224.94 Pa1 + 5.90 219.04 Mg 6 + 7 224.94 U 1 + 6.05 218.89 Mg6 + 7 224.94 Np1 + 6.20 218.74 Mg 6 + 7 224.94 Pu 1 + 6.06 218.88 Mg 6 + 7 224.94 Am 1 + 5.99 218.95 Mg6 + 7 224.94 Cm 1 + 6.02 218.92 Mg 6 + 7 224.94 Bk1 + 6.23 218.71 Mg6 + 7 224.94 Cf 1 + 6.30 218.64 Mg6 + 7 224.94 Es1 + 6.42 218.52 Mg7 + 8 265.90 Si 4 + 4 45.14 220.76 Mg7 + 8 265.90 P 4 + 4 51.37 214.53 Mg7 + 8 265.90 S 4 + 4 47.30 218.60 Mg7 + 8 265.90 K 3 + 3 45.72 220.18 Mg7 + 8 265.90 Ca3 + 3 50.91 214.99 Mg7 + 8 265.90 V 4 + 4 46.71 ■ 219.19 Mg7 + 8 265.90 Cr4 + 4 49.10 216.80 Mg7 + 8 265.90 Mn4 + 4 51.20 214.70 Mg7 + 8 265.90 . Co 4 + 4 51.30 214.60 g7 + 8 265.9 Ge4 + 4 45.71 220.19 Mg7 + 6 265.9<. As 4 + 4 50.13 215.77 Mg7 + 8 265.90 Br4 + 4 47.30 218.60 Mg7 + 8 265.90 Nb5 + 5 50.55 215.35 Mg7 + 8 265.90 Mo 4 + 4 46.40 . 219.50 Mg 7 + 8 265.90 La 4 + 4 49.95 215.95 Mg7 + 8 265.90 Lu4 + 4 45.19 220.71 Mg7 + 8 265.90 Bi 4 + 4 45.30 220.60 P 5 + 6 f 220.43 Al 1 + 1 5.99 214.44 Si 6 + 7 246.52 Al 3 + 3 28.45 218.07 Al 6 + 7 241.43 S 2 + 2 23.33 218.10 Al 6 + 7 241.43 CI2 + 2 23.81 217.62 Al 6 + 7 241.43 Sc3 + 3 24.76 216.67 Al 6 + 7 241.43 Ga2 + 2 20.51 220.92 Al 6 + 7 241.43 Se2 + 2 21.19 220.24 Al 6 + 7 241.43 Br2 + 2 21.80 219.63 Al 6 + 7 241.43 Kr2 + 2 24.36 217.07 Al 6 + 7 241.43 Rb2 + 2 27.28 214.15 Al 6 + 7 241.43 Y 3 + 3 20.52 220.91 Al 6 + 7 241.43 Zr3 + 3 22.99 218.44 Al 6 + 7 241.43 Nb3 + 3 25.04 216.39 Al 6 + 7 241.43 Mo 3 + 3 27.16 214.27 Al 6 + 7 241.43 Ag2 + 2 21.49 219.94 Al 6 + 7 241.43 Sb3 + 3 25.30 216.13 Al 6 + 7 241.43 Xe2 + 2 21.21 220.22 Al 6 + 7 241.43 Cs2 + 2 25.10 216.33 Al 6 + 7 241.43 Pr3 + 3 21.62 219.81 Al 6 + 7 241.43 Nd3 + 3 22.10 219.33 Al 6 + 7 241.43 Pm3 + 3 22.30 219.13 Al 6 + 7 241.43 Sm 3 + 3 23.40 218.03 Al 6 + 7 241.43 Eu3 + 3 24.90 216.53 Al 6 + 7 241.43 Gd3 + 3 20.63 220.80 Al 6 + 7 241.43 T 3 + 3 21.91 219.52 Al 6 + 7 241.43 Dy 3 + 3 22.80 218.63 Al 6 + 7 241.43 Ho 3 + 3 22.84 218.59 Al 6 + 7 241.43 .Er3 + 3 22.74 218.69 Al 6 + 7 241.43 Tm 3 + 3 23.68 217.75 Al 6 + 7 241.43 Yb3 + 3 25.03 216.40 Al 6 + 7 241.43 Lϋ3 + 3 20.96 220.47 Al 6 + 7 241.43 Hf 3 + 3 23.30 218.13 Al 6 + 7 241.43 Au 2 + 2 20.50 220.93 Al 6 + 7 241.43 Bi 3 + 3 25.56 215.87 Al 7 + 8 284.59 P 5 + 5 65.02 219.57 Al 7 + 8 284.59 CI 5 + 5 67.80 216.79 Al 7 + 8 284.59 Ca 4 + 4 67.10 217.49 Al 7 + 8 284.59 V 5 + 5 65.23 219.36 Al 7 + 8 284.59 Cr 5 + 5 69.30 215.29 Al 7 + 8 284.59 Ga 4 + 4 64.00 220.59 Al 7 + 8 284.59 As 5 + 5 63.63 220.96 Al 7 + 8 284.59 Se 5 + 5 68.30 216.29 Al 7 + 8 284.59 Kr 5 + 5 64.70 219.89 Al 7 + 8 284.59 Mo 6 + 6 68.00 216.59 Al 7 + 8 284.59 Pb 5 + 5 68.80 215.79 P 6 + 7 263.22 Si 4 + 4 45.14 218.08 Si 6 + 7 246.52 P 3 + 3 30.18 216.34 Si 6 + 7 246.52 Ar 2 + 2 27.63 218.89 Si 6 + 7 246.52 K 2 + 2 31 .63 214.90 i 6 + 7 246.52 Ti 3 + 3 27.49 219.03 i 6 + 7 246.52 V 3 + 3 29.31 217.21 i 6 + 7 246.52 Cr 3 + 3 30.96 215.56 i 6 + 7 246.52 Fe 3 + 3 30.65 215.87 i 6 + 7 246.52 Ga 3 + 3 30.71 215.81 i 6 + 7 246.52 As 3 + 3 28.35 218.17 i 6 + 7 246.52 Se 3 + 3 30.82 215.70 i 6 + 7 246.52 Rb 2 + 2 27.28 219.24 i 6 + 7 246.52 Mo 3 + 3 27.16 219.36 i 6 + 7 246.52 Tc 3 + 3 29.54 216.98 i 6 + 7 246.52 Ru 3 + 3 28.47 218.05 i 6 + 7 246.52 Rh 3 + 3 31.06 215.46 i 6 + 7 246.52 In 3 + 3 28.03 218.49 i 6 + 7 246.52 Sn 3 + 3 30.50 216.02 i 6 + 7 246.52 . Te 3 + 3 27.96 218.56 i 6 + 7 246.52 Xe 3 + 3 32.10 214.42 i 6 + 7 246.52 Tl 3 + 3 29.83 216.69 i 6 + 7 246.52 Pb 3 + 3 31 .94 214.58 i 6 + 7 246.52 Bi 3 + 3 25.56 220,96 i 7 + 8 303.17 S 6 + 6 88.05 215.12 i 7 + 8 303.17 K 5 + 5 82.66 220.51 i 7 + 8 303.17 Ca 5 + 5 84.41 218.76 Si 7 + 8 303.17 Zn 5 + 5 82.60 220.57 Si 7 + 8 303.17 Br 6 + 6 88.60 214.57 Si 7 + 8 303.17 Rb 6 + 6 84.40 218.77 Si 7 + 8 303.17 Bi 6 + 6 88.30 214.87 S 6 + 7 280.93 P 5 + 5 65.02 215.91 P 5 + 6 220.43 K 1 + " I 4.34 216.09 P 5 + 6 220.43 Ca 1 + " I 6.11 214.32 P 5 + 6 220.43 Ga 1 + I 6.00 214.43 P 5 + 6 220.43 Rb 1 + " I 4.18 216.25 P 5 + 6 220.43 Sr 1 + * I 5.70 214.73 P 5 + 6 220.43 Y 1 + I 6.38 214.05 P 5 + 6 220.43 In 1 + I 5.79 214.64 P 5 + 6 220.43 Cs 1 + I 3.89 216.54 P 5 + 6 220.43 Ba 1 + I 5.21 215.22 P 5 + 6 220.43 La 1 + I 5.58 214.85 P 5 + 6 220.43 Ce 1 + I 5.47 214.96 P 5 + 6 220.43 Pr 1 + " I 5.42 215.01 P 5 + 6 220.43 Nd 1 + I 5.49 214.94 P 5 + 6 220.43 Pm 1 + I 5.55 214.88 P 5 + 6 220.43 Sm 1 + I 5.63 214.80 P 5 + 6 220.43 Eu 1 + I 5.67 214.76 P 5 + 6 220.43 Gd 1 + I 6.14 214.29 P 5 + 6 220.43 Tb 1 + I 5.85 214.58 P 5 + 6 220.43 Dy 1 + I 5.93 214.50 P 5 + 6 220.43 Ho 1 + I 6.02 214.41 P 5 + 6 220.43 Er 1 + I 6.10 214.33 P 5 + 6 220.43 Tm 1 + ' I 6.18 214.25 P 5 + 6 220.43 Yb 1 + I 6.25 214.18 P '5 + 6 220.43 Lu 1 + I 5.43 215.00 P 5 + 6 220.43 Tl 1 + I 6.11 214.32 P 5 + 6 220.43 Ra 1 + I 5.28 215.15 P 5 + 6 220.43 Ac 1 + 1 5.20 215.23 P 5 + 6 220.43 Th 1 + 1 6.10 214.33 P 5 + 6 220.43 Pa 1 + I 5.90 . 214.53 P 5 + 6 220.43 U 1 + I 6.05 214.38 P 5 + 6 220.43 Np 1 + I 6.20 214.23 P 5 + 6 220.43 Pu 1 + 6.06 214.37 P 5 + 6 220.43 Am 1 + 5.99 214.44 P 5 + 6 220.43 Cm 1 + 6.02 214.41 P 5 + 6 220.43 Bk 1 + 6.23 214.20 P 5 + 6 220.43 Cf 1 + 6.30 214.13 P 5 + 6 220.43 Es 1 + 6.42 214.01 P 6 + 7 263.22 S 4 + 4 47.30 215.92 P 6 + 7 263.22 K 3 + 3 45.72 217.50 P 6 + 7 263.22 Ti 4 + 4 43.27 219.95 P 6 + 7 263.22 V 4 + 4 46.71 216.51 P 6 + 7 263.22 Cr 4 + 4 49.10 214.12 P 6 + 7 263.22 Ge 4 + 4 45.71 217.51 P 6 + 7 263.22 Se 4 + 4 42.94 220.28 P 6 + 7 263.22 Br 4 + 4 47.30 215.92 P 6 + 7 263.22 Sr 3 + 3 43.60 21 9.62 P 6 + 7 263.22 Mo 4 + 4 46.40 216.82 P 6 + 7 263.22 Sb 4 + 4 44.20 219.02 P 6 + 7 263.22 Eu 4 + 4 42.60 220.62 P 6 + 7 263.22 Gd 4 + 4 44.00 219.22 P 6 + 7 263.22 Ho 4 + 4 42.50 220.72 P 6 + 7 263.22 Er 4 + 4 42.60 220.62 P 6 + 7 263.22 Tm 4 + 4 42.70 220.52 P 6 + 7 263.22 Yb 4 + 4 43.70 219.52 P 6 + 7 263.22 Lu 4 + 4 45.19 218.03 P 6 + 7 263.22 P 4 + 4 42.32 220.90 P 6 + 7 263.22 Bi 4 + 4 45.30 217.92 P 7 + 8 309.41 Ar 6 + 6 91.01 218.40 P 7 + 8 309.41 Sc 5 + 5 91.66 217.75 P 7 + 8 309.41 Cr 6 + 6 90.56 218.85 P 7 + 8 309.41 Mn 6 + 6 95.00 214.41 P 7 + 8 309.41 Ge 5 + 5 93.50 215.91 P 7 + 8 309.41 Br 6 + 6 88.60 220.81 P 7 + 8 309.41 Sr 6 + 6 90.80 218.61 P 7 + 8 309.41 Y 6 + 6 93.00 . 216.41 S 6 + 7 280.93 K 4 + 4 60.91 220.02 S 6 + 7 280.93 V 5 + 5 65.23 215.70 s 6 + 7 280.93 Ga4 + 4 64.00 216.93 s 6 + 7 280.93 As 5 + 5 63.63 217.30 s 6 + 7 280.93 Kr5 + 5 64.70 216.23 s 6 + 7 280.93 Y 4 + 4 61.80 219.13 s 6 + 7 280.93 Mo 5 + 5 61.20 219.73 s 7 + 8 328.23 CI7 + 7 114.19 214.04 s 7 + 8 328.23 Ca6 + 6 108.78 219.45 s 7 + 8 328.23 Sc6 + 6 111.10 217.13 s 7 + 8 328.23 Ni 6 + 6 108.00 220.23 s 7 + 8 328.23 Zn6 + 6 108.00 220.23 s 7 + 8 328.23 Kr7 + 7 111.00 217.23 s 7 + 8 328.23 Sb6 + 6 108.00 220.23 CI7 + 8 348.28 Ca7 + 7 127.70 220.58 CI7 + 8 348.28 Y 6 + 6 128.12 220,16 CI7 + 8 348.28 Co 7 + 7 129.00 219,28 CI7 + 8 348.28 Ni7 + 7 133.00 215.28 CI7 + 8 348.28 Zn7 + 7 134.00 214.28 CI7 + 8 348.28 As 6 + 6 127.60 22068 CI7 + 8 348.28 Y 8 + 8 129:00 21928 n n β 54 (resonance shrinkage energy is given by ^ 27.21 eV; with n = 54, the resonance shrinkage energy is 734.67) Atom n nth Ion¬ Atom n nth Ion¬ Energy Oxidiz¬ ization Reduced ization Hole ed Energy Energy (eV) (eV) (eV) O 6 + 7 739.32 Li 1 + 1 5.39 733.92 F 7 + 8 953.89 Be 4 + 4 217.71 736.17 O 6 + 7 739.32 B 1 + 1 8.30 731.02 O 7 + 8 871.39 O 6 + 6 138.12 733.27 Q 6 + 7 739.32 Na1 + 1 5.14 734.18 O 6 + 7 739.32 Mg1 + 1 7.65 731.67 O 6 + 7 739.32 Al 1 + 1 5.99 733.33 O 6 + 7 739.32 Si 1 + 1 8.15 731.16 O 6 + 7 739.32 K 1 + 1 4.34 734.97 O 6 + 7 739.32 Ca1 + 1 6.11 733.20 6 + 7 739.32 Sc1 + 1 6.54 732.78 6 + 7 739.32 Ti 1 + 1 6.82 732.49 6 + 7 739.32 V 1 + 1 6.74 732.58 6 + 7 739.32 Cr 1 + 1 6.77 732.55 06 + 7 739.32 Mn1 + 1 7.43 731.88 06 + 7 739.32 Fe1 + 1 7.87 731.45 06 + 7 739.32 Co1 + 1 7.86 731.46 06 + 7 739.32 Ni 1 + 1 7.64 731.68 06 + 7 739.32 Cu1 + 1 7.73 731.59 06 + 7 739.32 Ga1 + 1 6.00 733.32 06 + 7 739.32 Ge1 + 1 7.90 731.42 06 + 7 739.32 Rb1 + 1 4.18 735.14 06 + 7 739.32 Sr 1 + 1 5.70 733.62 06 + 7 739.32 Y 1 + 6.38 732.93 06 + 7 739.32 Zr 1 + " 6.84 732.47 06 + 7 739.32 Nb1 + " I 6.88 732.43 06 + 7 739.32 Mo1 + I 7.10 732.22 06 + 7 739.32 Tc 1 + l 7.28 732.03 06 + 7 739.32 Ru1 + 1 7.37 731.95 06 + 7 739.32 Rh1 + 1 7.46 731.85 06 + 7 739.32 Pd1 + 1 8.34 730.97 06 + 7 739.32 Ag 1 + 1 7.58 731.74 06 + 7 739.32 Cd1 + 1 8.99 730.32 06 + 7 739.32 In 1 + 1 5.79 733.53 06 + 7 739.32 Sn1 + 1 7.34 731.97 O 6 + 7 739.32 Sb1 + 1 8.64 730.67 06 + 7 739.32 Te1 + 1 9.01 730.31 06 + 7 739.32 Cs1 + 1 3.89 735.42 06 + 7 739.32 . Ba1 + 1 5.21 734.10 06 + 7 739.32 La1 + 1 5.58 733.74 06 + 7 739.32 Ce1 + 1 5.47 733.85 06 + 7 739.32 Pr 1 + 1 5.42 733.89 06 + 7 739.32 Nd1 + 1 5.49 733.83 06 + 7 739.32 Pm 1 + 1 5.55 733.76 06 + 7 739.32 Sm 1 + 1 5.63 733.68 06 + 7 739.32 Eu1 + 1 5.67 733.65 06 + 7 739.32 Gd1+ 1 6.14 733.17 06 + 7 739.32 Tb1 + 1 5.85 733.47 O 6 + 7 739.32 Dy 1 + 1 5.93 733.39 06 + 7 739.32 Ho1 + 1 6.02 733.29 06 + 7 739.32 Er1 + 1 6.10 733.22 06 + 7 739.32 Tm 1 + 1 I 6.18 733.13 06 + 7 739.32 Yb1+ " I 6.25 733.06 06 + 7 739.32 Lu1 + ' 5.43 733.89 06 + 7 739.32 Hf 1 + ' I 6.60 732.72 06 + 7 739.32 Ta1 + ' I 7.89 731.42 06 + 7 739.32 W 1 + • I 7.98 731.34 O 6 + 7 739.32 Re1 + ■ I 7.88 731.43 06 + 7 739.32 Os1 + I 8.70 730.61 06 + 7 739.32 Ir 1 + I 9.10 730.22 06 + 7 739.32 Pt 1 + I 9.00 730.32 06 + 7 739.32 Au 1 + I 9.23 730.09 06 + 7 739.32 Tl 1 + I 6.11 733.21 06 + 7 739.32 Pb1 + l 7.42 731.90 06 + 7 739.32 Bi 1 + l 7.29 732.03 06 + 7 739.32 Po1 + l 8.42 730.90 O 6 + 7 739.32 Ra1 + 1 5.28 734.04 06 + 7 739.32 Ac1 + 1 5.20 734.11 06 + 7 739.32 Th 1 + 1 6.10 733.22 06 + 7 739.32 Pa1 + 1 5.90 733.41 06 + 7 739.32 U 1 + 1 6.05 733.27 0.6 + 7 739.32 Np1 + 1 6.20 . 733.11 06 + 7 739.32 Pu1 + 1 6.06 733.26 06 + 7 739.32 Am 1 + 1 5.99 733.33 06 + 7 739.32 Cm 1 + 1 6.02 733.29 06 + 7 739.32 Bk1 + 1 6.23 733.09 O 6 + 7 739.32 Cf 1 + 1 6.30 733.02 O 6 + 7 739.32 Es1 + 1 6.42 732.90 O 7 + 8, 871.39 0,6 + 5 , 138.12 733.27 O 7 + 8 871.39 Na5 + 5 138.3,9 . 733.00 O 7 + 8 871.39 Mg5 + 5 141.26 730.13 O 7 + 8 871.39 Sc7 + 7 138.00 733.39 0 7 + 8 871 .39 Ti 7 + 7 140.80 730.59 0 7 + 8 871 .39 Cu 7 + 7 139.00 732.39 0 7 + 8 871 .39 Zn 7 + 7 134.00 737.39 0 7 + 8 871 .39 Rb 8 + 8 136.00 735.39 0 7 + 8 871 .39 Te 7 + 7 137.00 734.39 F 7 + 8 953.89 P 6 + 6 220.43 733.46 Two-ion coupl es ( capable of producing energy holes for shrinking deuterium atoms nvolving cations and anions 5. The number in the colun following the i on, (n), is the nth ionization energy of the atom. For example, Ga 2+ + 30.71 eV = Ga 3+ + e " and H + e " = H- + 3.08 eV r Atom n nth Ion¬ Atom n nth Ion¬ Energy Oxidiz¬ ization Reduced ization Hole ed Energy Energy (eV) (eV) (eV) As 2 + 3 28.35 H 0.80 27.55 Ru 2 + 3 28.47 H 0.80 27.67 In 2 + 3 28.03 H 0.80 27.23 Te 2 + 3 27.96 H 0.80 27.16 Al 2 + 3 28.45 H 0.80 27.65 Ar 1 + 2 27.63 H 0.80 26.83 As 2 + 3 28.35 Li 0.61 27.74 Ru 2 + 3 28.47 Li I 0.61 27.86 In 2 + 3 28.03 Li I 0.61 27.42 Te 2 + 3 27.96 Li I 0.61 27.35 Al 2 + 3 28.45 Li I 0.61 27.84 Ar 1 + 2 27.63 L i l 0.61 27.02 Ti 2 + 3 27.49 L i - 1 0.61 26.88 As 2 + 3 28.35 B - l 0.30 28.05 Rb 1 + 2 27.28 . B - 1 0.30 26.98 Mo 2 + 3 27 16 B - 1 0.30 26.86 Ru 2 + 3 28.47 B - 1 0.30 28.17 In 2 + 3 28.03 B - 1 0.30 27.73 Te 2 + 3 27.96 B - 1 0.30 27.66 Al 2 + 3 28.45 B - 1 0.30 28.15 Ar 1 + 2 27.63 B - 1 0.30 27.33 Ti 2 + 3 27.49 B . 1 0.30 27.19 As 2 + 3 28.35 C I 1.12 27.23 Tc2 + 3 29.54 C I 1.12 28.42 Ru2 + 3 28.47 C I 1.12 27.35 In 2 + 3 28.03 C I 1.12 26.91 Te2 + 3 27.96 C I 1.12 26.84 N 1 + 2 29.60 C I 1.12 28.48 Al 2 + 3 28.45 C I 1.12 27.33 V 2 + 3 29.31 C I 1.12 28.19 As 2 + 3 28.35 0 I 147 26.89 Tc2 + 3 29.54 0 1 1.47 28.07 Ru2 + 3 28.47 O l 1.47 27.00 Tl 2 + 3 29.83 0 I 1.47 28.36 N 1 + 2 29.60 0 I 1.47 28.14 Al 2 + 3 28.45 0 I 1.47 26.98 V 2 + 3 29.31 O I 1.47 27.84 Ga2 + 3 30.71 F I 3.45 27.26 Se2 + 3 30.82 F l 3.45 27.37 Rh2 + 3 31.06 F I 3.45 27.61 Sn2 + 3 30.50 F I 3.45 27.05 Pb2 + 3 31.94 F I 3.45 28.49 K 1 + 2 31.63 F 1 3.45 28.18 Cr2 + 3 30.96 F 1 3.45 27.51 Fe2 3 30.65 F 1 3.45 27.20 As 2 + 3 28.35 Na I 0.52 27.83 Ru2 + 3 28.47 Na 1 0.52 27.95 In 2 + 3 28.03 Na 1 0.52 27.51 Te2 + 3 27.96 Na 1 0.52 27.44 Al 2 + 3 28.45 Na 1 0.52 27.93 Ar 1 + 2 27.63 . Na I 0.52 27.11 Ti 2 + 3 27.49 Na 1 0.52 26.97 As 2 + 3 28.35 Al 1 0.52 27.83 Ru2 + 3 28.47 Al 1 0.52 27.95 In 2 + 3 28.03 Al 1 0.52 27.51 Te2 + 3 27.96 Al 1 0.52 27.44 Al 2 + 3 28.45 Al 1 0.52 27.93 Ar 1 + 2 27.63 Al 1 0.52 27.11 Ti 2 + 3 27.49 Al -1 0.52 26.97 As 2 + 3 28.35 Si -1 1.39 26.96 Tc2 + 3 29.54 Si -1 1.39 28.15 Ru2 + 3 28.47 Si -1 1.39 27.08 Tl 2 + 3 29.83 Si -1 1.39 28.44 N 1 + 2 29.60 Si -1 1.39 28.21 Al 2 + 3 28.45 Si -1 1.39 27.06 V 2 + 3 29.31 Si -1 1.39 27.92 As 2 + 3 28.35 P -1 0.78 27.57 Ru2 + 3 28.47 P -1 0.78 27.69 In 2 + 3 28.03 p - ■ > 0.78 27.25 Te2 + 3 27.96 P 0.78 27.18 Al 2 + 3 28.45 P 0.78 27.67 Ar 1 + 2 27.63 P 0.78 26.85 Tc2 + 3 29.54 S I 2.07 27.47 Sn2 + 3 30.50 S I 2.07 28.43 Tl 2 + 3 29.83 S I 2.07 27.76 N 1 + 2 29.60 S I 2.07 27.53 P 2 + 3 30.18 S I 2.07 28.11 V 2 + 3 29.31 S I 2.07 27.24 Ga2 + 3 30.71 Cl I 3.61 27.10 Se2 + 3 30.82 Cl I 3.61 27.21 Rh2 + 3 31.06 Cl 1 3.61 27.45 Sn2 + 3 30.50 Cl 1 3.61 26.89 Xe2 + 3 32.10 Cl 1 3.61 28.49 Pb2 + 3 31.94 Cl 1 3.61 . 28.32 K 1 + 2 31.63 Cl 1 3.61 28.01 Cr2 + 3 30.96 Cl 1 3.61 27.35 Fe2 + 3 30.65 Cl 1 3.61 27.04 As 2 + 3 28.35 K 1 0.69 27.66 Ru2 + 3 28.47 K 1 0.69 27.78 In 2 + 3 28.03 K 1 0.69 27.34 Te2 + 3 27.96 K 1 0.69 27.27 Al 2 + 3 28.45 K 1 0.69 27.75 Ar 1 + 2 27.63 K 1 0.69 26.93 As 2 + 3 28.35 Fe 1 0.56 27.79 Ru 2 + 3 28.47 Fe I 0.56 27.91 In 2 + 3 28.03 Fe I 0.56 27.47 Te 2 + 3 27.96 Fe I 0.56 27.40 Al 2 + 3 28.45 Fe I 0.56 27.89 Ar 1 + 2 27.63 Fe I 0.56 27.07 Ti 2 + 3 27.49 Fe I 0.56 26.93 As 2 + 3 28.35 Co I 0.95 27.40 Ru 2 + 3 28.47 Co I 0.95 27.52 In 2 + 3 28.03 Co I 0.95 27.08 Te 2 + 3 27.96 Co I 0.95 27.01 Al 2 + 3 28.45 Co I 0.95 27.49 V 2 + 3 29.31 Co I 0.95 28.36 Tc 2 + 3 29.54 Cu I 1.82 27.72 Tl 2 + 3 29.83 Cu I 1.82 28.01 N 1 + 2 29.60 Cu l 1.82 27.78 P 2 + 3 30.18 Cu I 1.82 28.36 V 2 + 3 29.31 Cu I 1.82 27.49 Ga 2 + 3 30.71 Br I 3.36 27.35 Se 2 + 3 30.82 Br I 3.36 27.46 Rh 2 + 3 31 .06 Br I 3.36 27.70 Sn 2 + 3 30.50 Br I 3.36 27.14 P 2 + 3 30.18 Br I 3.36 26.82 K 1 + 2 31 .63 Br I 3.36 28.26 Cr 2 + 3 30.96 Br I 3.36 27.60 Fe 2 + 3 30.65 Br I 3.36 27.29 As 2 + 3 28.35 Rb I 0.30 28.05 Rb 1 + 2 27.28 Rb I 0.30 26.98 Mo 2 + 3 27.16 Rb I 0.30 26.86 Ru 2 + 3 28.47 . Rb I 0.30 28.17 In 2 + 3 28.03 Rb I 0.30 27.73 Te 2 + 3 27.96 Rb I 0.30 27.66 Al 2 + 3 28.45 Rb I 0.30 28.15 Ar 1 + 2 27.63 Rb I 0.30 27.33 Ti 2 + 3 27.49 Rb I 0.30 27.19 Ga 2 + 3 30.71 I I 3.06 27.65 Se 2 + 3 30.82 I I 3.06 27.76 Rh 2 + 3 31 .06 1 3.06 28.00 Sn 2 + 3 30.50 1 3.06 27.44 P 2 + 3 30.18 1 3.06 27.12 Cr 2 + 3 30.96 1 3.06 27.90 Fe 2 + 3 30.65 1 3.06 27.59 As 2 + 3 28.35 Cs 1 0.30 28.05 Rb 1 + 2 27.28 Cs 1 0.30 26.98 Mo 2 + 3 27.16 Cs 1 0.30 26.86 Ru 2 + 3 28.47 Cs 1 0.30 28.17 In 2 + 3 28.03 Cs 1 0.30 27.73 Te 2 + 3 27.96 Cs 1 0.30 27.66 Al 2 + 3 28.45 Cs 1 0.30 28.15 Ar 1 + 2 27.63 Cs 1 0.30 27.33 Ti 2 + 3 27.49 Cs 1 0.30 27.19 Tc 2 + 3 29.54 Se 1 170 27.84 Tl 2 + 3 29.83 Se 1 1.70 28.13 N 1 + 2 29.60 Se 1 1.70 27.90 P 2 + 3 30.18 Se 1 1.70 28.48 V 2 + 3 29.31 Se 1 1.70 27.61 Tc 2 + 3 29.54 Te 1 2.20 27.34 Sn 2 + 3 30.50 Te 1 2.20 28.30 Tl 2 + 3 29.83 Te 1 2.20 27.63 N 1 + 2 29.60 Te 1 2.20 27.40 P 2 + 3 30.18 Te 1 2.20 27.98 V 2 + 3 29.31 Te 1 2.20 27.11 Fe 2 + 3 30.65 Te 1 2.20 28.45 As 2 + 3 28.35 As 1 0.60 27.75 Ru 2 + 3 28.47 As 1 0.60 27.87 In 2 + 3 28.03 As 1 0.60 27.43 Te 2 + 3 27.96 As 1 0.60 27.36 Al 2 + 3 28.45 As 1 0.60 27.85 Ar 1 + 2 27.63 As 1 0.60 27.03 Ti 2 + 3 27.49 As 1 0.60 26.89 Tc 2 + 3 29.54 Sb 1 2.00 27.54 TI 2 + 3 29.83 Sb 1 2.00 27.83 N 1 + 2 29.60 Sb 1 2.00 27.60 P 2 + 3 30.18 Sb J 2.00 28.18 V 2 + 3 29.31 Sb 1 2.00 27.31 As 2 + 3 28.35 Bi I 0.70 27.65 Ru 2 + 3 28.47 Bi I 0.70 27.77 In 2 + 3 28.03 Bi I 0.70 27.33 Te 2 + 3 27.96 Bi 1 0.70 27.26 Al 2 + 3 28.45 Bi i 0.70 27.75 Ar 1 + 2 27.63 Bi 1 0.70 26.93 Tc 2 + 3 29.54 T l 1 2.10 27.44 Sn 2 + 3 - 30.50 T l I 2.10 28.40 Tl 2 + 3 29.83 T l I 2.10 27.73 N 1 + 2 29.60 T l l 2.10 27.50 P 2 + 3 30.18 T l I 2.10 28.08 V 2 + 3 29.31 T l I 2.10 27.21 Tc 2 + 3 29.54 Au 1 2.10 27.44 Sn 2 + 3 30.50 Au I 2.10 28.40 Tl 2 + 3 29.83 Au I 2.10 27.73 N 1 + 2 29.60 Au I 2.10 27.50 P 2 + 3 30.18 Au J 2.10 28.08 V 2 + 3 29.31 Au I 2.10 27.21 As 2 + 3 28.35 Hg I 154 26.81 Tc 2 + 3 29.54 Hg 1 1.54 28.00 Ru 2 + 3 28.47 Hg I 1.54 26.93 Tl 2 + 3 29.83 Hg I 1.54 28.29 N 1 + 2 29.60 Hg I 1.54 28.06 Al 2 + 3 28.45 Hg I 1.54 26.91 V 2 + 3 29.31 Hg I 1.54 27.77 As 2 + 3 28.35 As I 0.60 27.75 Ru 2 + 3 28.47 . As I 0.60 27.87 In 2 + 3 28.03 As I 0.60 27.43 Te 2 + 3 27.96 As I 0.60 27.36 Al 2 + 3 28.45 As I 0.60 27.85 Ar 1 + 2 27.63 As I 0.60 27.03 TI 2 + 3 27.49 As I 0.60 . 26.89 As 2 + 3 28.35 Ce I 120 27.15 Tc 2 + 3 29.54 Ce 1 1.20 28.34 Ru 2 + 3 28.47 Ce 1.20 27.27 In 2 + 3 28.03 Ce I 1.20 26.83 N 1 + 2 29.60 Ce I 1.20 28.40 Al 2 + 3 28.45 Ce I 1.20 27.25 V 2 + 3 29.31 Ce I 1.20 28.1 1 As 2 + 3 28.35 Fr I 0.46 27.89 Rb 1 + 2 27.28 Fr I 0.46 26.82 Ru 2 + 3 28.47 Fr I 0.46 28.01 In 2 + 3 28.03 Fr I 0.46 27.57 Te 2 + 3 27.96 Fr I 0.46 27.50 Al 2 + 3 28.45 Fr I 0.46 27.99 Ar 1 + 2 27.63 Fr I 0.46 27.17 Ti 2 + 3 27.49 Fr I 0.46 27.03 As 2 + 3 28.35 Ge I 1.20 27.15 Tc 2 + 3 29.54 Ge I 1.20 28.34 Ru 2 + 3 28.47 Ge I 1.20 27.27 In 2 + 3 28.03 Ge I 1.20 26.83 N 1 + 2 29.60 Ge I 1.20 28.40 Al 2 + 3 28.45 Ge I 1.20 27.25 V 2 + 3 29.31 Ge I 1.20 28.1 1 As 2 + 3 28.35 Sn I 1.25 27.10 Tc 2 + 3 29.54 Sn I 1.25 28.29 Ru 2 + 3 28.47 Sn I 1.25 27.22 N 1 + 2 29.60 Sn I 1.25 28.35 Al 2 + 3 28.45 Sn I 1.25 27.20 V 2 + 3 29.31 Sn 1 125 28.06 As 2 + 3 28.35 Pb I 1.05 27.30 Tc 2 + 3 29.54 Pb 1 1.05 28.49 Ru 2 + 3 28.47 Pb 1 105 27.42 In 2 + 3 28.03 Pb 1 105 26.98 Te 2 + 3 27.96 Pb 1 1.05 26.91 Al 2 + 3 28.45 Pb 1 1.05 27.40 V 2 + 3 29.31 Pb 1 1.05 28.26 Tc 2 + 3 29.54 Po 1 1.80 . 27.74 Tl 2 + 3 29.83 Po 1 1.80 28.03 N 1 + 2 29.60 Po 1 180 27.80 P 2 + 3 30.18 Po I 180 28.38 V 2 + 3 29.31 Po 1 1.80 27.51 Ga2 + 3 30.71 At I 2.80 27.91 Se2 + 3 30.82 At I 2.80 28.02 Rh2 + 3 31.06 At I 2.80 28.26 Sn2 + 3 30.50 At I 2.80 27.70 Tl 2 + 3 29.83 At I 2.80 27.03 N 1 + 2 29.60 At I 2.80 26.80 P 2 + 3 30.18 At I 2.80 27.38 Cr2 + 3 30.96 At I 2.80 28.16 Fe2 + 3 30.65 At I 2.80 27.85 As 2 + 3 28.35 Ge I 1.20 27.15 Tc2 + 3 29.54 Ge I 1.20 28.34 Ru2 + 3 28.47 Ge I 1.20 27.27 In 2 + 3 28.03 Ge I 1.20 26.83 N 1 + 2 29.60 Ge I 1.20 28.40 Al 2 + 3 28.45 Ge I 120 27.25 V 2 + 3 29.31 Ge 1 1.20 28.11 As 2 + 3 28.35 Ga I 0.37 27.98 Rb1 + 2 27.28 Ga I 0.37 26.91 Ru2 + 3 28.47 Ga I 0.37 28.10 In 2 + 3 28.03 Ga I 0.37 27.66 Te2 + 3 27.96 Ga I 0.37 27.59 Al 2 + 3 28.45 Ga I 0.37 28.08 Ar 1 + 2 27.63 Ga I 0.37 27.26 Ti 2 + 3 27.49 Ga - ■ I 0.37 27.12 As 2 + 3 28.35 In I 0.35 28.00 Rb1 + 2 27.28 In I 0.35 26.93 Mo 2 + 3 27.16 In I 0.35 26.81 Ru2 + 3 28.47 in I 0.35 28.12 In 2 + 3 * 28.03 _n " * I 0.35 27.68 Te 2 + ' 3 27.96 ' In " " I 0.35 27.61 Al 2 + 3 28.45 In - ■ I 0.35 28.10 ■ y. :'- AMV 2 27.63 In " ' - ' I 0.35 . 27.28 Ti 2 + 3 27.49 In 1 0.35 27.14 As 2 + 3 28.35 Ag 1 1.30 27.05 Tc 2 + 3 29.54 Ag 130 28.24 Ru 2 + 3 28.47 Ag 1.30 27.17 N 1 + 2 29.60 Ag 130 28.30 Al 2 + 3 28.45 Ag 1.30 27.15 V 2 + 3 29.31 Ag 1.30 28.01 Cations and anions with n = 16 (resonance shrinkage energy is given by 2 27.21 ; with n = 16, the resonance shrinkage energy is 217.68) Atom nth Ion¬ Atom n nth Ion¬ Energy Oxidiz¬ ization Reduced ization Hole ed Energy Energy (eV) (eV) (eV) Be 3 + 4 217.71 H 0.80 216.91 Be3+ 4 217.71 Li 0.61 217.10 Be3+ 4 217.71 B 0.30 217.41 Be3 + 4 217.71 C 1.12 216.59 Be3 + 4 217.71 O 1.47 216.25 P 5+ 6 220.43 O 1.47 218.96 P 5+ 6 220.43 F 3.45 216.98 Be3 + 4 217.71 Na 0.52 217.19 Be3+ 4 217.71 A l 0.52 217.19 Be3 + 4 217.71 Si 1.39 216.32 Be 3 + 4 217.71 P 0.78 216.94 Be3+ 4 217.71 S 2.07 215.64 P 5+ 6 220.43 S ; 2.07 218.36 P 5+ 6 220.43 Cl 3.61 216.82 Be3+ 4 217.71 K 0.69 217.02 Be3+ 4 217.71 Fe 0.56 217.15 Be3 + 4 217.71 Co 0.95 216.76 Be3 + 4 217.71 Cu 1.82 215.89 P 5+ 6 220.43 Cu 182 218.61 P 5+ 6 220.43 Br 3.36 217.07 Be3+ 4 217.71 Rb 0.30 217.41 P 5+ 6 220.43 I 3.06 . 217.37 Be3 + 4 217.71 Cs 0.30 217.41 Be3 + 4 217.71 Se 1.70 216.01 CM CM __ vo en o 0 ed Energy Energy (eV) (eV) (eV) 06+ 7 739.32 H -1 0.80 738.52 06+ 7 739.32 Li -1 0.61 738.70 06+ 7 739.32 C -1 1.12 738.20 06+ 7 739.32 O -1 1.47 737.85 06+ 7 739.32 F -1 3.45 735.87 06+ 7 739.32 Na -1 0.52 738.80 06+ 7 739.32 Al -1 0.52 738.80 06+ 7 739.32 Si -1 1.39 737.93 06+ 7 739.32 P -1 0.78 738.54 06+ 7 739.32 S -1 2.07 737.24 06+ 7 739.32 Cl 3.61 735.70 O 6+ 7 739.32 K I 0.69 738.62 06+ 7 739.32 Fe 0.56 738.76 06+ 7 739.32 Co I 0.95 738.36 06+ 7 739.32 Cu I 1.82 737.49 06+ 7 739.32 Br I 3.36 735.95 O 6+ 7 739.32 1 I 3.06 736.25 06+ 7 739.32 Se I 1.70 737.61 O 6+ 7 739.32 Te 1 2.20 737.11 06+ 7 739.32 As 1 0.60 738.72 06+ 7 739.32 Sb 1 2.00 737.32 06+ 7 739.32 Bi 1 0.70 738.61 06+ 7 739.32 Tl 1 2.10 737.22 06+ 7 739.32 Au 1 2.10 737.22 06+ 7 739.32 Hg 1 1.54 737.78 O 6+ 7 739.32 As 1 0.60 738.72 O 6+ 7 739.32 Ce 1 1.20 738.11 O 6+ 7 739.32 Fr 1 0.46 738.85 O 6+ 7 739.32 Ge 1 1.20 738.11 O 6+ 7 739.32 Sn 1 125 738.07 O 6+ 7 739.32 Pb 1 1.05 736.27 O 6+ 7 739.32 Po 1 1.80 737.52 O 6+ 7 739.32 At 1 2.80 736.52 O 6+ 7 739.32 Ge 1 1.20 738.11 0 6 + 7 739.32 Ga - 1 0.37 738.95 0 6 + 7 739.32 In - 1 0.35 738.97 « 0 6 + 7 739.32 Ag - 1 1.30 738.02 Some representative couples comprising a cation and a molecule capable of producing energy holes for shrinking deuterium atoms where the molecule is reduced. The number in the column following the ion or molecule, (n), is the nth ionization energy of the atom or molecule. For example, Ga 2 + + 30.71 eV - Ga 3+ + e~ and BF3 + e" - BF3 + 2.65 eV. Atom n nth Ion¬ Atom n nth Ion¬ Energy Oxidiz¬ ization Reduced ization Hole ed Energy Energy (eV) ., (eV) (eV) Ga 2 + 3 30.71 BF3 I 2.65 28.06 Se 2 + 3 30.82 BF 3 I 2.65 28.17 Tc 2 + 3 29.54 BF3 I 2.65 26.89 Rh 2 + 3 31.06 BF 3 I 2.65 28.41 Sn 2 + 3 30.50 BF3 I 2.65 27.85 Tl 2 + 3 29.83 BF 3 I 2.65 27.18 N 1 + 2 29.60 BF3 I 2.65 26.95 P 2 + 3 30.18 BF 3 I 2.65 27.53 Cr 2 + 3 30,96 BF3 I 2.65 28.31 Fe 2 + 3 30.65 BF 3 I 2.65 28.00 Se 2 + 3 30_82 NO2 I 3.91 26.91 Rh 2 + 3 31 .06 NO2 I 3.91 27.15 Xe 2 + 3 32.10 NO2 I 3.91 28.19 Pb 2 + . 3 31.94 NO2 I 3.91 28.03 K 1 + 2 31.63 NO2 I 3.91 27.72 Cr 2 + 3 30.96 Nθ2 I 3.91 27.05 As 2 + 3 28.35 02 I 0.45 27.90 Rb 1 + 2 27.28 02 I 0.45 26.83 Ru 2 + 3 28.47 02 I 0.45 28.02 In 2 + . 3 28.03 θ2 1 0.45 27.58 Te 2 + 3 27.96 θ2 ' 1 0.45 27.51 Al 2 + 3 28.45 02 1 0.45 28.00 Ar 1 + 2 27.63 θ2 1 0.45 27.18 Ti 2 + 3 27,49 θ2 1 0.45 27.04 As 2 + 3 28.35 SF6 -1 143 26.92 Tc2 + 3 29.54 SF6 -1 1.43 28.11 Ru2 + 3 28.47 SF6 -1 1.43 27.04 Tl 2 + 3 29.83 SFβ -1 1.43 28.40 N 1 + 2 29.60 SF6 -1 1.43 28.17 Al 2 + 3 28.45 SFβ -1 1.43 27.02 V 2 + 3 29.31 SF6 -1 1.43 27.88 Ga2 + 3 30.71 WF6 -1 2.74 27.97 Se2 + 3 30.82 WF6 -1 2.74 28.08 Tc2 + 3 29.54 WF6 -1 2.74 26.80 Rh2 + 3 31.06 WF6 -1 2.74 28.32 Sn2 + 3 30.50 WF6 -1 2.74 27.76 Tl 2 + 3 29.83 WF6 -1 2.74 27.09 N 1 + 2 29.60 WFβ -1 2.74 26.86 P 2 + 3 30.18 WF6 2.74 27.44 Cr2 + 3 30.96 WF6 2.74 28.22 Fe2 + 3 30.65 WF6 I 2.74 27.91 Ga2 + 3 30.71 UF6 I 2.91 27.80 Se2 + 3 30.82 UF6 I 2.91 27.91 Rh2 + 3 31.06 UF6 I 2.91 28.15 Sn2 + 3 30.50 UFβ 1 2.91 27.59 Tl 2 + 3 29.83 UF6 1 2.91 26.92 P 2 + 3 30.18 UF6 1 2.91 27.27 Cr2 + 3 30.96 UF6 1 2.91 28.05 Fe2 + 3 30.65 UF6 1 2.91 27.74 Tc2 + 3 29.54 CF 3 1 1.85 27.69 Tl 2 + 3 29.83 CF 3 1 1.85 27.98 N 1 + 2 29.60 CF 3 1 1.85 27.75 P 2 + 3 30.18 CF 3 1 1.85 28.33 V 2 + 3 29.31 CF 3 1 1.85 27.46 As 2 + 3 28.35 CCI3 1 1.22 27.13 Tc2 + 3 29.54 CCI3 1 1.22 28.32 Ru2 + 3 -28.47 CCI3 1 1.22 27.25 In 2 + 3 28.03 CCI3 1 1.22 26.81 N 1 + 2 29.60 CCI3 1 1.22 28.38 Al 2 + 3 28.45 CCI3 1 1.22 27.23 V 2 + 3 29.31 CCI3 - 1 1.22 28.09 Ga2 + 3 30.71 SiF3 - 1 3.35 27.36 Se2 + 3 30.82 SiF3 - 1 3.35 27.47 Rh2 + 3 31.06 SiF3 - 1 3.35 27.71 Sn2 + 3 30.50 SiF3 - 1 3.35 27.15 P 2 + 3 30.18 SiF3 - 1 3.35 26.83 K 1 + 2 31.63 SiF3 - 1 3.35 28.27 Cr2 + 3 30.96 SiF3 - 1 3.35 27.61 Fe2 + 3 30.65 SiF3 - 1 3.35 27.30 As 2 + 3 28.35 NH2 -1 1.12 27.23 Tc2 + 3 29.54 NH2 1.12 28.42 Ru2 + 3 28.47 NH2 - 1 1.12 27.35 In 2 + 3 28.03 NH2 I 1.12 26.91 Te2 + 3 27.96 NH2 1.12 26.84 N 1 + 2 29.60 NH2 1.12 28.48 Al 2 + 3 28.45 NH2 I 112 27.33 V 2 + 3 29.31 NH2 I 1.12 28.19 Tc2 + 3 29.54 PH2 I 1.60 27.94 Ru2 + 3 _ 28.47 PH2 I 1.60 26.87 Tl 2 + 3 29.83 PH2 I 1.60 28.23 N 1 + 2 ~ 29.60 PH2 I 1.60 28.00 Al 2 + 3 28.45 PH2 I 1.60 26.85 V 2 + 3 29.31 PH2 I 1.60 27.71 Tc2 + 3 29.54 CH I 1.83 27.71 TI2 + 3 29.83 CH I 1.83 28.00 N 1 + 2 29.60 CH I 1.83 27.77 P 2 + 3 30.18 CH 1 1.83 28.35 V 2 + 3 29.31 CH I 1.83 27.48 Tc2 + 3 29.54 SH l 2.19 27.35 Sn2 + 3 30.50 SH 1 2.19 28.31 Tl 2 + 3 29.83 SH 1 2.19 27.64 N 1 + 2 29.60 SH 1 2.19 27.41 ,p 2 + ~ 3 30.18 - SH . s - 2.19 27.99 V 2 + 3 29.31 SH 1 2.19 27.12 Fe2 + 3 30.65 SH 1 .2.19 28.46 Ga2 + 3 30.71 CN 1 3.17 27.54 Se2 + 3 30.82 CN -1 3.17 27.65 Rh2 + 3 31.06 CN -1 3.17 27.89 Sn2 + 3 30.50 CN -1 3.17 27.33 P 2 + 3 30.18 CN -1 3.17 27.01 K 1 + 2 31.63 CN -1 3.17 28.45 Cr2 + 3 30.96 CN -1 3.17 27.79 Fe2 + 3 30.65 CN -1 3.17 27.48 Tc2 + 3 29.54 SCN -1 2.17 27.37 Sn2 + 3 30.50 SCN -1 2.17 28.33 Tl 2 + 3 29.83 SCN -1 2.17 27.66 N 1 + 2 29.60 SCN -1 2.17 27.43 P 2 + 3 30.18 SCN 2.17 28.01 V 2 + 3 29.31 SCN 2.17 27.14 Fe2 + 3 30.65 SCN I 2.17 28.48 Ga2 + 3 30.71 SeCN I 2.64 28.07 Se2 + 3 30.82 SeCN I 2.64 28.18 Tc2 + 3 29.54 SeCN I 2.64 26.90 Rh2 + 3 31.06 SeCN I 2.64 28.42 Sn2 + 3 30.50 SeCN l 2.64 27.86 Tl 2 + 3 29.83 SeCN 1 2.64 27.19 N 1 + 2 29.60 SeCN 1 2.64 26.96 P 2 + 3 30.18 SeCN 1 2.64 27.54 Cr2 + 3 30.96 SeCN 1 2.64 28.32 Fe2 + 3 30.65 SeCN 1 2.64 28.01 s and molecular anions with n ■ 16 (reso nance shrinkag 3 energy is by jjj- 27.21 with n - 16, the resonance sh rinkage energy is 217.68) Atom n nth Ion¬ Atom n nth Ion¬ Energy Oxidiz¬ ization Reduced ization Hole ed Energy Energy (eV) (eV) (eV) P 5 + 6 220.43 BF3 1 2.65 217.78 P 5 + 6 220.43 Nθ2 1 , 3.91 216.52 Be 3 + 4 217.71 02 1 0.45 217.26 P 5 + 6 220.43 02 1 0.45 219.98 Be 3 + 4 217.71 SF6 1 1.43 216.28 P 5 + 6 220.43 SF6 1.43 219.00 P 5 + 6 220.43 WF6 2.74 217.69 P 5 + 6 220.43 UF6 I 2.91 217.52 P 5 + 6 220.43 CF3 I 1.85 218.58 Be 3 + 4 217.71 CCI3 I 1.22 216.49 P 5 + 6 220.43 CCI3 I 122 219.21 P 5 + 6 220.43 SiF3 1 3.35 217.08 Be 3 + 4 217.71 NH2 1 1.12 216.59 P 5 + 6 220.43 NH2 I 1.12 219.31 Be 3 + 4 217.71 PH2 I 1.60 216.1 1 P 5 + 6 220.43 PH2 I 1.60 218.83 P 5 + 6 220.43 CH I 1.83 218.60 P 5 + 6 220.43 SH l 2.19 218.24 P 5 + 6 220.43 CN 1 3.17 217.26 P 5 + 6 220.43 SCN 1 2.17 218.26 P 5 + 6 220.43 SeCN 1 2.64 217.79 Cations and molecular anions with n 54 (resonance shrinkage energy is given by 27.21 with n = 54, the resonance shrinkage energy is 734.67) Atom n nth Ion¬ Atom nth Ion¬ Energy Oxidiz¬ ization Reduced ization Hole ed Energy Energy (eV) (eV) (eV) O 6 + 7 739.32 BF3 2.65 736.66 O 6 + 7 739.32 NO2 3.91 735.41 0 6 + 7 739.32 02 0.45 738.86 0 6 + 7 739.32 SF6 1.43 737.89 O 6 + 7 739.32 WF6 2.74 736.58 O 6 + 7 739.32 UF6 2.91 736.41 0 6 + 7 739.32 CF3 1.85 737.47 0 6 + 7 739.32 CCI3 1.22 738.10 O 6 + 7 739.32 SiF3 3.35 735.97 O 6 + 7 739.32 NH2 1.12 . 738.20 O 6 + 7 739.32 PH2 1.60 737.72 O 6 + 7 739.32 CH 1.83 737.48 O 6 + 7 739.32 SH 2.19 737.13 0 6 + 7 739.32 CN - 1 3.17 736.15 0 6 + 7 739.32 SCN - 1 2.17 737.15 0 6 + 7 739.32 SeCN - 1 2.64 736.67 The fusion of deuterium to 3 He releases neutron which can effect the fusion of 6lJ to helium. In one embodiment of Coulombic Annihilation Fusion, 6|_i is present in the fusion reaction mixture of deuterium where fusion of deuterium further drives the fusion of 6|_i. Other atoms in addition to deuterium can be caused to fuse by Coulombic Annihilation as described for deuterium. The quantum of energy hole is calculated for the atoms involved and a reaction or process which removes this much energy and regenerates the atoms or molecules to be fused is effected until sufficient energy is removed from the Mills orbitals so that the internuclear distance is sufficient for the nuclear strong force to dominate the coulombic repulsive force. Fusion then occurs. Fusion Reactor The fusion reactor 50, shown in Figure 6 comprises a vessel 52 which contains the fusion reaction mixture 54, a heat exchanger 60, and a steam generator 62 where the heat exchanger 60 absorbs heat released by CAF and exchanges it with the steam generator 62 which absorbs heat from the exchanger 60 and produces steam. The fusion reactor 50 further comprises a turbine 70 which receives steam from the steam generator 62 and supplies mechanical power to a power generator 80 which converts the steam energy into electrical energy, which is received by a load 90 to produce work or for dissipation. The fusion reaction mixture 54 comprises a source of deuterium atoms 56 or a source of molecular deuterium, and a source of energy holes 58 which resonantly remove 27.21 eV ; n = 2, 3, 4,..., of energy from deuterium to effect shrinkage to the point of fusion. The source of deuterium can be deuterium gas, electrolysis of deuterium oxide, deuterium from hydrides, or deuterium from metal-deuterium solutions. A source of energy holes comprises a catalytic energy hole material 58, typically comprising electrochemical couples including the catalytic couples described in the Coulombic Annihilation Fusion Section. Thus, an exemplary fusion reaction mixture is molecular deuterium a salt of Pd 2 + and a lithium+ salt. Palladium absorbs molecular deuterium and the Pd 2+ /Lι + catalytic system effect resonant shrinkage of deuterium to the point of fusion. In one embodiment, the lithium is 6 Li in which case the neutrons released from fusion of deuterium effects the fusion of ^ Li to helium. In other embodiments, the fusionable material is one of any element of the periodic chart, and the energy of the holes of the said source of energy holes is resonant with the Mills orbital shrinkage energy which is calculated using Mills mechanics of the present invention and described for deuterium in Appendix VI. In the preferred embodiment, 2 H, 3H, or 6|J is used as the fusionable material. In all embodiments, the source of energy holes is one or more of an electrochemical, chemical, photochemical, thermal, free radical, sonic, or nuclear reactions, inelastic photon or particle scattering reactions. In the latter two cases, the present invention of a fusion reactor comprises a particle and/or photon source to supply the said energy holes. In all reaction mixtures a selected external energy device 75, such as an electrode may be used to supply an electrostatic potential or a current to decrease the activation energy of the resonant absorption of an energy hole. In another embodiment the fusion mixture 54, further comprises a surface or material to absorb atoms and/or molecules of the fusionable material 56. Such surfaces or materials to absorb deuterium, or tritium comprise transition elements and inner transition elements including iron, platinum, palladium, zirconium, vanadium, nickel, titanium, Sc, Cr, Mn, Co, Cu, Zn, Y, Nfr, Mo, Tc, Ru, Rh, Ag, Cd, La, Hf, Ta, W, Re, Os, Ir, Au, Hg, Ce, Pr, Nd, Pm, Sm, Eu L Gd, Tb, Oy, Ho, Er, Tm, Yb, Lu, Th, Pa, and U. Experimental S. Pons, et al, have demonstrated cold fusion with an electrochemical " cell that electrolyzes deuterium oxide to deuterium at a palladium electrode with lithium as the counter ion. That excess heat is released and that ' sdme fusion of deuterium is detectable is apparent by the present fiivibtfoπ. The third ionization energy of palladium is 32.93 eV and the ' ftfst ionizatϊ_J ~ energy of lithium is 5.392 eV. This system can catalytically generate energy holes of 32.93 eV - 5.392 eV = 27.538 eV The catalytic reaction is given in the Coulombic Annihilation Fusion Section. The quantum of energy needed to decrease a Mills orbital by ao ) is 27.21 eV. The energy difference between 27.538 eV and 27.21 eV is carried by a phonon or a translational or rotational mode. CAF occurs at a slower rate when sodium or potassium is used as the electrolyte because the energy hole produced by the Pd 2+ /Na+ system is 27.791 eV and the energy hole of the Pd 2+ /K+ system is 28.589 eV. The energy holes of the Pd 2+ /Li+ system are closer to the resonance quantum of 27.21 eV. Thus, it is not surprising that lithium is a superior counter ion to effect CAF. That cold fusion at a titanium electrode has been observed by S. E. Jones et al to proceed a faster rate than with the Pd 2+ / Li+ catalytic system is not surprising in that the catalytic reaction involves only one atom as the catalyst, and the third ionization energy of titanium is 27.491 eV which is close to the shrinkage quantum of 27.21 eV. The catalytic reaction appears in the Coulombic Annihilation Fusion Section. 27.21 eV of heat is released during a radius reducing cycle of the Mills orbital of the deuterium atom in the Pons and Jones systems. Approximately 100 KeV of heat energy is released by the shrinkage process before the nuclei approach sufficiently for fusion to occur. This heat is unaccountable by both research groups. Interestingly, this unaccountable heat was observed in electrochemical cells with palladium electrodes, Group I cation electrolytes, and aqueous solutions as long ago _ιs 1924 by Jirsa (Jirsa, F., Z. Physik, Chem.. 113, 241 (1924)). Thus, Pons and Jones' observation of the phenomenon of heat release due -to resonant Mills orbital shrinkage is not the first. Furthermore, physicist Francesco Scaramuzzi effected cold fusion of deuterium gas using shavings of titanium; whereas, in 1973, Catlett, et al., (Catlett, D. S., et al., The Journal of Chemical Physics, 58(8). p. 3432, (1973)) diffused deuterium gas into palladium and measured no fusion products by sensitive mass spectroscopy. According to the present .model of the atom, CAF was catalyzed by Ti + in the former experiment, and CAF was not possible in the latter due to the absence of the second element of a two-element catalytic couple such as Li+ of the Pd 2+ /Li + couple. Further Applications Mills. Mechanics, the present invention, is a means to derive a complete quantitative description of any atom, molecule, or material. The said descriptions can be used to device novel molecules, materials, and electronic devices; thus, they can eliminate much experimentation. And, they can be used to interpret the results of experimentation. For any atom, the radii of all Mills orbitals are calculated using the balance of forces as described in the One Electron Section, the Two Electron Section, and the Three Electron Section. The orbital energies are then calculated as- described in the said sections to give the complete mathematical description of any atom or ion. Thus, with the selection rules, described in the Section Rules Section, together with the orbital energies arid the principle of conservation of energy, all transitions are given. Bonding is calculated by minimizing the total energy stored in the electric and magnetic fields of the participating atoms as described in the Nature of the Chemical Bond Section. The resulting minimum for all atoms describes exactly any molecule or material. The physical properties can then be calculated from the following parameters: 1.) coordinates of the nuclei and Mills orbitals; 2.) the bond and orbital energies 3.) the bond energy as a function of said coordinates 4.) population of Mills orbitals (e.g., unpaired electron or two spin paired electrons in a given orbital) Furthermore, Mills mechanics is a means to calculate reaction coordinates as energy surfaces that describe the intermediates of a reaction; thus, reaction mechanisms are given. With this knowledge, novel syntheses and products can be engineered, catalysts can be developed, and yields of thf desired products increased. Also, phenomenon which occur too rapidly to be observed or have yet to be discovered (recent examples are cold fusion and high transition temperature superconductors) are described exεfctly " via Mills mechanics which provides a complete description of matter on the atomic and molecular level. Appendix I Proof that the condition for radiation by a charge density function is that it possesses components of its space-time Fourier Transform which are synchronous with waves traveling at the speed of light is given. Charge obeys superposition; thus, only a point charge need be considered. The proof starts with the Fourier components of the current produced by the moving charge. The electric field is found from the vector wave equation in Fourier space (k, ω space). The inverse Fourier transform is carried over the magnitude of k. The resulting expression demonstrates — CO — — — that the radiation field is proportional to J j _(- n ,ω), where J j _(k,ω) is the — — k space-time Fourier transform of the current perpendicular to k and n ≡? τrτ l κ l ; thus, the necessary condition for radiation by the charge is that its space-time Fourier transform possesses components which travel at the speed of light. II. The Source and Its Fourier Transforms Consider a charged particle of charge q and position r 0 (t). The charge density of the particle is described by p( 7, t) = qδ[7 - 7 0 (t)] (2.1 ) where δ( r - r 0 ) is the spatial unit impulse function. The current density i s J ( 7, t) = q7 0 (t)δ[7 - 7 0 (t)] . (2.2) The spatial Fourier transform represents the current density as a superposition of spatial exponentials, exp -j k- r. J( k, t) = J J j d3 k " q7 0 (t)δ[7 - 7 0 (t)] exp(-i k- 7) (2.3) - * i ' = qr 0 (t) exp(-i k- r 0 ) The full space time Fourier transform is of course, J( k r w}= J J J J dtd3 k J(r,t) exp(-i k- r) exp(iωt) (2.4) The inverse Fourier transform is J(7, t)= j J J d k3J (k,ω) exp(i k- 7) exp(-iωt) (2.5) III. The Electromagnetic Field The electric field obeys the vector wave equation The space-time Fourier transform of the vector wave equation is: 0)2_ k x [ kx E(k,ω) ] + -rr E(k,ω) « -iωμ 0 J(k,ω) (3.2) In the far-field, only the component perpendicular to k is of interest. Concentrating on this component one has _ _ -iωμ 0 nx[nχj(k,ω)] E ±( k ' ω >= k2 - ω 2/ c 2 ( 3 - 3 ) with IV-.fe The Inverse Spatial Fourier Transform < 3 - 4 ' The inverse space-time Fourier transform involves the integrals We shall retain the Fourier transform with respect to time and thus not carry out the integration over ω. But we shall focus on a spectral — — dω width dω of the field and thus write down expressions for E.(r,ω)— .We •i 2π separate the integrals into an integral over the magnitude of k, and into a double integral with respect to the angles θ and φ of k with respect to r. Jj dφdθsinθ The last integral can be carried out by contour integration. For k-r > 0, the contour must be closed into the negative imaginary half plane of k with the result dω . 1 . 2 ω 2 co f r dφdθsinθ E , (r,ω)- 2π = ( v -2π) -g dM 4π n-r ) (4.2) This expression may be rewritten in a way that lends itself to an appealing interpretation. The density of (linearly polarized) modes per unit volume and unit solid angle, p(ω,Ω), is 1 ω 2 ω dΩ p(ω,Ω) = dωdΩ = -(-) d( -)- (4.3) With this definition, one has ω — ω nx[nx J(— n,ω)]exp(i— n-r) (4.4) c c _ _ dω — ω The field E , (r,ω)— is proportional to -J(— n,ω) namely, the Fourier •>- 2π c compont. .t for which k = ω/c. Factors of ω that multiply the Fourier component of the current are due to the density of modes per unit volume and unit solid angle. An unaccelerated charge does not radiate in free space, not because it experiences no acceleration, but because it has no Fourier component. — ω — J(- n,ω) k c Indeed, from (2.3) J(k,ω) == J J ddttqqvv exp(-ik-vt + iωt) = 2πqvδ(ω - T<-v) (4.5) The only nonzero Fourier components are for where θ is the angle between v and k. The reason for the radiation of an accelerated charge is that the Fourier decomposition of the current acquires Fourier components that are "synchronous" with the light — w velocity, i.e. with the propagation constant |k| =— . Thus, for example, an c os JIating charge ^ 7 0 (t) « d sinω 0 t (4.7) has a Fourier spectrum J (k,ω) = - (m + 1)ω 0 ] + δ[ω - (m - 1)ω 0 ]} (4.8) where the Jm 's are Bessel functions of order m. These Fourier components can, and do, acquire phase velocities that are equal to the light velocity. For small kd only m = 0 remains and is approximately independent of k, v J 0 (ττcosθd) « 1 c V. Integration Over Angles Starting with (4.2), we note that the exponential is a strong function of θ whereas the component n x [ n x J] varies much more slowly and thus can be pulled out from under the integration. We have to integrate an expression of the form 2π 1 ω 2 d ω ω _ 2π c3 exp(i- -r ) where the upper limit on θ is ignored because of the rapid variation of the exponent. With this result introduced in (4.2) one has n'r ) (5" 1 ) Here, n is the direction of the radius vector 7. We note now that a factor of ω appears in front of the current. One may therefore interpret the source as containing the acceleration where -iω represents differentiation with respect to the time coordinate. It seems more natural to attribute the factor to the integration over all the modes, in particular because then Cherenkov radiation presents less of a mystery. Cherenkov radiation is produced by an unaccelerated particle, but since the velocity of light is less than c. the particle current can have Fourier components synchronous with . is the dielectric constant of the medium. Appendix II Space-time Fourier transform of Mills orbitals. The space-time Fourier transform in three dimensions in polar coordinates is given as follows: g(r, θ, φ, t)eκp (-/2π$rlco$ Θ cos θ ♦ sin Θ sin θ cos(φ-Φ) ♦ -®- 1]) χl sin θ dr dθ dφ dt with circular symmetry, G(S,Θ) - g(r, θ ) J 0 (2π$r sin Θ sin θ) exp (-/2π$r cos Θ cos θ) t-2 sin θ dr dθ with spherical symmetry. G(S) - g(r) sine (2sr) r 2 dr For separable variables f(r) g(θ) (φ) ttt) <----> F(s) 6(0) H(Φ) K(CD) Mills orbitals are separable into a product of functions of independent variables, r, θ , φ , and t. The radial functions are delta functions. The time functions are of the form e' ωt , the angular functions are spherical harmonics, sin or cosine trigonometric functions or sums of these functions, each raised to various powers. The space-time Fourier transform is derived of the separable variables for the angular space function of sin φ and sin θ. It follows from the space-time Fourier transform given below that other possible spherical harmonics angular functions give the same form of result as the transform of sin θ and sin φ. The space Fourier transform of f(r) = δ(r-ro) is given as follows: FCS) - δ(r - ri) sinc(2sr) r 2 dr The space Fourier transform of g(θ) = sin θ is given as follows where there is. no dependence on φ: 6(0) « $Jnθ J 0 (27lsr sin θ sin θ) eHp (-βJtsr cos 0 cos θ) sin θ r2 dθ dr G(Θ)- r2sin 2 θJ 0 (2πsr sin 0 sinθ) cos (27lsr cos 0 cos θ) dθ dr z - 27lsr sin0 sinθ G(Θ) - 2πf°° f π r $ in2θ ( ∑ HftlPrtlnΘ »lnft») Jo Jo n «0 nKn + ) cos(27t$rcos0 cosθ) dθdr cos(2π$rco$0 cosθ) dθdr co$(27C$rcosΘ cosθ) dθdr R e K)>-(l/2), z « 27Csrcos0 re 1 )!!!)* 1 ) (πsr cos0)υ — — sin 2υ θ cos(2πsrcos0 cosθ) dθdi ( πsr cos0 ) υnl-)r(υ+ JL ) 2 2 2 υ *2 ( πsrcosθ^ π $|n2υθ co$(2π$rco$0 co$ 0 )d (πsr co$ø) υ l )_T(υ*i-) Λ 2 2 (7tsr co$0) Hankel transform formula: f r -π/ 2 ) (r$) (1/2) Jυ(r$)dr . s (t/2 ) Jo Hankel transform relationship: f(„) <« = O H κ m f (κ) , m - 0, 1, 2 ... <«*«> u (, ) " ^(-i-)m[ y (m*υ-1/2) g ( y . m+υ)J 51 _» r υ r -d/2) , r$) (i/2) j υ , r$ , dr . $ ( i/2 ) -υ,-4-,υ, ,VIMI/J. s (t/2), r υ $(i/2) j (r$) dr .$__!__ ( jL )υι S 2υ, Jo s υ ds [°° r υ s ( i/2 ) j (r$)dr . s ( i/2 ) -2υ 2 υi $ υ-iυi s (i/2)-υ Jo υι υι I ) Γ_Ό*1 | — ^ ? & J(sr') dr' (πscos0) υ (2πcos0) υ+l ( -n^tπsinθ)^ ' " υ-i The space Fourier transform of h(φ) = sin φ is given as follows where there is no dependence on θ: Apply change of variable to the Fourier transform of g(θ) = sin θ. θ==>φ implies Ø=>Φ Λ H(φ) - Σ iϋ — ιπ sinφ ' 2 2 2υi . 2 υ υ-ϊ υ ( υ-i)f (πc o$ ø) 2 υ + ι 2 _ ι υι The time Fourier transform of K(t) 3 Re(eκp(jC0 ι t)) is given as follows: 1 δ (ω - ω, ) ♦ δ (CD ♦ CO l The space-time Fourier transform of a Mills orbital is of the following form: M(S, 0, Φ, CO) - F(S) G(0) H(Φ) K(CD) oo M ( s, Θ, Φ. ω) » 4ππ 2 sinc<2sπ) 4π I δ (co - ω fl ) ♦ δ (ω ω 1 )i The condition for radiation of a charge density function is given in Appendix I. The space-time Fourier transform of the charge density function must not have waves synchronous with waves traveling at the speed of light, that is synchronous with ®JI or synchronous with of the medium. Given the angular velocity, ω = ω n , the space-time Fourier transform of the Mills orbital is zero for s = — when (11.1 ) 2π(nn) = 2πr n = nλi = λ n (II.2) Λ where n = 1 n = 2, 3, 4, ... n - I 2 » l 3 > l 4 i — λi is the allowed wavelength for n = 1 ri is the allowed radius for n = 1 Thus, space-time harmonics of k do not exist. Thus, radiation due to charge motion does not occur in any medium when this boundary condition is met. Appendix III The solution to the Schrodinger equation is a wave function ψ (x). An interpretation of ψ (x) is required. Schrodinger postulated that ψ (x) represents the amplitude of the particle in some sense, and because the 5 intensity of a wave is the square of the amplitude the "intensity of the particle" is proportional to ψ * (x) ψ (x) [ψ * (x) is the complex conjugate of ψ (x)]. A controversy arose over the meaning of intensity. Schrodinger considered e ψ * (x) ψ (x) to be the charge density or e ψ * (x) ψ (x) to be the amount of charge between x and x + dx. Thus, he presumed the electron to 1 0 be spread all over the region. The electron has kinetic energy and angular momentum and energy must be conserved; thus, the motion of an electron must be time harmonic. It is demonstrated in Appendix I that emission of electromagnetic radiation occurs if the space-time Fourier transform possesses waves 1 5 that are light synchronous with waves traveling at the speed of light. It is demonstrated below that the Schrodinger wave equations have such components; thus, they must radiate. That no radiation is observed demonstrates the invalidity of these equations as an accurate description of an electron. 20 The angular functions of Schrodinger wave equations are spherical harmonics and their space^time Fourier transform is given in Appendix II as the transforms of g(θ), h(φ), and k(t). The radial solutions are of the form of a r raised to a power times a negative exponential of r. The space- tϊme Fourier transform of the radial function f(r) = re _r/a o follows: re~* r/a o) sinc(2sr) r 2 dr 30 ( r 2 e -(r/ β 0 ))/( 2 π$) sin 4π$r dr 35 Let r-r74π, dr' » (1/4π)dr r . $ dr . m*0 Let H -r, S -y, α-ϊ/4πa 0 ,n-2 1/4πf °° Λ 90/13126 126 Thus, the complete space-time Fourier transform of a Schrodinger wave equation is given as follows: ) m ^ι δ (ω- ω 0 ) * δ(ω * ω 0 )i ωn This transform has components — = k which are not zero and are synchronous with waves traveling at the speed of light. Thus, a charge density function given by the Schrodinger wave equation must radiate in accordance with Maxwell's Equations. Appendix IV Derivation of the Orbital Energy Stored in the Magnetic Fields of Two Paired Electrons Derivation of the Magnetic Field Consider Figure 2; the magnetic field must satisfy the following relationships: V- H - 0 in free space (IV.1 ) n x (H a H ) - Ϊ? (IV.2) (Ha Hb ) - 0 (IV.3) H = - V ψ (IV.4) • A 3 _fitL K = iψg sinθ (IV.5) μr n 3 JU Ha θ - Hb θ = r- . . sinθ (IV.6) -z μr n - To obtain He .the derivative of Ψ with respect to θ must be taken, and this suggests that the θ dependence of Ψ be taken as cos θ he field is finite at the origin and is zero at infinity; so, solutions of Laplace's equation in spherical coordinates are selected because they are consisten with these conditions. r Ψ = A (IV.8) r n cosθ ; r > r n The negative gradient of these potentials is H - (ir cosθ - ie sinθ) for r < r n rn (IV.9) sinθ) for r > r n (IV.10) The continuity conditions of Equations (IV.3), (IV.5), and (IV.6) and are applied to obtain the following relationships among the variables (IV.1 1 ) r n r n A C 3 e (IV.12) r n r n 2 μι * n 3 Solving the variables algebraically gives the magnetic fields of an electron: → → _ -eβntL_ Λ Λ Λ . Λ . H - „ r 3 Or cosθ - le sinθ) for r < r n (IV.13 μrn : — » efi Λ Λ H = g Or 2 cosθ - ie sinθ) for r > r n (IV.14 Derivation of the Energy The energy stored in the magnetic field of two electrons is 2π π oo Emag =2 r μ 0 J J JΗ≥r≥sinθdrdθdφ (IV.15 o o 0 Emag.total - Emag.external + Emag.internal (IV.16 Emag,internal 2 ( cos 2 θ + sin 2 θ ) r 2 sinθdrdθdφ (IV.17 2π π efi Emag,external 2 (4cos 2 θ + sin 2 θ) r 2 sinθdrdθdφ (IV.1 9 2μr3 2πμ 0 e 2 tτ 2 3μ2 rι 3 (IV.20 4πμ 0 e ft 2 2πμ 0 e 2 fT 2 : mag .total = 3μ 2 n3 3μ2 rι 3 (IV.21 2πμ 0 e 2 ft 2 Emag.total = μ 2 n 3 (IV.22 Appendix V The Hydrogen Molecule It can be shown easily that the internuclear distance for the dihydrogen, H 2 , is 0.748 A. Consider two hydrogen atoms, A and B, approaching each other along the x-axis as shown in Figure 3. The radius of each Mills orbital is a 0 . The electrostatic energy is ^interaction - 2 x y . 0 j A£ dv (V.1 ) We define this energy as Ej nteract j 0n> Recall that the electric field is zero for r > a 0 . Until the orbitsphere penetrate the energy of interaction, E interaction , is zero. As the atoms move closer, the Mills orbitals begin to penetrate. When the penetration is small, as shown in Figure 4, ^interaction decreases (is negative) because most of the electric field vectors from nucleus A in the overlap region are pointed in direct opposition to the B electric field vectors from nucleus B. As the atoms move closer and the overlap increases, the E interact j on will continue to decrease (become more negative). However, the decrease per unit volume will be smaller because a lower fraction of the A-vectors will be in direct opposition to the B-vectors. Figure 5 shows the two radial vectors and the net electric field vector (EAB) for tne P oint of intersection of the Mills orbitals. We see that E = EB - 2 ' (V.2) A 2 + EA 2 - g (V.3) From the angle θ, E VA - (£)3 ( .7) E A B = 2 ^3 (V.8) Therefore, (EAB) 2 il[ be less than [(EA) 2 + (EB) 2 ] when (a 0 ) 6 < (a 0 )4 < V - 9 > (a 0 ) 2 ao y 2 <-γ- or y < T ( v - 1 °) Thus, for y = 0 to y < a 0 /Vi E inte raction decreases. For y > a 0 /V2 E interaction increases. And for y = ιs a minimum. When y - RAB = xB = 2x ^ = 2 a 0 = 0.748 A (V.11) The experimental internuclear bond distance is 0.746 A Appendix VI Calculation of the Resonant Energy Hole to Effect Shrinkage of the Radius of the Mills Orbital of the Deuterium Atom. For the deuterium atom, the force relationship is given as follows: μv 2 _ ft 2 r ~ 4πe 0 r 2 The boundary condition for nonradiative Mills orbitals derived in Appendix II, 2πr = nλ, gives: v ~ μr * Consider the case where the electron in the ground state losses kinetic energy, 1/2 mv2, due to an inelastic collision for example, then the radius of the Mills orbital will shrink until the boundary condition is satisfied. The amount of energy which must be carried away (i.e., the magnitude of the energy hole absorbed) is calculated as follows: Let n = initial radius. Let r2 = final radius. The force balance is: μv 2 e 2 r ~ 4πε 0 r 2 Vo is introduced as a perturbation of the velocity and the magnitude of the velocity change of the electron from the initial to final Mills orbital is calculated as follows: e 2 f - V J j — i " 2( — μn - Vo)2 - 4πεor2 μ , ft 2 2ft . . . . 2 , e 2 — ( -5 — 5- Vo + Vo^) ■ « f2 μ 2 r-| 2 μri ^ 4πε 0 r2 2 . . 2 ^ — ϊl e 2 Vo - Vo μn + μ 2 rι 2 4πε 0 r2 ~ e 2 _ ft 2 °_ 4πε 0 ~ μa 0 For the ground state, the radius of the Mills orbital was determined in the One Electron Atom Section to be ao- Thus, the boundary condition is given as follows: 2πao = λ From the boundary condition, 2πr = nλ, with r < ao, the radius of any shrunken state is an integer fraction of the radius of the ground state. Thus, for the first shrunken state a 0 r = 2 , and in general a^ r2 = T a 0 Substituting r-j = ao and r2 = ~ r into the relationship for Vo gives n ft r- ft Vo = ± Vn - μa 0 μa 0 n=2,3,4 The angular velocity of the electron in ground state is and the angular velocity in the first shrunken state is — — . μa 0 Consider the velocity of the centripetal force equation: and the relationship resulting from the perturbation: In order to satisfy the boundary conditions, the first term of Vo, μa 0 ' must be negative so that it adds to the initial velocity to give the final velocity , and the kinetic energy due to the velocity component Vn must be removed to effect the shrinkage transition. μa 0 The magnitude of the energy hole which arises from this term is calculated as follows: E = « μ v2 β i-(^ — μa- 0 ) 2 n=2,3,4 Thus, the absorbed energy hole which effects shrinkage is quantized. For the shrinkage transition n = 1 to n = 2, the resonant energy loss to shrink a Mills orbital by a 0 ( -— - - — ) where ni is the quantum number of the initial orbital and n2 is the quantum number of the final orbital is given as follows: _____ (1 .05459 X 10-34)2 β μa 0 2 =s (9.10953 X 1 0"31 )(5.29177 X 10" 1 1 ) 2 E = 4.3598285 X 10-18j = 27.211682eV n Thus, shrinkage requires the electron to lose a resonance energy of 27.21 eV where n = 2, 3, 4 Notice that absorption of an energy hole reduces the radius; whereas, absorption of energy as a photon increases the radius. The former increases the coulombic force by the multiple of n; the latter decreases the coulombic force by the multiple of — where n is the integer of the transition; thus, the force balance, and the boundary conditions for nonradiation are satisfied. 1 34 Appendix VII Detailed Description of Figure 1. Mills Orbitals Mills orbitals are obtained by adding a constant sphere which is normalized to a spherical harmonic which is normalized. This function is 5 the charge density on the surface of the spherical delta function that comprises the Mills orbital. The former can be consider the base charge density whose current gives rise to magnetic spin, and the latter can be considered a charge density function which creates modulation of the former and whose traveling wave of current gives rise to orbital angular 1 0 momentum. The total charge of the Mills orbital for an electron is e and the total mass is μ. The application entitled ENERGY/ MATTER CONVERSION METHODS AND STRUCTURES filed April 21 , 1989 is herein incorporated by reference. These and further methods and embodiments arising from substitution 1 5 and modifications made by one of ordinary skill in the art are considered within the scope of the present invention. For instance, in the case of energy release through fusion according to the present invention, the fusion material may include more than one element or molecule, where corresponding energy holes are provided for each fusion element. 20 Therefore, the present invention is not limited except by the claims which follow.

Claims: CLAIMS What is claimed is: 1. A method of releasing energy, comprising the steps of: selecting a first element of matter having a nucleus and at least one electron orbital; selecting a second element of matter having a nucleus and, at least one electron orbital; determining the resonance shrinkage energy levels of the electron orbitals of said first and second elements of matter; providing two energy holes substantially equal to each of the resonance shrinkage energy levels of said first and second elements of matter; juxtaposing said first and second elements of matter and said energy holes, wherein; fusion of said first and second elements of matter is produced when the energy of said first and second elements of matter is removed by said energy holes from said electron orbitals to permit forces from each nucleus of said first and second element of matter to be attractive to form a common nucleus, providing the release of energy. 2. The method of claim 1 , wherein: said first and second elements of matter comprise the same element of matter. 3. The method of claim 1 , wherein said step of providing an energy hole for each fusionable element comprises the step of selecting a third element of matter having an ionization energy substantially equal to the ' resonance shrinkage energy of said first and second elements of matter. 4. The method of claim 3, further comprising the step of transferring energy between said juxtaposed first and second elements of matter and external energy apparatus, said energy hole to control the rate of fusion according to the relative equivalence of said energy hole and transferred energy to the energy levels of said first and second elements of matter. 5. The method of claim 1 , wherein the step of providing an energy hole comprises the steps of: selecting a plurality of elements of matter, each having an ionization energy, wherein each of said plurality of elements of matter are selected to produce a difference in ionization energies substantially equal to the energy resonance shrinkage energy of said first element of matter. 6. The method of claim 1 , wherein said first and second elements of matter comprise different elements of matter. 7. The method of claim 6, wherein said step of providing an energy hole for each of said first and second elements comprises the step of: selecting a third and fourth element of matter each having an ionization energy substantially equal to the resonance shrinkage energy of the respective first and second elements. 8. The method of claim 6, wherein said step of providing an energy hole for each of said first and second elements comprising the step of: selecting a plurality of elements providing a difference in ionization energies substantially equal to at least one of the resonance shrinkage energy of said first and second elements. 9. The method of claim 8, wherein the step of providing an energy hole includes the step of: selecting an additional element providing an ionization energy equal to the other resonance shrinkage energy of said first and second element. 10. The method of claim 5, further comprises the step of transferring energy between said juxtaposed first and second elements of matter and external energy apparatus, said energy hole to control the rate of fusion according to the relative equivalence of said energy hole and transferred energy to the resonance shrinkage energy levels of said first and second elements of matter. 1 1 . The method of claim 10, wherein the transfer of energy is provided by one of an externally applied electric, magnetic field, or heat transfer and acoustic energy. 12. The method of claim 1 , wherein the step of determining the resonance shrinkage energy comprises the step of calculating the said energy of the electron orbitals. 13. The method of claim 12, wherein the step of calculating comprises the steps of: equating the sum of the magnetic and coulombic forces with the centripetal force; introducing an energy hole into the centripetal force as a velocity deficit; and determining the energy hole by solving for the energy in the velocity deficit where the boundary conditions of Mills orbital, 2πr = nλ is observed. 14. The method of claim 1 , wherein: said first and second elements of matter have an atomic number of 26 or less. 15. The method of claim 1 , wherein the step of providing an energy hole comprises: providing a catalytic system. 16. The method of claim 15, wherein the step of providing a catalytic system comprises: providing an electrochemical reactant comprising at least one of a cation and an anion. 17. Apparatus for providing the release of energy, comprising: means for providing a first and second element of matter in a selected volume, each of said first and second elements having a nucleus and at least one electron at an orbital having a respective resonance shrinkage energy level; and a substance introduced into said selected volume for providing an energy hole in juxtaposition with said first and second elements of matter, said energy hole having a magnitude substantially equal to said resonance shrinkage energy, wherein: fusion of said first and second elements of matter is produced when the orbitals of said first and second elements of matter are reduced due to removal of orbital energy by said energy hole permitting forces from "each nucleus of said first and second elements of matter to form a common nucleus, providing the release of energy. 18. The apparatus of claim 17, wherein said substance comprises at least a third element of matter having an ionization energy substantially equal to the resonance shrinkage energy of each of said first and second elements of matter. 19. The apparatus of claim 18, wherein said substance further comprises at least an additional element of matter having an ionization energy, which in combination with the ionization energy of said third element produce said energy hole substantially equal to the resonance shrinkage energy of at least one of said first and second elements of matter. 20. The apparatus of claim 18, wherein: said first and second elements of matter are the same elements. 21 . The apparatus of claim 20, wherein: * sard first and second elements of matter have an atomic number of 26 or less. 22. The apparatus of claim 18, wherein: said first and second elements of matter comprises one of 2 H, 3H , 6 Li; and said third element comprises Ti 2+ . ,23. The apparatus of claim 22, wherein said first and second elements o-f matter comprise deuterium and said third element comprises one of: single-ion capable of producing energy holes for shrinking deuterium atoms. The number following the atomic symbol (n) is the nth ionization energy of tire atom. That is for example, Ti 2+ + 27.49 eV = Ti 3 + + e\ Catalytic Ion n nth ionization energy Al 2 + 3 28.45 Ar " * + 2 27.63 Ti2 + 3 27.49 As 2 + 3 28.35 Rb 1 + 2 27.28 Mo 2+ 3 27.16 Ru 2 + 3 28.47 ln 2 + 3 28.03 Te 2 + 3 27.96 n n = 16 (resonance shrinkage energy is given by -^ 27.21 ; with n = 16, the resonance shrinkage energy is 217.68) Catalytic Ion n nth ionization energy Be3+ 4 217.71 p5+ 6 220.43 24. The apparatus of claim 20, wherein: said first and second elements of matter comprises 2 H and H; and said third and said additional element comprise Pd 2+ and Li+. 25. The apparatus of claim 20, wherein said first and second elements of matter comprise deuterium and said third and fourth elements of matter comprise on of the following two-ion couples: Two-ion couples capable of producing energy holes for shrinking deuterium atoms. The number in the column following the ion, (n), is the nth ionization energy of the atom. That is for example, Pd 2+ + 32.93 eV = Pd3+ + e" and Li+ + e" = Li + 5.39 eV. Atom n nth Ion¬ Atom n nth Ion¬ Energy Oxidiz¬ ization Reduced ization Hole ed Energy Energy (eV) (eV) (eV) Ne1 + 2 40.96 H 1 + 13.60 27.36 Ar 2 + 3 40.74 H 1 + 13.60 27.14 Sn3 + 4 40.73 H 1 + 13.60 27.14 Pm 3 + 4 41.10 H 1 + 13.60 27.50 Sm 3 + 4 41.40 H 1 + 13.60 27.80 Dy3 + 4 41.50 H 1 + 13.60 27.90 Kr3 + 4 52.50 He1 + 24.59 27.91 Rb3 + 4 52.60 He1 + 24.59 28.01 K 4 + 5 82.66 He 2 + 2 54.42 28.24 Zn4 + 5 82.60 He 2 + 2 54.42 28.18 Se5 + 6 81.70 He 2 + 2 54.42 27.28 He1 + 2 54.42 Rb2 + 2 27.28 27.14 Zr4 + 5 81.50 He2 + 2 54.42 27.08 He1 + 2 54.42 Mo3 + 3 27.16 27.26 Si 2 + 3 33.49 Li 1 + 5.39 28.10 Mn2 + 3 33.67 Li 1 + 5.39 28.27 Co2 + 3 33.50 Li 1 + 5.39 28.11 Pd2 + 3 32.93 Li 1 + 5.39 27.54 I 2 + 3 33.00 Li 1 + 5.39 27.61 Hf 3 + 4 33.33 Li 1 + 5.39 27.94 Li 1 + 2 75.64 C 3 + 3 47.89 27.75 Li 1 + 2 75.64 N 3 + 3 47.45 28.19 Li 1 + 2 75.64 Na2 + 2 47.29 28.35 Li 1 + 2 75.64 S 4 + 4 47.30 2B.34 Cu5 + 6 103.00 Li 2 + 2 75.64 . 27.36 Li 1 + 2 75.64 Br4 + 4 47.30 28.34 Br 6 + 7 103.00 Li 2 + 2 75.64 27.36 V 6 + 7 150.17 Li 3 + 3 122.45 27.72 Li 2 + 3 122.45 Mn6 + 6 95.00 27.45 Cu2 + 3 36.83 Be1 + 9.32 27.51 Kr 2 + 3 36.95 Be1 + 9.32 27.63 Cd2 + 3 37.48 Be 1 + 9.32 28.16 Te3 + 4 37.41 Be1 + 9.32 28.09 Ce3 + 4 36.76 Be1 + 9.32 27.44 K 2 + 3 45.72 Be 2 + 2 18.21 27.51 V 3 + 4 46.71 Be 2 + 2 18.21 28.50 Ge3 + 4 45.71 Be 2 + 2 18.21 27.50 Mo 3 + 4 46.40 Be 2 + 2 18.21 28.19 Bi3 + 4 45.30 Be2 + 2 18.21 27.09 Be2 + 3 153.89 Ne5 + 5 126.21 27.68 Be2 + 3 153.89 Kr8 + 8 126.00 27.89 Be2 + . 3 153.89 Mo7 + 7 126.80 27.09 Be3 + 4 - 217.71 Al 6 + 6 190.47 27.24 Br2 + 3 36.00 B 1 + 1 8.30 27.70 Ce3 + 4 36.76 B 1 + 1 8.30 28.46 Cl 3 + 4 53.46 B 2 + 2 25.15 28.31 Kr 3 + 4 52.50 B 2 + 2 25.15 27.35 Rb3 + 4 52.60 B 2 + 2 25.15 27.45 B 2 + 3 37.93 P 1 + 1 10.49 27.44 P 4 + 5 65.02 B 3 + 3 37.93 27.09 B 2 + 3 37.93 S 1 + 1 10.36 27.57 V 4 + 5 65.23 B 3 + 3 37.93 27.30 B 2 + 3 37.93 As 1 + 1 9.81 28.12 B 2 + 3 .37.93 Se1 + 1 9.75 28.18 B 2 + 3 37.93 I 1 + 1 10.45 27.48 B 2 + 3 37.93 Ba2 + 2 10.00 27.93 B 2 + 3 37.93 Ce2 + 2 10.85 27.08 B 2 + 3 37.93 Pr2 + 2 10.55 27.38 B 2 + 3 37.93 Nd2 + 2 10.73 27.20 B 2 + 3 37.93 Pm 2 + 2 10.90 27.03 B 2 + 3 37.93 Hg1 + 1 10.44 27.49 B 2 + 3 37.93 Rn 1 + 1 10.75 27.18 B 2 + 3 37.93 Ra2 + 2 10.15 27.78 CI2 + 3 39.61 C 1 + 1 11.26 28.35 Zn2 + 3 39.72 C 1 + 1 11.26 28.46 Nb3 + 4 38.30 C 1 + 1 11.26 27.04 Pr3 + 4 38.98 C 1 + 1 11.26 27.72 Kr3 + 4 52.50 C 2 + 2 24.38 28.12 Rb3 + 4 52.60 C 2 + 2 24.38 28.22 C 2 + 3 47.89 P 2 + 2 19.73 28.16 Ar 4 + 5 75.02 C 3 + 3 47.89 27.13 Fe4 + 5 75.00 C 3 + 3 47.89 27.11 Ni4 + 5 75.50 C 3 + 3 47.89 27.61 C 2 + 3 47.89 Cu2 + 2 20.29 27.60 C 2 + 3 47.89 Ga2 + 2 20.51 27.38 C 2 + 3 47.89 Y 3 + 3 20.52 27.37 C 2 + 3 47.89 Pd2 + 2 19.43 28.46 C 2 + 3 47.89 Ce3 + 3 20.20 27.69 C 2 + 3 47.89 Gd3 + 3 20.63 27.26 C 2 + 3 47.89 Au 2 + 2 20.50 27.39 C 2 + 3 47.89 Tl 2 + 2 20.43 27.46 Sc4 + 5 91.66 C 4 + 4 64.49 27.17 C 3 + 4 64.49 Cu3 + 3 36.83 27.66 C 3 + 4 64.49 Br3 + 3 36.00 28.49 C 3 + 4 64.49 Kr3 + 3 36.95 27.54 C 3 + 4 64.49 Cd3 + 3 37.48 27.01 C 3 + 4 64.49 Te4 + 4 37.41 27.08 C 3 + 4 64.49 Ce4 + 4 36.76 27.73 Se3 + 4 42.94 N 1 + 14.53 28.41 Eu3 + 4 42.60 N,1 + 14.53 28.07 Ho3 + 4 42.50 N 1 + 14.53 27.97 Er3 + 4 42.60 N 1 + 14.53 28.07 Tm 3 + 4 42.70 N 1 + 14.53 28.17 Pb3 + 4 42.32 N 1 + 14.53 27.79 Sr3 + 4 57.00 N 2 + 2 29.60 27.40 N 2 + 3 47,45 P 2 + 2 19.73 27.72 Ar4 + 5 75.02 N 3 + 3 47.45 . 27.57 Fe4 + 5 75.00 N 3 + 3 47.45 27.55 Ni4 + 5 75.50 N 3 + 3 47.45 28.05 N 2 + 3 47.45 Cu2 + 2 20.29 27.16 N 2 + 3 47.45 Pd2 + 2 19.43 28.02 N 2 + 3 47.45 I 2 + 2 19.13 28.32 N 2 + 3 47.45 La3 + 3 19.18 28.27 N 2 + 3 47.45 Ce3 + 3 20.20 27.25 N 2 + 3 47.45 TI2 + 2 20.43 27.02 N 3 + 4 77.47 Cr4 + 4 49.10 28.37 N 3 + 4 77.47 As 4 + 4 50.13 27.34 N 3 + 4 77.47 La 4 + 4 49.95 27.52 Ne4 + 5 126.21 N 5 + 5 97.89 28.32 Fe6 + 7 125.00 N 5 + 5 97.89 27.11 Kr7 + 8 126.00 N 5 + 5 97.89 28.11 N 6 + 7 125.00 N 5 + 5 97.89 27.11 N 4 + 5 97.89 Te6 + 6 70.70 27.19 Ne1 + 2 40.96 0 1 + 13.62 27.34 Ar 2 + 3 40.74 0 1 + 13.62 27.12 Sn3 + 4 40.73 0 1 + 13.62 27.12 Pm3 + 4 41.10 0 1 + 13.62 27.48 Sm3 + 4 41.40 01 + 13.62 27.78 Dy 3 + 4 41.50 0 1 + 13.62 27.88 F 2 + 3 62.71 02 + 2 35.12 27.59 Ne2 + 3 63.45 02 + 2 35.12 28.33 01 + 2 35.12 Mg1 + 7.65 27.47 0 1 + 2 35.12 Ti 1 + 6.82 28.30 01 + 2 35.12 V 1 + 6.74 28.38 0 1 + 2 35.12 Cr1 + 6.77 28.35 01 + 2 35.12 Mn1 + 7.43 27.68 0 1 + 2 . 35.12 Fe1 + 7.87 27.25 01 + 2 35.12 Co1 + 7.86 27.26 0 1 + 2 35.12 Ni 1 + 7.64 27.48 O 1 + 2 35.12 Cu1 + 7.73 27.39 0 1 + 2 35.12 Ge1 + 7.90 27.22 01 + 2 35.12 Zr 1 + 6.84 28.28 O 1 + 2 35.12 Nb1 + 6.88 28.24 O 1 + 2 35.12 Mo1 + 7.10 28.02 0 1 + 2 35.12 Tc1 + 7.28 27.84 0 1 + 2 35.12 Ru1 + 7.37 27.75 0 1 + 2 35.12 Rh1 + 7.46 27.66 0 1 + 2 35.12 Ag 1 + 7.58 27.54 0 1 + 2 35.12 Sn1 + 7.34 27.77 0 1 + 2 35.12 Ta1 + 7.89 27.23 0 1 + 2 35.12 W 1 + 7.98 27.14 0 1 + 2 35.12 Re1 + 7.88 27.24 0 1 + 2 35.12 Pb1 + 7.42 27.70 0 1 + 2 35.12 Bi 1 + 7.29 27.83 02 + 3 54.93 Ar2 + 2 27.63 27.30 K 4 + 5 82.66 03 + 3 54.93 27.73 02 + 3 54.93 Ti 3 + 3 27.49 27.44 Zn4 + 5 82.60 03 + 3 54.93 27.67 02 + 3 54.93 Rb2 + 2 27.28 27.65 O 2 + 3 54.93 Mo3 + 3 27.16 27.77 0 3 + 4 77.41 Cr4 + 4 49.10 28.31 03 + 4 77.41 As 4 + 4 50.13 27.28 O 3 + 4 77.41 La 4 + 4 49.95 27.46 Mg4 + 5 141.26 05 + 5 113.90 27.36 05 + 6 138.12 Sc6 + 6 111.10 27.02 Cu7 + 8 166.00 06 + 6 138.12 27.88 O 5 + 6 138.12 Kr7 + 7 111.00 27.12 Si 3 + 4 45.14 F 1 + 1 17.42 27.72 K 2 + 3 45.72 F 1 + 1 17.42 28.30 Ge3 + 4 45.71 F.-.1 + 1 17.42 28.29 Lu3 + 4 45.19 F 1 + 1 17.42 27.77 Bi 3 + 4 45.30 F ,1 + 1 17.42 27.88 F 2 + 3 62.71 F 2 + 2 34.97 27.74 Ne2 + 3 63.45 F 2 + 2 34.97 28.48 F 1 + 2 34.97 Mg1 + 1 7.65 27.32 F 1 + 2 34.97 Sc1 + 1 6.54 28.43 F 1 + 2 34.97 Ti 1 + 1 6.82 28.15 F 1 + 2 34.97 V 1 + 1 6.74 28.23 F 1 + 2 34.97 Cr1 + 1 6.77 . 28.20 F 1 + 2 34.97 Mn1 + 1 7.43 27.54 F 1 + 2 34.97 Fe1 + 1 7.87 27.10 F 1 + 2 34.97 Co1 + 7.86 27.11 F 1 + 2 34.97 Ni 1 + 7.64 27.34 F 1 + 2 34.97 Cu1 + 7.73 27.24 F 1 + 2 34.97 Ge1 + 7.90 27.07 F 1 + 2 34.97 Zr1 + 6.84 28.13 F 1 + 2 34.97 Nb1 + 6.88 28.09 F 1 + 2 34.97 Mo1 + 7.10 27.87 F 1 + 2 34.97 Tc 1 + 7.28 27.69 F 1 + 2 34.97 Ru1 + 7.37 27.60 F 1 + 2 34.97 Rh1 + 7.46 27.51 F 1 + 2 34.97 Ag 1 + 7.58 27.39 F 1 + 2 34.97 Sn 1 7.34 27.63 F 1 + 2 34.97 Hf 1 + 6.60 28.37 F 1 + 2 34.97 Ta1 + 7.89 27.08 F 1 + 2 34.97 Re1 + 7.88 27.09 F 1 + 2 34.97 Pb1 + 7.42 27.55 F 1 + 2 34.97 Bi 1 + 7.29 27.68 F 2 + 3 62.71 F 2 + 2 34.97 27.74 F 2 + 3 62.71 S 3 + 3 34.83 27.88 Ar 5 + 6 91.01 F 3 + 3 62.71 28.30 Cr5 + 6 90.56 F 3 + 3 62.71 27.85 F 2 + 3 62.71 Ni3 + 3 35.17 27.54 F 2 + 3 62.71 Ge3 + 3 34.22 28.49 Sr5 + 6 90.80 F 3 + 3 62.71 28.09 F 2 + 3 62.71 Zr4 + 4 34.34 28.37 F 2 + 3 62.71 Ag 3 + 3 34.83 27.88 F 4 + 5 114.24 F 4 + 4 87.14 27.10 CI6 + 7 114.19 F 4 + 4 87.14 27.06 F 3 + 4 - 87.14 Ar 4 + 4 59.81 27.33 F 3 + 4 87.14 Zn4 + 4 59.40 27.74 F 3 + 4 87.14 Br5 + 5 59.70 27.44 F 3 + 4 87,14 Te5 + 5 58.75 28.39 F 4 + 5 114 * 24 F 4 + 4 87.14 27.10 Mg4 + 5 141.26 F 5 + 5 114.24 . 27.02 F 6 + 7 185.18 F 6 + 6 157.16 28.02 Cr 7 + 8 184.70 F 6 + 6 157.16 27.54 F 5 + 6 157.16 Co 7 + 7 129.00 28.16 F 5 + 6 157.16 Y 8 + 8 129.00 28.16 F 6 + 7 185.18 F 6 + 6 157.16 28.02 F 6 + 7 185.18 Ne6 + 6 157.93 27.25 F 6 + 7 185.18 Co 8 + 8 157.00 28.18 Cr3 + 4 49.10 Ne1 + 1 21.56 27.54 La3 + 4 49.95 Ne1 + 1 21.56 28.39 Ne1 + 2 40.96 Cl 1 + 1 12.97 28.00 Ne1 + 2 40.96 Sc2 + 2 12.80 28.16 Ne1 + 2 40.96 Ti 2 + 2 13.58 27.38 Cr4 + 5 69.30 Ne2 + 2 40.96 28.34 Se4 + 5 68.30 Ne2 + 2 40.96 27.34 Ne1 + 2 40.96 Zr2 + 2 13.13 27.83 Mo 5 + 6 68.00 Ne2 + 2 40.96 27.04 Ne1 + 2 40.96 Lu2 + 2 13.90 27.06 Pb4 + 5 68.80 Ne2 + 2 40.96 27.84 Ar 5 + 6 91.01 Ne3 + 3 63.45 27.56 Sc4 + 5 91.66 Ne3 + 3 63.45 28.21 Cr5 + 6 90.56 Ne3 + 3 63.45 27.11 Ne2 + 3 63.45 Ni 3 + 3 35.17 28.28 Ne2 + 3 63.45 Br3 + 3 36.00 27.45 Sr5 + 6 90.80 Ne3 + 3 63.45 27.35 Ar 6 + 7 124.32 Ne4 + 4 97.11 27.21 Ne3 + 4 97.11 Cr5 + 5 69.30 27.81 Fe6 + 7 125.00 Ne4 + 4 97.11 27.89 Nb6 + 7 125.00 Ne4 + 4 97.11. 27.89 Ne3 + 4 97.11 Pb5 + 5 68.80 28.31 Ne4 + 5 126.21 Na4 + 4 98.91 27.30 Al 4 + 5 153.71 Ne5 + 5 126.21 27.50 Ne4 + 5 126.21 Fe6 + 6 99.00 27.21 Ne4 + 5 126.21 Rb7 + 7 99.20 27.01 Si2 + 3 33.49 Na1 + 5.14 28.35 Co 2 + 3 33„50 r .Na 1 + . 5,14 -28.36 Pd2 + 3 32.93 Na1 + 5.14 27.79 I 2 + 3 33.00 Na1 + 5.14 ,27.86 Hf 3 + 4 33.33 Na1 + 5.14 28.19 Na1 + 2 47.29 Al 2 + 2 18.83 28.46 Na1 + 2 47.29 P 2 + 2 19.73 27.56 Ar 4 + 5 75.02 Na2 + 2 47.29 27.73 Fe4 + 5 75.00 Na2 + 2 47.29 27.71 Ni4 + 5 75.50 Na2 + 2 47.29 28.21 Na1 + 2 47.29 Pd2 + 2 19.43 27.86 Na1 + 2 47.29 In 2 + 2 18.87 28.42 Na1 + 2 47.29 I 2 + 2 19.13 28.15 Na1 + 2 47.29 La 3 + 3 19.18 28.11 Na1 + 2 47.29 Ce3 + 3 20.20 27.09 Na3 + 4 98.91 Na3 + 3 71.64 27.27 K 5 + 6 100.00 Na3 + 3 71.64 28.36 Na2 + 3 71.64 Ti 4 + 4 43.27 28.37 Ti 4 + 5 99.22 Na3 + 3 71.64 27.58 Fe 5 + 6 99.00 Na3 + 3 71.64 27.36 Rb6 + .7 99.20 Na3 + 3 71.64 27.56 Na2 + 3 71.64 Sr3 + 3 43.60 28.04 Na2 + 3 71.64 Sb4 + 4 44.20 27.44 Na2 + 3 71.64 Gd4 + 4 44.00 27.64 Na2 + 3 71.64 Yb4 + 4 43.70 27.94 Na3 + 4 98.91 Na3 + 3 71.64 27.27 Kr7 + 8 126.00 Na4 + 4 98.91 27.09 Na3 + 4 98.91 Rb5 + 5 71.00 27.91 Na3 + 4 98.91 Sr5 + 5 71.60 27.31 Mo6 + 7 126.80 Na4 + 4 98.91 27.89 Na3 + 4 98.91 Te6 + 6 70.70 28.21 Si 4 + .5 166.77 Na5 + 5 138.39 28.38 Na4 + 5 138.39 Sc6 + 6 111.10 27.29 Cu7 + 8 166.00 Na5 + 5 138.39 27.61 Na4 + 5 138.39 Kr7 + 7 111.00 27.39 S 2 + 3 34.83 Mg1 + 1 7.65 27.18 Ni2 + 3 35.17 Mg1 + 1 7.65 27.52 Br2 + 3 36.00 Mg1 + 1 7.65 28.35 Ag2 + 3 34.83 Mg1 + 1 7.65 27.18 Ti 3 + 4 43.27 Mg2 + 2 15.03 28.23 Se3 + 4 42.94 Mg2 + 2 15.03 27.91 Eu3 + 4 42.60 Mg2 + 2 15.03 27.56 Ho 3 + 4 42.50 Mg2 + 2 15.03 27.47 Er3 + 4 42.60 Mg2 + 2 15.03 27.56 Tm 3 + 4 42.70 Mg2 + 2 15.03 27.67 Pb3 + 4 42.32 Mg2 + 2 15.03 27.28 Ni5 + 6 108.00 Mg3 + 3 80.14 27.86 Zn5 + 6 108.00 Mg3 + 3 80.14 27.86 Mg2 + 3 80.14 Kr4 + 4 52.50 27.64 Mg2 + 3 80.14 Rb4 + 4 52.60 27.54 Sb5 + 6 108.00 Mg3 + 3 80.14 27.86 Mg3 + 4 109.24 Se6 + 6 81.70 27.54 Mg 3 + 4 109.24 Zr 5 + 5 81.50 27.74 Te6 + 7 137.00 Mg4 + 4 109.24 27.76 Mg 4 + 5 141.26 CI7 + 7 114.19 27.07 Ti 7 + 8 168.50 Mg5 + 5 141.26 27.24 Mg 5 + 6 186.50 Sc8 + 8 158.70 27.80 Mg6 + 7 224.94 Mn8 + 8 196.46 28.48 Si 2 + 3 33.49 Al 1 + 5.99 27.51 Mn2 + 3 33.67 Al 1 + 5.99 27.68 Co2 + 3 33.50 Al 1 + 5.99 27.51 Ge2 + 3 34.22 Al 1 + 5.99 28.23 Zr3 + 4 34.34 Al 1 + 5.99 28.35 I 2 + 3 33.00 Al 1 + 5.99 27.01 Hf 3 + 4 33.33 Al 1 + 5.99 27.34 Hg2 + 3 34.20 Al 1 + 5.99 28.21 S 3 + 4 47.30 AI2 + 2 18.83 28.47 V 3 + 4 46.71 Al 2 + 2 18.83 27.86 Br3 + 4 47.30 AI2 + 2 18.83 28.47 Mo3 + 4 46.40 Al 2 + 2 18.83 27.57 Sb4 + 5 56.00 Al 3 + 3 28.45 27.55 Bi 4 + 5 56.00 AI3 + 3 28.45 27.55 Ca7 + 8 147.24 AI4 + 4 119.99 27.25 Al 3 + 4 119.99 Sc5 + 5 91.66 2a.33 Al 4 + 5 153.71 Kr8 + 8 126.00 27.71 Al 5 + 6 190.47 Ni 8 + 8 162.00 28.47 Ni2 + 3 35.17 Si 1 + 1 8.15 27.02 Br2 + 3 36.00 Si 1 + 1 8.15 27.85 Sr2 + 3 43.60 Si 2 + 2 16.34 27.25 Sb3 + 4 44.20 Si 2 + 2 16.34 27.86 Gd3 + 4 44.00 Si 2 + 2 16.34 27.66 Yb3 + 4 43.70 Si 2 + 2 16.34 27.36 K 3 + 4 60.91 Si 3 + 3 33.49 27.42 Si 2 + 3 .; 33.49 Ca1 + 1 6.11 27.38 Si 2 + 3 33.49 Ga1 + 1 6.00 27.49 Si 2 + 3 33.49 Sr1 + 1 5.70 27.80 Si 2 + 3 33.49 Y 1 + 1 6.38 27.11 Y 3 + 3 61.80 Si 3 + 3 33.49 28.31 Mo 4 + 5 61.20 Si 3 + 3 33.49 27.71 Si 2 + 3 33.49 In 1 + 5.79 27.71 Si 2 + 3 33.49 Ba1 + 5.21 28.28 Si 2 + 3 33.49 La1 + 5.58 27.92 Si 2 + 3 33.49 Ce1 + 5.47 28.02 Si 2 + 3 , 33.49 Pr 1 + 5.42 28.07 Si 2 + 3 33.49 Nd1 + 5.49 28.00 Si 2 + 3 33.49 Pm 1 + 5.55 27.94 Si 2 + 3 33.49 Sm 1 + 5.63 27.86 Si 2 + 3 33.49 Eu1 + 5.67 27.83 Si2 + 3 33.49 Gd1 + 6.14 27.35 Si 2 + 3 33.49 Tb1 + 5.85 27.64 Si 2 + 3 33.49 Dy 1 + 5.93 27.57 Si 2 + 3 33.49 Ho1 + 6.02 27.47 Si2 + 3 33.49 Er 1 + 6.10 27.39 Si 2 +. 3 33.49 Tm 1 + 6.18 27.31 Si 2 + 3 33.49 Yb1 + 6.25 27.24 Si 2 + 3 33.49 Lu1 + 5.43 28.07 Si 2 + " 3 33.49 Tl 1 + 6.11 27.38 Si 2 + 3 33.49 Ra1 + 5.28 28.21 Si 2 + 3 33.49 Ac 1 + 5.20 28.29 Si 2 + 3 33.49 Th 1 + 6.10 27.39 Si 2 + 3 33.49 Pa1 + 5.90 27.59 Si 2 + 3. 33,49 U 1 + 6.05 27.44 Si 2 + 3 33.49 Np1 + 6.20 27.29 Si 2 + 3 33.49 Pu 1 + 6.06 27.43 Si 2 + 3 33.49 Am 1 + 5.99 27.50 Si 2 + 3 33.49 Cm 1 + 6.02 27.47 Si 2-ι- 3 33.49 Bk1 + 6.23 27.26 Si 2 + 3 33.49 Cf 1 + 6.30 27.19 Si 2 + 3 33.49 Es1 + 6.42 27.07 S 4 + 5 72.68 Si 4 + 4 45.14 27.54 Sc3 + 4 73.47 Si 4 + 4 45.14 28.33 Mn 4 + 5 72.40 Si 4 + 4 45.14 27.26 Si 3 + 4 45.14 Co 2 + 2 17.06 28.08 Si 3 + 4 45.14 Zn2 + 2 17.96 27.18 Si 3 + 4 45.14 Ru2 + 2 16.76 28.38 Si 3 + 4 45.14 Rh2 + 2 18.08 27.06 Si 3 + 4 45.14 Cd2 + 2 16.91 28.23 Sn4 + 5 72.28 Si 4 + 4 45.14 27.14 Si 3 + 4 45.14 Bi2 + 2 16.69 28.45 Si 4 + 5 166.77 Cu7 + 7 139.00 27.77 Nb3 + 4 38.30 P 1 + 1 10.49 27.81 Pr3 + 4 38.98 P 1 + 1 10.49 28.49 S 3 + 4 47.30 P 2 + 2 19.73 27.57 Br3 + 4 47.30 P 2 + 2 19.73 27.57 P 3 + 4 51.37 S 2 + 2 23.33 28.04 P 3 + 4 51.37 CI2 + 2 23.81 27.56 Co4 + 5 79.50 P 4 + 4 51.37 28.13 P 3 + 4 51.37 Kr2 + 2 24.36 27.01 Kr5 + 6 78.50 P 4 + 4 51.37 27.13 P 3 + 4 51.37 Zr3 + 3 22.99 28.38 P 3 + 4 51.37 Sm 3 + 3 23.40 27.97 P 3 + 4 51.37 . Tm 3 + 3 23.68 27.69 P 3 + 4 51.37 Hf 3 + 3 23.30 28.07 P 4 + 5 65.02 Cu3 + 3 36.83 28.19 Ge4 + 5 93.50 P 5 + 5 65.02 28.48 P 4 + 5 65.02 Kr3 + 3 36.95 28.07 Y 5 + 6 93.00 P 5 + 5 65.02 27.98 P 4 + 5 65.02 Cd3 + 3 37.48 27.54 P 4 + 5 65.02 Te4 + 4 37.41 27.61 P 4 + 5 65.02 Ce4 + 4 36.76 28.27 P 5 + 6 220.43 Br8 + 8 192.80 27.63 P 7 + 8 309.41 S 7 + 7 280.93 28.48 Nb3 + 4 38.30 S 1 + 1 10.36 27.94 Cd2 + 3 37.48 S 1 + 1 10.36 27.12 Te3 + 4 37.41 S 1 + 1 10.36 27.05 Ca2 + 3 50.91 S 2 + 2 23.33 27.58 Mn3 + 4 51.20 S 2 + 2 23.33 27.87 Co3 + 4 51.30 S 2 + 2 23.33 27.97 Nb4 + 5 50.55 S 2 + 2 23.33 27.22 S 2 + 3 34.83 Sc1 + 6.54 28.29 S 2 + 3 34.83 Ti 1 + 6.82 28.01 S 2 + 3 34.83 V 1 + 6.74 28.09 S 2 + 3 34.83 Cr 1 + 6.77 28.06 S 2 + 3 34.83 Mn1 + 7.43 27.40 S 2 + 3 34.83 Ni 1 + 7.64 27.20 S 2 + 3 34.83 Cu1 + 7.73 27.10 S 2 + 3 34.83 Y 1 + 6.38 28.45 S 2 + 3 34.83 Zr1 + 6.84 27.99 S 2 + 3 34.83 Nb1 + 6.88 27.95 S 2 + 3 34.83 Mo1 + 7.10 27.73 S 2 + 3 34.83 Tc1 + 7.28 27.55 S 2 + 3 34.83 Ru1 + 7.37 27.46 S 2 + 3 34.83 Rh1 + 7.46 27.37 S 2 + 3 34.83 Ag1 + 7.58 27.25 S 2 + 3 34.83 Sn 1 + 7.34 27.49 S 2 + 3 34.83 Hf 1 + 6.60 28.23 S 2 + 3 34.83 Pb1 + 7.42 27.41 S 2 + 3 34.83 . 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Co 4 + 4 51.30 28.20 Co 7 + 8 157.00 Co 7 + 7 129.00 28.00 Co 7 + 8 157.00 Co 7 + 7 129.00 28.00 Co 7 + 8 157.00 Y 8 + 8 129.00 28.00 Ni2 + 3 35.17 Ni 1 + 1 7.64 27.53 Br2 + 3 36.00 Ni 1 + 1 7.64 28.36 Ag2 + 3 34.83 Ni 1 + 1 7.64 27.20 Ge3 + 4 45.71 Ni 2 + 2 18.17 27.54 Mo3 + 4 46.40 Ni 2 + 2 18.17 28.23 Lu3 + 4 45.19 Ni2 + 2 18.17 27.02 Bi 3 + 4 45.30 Ni 2 + 2 18.17 27.13 Ni2 + 3 35.17 Ni 1 + 7.64 27.53 Ni2 + 3 35.17 Cu1 + 7.73 27.44 Ni 2 + 3 35.17 Ge1 + 7.90 27.27 As 4 + 5 63.63 Ni3 + 3 35.17 28.46 Ni2 + 3 35.17 Zr1 + 6.84 28.33 Ni2 + 3 35.17 Nb1 + 6.88 28.29 Ni2 + 3 35.17 Mo1 + 7.10 28.07 Ni2 + 3 35.17 Tc1 + 7.28 27.89 Ni2 + 3 35.17 Ru1 + 7.37 27.80 Ni 2 + 3 35.17 Rh1 + 7.46 27.71 Ni2 + 3 35.17 Ag 1 + 7.58 27.59 Ni2 + 3 35.17 Sn 1 + 7.34 27.83 Ni2 + 3 35.17 Ta1 + 7.89 27.28 Ni2 + 3 35.17 W 1 + 7.98 27.19 Ni2 + 3 35.17 Re1 + 7.88 27.29 Ni2 + 3 35.17 Pb1 + 7.42 27.75 Ni2 + 3 35.17 Bi 1 + 7.29 27.88 Zn4 + 5 82.60 Ni 4 + 4 54.90 27.70 Ni 3 + 4 54.90 Rb2 + 2 27.28 27.62 Ni 3 4 54.90 Mo3 + 3 27.16 27.74 Cu5 + 6 103.00 Ni 5 + 5 75.50 27.50 Ni4 + 5 75.50 Br4 + 4 47.30 28.20 Br 6 + 7 103.00 Ni 5 + 5 75.50 27.50 Nb5 + 6 102.60 Ni 5 + 5 75.50 27.10 Ni5 + 6 108.00 Cu5 + 5 79.90 28.10 Rb7 + 8 136.00 Ni6 + 6 108.00 28.00 Ni7 + 8 162.00 Zn7 + 7 134.00 28.00 Br2 + 3 36.00 Cu1 + 1 7.73 28.27 Ag2 + 3 34.83 Cu1 + 1 7.73 27.10 Br 3 + 4 47.30 Cu2 + 2 20.29 27.01 Cu2 + 3 36.83 Zn1 + 1 9.39 27.44 Ga3 + 4 64.00 Cu3 + 3 36.83 27.17 Cu2 + 3 36.83 As 1 + 1 9.81 27.02 Cu2 + 3 36.83 Se1 + 1 9.75 27.08 Kr4 + 5 64.70 Cu3 + 3 36.83 27.87 Cu2 + 3 36.83 Pd1 + 8.34 28.49 Cu2 + 3 36.83 Cd1 + 8.99 27.84 Cu2 + 3 36.83 Sb1 + 8.64 28.19 Cu2 + 3 36.83 Te1 + 9.01 27.82 Cu2 + 3 36.83 Os1 + 8.70 28.13 Cu2 + 3 36.83 Ir 1 + 9.10 27.73 Cu2 + 3 36.83 Pt 1 + 9.00 27.83 Cu2 + 3 36.83 Au 1 + 9.23 27.61 Cu2 + 3 36.83 Po1 + 8.42 28.41 Zn4 + 5 82.60 Cu4 + 4 55.20 27.40 Cu3 + 4 55.20 Rb2 + 2 27.28 27.92 Cu3 + 4 55.20 Mo3 + 3 27.16 28.04 Cu3 + 4 55.20 In 3 + 3 28.03 27.17 Cu3 + 4 55.20 Te3 + 3 27.96 27.24 Zn5 + 6 108.00 Cu5 + 5 79.90 28.10 Cu4 + 5 79.90 Kr4 + 4 52.50 27.40 Cu4 + 5 79.90 Rb4 + 4 52.60 27.30 Sb5 + 6 108.00 Cu5 + 5 79.90 28.10 Cu6 + 7 139.00 Kr7 + 7 111.00 28.00 Kr2 + 3 36.95 Zn1 + 1 9.39 27.56 Cd2 + 3 37.48 Zn1 + 1 9.39 28.09 Te3 + 4 37.41 Zn 1 + 1 9.39 28.02 Ce3 + 4 36.76 Zn1 + 1 9.39 27.36 Ge3 + 4 45.71 Zn2 + 2 17.96 27.75 Mo3 + 4 46.40 Zn2 + 2 17.96 28.44 Lu3 + 4 45.19 Zn2 + 2 17.96 27.23 Bi 3 + 4 45.30 • Zn2 + 2 17.96 27.34 Zn2 + 3 39.72 Br 1 + 1 11.81 27.91 Zn2 + 3 39.72 Y 2 + 2 12.24 27.48 Mo 5 + 6 68.00 Zn3 + 3 39.72 28.28 Zn2 + 3 39.72 Xe1 + 1 12.16 £7.59 Zn2 + 3 39.72 Eu2 + 2 11.24 28.48 Zn2 + 3 39.72 Gd2 + 2 12.09 27.63 Zn2 + 3 39.72 Tb2 + 2 11.52 28.20 Zn2 + 3 39.72 Dy 2 + 2 11.67 28.05 Zn2 + 3 39.72 Ho 2 + 2 11.80 27.92 Zn2 + 3 39.72 Er2 + 2 11.93 27.79 Zn2 + 3 39.72 Tm2 + 2 12.05 27.67 Zn2 + 3 39.72 Yb2 + 2 12.18 27.54 Zn3 + 4 59.40 Rh3 + 3 31.06 28.34 Zn3 + 4 59.40 Xe3 + 3 32.10 27.30 Zn 3 + 4 59.40 Pb3 + 3 31.94 27.46 Kr6 + 7 111.00 Zn5 + 5 82.60 28.40 Rb7 + 8 136.00 Zn6 + 6 108.00 28.00 Zn6 + 7 134.00 Sr7 + 7 106.00 28.00 Ge2 + 3. 34.22 Ga1 + 6.00 28.22 Zr3 + 4 34.34 Ga1 + 6.00 28.34 I 2 + 3 33.00 ~ Ga1 + 6.00 27.00 Hf 3 + 4 33.33 Ga1 + 6.00 27.33 Hg2 + 3 34.20 Ga1 + 6.00 28.20 Te4 + 5 58.75 Ga3 + 3 30.71 28.04 Ga3 + ■4 64.00 Br3 + 3 36.00 28.00 Ga3 + 4 -. 64.00 Kr3 + 3 36.95 27.05 Ga3 + * 4 • 64.00 Ce4 + 4 36.76 27.24 Br2 + 3 36.00 Ge1 + 1 7.90 28.10 Se3 + 4 42.94 Ge2 + 2 15.93 27.01 Sr2 + 3 43.60 Ge2 + 2 15.93 27.67 Sb3 + 4 44.20 Ge2 + 2 15.93 28.27 Gd3 + ' 4 44.00 Ge2 + 2 15.93 28.07 Yb3 + 4 43.70 Ge2 + 2 15.93 27.77 Ger2 + 3 34.22 Y 1 + 1 6.38 27.84 Y 3 + 4 61.80 Ge3 + 3 34.22 27.58 Ge2 + 3 34.22 • Zr 1 + 6.84 27.38 Ge2 + 3 34.22 Nb1 + 6.88 27.34 Ge2 + 3 34.22 Mo1 + 7.10 27.12 Ge2 + 3 34.22 In 1 + 5.79 28.43 Ge2 + 3 34.22 Gd1 + 6.14 28.08 Ge2 + 3 34.22 Tb1 + 5.85 28.37 Ge-2 + 3 34.22 Dy 1 + 5.93 28.29 Ge2 -. 3 34.22 Ho1 + 6.02 28.20 Ge2 + 3 34.22 Er1 + 6.10 28.12 Ge2 + 3 34.22 Tm 1 + 6.18 28.04 Ge2 + 3 34.22 Yb1 + 6.25 27.97 Ge2 + 3 34.22 Hf 1 + 6.60 27.62 Ge2 + 3 34.22 Tl 1 + 6.11 28.11 Ge2 + 3 34.22 Th 1 + 6.10 28.12 Ge2 + 3 34.22 Pa1 + 5.90 28.32 Ge2 + 3 34.22 U 1 + 6.05 28.17 Ge2 + 3 34.22 Np1 + 6.20 28.02 Ge2 + 3 34.22 Pu 1 + 6.06 28.16 Ge2 + 3 34.22 Am 1 + 5.99 28.23 Ge2 + 3 34.22 Cm 1 + 6.02 28.20 Ge2 + 3 34.22 Bk1 + 6.23 27.99 Ge2 + 3 34.22 Cf 1 + 6.30 27.92 Ge2 + 3 34.22 Es1 + 6.42 27.80 Ge3 + 4 45.71 As 2 + 2 18.63 27.08 Ge3 + 4 45.71 Rh2 + 2 18.08 27.63 Ge3 + 4 45.71 Te2 + 2 18.60 27.11 Ge3 + 4 45.71 Pt2 + 2 18.56 27.15 Kr2 + 3 36.95 As 1 + 1 9.81 27.14 Nb3 + 4 38.30 As 1 + 1 9.81 28.49 Cd2 + 3 37.48 As 1 + 1 9.81 27.67 Te3 + 4 37.41 As 1 + 1 9.81 27.60 Mo3 + 4 46.40 As 2 + 2 18.63 27.77 Sb4 + 5 56.00 As 3 + 3 28.35 27.65 Bi 4 + 5 56.00 As 3 + 3 28.35 27.65 As 3 + 4 50.13 Br2 + 2 21.80 28.33 Kr5 + 6 78.50 As 4 + 4 50.13 28.37 As 3 + 4 50.13 . 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X_ en N N N N N N N N N N N N N N N N < X CO LU Q X LU |- CL Z Z Z Z Z Z Z Z Z Z Nb3 + 4 38.30 Ra2 + 2 10.15 28.15 N 4 + 5 50.55 Nd3 + 3 22.10 28.45 Nb4 + 5 50.55 Pm3 + 3 22.30 28.25 Nb4 + 5 50.55 Sm 3 + 3 23.40 27.15 Nb4 + 5 50.55 Dy3 + 3 22.80 27.75 Nb4 + 5 50.55 Ho3 + 3 22.84 27.71 Nb4 + 5 50.55 Er3 + 3 22.74 27.81 Nb4 + 5 50.55 Hf 3 + 3 23.30 27.25 Mo7 + 8 153.00 Nb7 + 7 125.00 28.00 Ag2 + 3 34.83 Mo1 + 1 7.10 27.73 Hg2 + 3 34.20 Mo1 + 1 7.10 27.10 Sb3 + 4 44.20 Mo 2 + 2 16.15 28.05 Gd3 + 4 44.00 Mo2 + 2 16.15 27.85 Yb3 + 4 43.70 Mo2 + 2 16.15 27.55 Mo3 + 4 46.40 Rh2 + 2 18.08 28.32 Mo3 + 4 46.40 In 2 + 2 18.87 27.53 Mo3 + 4 46.40 Te2 + 2 18.60 27.80 Mo3 + 4 46.40 I 2 + 2 19.13 27.27 Mo3 + 4 46.40 La3 + 3 19.18 27.22 Mo3 + 4 46.40 Pt 2 + 2 18.56 27.84 Mo3 + 4 46.40 Hg2 + 2 18.76 27.64 Mo4 + 5 61.20 Pd3 + 3 32.93 28.27 Mo 4 + 5 61.20 I 3 + 3 33.00 28.20 Mo 4 + 5 61.20 Hf 4 + 4 33.33 27.87 Bi 5 + 6 88.30 Mo 5 + 5 61.20 27.10 Mo 5 + 6 68.00 Sn4 + 4 40.73 27.27 Mo 5 + 6 68.00 Nd4 + 4 40.41 27.59 Mo 5 + 6 68.00 Tb4 + 4 39.80 28.20 Ag2 + 3 34.83 . Tc1 + 1 7.28 27.55 Eu3 + 4 42.60 Tc2 + 2 15.26 27.34 Ho3 + 4 42.50 Tc2 + 2 15.26 27.24 Er3 + 4 42.60 Tc2 + 2 15.26 27.34 Tmθ + 4 42.70 Tc2 + 2 15.26 27.44 Yb3 + 4 43.70 Tc2 + 2 15.26 • 28.44 Pb3 + 4 42.32 Tc2 + 2 15.26 27.06 Ag2 + 3 34.83 Ru1 + 1 7.37 27.46 Sb3 + . 4 44.20 Ru2 + 2 16.76 27.44 Gd3 + 4 44.00 Ru2 + 2 16.76 27.24 Lu3 + 4 45.19 Ru2 + 2 16.76 28.43 Sb4 + 5 56.00 Ru3 + 3 28.47 27.53 Bi 4 + 5 56.00 Ru3 + 3 28.47 27.53 Ag 2 + 3 34.83 Rh1 + 1 7.46 27.37 Lu3 + 4 45.19 Rh2 + 2 18.08 27.11 Bi 3 + 4 45.30 Rh2 + 2 18.08 27.22 Te4 + 5 58.75 Rh3 + 3 31.06 27.69 Rh2 + 3 31.06 Cs1 + 3.89 27.17 Ce3 + 4 36.76 Pd1 + 8.34 28.42 Pd2 + 3 32.93 In 1 + 5.79 27.14 Pd2 + 3 32.93 Ba1 + 5.21 27.72 Pd2 + 3 32.93 La1 + 5.58 27.35 Pd2 + 3 32.93 Ce1 + 5.47 27.46 Pd2 + 3 32.93 Pr 1 + 5.42 27.51 Pd2 + 3 32.93 Nd1 + 5.49 27.44 Pd2 + 3 32.93 Pm 1 + 5.55 27.38 Pd2 + 3 32.93 Sm 1 + 5.63 27.30 Pd2 + 3 32.93 Eu1 + 5.67 27.26 Pd2 + 3 32.93 Tb1 + 5.85 27.08 Pd2 + 3 32.93 Dy1 + 5.93 27.00 Pd2 + 3 32.93 Lu 1 + 5.43 27.50 Pd2 + 3 32.93 Ra1 + 5.28 27.65 Pd2 + 3 32.93 Ac1 + 5.20 27.73 Pd2 + 3 32.93 Pa1 + 5.90 27.03 Ag2 + 3 34-83 Ag 1 + 7.58 27.25 La3 + 4 49.95 Ag2 + 2 21.49 28.46 Ag2 + 3 34.83 Ag 1 + 7.58 27.25 Ag2 + 3 34.83 Sn1 + 7.34 27.49 Ag2 + 3 34.83 Hf 1 + 6.60 28.23 Ag2 + 3 34.83 Pb1 + 7.42 27.41 Ag2 +, 34.83 Bi .1 + 7,29 27.54 Ag2 + 3 34.83 Es1 + 6.42 28.41 Cd2 + 3 37.48 Cd1 + 8.99- 28.49 Te3 + 4 37.41 Cd1 + 8.99 28.42 Ce3 + 4 36.76 Cd1 + 1 8.99 27.76 Sb3 + 4 44.20 Cd2 + 2 16.91 27.29 Gd3 + 4 44.00 Cd2 + 2 16.91 27.09 Lu3 + 4 45.19 Cd2 + 2 16.91 28.28 Bi 3 + 4 45.30 Cd2 + 2 16.91 28.39 Cd2 + 3 37.48 Cd1 + 8.99 28.49 Cd2 + 3 37.48 Te1 + 9.01 28.47 Cd2 + 3 37.48 I 1 + 10.45 27.03 Cd2 + 3 37.48 Ba2 + 2 10.00 27.48 Cd2 + 3 37.48 Ir 1 + 9.10 28.38 Cd2 + 3 37.48 Pt 1 + 9.00 28.48 Cd2 + 3 37.48 Au 1 + 9.23 28.25 Cd2 + 3 37.48 Hg1 + 10.44 27.04 Cd2 + 3 37.48 Ra2 + 2 10.15 27.33 I 2 + 3 33.00 In 1 + 5.79 27.21 Hf 3 + 4 33.33 In 1 + 5.79 27.54 Hg2 + 3 34.20 In 1 + 5.79 28.41 Sb4 + 5 56.00 In 3 + 3 28.03 27.97 Bi4 + 5 56.00 In 3 + 3 28.03 27.97 In 3 + 4 54.00 Bi3 + 3 25.56 28.44 Eu3 + 4 42.60 Sn2 + 2 14.63 27.97 Ho3 + 4 42.50 Sn2 + 2 14.63 27.87 Er3 + 4 42.60 Sn2 + 2 14.63 27.97 Tm 3 + 4 42.70 Sn2 + 2 14.63 28.07 Pb3 + 4 42.32 Sn2 + 2 14.63 27.69 Te4 + 5 58.75 Sn3 + 3 30.50 28.25 Pb4 + 5 68.80 Sn4 + 4 40.73 28.07 Sn4 + 5 72.28 Sb4 + 4 44.20 28.08 Sn4 + 5 72.28 . Gd4 + 4 44.00 28.28 Sn4 + 5 72.28 Lu 4 + 4 45.19 27.09 Ce3 + 4 36.76 Sb1 + 1 8.64 28.12 Sb3 + 4 44.20 Sb2 + 2 16.53 27.67 Gd3 + 4 . 44.00 Sb 2 + 2 16.53. 27.47 Yb3 + 4 43.70 Sb2 + 2 16.53 27.17 Sb3 + 4 44.20 Sb2 + 2 16.53 27.67 Sb3 + 4 44.20 Bi2 + 2 16.69 27.51 Sb4 + 5 56.00 Te3 + 3 27.96 28.04 Te3 + 4 37.41 Te 1 + 1 9.01 28.40 Ce3 + 4 36.76 Te1 + 1 9.01 27.75 Bi 4 + 5 56.00 Te3 + 3 27.96 28.04 Te3 + 4 37.41 Te1 + 1 9.01 28.40 Te3 + 4 37.41 Ba2 + 2 10.00 27.41 Te3 + 4 37.41 Ir 1 + 1 9.10 28.31 Te3 + 4 37.41 Pt 1 + 1 9.00 28.41 Te3 + 4 37.41 Au 1 + 1 9.23 28.18 Te3 + 4 37.41 Ra2 + 2 10.15 27.26 Te5 + 6 70.70 Eu4 + 4 42.60 28.10 Te5 + 6 70.70 Ho 4 + 4 42.50 28.20 Te5 + 6 70.70 Er4 + 4 42.60 28.10 Te5 + 6 70.70 Tm 4 + 4 42.70 28.00 Te5 + 6 70.70 Pb4 + 4 42.32 28.38 I 2 + 3 33.00 Ba1 + 5.21 27.79 I 2 + 3 33.00 La1 + 5.58 27.42 I 2 + 3 33.00 Ce1 + 5.47 27.53 1 2 + 3 33.00 Pr 1 + 5.42 27.58 1 2 + 3 33.00 Nd1 + 5.49 27.51 1 2 + 3 33.00 Pm 1 + 5.55 27.45 1 2 + 3 33.00 Sm 1 + 5.63 27.37 1 2 + 3 33.00 Eu1 + 5.67 27.33 1 2 + 3 33.00 Tb1 + 5.85 27.15 1 2 + 3 33.00 Dy1 + 5.93 27.07 1 2 + 3 33.00 Lu 1 + 5.43 27.57 1-2 + 3 33.00 Ra1 + 5.28 27.72 1 2 + 3 33.00 Ac 1 + 5.20 27.80 1 2 + 3 33.00 • Pa1 + 5.90 27.10 1 2 + 3 33.00 Am 1 + 5.99 27.01 Nd3 + 4 40.41 Xe1 + 12.13 28.28 Tb3 + 4 39.80 Xe1 + 12.13 27.67 Xe2 + 3 32.10 Cs1 + 3.89 28.21 Pb2 + 3 31.94 Cs1 + 3.89 • 28.04 Hf 3 + 4 33.33 Ba1 + 5.21 28.12 Hf 3 + 4 33.33 La1 + 5.58 27.75 00 ON O. CM co m m "fr in τ- CD C CO CO CD CO "^ τ- CO C in cθ τ- "fr CD τ- CO in cθ "fr CM CO CD CO CJ) Oθ O O) CO CO CD O 1— W (O i- 0 (O S lO CO O) 'vt ^ W O O N '«f CO i- O W OO CO '!j- CO W CO N CVI Ov N CO S S CO N N N N CO CO N S CO S CO ω oO CO N N N N N N OO N ω oO CO CO CO N N Xf) CM CM CN CM CN CM CM CN CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM P B c* cD CM θ θ o q τ- co τ- τ- cM d T- CM CM CM CM CO CO CO CO CO CO CO CM CM CM CM CM CM CM CM CM CM CM τ- τ- CM CM CM CN "fr -- CM + + + + + + + + + + + + + + + + + + + + "r + T + J +- J +- J +- + ■ J +- J +- J +- + τ + _ τ + CM r- CM CM CM ^ ^ CN CM CM CM oj T - T- CM CO CO CO CO CO CO CO 1— CM T— - " T- CM ^ CM - _ ■* ^ CM co ■ σ b _Q , >» . O _ t- <D CQ tn r ~ ^.. ZZl O - -. XJ _ E_ ιE_ _3ι j_Q_ι _>—» w I__ C.:- T__J Tw> k. C -Q O C 3 —I CL in z Q- Q X LU U U θ _= Q- < Q- Q_ _L Z Q- C LU I- Q X LU DC Z CD UJ - >- Z Q- I s - co ιn ιn ιn ιn ιn ιn ιn co oo co cD CD CD co co co oD co co co co co co o3 co co cθ τ- τ- τ- τ- o co o C_D O) 0) CD CJ> 0) 0) C3) CO CJ) l s - l s - l- l- l s - CO CJ) C_D CJ) _D OT O) p p c3) CJ) CJ) CO d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d τ-^ tO _ , ^ ^ 't ^ '!|- 't CO CO . CO CO CO C C CO CO CO CO C CO CO CO «O C CO CO ^ _ i _' CO C x. "fr "fr "fr "fr "fr- "* "fr "fr- "fr ^* "fr "fr "fr "* "* "fr "fr "fr "fr ^* "fr "fr "fr "fr ^ "fr _* -^ CM CM CO CO Hf 3 + 4 33.33 Sm 1 + 1 5.63 27.70 Sm3 + 4 41.40 Lu2 + 2 13.90 27.50 Pb4 + 5 68.80 Sm 4 + 4 41.40 27.40 Hf 3 + 4 33.33 Eu1 + 1 5.67 27.66 Eu3 + 4 42.60 Hf 2 + 2 14.90 27.70 Eu3 + 4 42.60 Pb2 + 2 15.03 27.57 Hf 3 + 4 33.33 Gd1 + 1 6.14 27.19 Hg2 + 3 34.20 Gd1 + 1 6.14 28.06 Tb3 + 4 39.80 Gd2 + 2 12.09 27.71 Gd3 + 4 44.00 Bi 2 + 2 16.69 27.31 Hf 3 + 4 33.33 Tb1 + 1 5.85 27.48 Hg2 + 3 34.20 Tb 1 + 1 5.85 28.35 Tb3 + 4 39.80 Tb2 + 2 11.52 28.28 Tb3 + 4 39.80 Tb2 + 2 11.52 28.28 Tb3 + 4 39.80 Dy 2 + 2 11.67 28.13 Tb3 + 4 39.80 Ho 2 + 2 11.80 28.00 Tb3 + 4 39.80 Er2 + 2 11.93 27.87 Tb3 + 4 39.80 Tm2 + 2 12.05 27.75 Tb3 + 4 39.80 Yb2 + 2 12.18 27.62 Hf 3 + 4 33.33 Dy 1 + 1 5.93 27.40 Hg2 + 3 34.20 Dy 1 + 1 5.93 28.27 Dy3 + 4 41.50 Lu2 + 2 13.90 27.60 Pb4 + 5 68.80 Dy 4 + 4 41.50 27.30 Hf 3 + 4 33.33 Ho1 + 1 6.02 27.31 Hg2 + 3 34.20 Ho1 + 1 6.02 28.18 Ho3 + 4 42.50 Hf 2 + 2 14.90 27.60 Ho 3 + 4 42.50 Pb2 + 2 15.03 27.47 Hf 3 + 4 33.33 Er1 + 1 6.10 27.23 Hg2 + 3 34.20 • Er1 + 1 6.10 28.10 Er3 + 4 42.60 Hf 2 + 2 14.90 27.70 Er3 + 4 42.60 Pb2 + 2 15.03 27.57 Hf 3 + 4 33.33 Tm 1 + 1 6.18 27.15 Hg2 + 3 34.2Q Tm 1 + 1 6.18 28.02 Tm 3 + 4 42.70 Hf 2 + 2 14.90 27.80 Tm 3 + 4 42.70 Pb2 + 2 15.03 27.67 Hf 3 + 4 33.33 Yb1 + 1 6.25 27.08 Hg2 + 3 34.20 Yb1 + 1 6.25 27.95 Yb3 + 4 43.70 Bi 2 + 2 16.69 27.01 Hf 3 + 4 33.33 Lu 1 + 1 5.43 27.90 Pb3 + 4 42.32 Lu2 + 2 13.90 28.42 Lu3 + 4 45.19 Bi2 + 2 16.69 28.50 Hg2 + 3 34.20 Hf 1 + 1 6.60 27.60 Pb3 + 4 42.32 Hf 2 + 2 14.90 27.42 Hf 3 + 4 33.33 Tl 1 + 1 6.11 27.22 Hf 3 + 4 33.33 Ra1 + 1 5.28 28.05 Hf 3 + 4 33.33 Ac 1 + 1 5.20 28.13 Hf 3 + 4 33.33 Th 1 + 1 6.10 27.23 Hf 3 + 4 33.33 Pa1 + 1 5.90 27.43 Hf 3 + 4 33.33 U 1 + 1 6.05 27.28 Hf 3 + 4 33.33 Np1 + 1 6.20 27.13 Hf 3 + 4 33.33 Pu 1 + 1 6.06 27.27 Hf 3 + 4 33.33 Am 1 + 1 5.99 27.34 Hf 3 + 4 33.33 Cm 1 + 1 6.02 27.31 Hf 3 + 4 33.33 Bk1 + 1 6.23 27.10 Hf 3 + 4 33.33 Cf 1 + 1 6.30 27.03 Hg2 + 3 34.20 Tl 1 + 1 6.11 28.09 Hg2 + 3 34.20 Th 1 + 1 6.10 28.10 Hg2 + 3 34.20 Pa1 + 1 5.90 28.30 Hg2 + 3 34.20 U 1 + 1 6.05 28.15 Hg2 + 3 34.20 Np1 + 1 6.20 28.00 Hg2 + 3 34.20 Pu 1 + 1 6.06 28.14 Hg2 + 3 34.20 Am 1 + 1 5.99 28.21 Hg2 + 3 34.20 Cm 1 + 1 6.02 28.18 Hg2 + 3 34.20 Bk1 + 1 6.23 27.97 Hg2 + 3 34.20 • Cf 1 + 1 6.30 27.90 Hg2 + 3 34.20 Es 1 + 1 6.42 27.78 Pb3 + 4 42.32 Pb2 + 2 15.03 27.29 Pb3 + 4 42.32 Pb2 + 2 15.03 27.29 n - 16 (resonance shrinkage energy is given by 27.21 eV ; with n - 16, the resonance shrinkage energy is 217.68) Atom n nth Ion- Atom n nth Ion- Energy 00 O "fr m "_- | s - CM 00 "fr 00 τ- C0 CD C0 O lO W N N CO N Cn CD N N N N N N N N N 0 m oo m o r- co co co cM -_- cM i- co τ- CD ^ C S CO τ- ( CD OI O) S C in α) CD N CO ( X H "fr CD CJ) in i- ιn o cD CD oθ "fr cJ) oo cD OT CD σ) in co ιn o oo co i s - CD in σ) i- cD CD co ι ι— T— T— T— T— T— CM T— T— T— T— Ύ— T— T— T— T— 1— T— T— T— CM T— T— T— T— T— T— T— T— T— T— T— OV XT) CM CM CM CM CM CN CN CM CM CM CM CM CM CN CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM P B P. C o >; _-. 0) 0) 0) 0) m CM T- 0 m co "fr T- "fr l- CM "fr O O CO O OO τ- 0 0 0 O O O O O O O > m m co cθ "fr co cM co T- O) T- co r s - CM I s - p p p i- CN p "fr τ- "fr CD o co m m co r-. f s - +-: m CO Φ Φ j . j . _o m C vj CJ) co oo ιn o ) C ) c d d d c_ d d d "fr d d τ- τ- ' cM "fr O) T- CM CM CM c N LU CM CM CM T- CM "fr "fr CO "fr "fr CO -* "fr "fr "fr "fr CO "fr "fr "fr "fr "fr C O "fr "fr "fr "fr "fr T— T- T— CO CM CM CM "fr CO CO "fr CO "fr CO CO "fr "fr "fr "fr "fr "fr "fr "fr "fr "fr "fr "fr -** "fr X3 φ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + o 3 T- T- CO T- CM CM CM co c θ " f r C θ "s ω w , fr , " f r , si" , ' :," ,:,' " f r "fr "fr "fr "fr * ^ "fr XJ Φ Φ Φ Φ Φ ._ —— _ ,_ cc Φu» XJ-»» —— C_ X. Iι__ Ό_ Ec; Ec_; ____ι_ 7w3 -Q 3 ^» __ι . E oo φ X X CQ CQ CQ CQ C ϋ < _- N CO DC CO C CO Q- Z CL C LU CD l- Q X LU I — >- DC I s - ≥c~- σ ) co ^ co cN "fr σ) ^ co ι- ι- ι s - ι s - ι- ι s - ι- ι s - ι s - ι- ι s - ι s - ι ^ .i; g ) > o ^ ro ^ w (. θ (. '<. <o co {o co co co co co co co co co co co co co co co co co co co co " φ C_O. Φ __ 0) T- "fr o o "fr c_D ^ T- 0) 0) 0) 0) C) cj) c_) CJ) CJ) CJ> 0) 0 cn c) CJ) <_n c) cj) C) OT co "fr cN CN "fr CM co cN ^ ιn ιn ιn ιn ιn ιn ιn ιn ιn ιn ιn ιn ιn ιn ιn ιn ιn ιn ιn ιn ιn ιn ιn CM CM CM CM CO CM CM CN CM CN CM CM CM CM CM CM CM CN CM CM CN CM CM CM CM CM CN CN CM CM CM CM 0O N N ( D W N M N N ^ ^ \. ^ ^ ^ ^ ^ ^ ^ τf ^ ^ ^ _- ^ ^ τt- '* \f 'vt τ|- ^ + + + + + + + + + + + + + + + + + + + + + + + + tD CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO < CQ CQ CQ CQ CQ CQ CQ CQ CQ CQ CQ CQ CQ CQ CQ CQ CQ ω cQ CQ CQ CQ CQ CM CM CO co B 3 + 4 259.37 Pb4 + 4 42.32 217.05 B 3 + 4 259.37 Bi 4 + 4 45.30 214.07 B 4 + 5 340.22 Ne5 + 5 126.21 214.01 B 4 + 5 340.22 Al 4 + 4 119.99 220.23 B 4 + 5 340.22 Ar7 + 7 124.32 215.90 B 4 + 5 340.22 Ti 6 + 6 119.36 220.86 B 4 + 5 340.22 Mn7 + 7 119.27 220.95 B 4 + 5 340.22 Fe7 + 7 125.00 215.22 B 4 + 5 340.22 Kr8 + 8 126.00 214.22 B 4 + 5 340.22 Sr8 + 8 122.30 217.92 B 4 + 5 340.22 Nb7 + 7 125.00 215.22 Ne7 + 8 239.09 C 2 + 2 24.38 214.71 Al 6 + 7 241.43 C 2 + 2 24.38 217.05 Na7 + 8 264.18 C 3 + 3 47.89 216.29 Mg7 + 8 265.90 C 3 + 3 47.89 218.01 P 6 + 7 263.22 C 3 + 3 47.89 215.33 Al 7 + 8 284.59 C 4 + 4 64.49 220.10 S 6 + 7 280.93 C 4 + 4 64.49 216.44 C 4 + 5 392.08 Na6 + 6 172.15 219.93 C 4 + 5 392.08 V 8 + 8 173.70 218.38 C 4 + 5 392.08 Zn8 + 8 174.00 218.08 Si 6 + 7 246.52 N 2 + 2 29.60 216.92 Na7 + 8 264.18 N 3 + 3 47.45 216.73 Mg7 + 8 265.90 N 3 + 3 47.45 218.45 P 6 + 7 263.22 N 3 + 3 47.45 215.77 S 7 + 8 328.23 05 + 5 113.90 214.33 F 7 + 8 953.89 0 7 + 7 739.32 214.57 S 6 + 7 280.93 F 3 + 3 62.71 218.22 Si 7 + 8 303.17 • F 4 + 4 87.14 216.03 Ne7 + 8 239.09 Ne1 + 1 21.56 217.53 Al 6 + 7 241.43 Ne1 + 1 21.56 219.87 S 6 + 7 280.93 Ne3 + 3 63.45 217.48 Ne7 + 8 239.09 Ne1 + 1 21.56 217.53 Ne7 + 8 239.09 Al 2 + 2 18.83 220.26 Ne7 + 8 239.09 P 2 + 2 19.73 219.36 Ne7 + 8 239.09 S 2 + 2 23.33 215.76 Ne7 + 8 239.09 CI2 + 2 23.81 215.28 Ne7 + 8 239.09 Sc3 + 3 24.76 214.33 Ne7 + 8 239.09 Ni2 + 2 18.17 220.92 Ne7 + 8 239.09 Cu2 + 2 20.29 218.80 Ne7 + 8 239.09 Ga2 + 2 20.51 218.58 Ne7 + 8 239.09 As 2 + 2 18.63 220.46 Ne7 + 8 239.09 Se2 + 2 21.19 217.90 Ne7 + 8 239.09 Br2 + 2 21.80 217.29 Ne7 + 8 239.09 Kr2 + 2 24.36 214.73 Ne7 + 8 239.09 Y 3 + 3 20.52 218.57 Ne7 + 8 239.09 Zr3 + 3 22.99 216.10 Ne7 + 8 239.09 Nb3 + 3 25.04 214.05 Ne7 + 8 239.09 Pd2 + 2 19.43 219.66 Ne7 + 8 239.09 Ag2 + 2 21.49 217.60 Ne7 + 8 239.09 In 2 + 2 18.87 220.22 Ne7 + 8 239.09 Te2 + 2 18.60 220.49 Ne7 + 8 239.09 I 2 + 2 19.13 219.96 Ne7 + 8 239.09 Xe2 + 2 21.21 217.88 Ne7 + 8 239.09 La3 + 3 19.18 219.91 Ne7 + 8 239.09 Ce3 + 3 20.20 ' 218.89 Ne7 + 8 239.09 Pr3 + 3 21.62 217.47 Ne7 + 8 239.09 Nd3 + 3 22.10 216.99 Ne7 + 8 239.09 Pm3 + 3 22.30 216.79 Ne7 + 8 239.09 Sm3 + 3 23.40 215.69 Ne7 + 8 239.09 Eu3 + 3 24.90 214.19 Ne7 + 8 239.09 Gd3 + 3 20.63 218.46 Ne.7 + 8 239.09 Tb3 + 3 21.91 217.18 Ne7 + 8 239.09 Dy 3 + 3 22.80 216.29 Ne7 + 8 239.09 ' Ho 3 + 3 22.84 216.25 Ne7 + 8 239.09 Er3 + 3 22.74 216.35 Ne7 + 8 239.09 Tm 3 + 3 23.68 215.41 Ne7 + 8 239.09 Yb3 + 3 25.03 214.06 Ne ' 7-κ 8 239.09 Lu 3 + 3 20796 218.13 Ne7 + 8 239.09 Hf 3 + 3 23.30 215.79 Ne7 + 8 239.09 Pt2 + 2 18.56 220.53 Ne7 + 8 239.09 Au 2 + 2 20.50 218.59 Ne7 + 8 239.09 Hg2 + 2 18.76 220.33 Ne7 + 8 239.09 Tl 2 + 2 20.43 218.66 Mg6 + 7 224.94 Na1 + 1 5.14 219.80 P 5 + 6 220.43 Na1 + 1 5.14 215.29 Na7 + 8 264.18 Na2 + 2 47.29 216.89 Mg7 + 8 265.90 Na2 + 2 47.29 218.61 P 6 + 7 263.22 Na2 + 2 47.29 215.93 Na7 + 8 264.18 Na2 + 2 47.29 216.89 Na7 + 8 264.18 Si4 + 4 45.14 219.04 Na7 + 8 264.18 S 4 + 4 47.30 216.88 Na7 + 8 264.18 K 3 + 3 45.72 218.46 Na7 + 8 264.18 Ti4 + 4 43.27 220.91 Na7 + 8 264.18 V 4 + 4 46.71 217.47 Na7 + 8 264.18 Cr4 + 4 49.10 215.08 Na7 + 8 264.18 Ge4 + 4 45.71 218.47 Na7 + 8 264.18 As 4 + 4 50.13 214.05 Na7 + 8 264.18 Br4 + 4 47.30 216.88 Na7 + 8 264.18 Sr3 + 3 43.60 220.58 Na7 + 8 264.18 Mo 4 + 4 46.40 217.78 Na7 + 8 264.18 Sb4 + 4 44.20 219.98 Na7 + 8 264.18 La4 + 4 49.95 214.23 Na7 + 8 264.18 Gd4 + 4 44.00 220.18 Na7 + 8 264.18 Yb4 + 4 43.70 220.48 Na7 + 8 264.18 Lu4 + 4 45.19 218.99 Na7 + β 264.18 Bi 4 + 4 45.30 218.88 Mg6 + 7 224.94 Mg1 + 1 7.65 217.29 S 7 + 8 328.23 Mg4 + 4 109.24 218.99 Mg6 + 7 224.94 Mg1 + 7.65 217,29 Mg6 + 7 224.94 • Al 1 + 5.99 218.95 Mg6 + 7 224.94 Si 1 + .8.15 216.79 Mg6 + 7 224.94 P 1 + 10.49 214.45 Mg 6 + 7 224.94 S 1 + 10.36 214.58 Mg6 + 7 224.94 K _ + "4.34 ,220.60 Mg6 + 7 224.94 Ca1 + 6.11 218.83 Mg 6 + 7 224.94 Sc1 + 6.54 218.40 Mg6 + 7 224.94 Ti 1 + 6.82 218.12 Mg6 + 7 224.94 V 1 + ' 6.74 218.20 Mg6 + 7 224.94 cn + j 6.77 218.17 Mg6 + 7 224.94 Mn1 + " 7.43 217.51 Mg 6 + 7 224.94 Fe1 + ' 7.87 217.07 Mg6 + 7 224.94 Co1 + " I 7.86 217.08 Mg6 + 7 224.94 Ni 1 + " I 7.64 217.31 Mg6 + 7 224.94 Cu1 + " I 7.73 217.21 Mg6 + 7 224.94 Zn1 + " I 9.39 215.55 Mg6 + 7 224.94 Ga1 + " I 6.00 218.94 Mg6 + 7 224.94 Ge1+ ' I 7.90 217.04 Mg 6 + 7 224.94 As 1 + I 9.81 215.13 Mg6 + 7 224.94 Se1 + " I 9.75 215.19 Mg6 + 7 224.94 Rb1 + I 4.18 220.76 Mg 6 + 7 224.94 Sr 1 + I 5.70 219.24 Mg6 + 7 224.94 Y 1 + I 6.38 218.56 Mg6 + 7 224.94 zn + I 6.84 218.10 Mg6 + 7 224.94 Nb1 + I 6.88 218.06 Mg6 + 7 224.94 Mo1 + 1 7.10 217.84 Mg6 + 7 224.94 Tc1 + I 7.28 217.66 Mg6 + 7 224.94 Ru1 + I 7.37 217.57 Mg6 + 7 224.94 Rh1 + l 7.46 217.48 Mg6 + 7 224.94 Pd1 + I 8.34 216.60 Mg6 + 7 224.94 Ag 1 + " 1 7.58 217.36 Mg6 + 7 224.94 Cd1 + 1 8.99 215.95 Mg6 + 7 224.94 In 1 + 1 5.79 219.15 Mg6 + 7 224.94 Sn 1 + 1 7.34 217.60 Mg6 + 7 224.94 Sb1 + 1 8.64 216.30 Mg6 + 7 224.94 Te1 + 1 9.01 215.93 Mg 6 + 7 224.94 I 1 + 1 10.45 214.49 Mg6 + 7 224.94 Ba1 + 1 5.21 219.73 Mg6 + 7 224.94 Ba2+ ; 2 10.00 214.94 Mg6 + 7 224.94 La1 + 1 5.58 219.36 Mg6 + 7 224.94 Ce1 + 1 5.47 219.47 Mg6 + 7 224.94 Ce2+ - 2 10.85 214.09 Mg6 + 7 224.94 Pr 1 + 1 5.42 219.52 Mg6 + 7 224.94 Pr 2 + 2 10.55 214.39 Mg 6 + 7 224.94 Nd1 + 1 5.49 219.45 Mg 6 + 7 224.94 Nd2+ ϊ > 10.73 214.21 Mg6 + 7 224.94 Pm 1 + 1 5.55 219.39 Mg6 + 7 224.94 Pm2+ Σ 10.90 214.04 Mg6 + 7 224.94 Sm 1 + 1 5.63 219.31 Mg6 + 7 224.94 Eu1 + - 5.67 219.27 Mg6 + 7 224.94 Gd1+ 1 I 6.14 218.80 Mg6 + 7 224.94 Tb1 + < 5.85 219.09 Mg6 + 7 224.94 Dy 1 + 5.93 219.01 Mg6 + 7 224.94 Ho1 + - I 6.02 218.92 Mg 6 + 7 224.94 Er 1 + " I 6.10 218.84 Mg6 + 7 224.94 Tm 1 + " I 6.18 218.76 Mg 6 + 7 224.94 Yb1 + ' I 6.25 218.69 Mg6 + 7 224.94 Lu1 + " I 5.43 219.51 Mg 6 + 7 224.94 Hf 1 + ' I 6.60 218.34 Mg6 + 7 224.94 Ta1 + " I 7.89 217.05 Mg 6 + 7 224.94 W 1 + I 7.98 216.96 Mg6 + 7 224.94 Re1 + I 7.88 217.06 Mg6 + 7 224.94 Os1 + I 8.70 216.24 Mg6 + 7 224.94 Ir 1 + 1 9.10 215.84 Mg 6 + 7 224.94 Pt 1 + 1 9.00 215.94 Mg6 + 7 224.94 Au 1 + 1 9.23 215.71 Mg 6 + 7 224.94 Hg1 + 1 10.44 214.50 Mg6 + 7 224.94 Tl 1 + 1 6.11 218.83 Mg 6 + 7 224.94 Pb1 + 1 7.42 217.52 Mg 6 + 7 224.94 Bi 1 + 1 7.29 217.65 Mg6 + 7 224.94 Po 1 + 1 8.42 216.52 Mg6 + 7 224.94 Rn1 + 1 10.75 214.19 Mg6 + 7 224.94 Ra1 + 1 5.28 219.66 Mg6 + 7 224.94 Ra2+ ; 2 10.15 214.79 Mg6 + 7 224.94 Ac 1 + 1 5.20 219.74 Mg6 + 7 224.94 Th 1 + 1 6.10 218.84 Mg6 + 7 224.94 Pa1 + 1 5.90 219.04 Mg6 + 7 224.94 U 1 + 1 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CM CM CO CO P 6 + 7 263.22 Mo 4 + 4 46.40 216.82 P 6 + 7 263.22 Sb4 + 4 44.20 219.02 P 6 + 7 263.22 Eu 4 + 4 42.60 220.62 P 6 + 7 263.22 Gd4 + 4 44.00 219.22 P 6 + 7 263.22 Ho4 + 4 42.50 220.72 P 6 + 7 263.22 Er4 + 4 42.60 220.62 P 6 + 7 263.22 Tm 4 + 4 42.70 220.52 P 6 + 7 263.22 Yb4 + 4 43.70 219.52 P 6 + 7 263.22 Lu4 + 4 45.19 218.03 P 6 + 7 263.22 Pb4 + 4 42.32 220.90 P 6 + 7 263.22 Bi 4 + 4 45.30 217.92 P 7 + 8 309.41 Ar 6 + 6 91.01 218.40 P 7 + 8 309.41 Sc5 + 5 91.66 217.75 P 7 + 8 309.41 Cr6 + 6 90.56 218.85 P 7 + 8 309.41 Mn6 + 6 95.00 214.41 P 7 + 8 309.41 Ge5 + 5 93.50 215.91 P 7 + 8 309.41 Br6 + 6 88.60 220.81 P 7 + 8 309.41 Sr6 + 6 90.80 218.61 P 7 + 8 309.41 Y 6 + 6 93.00 216.41 S 6 + 7 280.93 K 4 + 4 60.91 220.02 S 6 + 7 280.93 V 5 + 5 65.23 215.70 S 6 + 7 280.93 Ga4 + 4 64.00 216.93 S 6 + 7 280.93 As 5 + 5 63.63 217.30 S 6 + 7 280.93 Kr5 + 5 64.70 216.23 S 6 + 7 280.93 Y 4 + 4 61.80 219.13 S 6 + 7 280.93 Mo5 + 5 61.20 219.73 S 7 + 8 328:23 CI7 + 7 114.19 214.04 S 7 + 8 328.23 Ca6 + 6 108.78 219.45 S 7 + 8 328.23 Sc6 + 6 111.10 217.13 S 7 + 8 328.23 Ni 6 + 6 108.00 220.23 S 7 + 8 328.23 Zn6 + 6 108.00 220.23 S 7 + 8 328.23 Kr7 + 7 111.00 217.23 S<7 + 8 328.23 Sb6 + 6 108.00 220.23 CI7 + 8 348.28 Ca7 + 7 127.70 220.58 CI7 + 8 348.28 V 6 + 6 128.12 220.16 CI7 + 8 348.28 Co7 + 7 129.00 219.28 CI7 + 8 348.28 Ni 7 + 7 133.00 215.28 CI7 + 8 348.28 Zn7 + 7 134.00 214.28 CI7 + 8 348.28 As 6 + 6 127.60 220.68 CI7 + 8 348.28 Y 8 + 8 129.00 219.28 n = 54 (resonance shrinkage energy is given by -r 27.21 e V; with n- 54, the resonance shrinkage energy ' is 734.67) Atom n nth Ion¬ Atom n nth Ion¬ Energy Oxidiz¬ ization Reduced ization Hole ed Energy Energy (eV) (eV) (eV) 06 + 7 739.32 Li 1 + 5.39 733.92 F 7 + 8 953.89 Be 4 + 4 217.71 736.17 O 6 + 7 739.32 B 1 + 8.30 731.02 07 + 8 871.39 0 6 + 138.12 733.27 06 + 7 739.32 Na1 + 5.14 734.18 06 + 7 739.32 Mg 1 + 7.65 731.67 06 + 7 739.32 Al 1 + 5.99 733.33 06 + 7 739.32 Si 1 + 8.15 731.16 06 + 7 739.32 K 1 + 4.34 734.97 O 6 + 7 739.32 Ca1 + 6.11 733.20 06 + 7 739.32 Sc1 + 6.54 732.78 O 6 + 7 739.32 Ti 1 + 6.82 732.49 06 + 7 739.32 V 1 + 6.74 732.58 06 + 7 739.32 Cr 1 + 6,77 732.55 O 6 + 7 739.32 Mn1 + 7.43 731.88 06 + 7 739.32 Fe1 + 7.87 731.45 06 + 7 739.32 Co1 + 7.86 731.46 O 6 + 7 739.32 Ni 1 + 7.64 731.68 06 + 7 739.32 Cu 1 + 7.73 731.59 06 + 7 .739.32 Ga1 + 6.00 733.32 06 + 7 739.32 Ge1 + 7.90 731.42 06 + 7 739,32 Rb1 + 4.18 .735.14 06 + 7 739.32 Sr 1 + 5.70 733.62 06 + 7 739.32 Y 1 + 6.38 732.93 06 + 7 739.32 Zr 1 + 6.84 732.47 06 + 7 739.32 Nb1 + 1 6.88 732.43 O 6 + 7 739.32 Mo1 + 1 7.10 732.22 06 + 7 739.32 Tc1 + 1 7.28 732.03 06 + 7 739.32 Ru 1 + 1 7.37 731.95 06 + 7 739.32 Rh1 + 1 7.46 731.85 06 + 7 739.32 Pd1 + 1 8.34 730.97 06 + 7 739.32 Ag 1 + 1 7.58 731.74 06 + 7 739.32 Cd1 + 1 8.99 730.32 06 + 7 739.32 In 1 + 1 5.79 733.53 06 + 7 739.32 Sn1 + 1 7.34 731.97 06 + 7 739.32 Sb1 + w 8.64 730.67 06 + 7 739.32 Te1 + - 9.01 730.31 06 + 7 739.32 Cs1 + ■ I 3.89 735.42 06 + 7 739.32 Ba1 + ' I 5.21 734.10 06 + 7 739.32 La1 + ■ I 5.58 733.74 06 + 7 739.32 Ce1 + " I 5.47 733.85 06 + 7 739.32 Pr 1 + I 5.42 733.89 O 6 + 7 739.32 Nd1 + I 5.49 733.83 06 + 7 739.32 Pm 1 + l 5.55 733.76 06 + 7 739.32 Sm 1 + I 5.63 733.68 06 + 7 739.32 Eu1 + l 5.67 733.65 06 + 7 739.32 Gd1 + 1 6.14 733.17 06 + 7 739.32 Tb1 + 1 5.85 733.47 06 + 7 739.32 Dy 1 + 1 5.93 733.39 O 6 + 7 739.32 Ho1 + 1 6.02 733.29 06 + 7 739.32 Er1 + 1 6.10 733.22 Θ 6 + 7 739.32 Tm 1 + 1 6.18 733.13 06 + 7 739.32 Yb1 + 1 6.25 733.06 0'6 + 7 739.32 ■ Lu 1 + 1 5.43 733.89 06 + 7 739.32 Hf 1 + 1 6.60 732.72 06 + 7 739.32 Ta1 + 1 7.89 731.42 O 6 + 7 739.32 W 1 + 1 7.98 731.34 OS + 7 739.32 <Re1 + 1 7.S8 731.43 O 6 + 7 739.32 0s1 + 1 8.70 730.61 O 6 + 7 739.32 Ir 1 + 1 9.10 730.22 O 6 + 7 739.32 Pt 1 + 1 9.00 730.32 0 6 + 7 739.32 Au 1 + 9.23 730.09 0 6 + 7 739.32 Tl 1 + 6.11 733.21 0 6 + 7 739.32 P 1 + 7.42 731 .90 0 6 + 7 739.32 Bi 1 + 7.29 732.03 0 6 + 7 739.32 Po 1 + 8.42 730.90 0 6 + 7 739.32 Ra 1 + 5.28 734.04 O 6 + 7 739.32 Ac 1 + 5.20 734.1 1 0 6 + 7 739.32 Th 1 + 6.10 733.22 0 6 + 7 739.32 Pa 1 + 5.90 733.41 O 6 + 7 739.32 U 1 + 6.05 733.27 0 6 + 7 739.32 Np 1 + 6.20 733.1 1 0 6 + 7 739.32 Pu 1 + 6.06 733.26 O 6 + 7 739.32 Am 1 + 5.99 733.33 0 6 + 7 739.32 Cm 1 + 6.02 733.29 O 6 + 7 739.32 Bk 1 + 6.23 733.09 0 6 + 7 739.32 Cf 1 + 6.30 733.02 0 6 + 7 739.32 Es 1 + 6.42 732.90 0 7 + 8 871.39 0 6 + 6 138.12 733.27 0 7 + 8 871.39 Na 5 + 5 138.39 733.00 O 7 + 8 871.39 Mg 5 + 5 141 .26 730.13 0 7 + 8 871.39 Sc 7 + 7 138.00 733.39 0 7 + 8 871.39 Ti 7 + 7 140.80 730.59 0 7 + 8 871.39 Cu 7 + 7 139.00 732.39 0 7 + 8 871.39 Zn 7 + 7 134.00 737.39 0 7 + 8 871 .39 Rb 8 + 8 136.00 735.39 0 7 + 8 871.39 Te 7 + 7 137.00 734.39 F 7 + 8 953.S9 P. 6 + 6 220.43 733.46 Two-ion couples capable of producing energy holes for shrinking deuterium atoms involving cations and anions. The number in the column following the ion, (n), is the nth ionization energy of the atom. For example, Ga 2+ +■ 30.71 eV = Ga3+ + e" and H + e " - H- + 3.08 eV . Atom n nt Ion¬ Atom n nth lon- Energy Oxidiz¬ ization Reduced ization • Hole ed Energy Energy (eV) (eV) (eV) As 2 + 3 28.35 H 0.80 27.55 Ru 2 + 3 28.47 H 0.80 27.67 In 2 + 3 28.03 H 0.80 27.23 Te 2 + 3 27.96 H 0.80 27.16 Al 2 + 3 28.45 H I 0.80 27.65 Ar 1 + 2 27.63 H I 0.80 26.83 As 2 + 3 28.35 Li I 0.61 27.74 Ru 2 + 3 28.47 Li I 0.61 27.86 In 2 + 3 28.03 Li I 0.61 27.42 Te 2 + 3 27.96 L i I 0.61 27.35 Al 2 + 3 28.45 Li I 0.61 27.84 Ar 1 + 2 27.63 Li I 0.61 27.02 Ti 2 + 3 27.49 Li I 0.61 26.88 As 2 + 3 28.35 B I 0.30 28.05 Rb 1 + 2 27.28 B I 0.30 26.98 Mo 2 + 3 27.16 B I 0.30 26.86 Ru 2 + 3 28.47 B I 0.30 28.17 In 2 + 3 28.03 B I 0.30 27.73 Te 2 + 3 27.96 B I 0.30 27.66 Al 2 + 3 28.45 B I 0.30 28.15 Ar 1 + 2 27.63 B I 0.30 27.33 Ti 2 + 3 27.49 B I 0.30 27.19 As 2 + 3 28.35 C I 1.12 27.23 Tc 2 + 3 29.54 C I 1.12 28.42 Ru 2 + 3 28.47 C I 1.12 27.35 In 2 + 3 28.03 C I 1.12 26.91 Te + 3 27.96 C I 1.12 26.84 N 1 + 2 29.60 C I 1.12 28.48 Al 2 + 3 28.45 • C I 1.12 27.33 V 2 + 3 29.31 C I 1.12 28.19 As 2 + 3 28.35 0 1 1.47 26.89 Tc 2 + 3 29.54 O 1 1.47 28.07 Ru 2 + 3 28.47 O I 1.47 27.00 Tl 2 + 3 29.83 0 I 1.47 28.36 N 1 + 2 29.60 0 l 1.47 28.14 Al 2 + 3 28.45 O 1 1.47 26.98 V 2 + 3 29.31 0 -1 1.47 27.84 Ga2 + 3 30.71 F -1 3.45 27.26 Se2 + 3 30.82 F -1 3.45 27.37 Rh2 + 3 31.06 F -1 3.45 27.61 Sn2 + 3 30.50 F -1 3.45 27.05 Pb2 + 3 31.94 F -1 3.45 28.49 K 1 + 2 31.63 F -1 3.45 28.18 Cr2 + 3 30.96 F -1 3.45 27.51 Fe2 3 30.65 F -1 3.45 27.20 As 2 + 3 28.35 Na -1 0.52 27.83 Ru2 + 3 28.47 Na 0.52 27.95 In 2 + 3 28.03 Na 0.52 27.51 Te2 + 3 27.96 Na 0.52 27.44 Al 2 + 3 28.45 Na I 0.52 27.93 Ar 1 + 2 27.63 Na 0.52 27.11 Ti 2 + 3 27.49 Na I 0.52 26.97 As 2 + 3 28.35 Al I 0.52 27.83 Ru2 + 3 28.47 Al I 0.52 27.95 In 2 + 3 28.03 Al I 0.52 27.51 Te2 + 3 27.96 A I I 0.52 27.44 Al 2 + 3 28.45 Al I 0.52 27.93 Ar 1 + 2 27.63 Al I 0.52 27.11 Ti 2 + 3 27.49 Al I 0.52 26.97 As 2 + 3 28.35 Si l 1.39 26.96 Tc2 + 3 29.54 Si- I 1.39 28.15 Ru2 + 3 28.47 Si I 1.39 27.08 Tl 2 + 3< 29.83 Si 1 1.39 28.44 N 1 + 2 29.60 Si 1 1.39 28.21 Al 2 + 3 28.45 Si 1 1.39 27.06 V 2 + 3 29.31 Si 1 1.39 27.92 As 2 + 3. 28.35 P 1 0.78 27.57 Ru2 + 3 28.47 P 1 0.78 27.69 In, 2.+ 3 28.03. P 1 0.78' 27.25 Te2 + 3 27.96 P 1 0.78 27.18 Al 2 + 3 28.45 P 1 0.78 27.67 Ar 1 + 2 27.63 P 1 0.78 26.85 Tc2 + 3 29.54 S I 2.07 27.47 Sn2 + 3 30.50 S I 2.07 28.43 Tl 2 + 3 29.83 S I 2.07 27.76 N 1 + 2 29.60 S I 2.07 27.53 P 2 + 3 30.18 S I 2.07 28.11 V 2 + 3 29.31 S I 2.07 27.24 Ga2 + 3 30.71 Cl I 3.61 27.10 Se2 + 3 30.82 Cl I 3.61 27.21 Rh2 + 3 31.06 Cl I 3.61 27.45 Sn2 + 3 30.50 Cl I 3.61 26.89 Xe2 + 3 32.10 Cl I 3.61 28.49 Pb2 + 3 31.94 Cl I 3.61 28.32 K 1 + 2 31.63 Cl I 3.61 28.01 Cr2 + 3 30.96 Cl I 3.61 27.35 Fe2 + 3 30.65 Cl I 3.61 27.04 As2 + 3 28.35 K I 0.69 27.66 Ru2 + 3 28.47 K I 0.69 27.78 In2 + 3 28.03 K I 0.69 27.34 Te2 + 3 27.96 K I 0.69 27.27 Al 2 + 3 28.45 K I 0.69 27.75 Ar 1 + 2 27.63 K I 0.69 26.93 As2 + 3 28.35 Fe I 0.56 27.79 Ru2 + 3 28.47 Fe I 0.56 27.91 In 2 + 3 28.03 Fe I 0.56 27.47 Te2 + 3 27.96 Fe 1 0.56 27.40 Al 2 + 3 28.45 Fe 1 0.56 27.89 Ar 1 + 2 27.63 Fe 1 0.56 27.07 Ti 2 + 3 27.49 Fe 1 0.56 26.93 As 2 + 3 28.35 Co 1 0.95 27.40 Ru2 + 3 28.47 Co 1 0.95 27.52 In 2 + 3 28.03 Co 1 0.95 27.08 Te2 + 3 27.96 Co 1 0.95 27.01 Al 2 + 3 28.45 Co 1 0.95 27.49 V 2 + 3 29.31 Co 1 0.95 28.36 Tc2 + 3 29.54 Cu 1 1.82 27.72 Tl 2 + 3 29.83 Cu 1 1.82 28.01 N 1 + 2 29.60 Cu 1 1.82 27.78 P 2 + 3 30.18 Cu 1 1.82 28.36 V 2 + 3 29.31 Cu 1 1.82 27.49 Ga2 + 3 30.71 Br 1 3.36 27.35 Se2 + 3 30.82 Br 1 3.36 27.46 Rh2 + 3 31.06 Br 1 3.36 27.70 Sn2 + 3 30.50 Br 1 3.36 27.14 P 2 + 3 30.18 Br 1 3.36 26.82 K 1 + 2 31.63 Br 1 3.36 28.26 Cr2 + 3 30.96 Br 1 3.36 27.60 Fe2 + 3 30.65 Br 1 3.36 27.29 As2 + 3 28.35 Rb 1 0.30 28.05 Rb1 + 2 27.28 Rb 1 0.30 26.98 Mo2 + 3 27.16 Rb 1 0.30 26.86 Ru2 + 3 28.47 Rb 1 0.30 28.17 In 2 + 3 28.03 Rb 1 0.30 27.73 Te2 + 3 27.96 Rb 1 0.30 27.66 Al 2 + 3 28.45 Rb 1 0.30 28.15 Ar 1 + 2 27.63 Rb 1 0.30 27.33 Ti 2 + 3 27.49 Rb 1 0.30 27.19 Ga2 + 3 30.71 1 3.06 27.65 Se2 + 3 30.82 1 3.06 27.76 Rh2 + 3 31.06 1 3.06 28.00 Sn2 + 3 30.50 1 3.06 27.44 P 2 + 3 30.18 1 3.06 27.12 Cr2 + 3 30.96 1 3,06 27.90 Fe2 + 3 30.65 1 3.06 27.59 As2 + 3 28.35 Cs 1 0.30 28.05 Rb1 + 2 27.28 Cs 1 0.30 26.98 Mo2 + 3 27.16 Cs 1 0.30 26.86 Ru2 + 3 28.47 Cs 1 0.30 28.17 In 2 + 3 28.03 Cs 1 0.30 27.73 Te2 + 3 27.96 Cs 1 0.30 27.66 Al 2 + 3 28.45 Cs 1 0.30 28.15 Ar 1 + 2 27.63 Cs 1 0.30 27.33 Ti 2 + 3 27.49 Cs 1 0.30 27.19 Tc 2 + 3 29.54 Se 1 1.70 27.84 Tl 2 + 3 29.83 Se 1 1.70 28.13 N 1 + 2 29.60 Se 1 1.70 27.90 P 2 + 3 30.18 Se 1 1.70 28.48 V 2 + 3 29.31 Se 1 1.70 27.61 Tc 2 + 3 29.54 Te 1 2.20 27.34 Sn 2 + 3 30.50 Te 1 2.20 28.30 Tl 2 + 3 29.83 Te 1 2.20 27.63 N 1 + 2 29.60 Te 1 2.20 27.40 P 2 + 3 30.18 Te 1 2.20 27.98 V 2 + 3 29.31 Te 1 2.20 27.1 1 Fe 2 + 3 30.65 Te 1 2.20 28.45 As 2 + 3 28.35 As 1 0.60 27.75 Ru 2 + 3 28.47 As 1 0.60 27.87 In 2 + 3 28.03 As 1 0.60 27.43 Te 2 + 3 27.96 As 1 0.60 27.36 Al 2 + 3 28.45 As 1 0.60 27.85 Ar 1 + 2 27.63 As 1 0.60 27.03 Ti 2 + 3 27.49 As 1 0.60 26.89 Tc 2 + 3 29.54 Sb 1 2.00 27.54 Tl 2 + 3 29.83 Sb 1 2.00 27.83 N 1 + 2 29.60 Sb 1 2.00 27.60 P 2 + 3 30.18 Sb 1 2.00 28.18 V 2 + 3 29.31 Sb 1 2.00 27.31 As 2 + 3 28.35 Bi 1 0.70 27.65 Ru 2 + 3 28.47 Bi 1 0.70 27.77 In 2 + 3 28.03 Bi 1 0.70 27.33 Te 2 + 3 27.96 Bi 1 0.70 27.26 Al 2 + 3 28.45 . Bi 0.70 27.75 Ar 1 + 2 27.63 Bi 0.70 26.93 Tc 2 + 3 29.54 T l 2.10 27.44 Sn 2 + 3 30.50 T l I 2.10 28.40 Tl 2 + 3 29.83 T l I 2.10 27.73 N 1 + 2 29.60 Tl I 2.10 27.50 P 2 + 3 30.18 T l I 2.10 28.08 V 2 + 3 29.31 T l 2.10 27.21 Tc2 + 3 29.54 Au -1 2.10 27.44 Sn2 + 3 30.50 Au -1 2.10 28.40 Tl 2 + 3 29.83 Au -1 2.10 27.73 N 1 + 2 29.60 Au -1 2.10 27.50 P 2 + 3 30.18 Au -1 2.10 28.08 V 2 + 3 29.31 Au -1 2.10 27.21 As 2 + 3 28.35 Hg -1 1.54 26.81 Tc2 + 3 29.54 Hg -1 1.54 28.00 Ru2 + 3 28.47 Hg -1 1.54 26.93 Tl 2 + 3 29.83 Hg 1.54 28.29 N 1 + 2 29.60 Hg -1 1.54 28.06 Al 2 + 3 28.45 Hg 1.54 26.91 V 2 + 3 29.31 Hg -ι 1.54 27.77 As2 + 3 28.35 As 0.60 27.75 Ru2 + 3 28.47 As I 0.60 27.87 In 2 + 3 28.03 As I 0.60 27.43 Te2 + 3 27.96 As I 0.60 27.36 Al 2 + 3 28.45 As I 0.60 27.85 Ar 1 + 2 27.63 As I 0.60 27.03 Ti 2 + 3 27.49 As I 0.60 26.89 As 2 + 3 28.35 Ce I 1.20 27.15 Tc2 + 3 29.54 Ce 1 1.20 28.34 Ru2 + 3 28.47 Ce 1 1.20 27.27 In 2 + 3 28.03 Ce 1 1.20 26.83 N 1 + 2 29.60 Ce 1 1.20 28.40 Al 2 + 3 28.45 Ce 1 1.20 27.25 V 2 + 3 29.3 Ce 1 1.20 28.11 As 2 + 3 28.35 Fr 1 0.46 27.89 Rb1 + 2 27.28 Fr 1 0.46 26.82 Ru2 + 3 28.47 Fr 1 0.46 28.01 In 2 + 3 28.03 Fr 1 0.46 27.57 Te2 + 3 27.96 Fr 1 0.46 27.50 Al 2 + 3 28.45 Fr 1 0.46 27.99 Ar 1 + 2 27.63 Fr 1 0.46 27.17 Ti 2 + 3 27.49 Fr 1 0.46 27.03 As 2 + 3 28.35 Ge 1 1.20 27.15 Tc2 + 3 29.54 Ge -1 1.20 28.34 Ru2 + 3 28.47 Ge -1 1.20 27.27 In 2 + 3 28.03 Ge -1 1.20 26.83 N 1 + 2 29.60 & -1 1.20 28.40 Al 2 + 3 28.45 Ge -1 1.20 27.25 V 2 + 3 29.31 Ge -1 1.20 28.11 As2 + 3 28.35 Sn -1 1.25 27.10 Tc2 + 3 29.54 Sn 1.25 28.29 Ru2 + 3 28.47 Sn 1.25 27.22 N 1 + 2 29.60 Sn I 1.25 28.35 Al 2 + 3 28.45 Sn I 1.25 27.20 V 2 + 3 29.31 Sn I 1.25 28.06 As2 + 3 28.35 Pb I 1.05 27.30 Tc2 + - 3 29.54 Pb I 1.05 28.49 Ru2 + 3 28.47 Pb I 1.05 27.42 In 2 + 3 28.03 Pb I 1.05 26.98 Te2 + 3 27.96 Pb I 1.05 26.91 Al 2 + 3 28.45 Pb I 1.05 27.40 V 2 + 3 29.31 Pb I 1.05 28.26 Tc2 + 3 29.54 Po I 1.80 27.74 Tl 2 + 3 29.83 Po I 1.80 28.03 N 1 + 2 29.60 Po I 1.80 27.80 P 2 + 3 30.18 Po 1 1.80 28.38 V 2 + 3 29.31 Po 1 1.80 27.51 Ga2 + 3 30.71 At 1 2.80 27.91 Se2 + 3 30.82 At 1 2.80 28.02 Rh2 + 3 31.06 At 1 - 2.80 28.26 Sn2 + 3 30.50 At 1 2.80 27.70 Tl 2 + 3 29.83 • At 1 2.80 27.03 N 1 + 2 29.60 At 1 2.80 26.80 P 2 + 3 30.18 At 1 2.80 27.38 Cr2 + 3 30.96 At 1 2.80 28.16 Fe2 + 3 30.65 At 1 2.80 27.85 As 2 + 3 28.35 Ge 1 1.20 27.15 Tc2 + 3 29.54 Ge 1 1.20 28.34 Ru2 + 3 28.47 Ge 1 1.20 27.27 In 2 + 3 28.03 Ge -1 1.20 26.83 N 1 + 2 29.60 Ge -1 1.20 28.40 Al 2 + 3 28.45 Ge -1 1.20 27.25 V 2 + 3 29.31 Ge -1 1.20 28.11 As2 + 3 28.35 Ga -1 0.37 27.98 Rb1 + 2 27.28 Ga -1 0.37 26.91 Ru2 + 3 28.47 Ga -1 0.37 28.10 In 2 + 3 28.03 Ga -1 0.37 27.66 Te2 + 3 27.96 Ga -1 0.37 27.59 Al 2 + 3 28.45 Ga 0.37 28.08 Ar 1 + 2 27.63 G_ 0.37 27.26 Ti 2 + 3 27.49 Ga I 0.37 ' 27.12 As 2 + 3 28.35 In I 0.35 28.00 Rb1 + 2 27.28 In I 0.35 26.93 Mo 2 + 3 27.16 In I 0.35 26.81 Ru2 + 3 28.47 In I 0.35 28.12 In 2 + 3 28.03 In 1 0.35 27.68 Te2 + 3 27.96 In i 0.35 27.61 Al 2 + 3 28.45 In 1 0.35 28.10 Ar 1 + 2 27.63 In 1 0.35 27.28 Ti 2 + 3 27.49 In 1 0.35 27.14 As 2 + 3 28.35 Ag 1 1.30 27.05 Tc2 + 3 29.54 Ag 1 1.30 28.24 Ru2 + 3 28.47 Ag 1 1.30 27.17 N 1 + 2 29.60 Ag 1 1.30 28.30 Al 2 + 3 28.45 Ag 1 1.30 27.15 V.2 + 3 ,29.31 Ag 1 1.30 28.01 Cations and anions with n : = 16 (resonanc e shrinkage energy is gi n by g 27.21; with n = 16, the resonance shrinkage < snergy is 21 " Atom n nth Ion¬ Atom n nth Ion¬ Energy Oxidiz¬ ization Reduced ization Hole ed Energy Energy (eV) (eV) (eV) ' Be 3 + 4 217.71 H 1 0.80 216.91 Be 3 + 4 217.71 Li 1 0.61 217.10 00 ©V ©N τ- σ) uo _D co σ> cn cN "fr "fr co cM CM in cD CD τ- r- τ- | s . —- τ- co co CO CO r- CO CO CO N O C "fr in CM CJ) CΛ τ- τ- CO CJ) CO C Oθ O τ- r s -. CO CD O "fr CO "fr O _- CM Oθ "fr O l s - CO CO τ- 00 o N CD CD CD (D S N CD CD m ϋ0 (O N (D in 00 N S N (D 00 C0 N 'M N σ) 00 IX) CD 0O N σ ©\ CΛ CM CM CM CM CM CM CM CM CM CM CM CM CM CN CM CM CM CM CM CM CM CN CM CM CM CM CM CM CM CM CM CM CN CM C P B O CM f s - l s - in CM CM 0) 00 l s - l s - T- 0) CD in CM CM CD O CD O O O O O O O O O O O "fr "fr O O θ τ- ' τ- , τ- d o d τ- ' o d o o o τ- τ- d o d θ τ- ' τ- ' cM θ d cM ' o o cM τ^ τ- ' o φ O CO _Q — — — 3 a) rj) CO CO o (D U θ O l-. Z < . l . C ϋ _ 8 3 3 — ___ CO φ Φ φ ( O U CQ £ _ O CO CO < < CO CQ CQ I- < X X < < o CM t— τ- τ- CO CO τ- τ— T— T- T- CO CO T- T- T— T— CO CO τ- C r r CO C τ- CO C r C C CO r CO r C r s - ι- ι- "fr "fr i s - ι- ι s - ι s - ι s - "fr "_- ι- ι- ι s - rs- "fr "fr l- "fr l s - l s - "fr "fr l s - "fr "fr l s - "fr "fr "fr l- "fr l s - "fr ι s - ι- ι s - o o ι s - t s - ι s - ι s - o o ι s - rs- ι s - ι s - o o ι- o r s - ι s - o o i s - o o rs. o o o r s - o r- o τ- τ- τ- CN CM τ- τ- τ- τ- τ- CM CM τ- τ- τ- τ- CN CN τ- CN τ- τ- CM CN τ- CN CM τ- CM CM CM τ- CM τ- CM CM CM CM CN CM CM CM CM CM CN CM CM CM CM CM CM CM CM CM CN CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM ^ ^ ^ ω D ". ^ ^ ^ ^ ω ω ^ ^ "t "f ω Φ _- Φ t "t ω Φ ^ φ φ 'fr ω D CD ^ ω _- ω + + + + + + + + + + + + + + + + + + + + + + + + + + + CO ∞ CO i^ iβ CO CO CO CO ^ ^ O CO O ^ ^ CO ^ CO CO i^ μ- j CO ^ ^ W φ φ φ φ φ φ φ φ φ φ φ φ φ φ φ φ φ φ φ m m m θ- CL m ω ω m ffl CL Q. ffl m m ffl Q. Q. CQ CL CQ CQ Q. Q. CQ Q- Q. CQ Q- Q. Q. CQ Q. CQ α. 00 ON ©V ©V Xf) P CM CM co c l eceu Ga2 + 3 30.71 BF 3 -1 2.65 28.06 Se2 + 3 30.82 BF 3 2.65 28.17 Tc2 + 3 29.54 BF 3 2.65 26.89 Rh2 + 3 31.06 BF 3 2.65 28.41 Sn2 + 3 30.50 BF 3 I 2.65 27.85 Tl 2 + 3 29.83 BF 3 -1 2.65 27.18 N 1 + 2 29.60 BF 3 2.65 26.95 P 2 + 3 30.18 BF 3 2.65 27.53 Cr2 + 3 30.96 BF 3 2.65 28.31 Fe2 + 3 30.65 BF 3 2.65 28.00 Se2 + 3 30.82 N02 3.91 26.91 Rh2 + 3 31.06 Nθ2 I 3.91 27.15 Xe2 + 3 32.10 N02 I 3.91 28.19 Pb2 + 3 31.94 Nθ2 I 3.91 28.03 K 1 + 2 31.63 Nθ2 I 3.91 27.72 Cr2 + 3 30.96 Nθ2 I 3.91 27.05 As 2 + 3 28.35 02 I 0.45 27.90 Rb1 + 2 27.28 02 I 0.45 26.83 Ru2 + 3 28.47 0 2 I 0.45 28.02 In 2 + 3 28.03 02 I 0.45 27.58 Te2 + 3 27.96 0 2 I 0.45 27.51 Al 2 + 3 28.45 θ2 I 0.45 28.00 Ar 1 + 2 27.63 0 2 l 0.45 27.18 Ti 2 + 3 27.49 θ2 1 0.45 27.04 As 2 + 3 28.35 SF6 1 1.43 26.92 Tc2 + 3 29.54 SF6 1 1.43 28.11 Ru2 + 3 28.47 SF6 l 1.43 27.04 Tl 2 + 3 29.83 SF6 l 1.43 28.40 N 1 + 2 29.60 . SF6 1 1.43 28.17 Al 2 + 3 28.45 SF6 1 1.43 27.02 V 2 + 3 29.31 SF6 1 1.43 27.88 Ga2 + 3 30.71 WF6 1 2.74 27.97 Se2 + 3 30.82 WF6 1 2.74 28.08 Tc2 + 3 29.54 WF6 1 2.74 • 26.80 Rh2 + 3 31.06 WF6 1 2.74 28.32 Sn2 + 3 30.50 WF6 1 2.74 27.76 Tl 2 + 3 29.83 WF6 I 2.74 27.09 N 1 + 2 29.60 WF6 2.74 26.86 P 2 + 3 30.18 WF6 I 2.74 27.44 Cr2 + 3 30.96 WF6 I 2.74 28.22 Fe2 + 3 30.65 WF6 I 2.74 27.91 Ga2 + 3 30.71 UF6 I 2.91 27.80 Se2 + 3 30.82 UF6 I 2.91 27.91 Rh2 + 3 31.06 UF6 I 2.91 28.15 Sn2 + 3 30.50 UF6 I 2.91 27.59 Tl 2 + 3 29.83 UF6 I 2.91 26.92 P 2 + 3 30.18 UF6 I 2.91 27.27 Cr2 + 3 30.96 UF6 I 2.91 28.05 Fe2 + 3 30.65 UF6 I 2.91 27.74 Tc2 + 3 29.54 CFs I 1.85 27.69 Tl 2 + 3 29.83 CFs I 1.85 27.98 N 1 + 2 29.60 CFs I 1.85 27.75 P 2 + 3 30.18 CFs I 1.85 28.33 V 2 + 3 29.31 CFs I 1.85 27.46 As 2 + 3 28.35 CCI 3 I 1.22 27.13 Tc2 + 3 29.54 CCIs I 1.22 28.32 Ru2 + 3 28.47 CCIs I 1.22 27.25 In 2 + 3 28.03 CCI 3 I 1.22 26.81 N 1 + 2 29.60 CCI 3 I 1.22 28.38 Al 2 + 3 28.45 CCI 3 I 1.22 27.23 V 2 + 3 29.31 ccι 3 I 1.22 28.09 Ga2 + 3 30.71 SiF 3 I 3.35 27.36 Se2 + 3 30.82 ' SiF 3 l 3.35 27.47 Rh2 + 3 31.06 SiF 3 I 3.35 27.71 Sn2 + 3 30.50 • SiF 3 I 3.35 27.15 P 2 + 3 30.18 SiF 3 I 3.35 26.83 K 1 + 2 31.63 SiF 3 I 3.35 28.27 Cr2 + 3 30.96 SiF 3 1 3.35 27.61 Fe2 + 3 30.65 SiF 3 i 3.35 27.30 As2 + 3 28.35 NH2 1 1.12 27.23 Tc2 + 3 29.54 NH2 1 1.12 28.42 Ru2 + 3 28.47 NH2 1 1.12 27.35 In 2 + 3 28.03 NH2 -1 1.12 26.91 Te2 + 3 27.96 NH2 -1 1.12 26.84 N 1 + 2 29.60 NH2 -1 1.12 28.48 Al 2 + 3 28.45 NH2 -1 1.12 27.33 V 2 + 3 29.31 NH2 -1 1.12 28.19 Tc2 + 3 29.54 PH2 -1 1.60 27.94 Ru2 + 3 28.47 PH2 -1 1.60 26.87 Tl 2 + 3 29.83 PH2 -1 1.60 28.23 N 1 + 2 29.60 PH2 -1 1.60 28.00 Al 2 + 3 28.45 PH2 -1 1.60 26.85 V 2 + 3 29.31 PH2 -1 1.60 27.71 Tc2 + 3 29.54 CH 1.83 27.71 Tl 2 + 3 29.83 CH 1.83 28.00 N 1 + 2 29.60 CH 1.83 27.77 P 2 + 3 30.18 CH 1.83 28.35 V 2 + 3 29.31 CH I 1.83 27.48 Tc2 + 3 29.54 SH I 2.19 27.35 Sn2 + 3 30.50 SH I 2.19 28.31 Tl 2 + 3 29.83 SH I 2.19 27.64 N 1 + 2 29.60 SH I 2.19 27.41 P 2 + 3 30.18 SH I 2.19 27.99 V 2 + 3 29.31 SH I 2.19 27.12 Fe2 + 3 30.65 SH 1 2.19 28.46 Ga2 + 3 30:71 CN 1 3.17 27.54 Se2 + 3 30.82 CN 1 3.17 27.65 Rh2 + 3 31.06 CN 1 3.17 27.89 Sπ2 + 3 30.50 CN 1 - 3.17 ■ - 27.33 P 2 + 3 30.18 CN 1 3.17 27.01 K 1 + 2 31.63 - CN 1 3.17 28.45 Cr2 + 3 30.96 CN 1 3.17 27.79 Fe2 + 3 30.65 CN 1 3.17 27.48 Tc2 + 3 29.54 SCN 1 2.17 27.37 Sn2 + 3 30.50 " SCN 1 2.17 - • 28.33 Tl 2 + 3 29.83 SCN 1 2.17 • 27.66 N 1 + 2 29.60 SCN 1 2.17 27.43 P 2 + 3 30.18 SCN 1 2.17 28.01 CD co CO o CJ) CM 00 CJ) T— 00 O) T- CM CJ) CM o CO in in "fr CM O in CO l- I s - O) CO CJ) I s - I s - oo CD O) I s - CO O) CD CM CM CM CM CM CM CM CM CM CM CN CM CM 'Λ W C C "fr T- in cM CM in cM CM O "fr "_- "fr "fr I s - O) 00 CM CM CO T- CD d d τ- : τ- ' CM CM CD o CM CM CM CO P 5 + 6 220.43 CH 1 1.83 218.60 P 5 + 6 220.43 SH 1 2.19 218.24 P 5 + 6 220.43 CN 1 3.17 217.26 P 5 + 6 220.43 SCN 1 2.17 218.26 P 5 + 6 220.43 SeCN 1 2.64 217.79 Cations and molecular anions with n = 54 (resonance shrinkage energy is given by 27.21 with n - 54, the resonance shrinkage energy is 734.67) Atom n nth Ion¬ Atom n nth Ion¬ Energy Oxidiz¬ ization Reduced ization Hole ed Energy Energy (eV) (eV) (eV) 0 6 + 7 739.32 BF3 - 1 2.65 736.66 0 6 + 7 739.32 N02 - 1 3.91 735.41 O 6 + 7 739.32 02 - 1 0.45 738.86 O 6 + 7 739.32 SF6 - 1 1.43 737.89 0 6 + 7 739.32 WF6 - 1 2.74 736.58 O 6 + 7 739.32 UF6 - 1 2.91 736.41 0 6 + 7 739.32 CF 3 - 1 1.85 737.47 0 6 + 7 739.32 CCI3 - 1 1.22 738.10 O 6 + 7 739.32 SiF3 - 1 3.35 735.97 O 6 + 7 739.32 NH 2 - 1 1.12 738.20 O 6 + 7 739.32 PH2 - 1 1.60 737.72 O 6 + 7 739.32 CH - 1 1.83 737.48 0 6 + 7 739.32 SH - 1 2.19 737.13 0 6 + 7. 739.32 CN - 1 3 7 736.15 0 6 + 7 739.32 SCN - 1 2.17 737.15 O 6 +. 7 739.32 SeCN - 1 2.64 736.67 26. The apparatus of claim 19, wherein said energy hole is provided by one of the following three-ion couples: Atom (eV) Ato m(s) (eV) I Energy Hole Oxidized Reduced (eV) B 3 37.48 Li 1 5.392 .27.40 Na 1 5.139 Cd 3 37.48 Na 1 5.139 27.20 Na 1 5.139 27. The apparatus of claim 17, further including: external energy apparatus; means for providing a transfer of energy between said juxtaposed first and second elements of matter and said substance, and said external energy apparatus for controlling the rate of said fusion according to the relative equivalence of said energy hole and resonance shrinkage energy * transferred to said first and second elements of matter. 28. The apparatus of claim 27, wherein said means for providing a transfer of energy comprises means for applying one of an electric, a magnetic field, transfer of heat and acoustic energy to said selected volume. 29. The apparatus of claim 17, further comprising: means for receiving said release of energy from said volume; : d means for transferring the received released energy to external load apparatus for dissipation and production of work. 30. The apparatus of claim 29, wherein: said means for receiving comprises heat exchanger means for providing a flow of heat in a selected medium; and said means for transferring comprises turbine means for receiving said heat flow and providing one of electrical and mechanical power therefrom. 31 . A method of determining the energy levels of the electron orbitals of an element of matter, comprising the steps of: determining the centripetal force of each electron orbital; determining the gradient of said electrostatic potential of said element, of matter; determining the radius of each electron orbital shell according to the centripetal force and the gradient of said electrostatic potential; and determine the energy level according to the radius of said electron orbital. 32. The method of claim 31 , further providing the step of providing relativistic corrections of the determined energy. 33. The method of claim 31 , where the steps of determining the gradient comprises: and the step of determining the energy level according to the radius comprises: mv 2 'centripetal = r 34. The method of claim 31 , further including the steps of: determining the gradient of the angular momentum of each said electron; determining the radius of each Mills electron orbital shell according to the centripetal force, gradient of said electrostatic potential and the gradient of said angular momentum; determining the electrostatic energy of each electron orbital according to the radius of each Mills electron orbital shell; determining the magnetic energy of each electron orbital according to the radius of each electron orbital shell; and adding the electrostatic and magnetic energy to provide said electron orbital energy level. 35. The method of claim 34, further including the step of providing relativistic correction of the determined energy. 36. A method of determining the internuclear distance of a chemical bond, comprising the steps of: determining the decrease in electron electrostatic energy as internuclear distance 2y decreases; determining the increase in nuclear repulsive energy as internuclear distance 2y decreases; and determining the distance 2y at which point the change in electrostatic energy and nuclear repulsive energy are substantially equal, to provide the internuclear distance of a chemical bond, wherein the total energy stored in the resulting electric field is a minimum. 37. For use in the production of coulombic annihilation fusion, an energy hole of energy E, comprising a first element of matter selected according to a corresponding ionization potential; and at least one second element of matter selected according to a corresponding ionization potential, wherein the combination of the ionization potentials provides a net positive ionization potential substantially equal to E. 38. An apparatus of claim 22, wherein the source of an energy hole is a single cation, neutral atom, or anion or a single molecule which is a cation, neutral molecule or anion, or is a combination of said species wherein the said energy hole is substantially equivalent to n/2 27.21 eV where n - 2, 3, 4,... . 39. A method of releasing energy, comprising the steps of: selecting a first element of matter having a nucleus and at least one electron orbital; selecting a second element of matter having a nucleus and at least one electron orbital; determining the resonance shrinkage energy levels of the electron orbitals of said first and second elements of matter; providing two energy holes substantially equal to each of the resonance shrinkage energy levels of said first and second elements of matter; juxtaposing said first and second elements of matter and said energy holes, wherein; a non-fusion release of energy is produced when the energy of said electron orbitals is removed by said energy holes. 40. A composition of matter, comprising: a transition element, m, having a large population of electrons receptive of energy from one of an electric and magnetic field to urge formation of Cooper electron pairs; and a plurality of materials, A, B, C, and D having strong bond energies and a lattice of two of less dimensions, wherein A, B, C, and D each are of different atoms, different oxidation states of the same atom, and different oxidation states of different atoms, in a cell arrangement, D — having superconductor properties.

Inventors: MILLS RANDELL L, MILLS, RANDELL, L.
Applicants: MILLS RANDELL L, MILLS, RANDELL, L.
Application year: 1990
Main classification: G21B1
IPC codes: C01G1, G21B3