Extended Abstract Title (14 pt, Times New Roman

Fusion Energies Based on Matter-Antimatter Interaction Mohamed Assad Abdel-Raouf Physics Department, E-mail: [email protected] College of Science, U.A.E. University, Al-Ain, P.O. Box: 17555, U.A.E.

Abstract Recently, the problem of "Global Warming" has raised vigorous interest among scientists around the world in the development of environmentally friendly sources of energy. Contradictions between two facts, namely continues increasing of energy demands, as an indispensible factor for the continuous improvement of the quality of human life, and the environmental side effects of the present forms of energy, have to be resolved on scientific basis. It is obvious that the aimed clean forms of energy should depend on unlimited resources. Consequently, the expression "Renewable Energies" has boomed, with which one usually means "Solar" and "Wind" energies. The scientific limitations of these sources are well known. In this work a brief account is presented on nuclear fusion energies as ultimate sources for the fulfillment of our goals. Our main purpose, however, is to shed light on the possibility of producing huge amount of energies based on Matter-Antimatter Annihilation". Particularly, a scenario is discussed for cold fusion processes based matter-antimatter annihilation. The advantage of this form of energy is threefold: it is considerably larger than fusion energies obtained from conventional nuclear reactions, it is cold and CONTROLABLE.

1. INTRODUCTION The equivalence between matter and energy goes back to 1905 when one of the most fascinating papers in Physics was published by Albert Einstein [1]. It was clear that a tiny piece of matter of mass m is in fact equivalent to an energy E = m c2, where c is the speed of light. This rigorous statement was never experimentally tested until 1938, when Otto Hahn and Strassmann [2] discovered the fission of Uranium and established the basic concept of the production of nuclear energy. Huge amount of energy was also expected to be produced on the basis of the same equation from the contrary nuclear process in which two light nuclei fuse together leading to a new nucleus with mass less than the sum of the masses of the original nuclei. The ultimate experiment which supports this fact was thought of in 1920 [3]. In this case, precise measurements of the masses of many different atoms, among them hydrogen and helium, showed that four hydrogen nuclei were heavier than a helium nucleus. The importance of these measurements was recognized immediately by astrophysicists [4] who argued that the mass difference between four atoms of hydrogen and a helium atom indicates that the sun could shine by converting hydrogen atoms into helium. This burning of Hydrogen into Helium would (according to E=mc2) release about 0.7% of the mass equivalent of the energy. In principle, this would allow the sun to shine for about 100 billion years. In 1939, Hans Bethe [5] described a quantitative theory explaining the fusion generation of energy in the stars (including our sun).The uncontrollable thermonuclear fusion of Hydrogen Isotopes (Deuteriums and Tritiums) was realized in 1952(USA) and 1953 (Russia). The fusion temperatures are 5.0 x107 °C for Deuterium with Tritium and 4.0x108 °C for Tritium with Tritium. In general, (see also [6]-[9]), there are two types of fusion reactions: (1) those that preserve the number of protons and neutrons and (2) those that involve a conversion between protons and neutrons. Reactions of the first type are most important for practical fusion energy production, whereas those of the second type are crucial to the initiation of star burning. An important fusion reaction for practical energy generation is that between Deuterium and Tritium (the D-T fusion reaction). It produces helium (He) and a neutron (n) and is written D + T → He + n. The amount of released energy is 2.8 × 10−12 joule. The H-H fusion reaction is also exoergic, it releases 6.7 × 10−14 joule. To develop a sense for these figures, one might consider that one metric ton (1,000 kg, or almost 2,205 pounds) of Deuterium would contain roughly 3 × 1032 atoms. If one ton of Deuterium were to be consumed through the fusion reaction with Tritium, the energy released would be 8.4 × 1020 joules. This can be compared with the energy content of one ton of coal—namely, 2.9 × 1010 joules. In other words, one ton of Deuterium has the energy equivalent of approximately 29

1

billion tons of coal. Trials to obtain controllable fusion energies, i.e. energies for industrial applications, have been improved ever since [3]. The most interesting ones, however, are the "Joint European Torus (JET)" which was constructed at the UK and the US "Tokamak Fusion Test Reactor (TFTR)". In both cases deuterium and tritium fuels are employed, and the resultant power was larger than 10 megawatts, produced for short time due to the limitations set by the magnets. The Japanese tokamak (TRIAM) can be operated stably for much longer period, about 5 hours, but produces less energy. The main drawback of these projects is that they consume power to start the production more than what they produce. Another completely different source of energy is thought of on the basis of matter-antimatter annihilation [10], [11]. The existence of antiparticles was predicted by Paul Dirac in 1930 [12], [13] as one of the possible roots of Einstein's quadratic relation between relativistic energy and momentum of a moving free electron. A confirmation for this existence was given two years later by Anderson [14]. Deutsch [15] was the first to show that an electron and an antielectron (positron) could build up a bound state (called Positronium) with a lifetime between 10-10 and 10-7 second and a ground state energy -6.8 eV. It annihilates, (following Einstein's equation E = m c2), yielding two γ photons each with 511 keV. Thus, observation of a spectral emission line at 511 keV indicates that a positron-electron pair has been annihilated. The most important developments in the field of antimatter was the discovery of antiprotons [16], their cooling, trapping and the formation of Antihydrogen at CERN Laboratory [17], [18] as well as the synthesizing of Protoniums [19]-[21]. Antiprotons are produced at CERN, by accelerating protons in the Proton Synchrotron (PS) to an energy of 26 GeV, and then smashed into an iridium rod. The protons bounce off the iridium nuclei with enough energy for matter to be created. A range of particles and antiparticles are formed, and the antiprotons are separated off using magnets in vacuum. The formation energy is equivalent to a temperature of 10 trillion K (1013 K). For each 200,000 protons hitting, one antiproton is produced. In 2006, the mass of the antiproton, was measured [22] and found to be 1,836.153674(5) times more massive than an electron. This is exactly the same as the mass of a "regular" proton. Also, almost 1012 (far less than a nanogram) could be trapped in two days. The two particles have opposite charges, but the same spin (1/2) and isospin (1/2). Both are Fermions and grouped as Hadrons. It takes 5x104 years for p- → μ− + X and 3x105 years for p- → e− + γ annihilations. The lowest temperature to which they can be cooled is 4.2 K. Proton-Antiproton pair annihilates at rest yielding 2 photons (X-rays) with a combined energy of 1.88 GeV. The maximum antiproton energy after reacceleration in Fermilab is 1.0 TeV, a factor of 1 million greater. So 2.0 TeV = 2x1012 eV = 3.2 x 10-7 Joule can be produced from one collision. The maximum energy produced by the LHC at CERN (in 2013) is 14 TeV, i.e. 2x14TeV= 4.48x10-6 Joule. Thus, the total gained energy is equal to (4.48x10-6) x1012= 4.48x106 Joule. This amount will be enhanced if Antiprotons were converted to Antihydrogens and the annihilation of Hydrogen-Antihydrogen is considered in this case an extra 1.022x109eV (= 1.635x10-10 Joule) or total of 1.3x103 Joule will be added. On the other hand, it is interesting to indicate that the most efficient chemical reaction provides about 1x10 7 Joule/kg, nuclear fission 8x1013 Joule/kg, nuclear fusion 3x1014 Joule/kg, whilst complete annihilation of matter-antimatter yields 9x1016 Joule/kg. (Remember that a kilogram of Antihydrogen contains 6.02x10 26 Atom). In other words, kilogram for kilogram matter-antimatter annihilation releases about ten billion times more energy than the hydrogen/oxygen mixture that powers the space shuttles main engines and more than 300 times the fusions at the sun's core. Recently, the use of matter-antimatter fusion as a source of energy has gained tremendous interest among space scientists and engineers (see [23]-[27]). Particularly, the development of an antimatter engine for rockets, space shuttles and spacelabs has been considered as highly challenging idea, In this case antihydrogen could be used as a fuel to power the proposed engine. The small antihydrogen microcrystals, each weighing about a microgram and having the energy content of 20 kg of LOX/hydrogen, would be extracted electromagnetically from a storage trap, directed by electric fields down a vacuum line with shutters (to maintain the trap vacuum) , then electrostatically ejected with a carefully selected velocity into the rocket chamber, where the antiprotons would annihilate with the reaction fluid, heating it up to provide high thrust at high specific impulse. The annihilation cross section increases dramatically at low relative velocity, so the annihilation process occurs mostly at the center of the chamber. Comparing the specific impulse, as measure of efficiency, of Space Shuttle Main Engine produced by different sources of energy, we notice that it is now 455 seconds, nuclear fission could increase it to 10,000 seconds, nuclear fusion could provide 60,000 to 100,000 seconds, while matter/antimatter annihilation up to 100,000 to 1,000,000

2

seconds. Clearly, this means that the advantage of using matter-antimatter as a fuel in space is twofold: (1) The energy source is extremely light, which means that the mass of the whole Space Shuttle would be considerably small (about 100 tons). (2) The yield is extremely larger than that of any other fuel, a matter which enables faster and longer trips. For example an Earth-Mars round trip with 30 days stay would last 120 days, Earth-Jupiter round trip with 90 day stay could be covered in no more than 18 Months, and Earth-Pluto one way trip could be managed within 3 years. The first goal of the present work is to show that a system composed of Hydrogen and Antihydrogen could be formed in nature and it is stable against dissociation of any kind. Our second goal is to draw the attention of space scientists and engineers to the possible employment of these molecules as fuel for space engines. It is anticipated that the production of such exotic molecules would increase the pre-annihilation time and, consequently, improve the practical use of antimatter, particularly as a fuel for space engines. As a chemical compound, it might be possible to synthesize frozen H H molecules and employ them, (as alternatives to frozen H2 [29], which possesses frizzing point at -259 deg C and density 0.0855/cc), as fuel for space engines. Our third goal is to draw the attention of searchers for alternative sources of energy to the possible employment matter-antimatter annihilation in general, and Hydrogen-Antihydrogen exotic molecules in particular, as incomparable distinguished sources for environmentally friendly energy. In order to reach this goal we propose a scenario for possible use H H as props for cold fusion. The paper contains other three sections. Section 2 is devoted to the mathematical representation of the problem. Section 3 deals with the results and discussions of our calculations. In section 4, a scenario is proposed for a cold fusion process based on Hydrogen-Antihydrogen or Positronium-Protonium annihilation. The paper ends with the conclusions drawn from our work followed by a complete list of references mentioned in the text.

2. MATHEMATICAL FORMALISM AND VARIATIONAL APPROACH Let m1-, m2+, ma-, and mb+ be four charged particle, (say the first and third are particles, while the other two are antiparticles), with internal distances as illustrated in Fig. (1); the total Hamiltonian of such a four-body system has the form H 

2 2m1

12 

2 2ma

 2a 

2 2m2

 22 

2 2mb

 2b  Z 2 e 2 (

1 1 1 1 1 1      ) r1a r2b r12 r1b r2 a rab

(1)

At any moment, different quasi atomic (two-body) and ionic (three + one) clusters are possible. Let us assume that (m1-, m2+) and (ma-, mb+) are two possible dissociating clusters with binding energies E12 = - μ12 e2/(2 ħ2) and Eab = - μab e2/(2 ħ2), (2) where μ12 = m1m2/(m1+m2) and μab = mamb/(ma+mb), (3) are the reduced masses, respectively. The following two cases could be distinguished Case I: m1 = ma = m and m2 = mb = M where m « M (4) Case II: m1 = m2 = m and ma = mb = M where m « M (5) Case I corresponds to the dissociation to an atom and an antiatom. The second case yields two separate tiny and heavy particle-antiparticle pairs. It is obvious that case II assigns the lowest dissociation threshold. The dissociation to an ion and a particle (or antiparticle) is also possible. However, the ion-particle binding energy is higher than case II. To absolutely guarantee that the four-body system is bound, it must have a total energy lower than the sum of the binding energies of the constituents of all possible dissociation channels. Let us now define the binding energy W(σ) by W(σ) = E(σ) - (E12 + Eab) (6) Clearly, the system is bound if and only if W(σ) ≤ 0, (7) i.e. if the total energy E(σ) is located, (on the negative part of the real axis of the energy complex plane belonging to the Hamiltonian H), lower than the sum of the binding energies (to be referred to as Ethreshold or Ethr) of the dissociated clusters. σ is the ration between the light and heavy masses. Dividing (6) by Ethr leads to ω (σ) = ε (σ) - 1 , (8a)

3

Fig. 1: Relative coordinates of the Four-Body System where ε (σ) = E(σ) /Ethr, and ω (σ) Thus

= W(σ) /Ethr, with

Ethr = (E12 + Eab),

(8b)

ω (σ) ≥ 0,

(9)

is a sufficient condition for the existence of the four-body system. Since, the potential energy part of H does not depend on the masses, therefore, the total Hamiltonian can be written as 2 1 1 1 1 1 1 H  [M (12   2a )  m( 22   2b )]  Z 2 e 2 (      ). (10) 2mM r12 ra b r1a r2 a r1b r2b It is understood here that the indices 1, 2, a and b are dummy. Writing the mass ratio as σ = m/M ,

(11a)

and the reduced mass  as (11b)

1 1 M  m 1     ,  m M mM m 1

the Hamiltonian can be rewritten in the form: H 

2 2  ( M  m)



[M (12   2a )  m( 22   2b )]  Z 2 e 2 (

1 1 1 1 1 1      ) r12 ra b r1a r2 a r1b r2b

2 1  1 1 1 1 1 1 [ (12   2a )  ( 22   2b )]  Z 2 e 2 (      ). 2 1   1 r12 ra b r1a r2 a r1b r2b

Now, let us define the units of energy and length, respectively, as

 Z 4e4 2 2

The unit of energy

(14a)

2  Z 2e2

The unit of length

(14b)

Multiply the Hamiltonian by the reciprocal of the energy unit leaves us with

4

(12)

(13)

H 

 (

2  2 2 2 [ 1 (12   2a )   ( 22   2b )]  Z 2 e 2 24 4 ( 1  1  1  1  1  1 ) 4 4 2  Z e 1   1   Z e r12 rab r1a r2 a r1b r2b

1  2 1 1 1 1 1 1 )2[ (12   2a )  ( 22   2b )]  2( )(      ). 1  1 Z e  Z 2 e 2 r12 ra b r1a r2 a r1b r2b

2 2

2

Since we took

2 Z2 e2

(15)

to be equal to unity, then the Hamiltonian could finally be given by;

1 H { [12   2a   ( 22   2b )]}T  { 2  2  2  2  2  2 }V , 1 r12 ra b r1a r2 a r1b r2b

(16)

where T is the total kinetic energy operator of the system, while V is its total potential energy. Now, if {  k

} is the set of exact wavefunctions of the four-body system, such that;  k   k ( r1 , r2 ,  ) ,

(17)

 k   k    k k d   kk ,

And

(18)

where d is the volume element, therefore, the bound-states of the system are identical with the negative spectrum of the Hamiltonian within the space {  k } , i.e., they are the eigenvalues of the Schrödinger equation

H  k  Ek  k

,

(19)

,

(20)

and can be determined by;

Ek   k H  k such that

E k  E k 1 ,

for all k  1 .

(21)

Obviously, if E k  0 for all k's, then the total Hamiltonian H does not possess any negative spectrum and the quantum mechanical system cannot form a bound-state, in other words, the molecule consisting of the four bodies (m1-, m2+, ma-, and mb+) simply cannot exist. Let us now introduce a short account on the variational approach employed for calculating the total and binding energies of the system. The method can be displayed as follows: consider the non-relativistic time independent quantum mechanical system defined in the preceding section, The Schrödinger's equation is equivalent in form to the conventional eigenvalue problem:

H E

,

(22)

or (23) ( H  E)   0 , where E and H are the total energy and Hamiltonian, respectively, of a quantum mechanical system described by the vector  . The Schrödinger constraint can be stated according to eq. (23) as follows: a true physical system or process described by the observable ( H  E) is well expressed, microscopically, by the expansion space  if and only if Schrödinger vector (23) fulfills the variational principle:

  H  E   0,

( H  E) 

defines a null space. Also, eq.

(24)

and possesses the eigenvalues:

5

Ek   k H  k

k k

.

(25)

Eqs. (23), (24) and (25) imply a one-to-one correspondence between the

Ek 's

and

k 's

once the

degeneracy has been removed. Consequently one can order the E k 's such that

E k  E k 1 , where

for k  1, 2,  ,

(26)

E 1 is the first (lowest) eigenvalue.

Now, the verification of Schrödinger's constraint requires the exact knowledge of the terms E, H and



.

In practice, however,  is always unknown and the parameter E is not given for the boundary value problems. For this, there was a necessity of using approximate methods to get a solution for physical problems. In Rayleigh-Ritz variational method a trial expansion space  ( n) is selected which defines a hypothetical t physical system such that n

 (t n )   a k  tk

,

(27)

k

where n is the dimension of

 (tkn)

, and

 (tkn)  (tkn)   kk , where

for k , k   1, 2,  , n

(28)

 kk is the Kroneker-delta. eq. (28) will then reduce to

  (t n) H  E  (t n)  0 All

,

 (tkn ) ' s

.

(29)

are, due to Rayleigh-Ritz variational method, generated from one basis set of vectors

{ i }  D H

where

DH

is the H-domain, i.e., n

 (tkn )   cik  i

(30)

.

i 1

Consequently, eq. (29) can be written for each k as the system of secular equations:

n

 c jk [ i H  j j 1

 E nk  i  j

] 0,

which is meaningful if and only if the determinant

 nk  det ( H ij  E nk Sij )  0 Where And

6

i  1, 2, , n ,  nk ,

(31)

satisfies the relation (32)

H ij  i H  j

(33a)

Sij   i  j

(33b)

. The eigenvalues obtained by (31) are ordered such that;

E n1  E n 2    E n n

(34)

,

is satisfied.

3. RESULTS and DISCUSSIONS In order to calculate the eigenfunctions and eigenvalues of the Hamiltonian (15), or (16), using eqs. (30)(34), we chose the Hylleraas coordinate system

si  ( ria  rib ) rab

;

i  1, 2

t i  ( ria  rib ) rab

;

i  1, 2

sa  ( r1a  r2 a ) r12

,

sb  ( r1b  r2 b ) r12 ,

t a  ( r1a  r2 a ) r12

,

t b  ( r1b  r2 b ) r12 ,

u  r12 rab

,

v  rab .

Furthermore, we selected the elements of the complete set

j 

m s1 j

n s2 j

e

  j ( s1  s2 )

k t1 j

{  i } as

 t2 j

cosh [ j ( t1  t 2 ) ] u

pj

v

qj

e

  jv

.

Hydrogen-Antihydrogen exotic molecules correspond to case I defined at eq. (4), where m1 = ma =me and m2 = mb= M, where me (=1/2 in Hartree a.u.) and M are the masses of the electron (positron) and proton (antiproton), respectively. The reduced masses, eq. (3), reduced to μ 12 = μab = me and M is set to be infinite . The threshold energy is now given by Ethr= -1 Hartree = - 27.2 eV. Thus, eqs (8b) state that ε (σ) = E(σ), and ω (σ) = W(σ) . The optimization of the nonlinear parameters of the wavefunction provide us with i = 1.95, i = 0.87 and i = 1.53 when the first five components of the set {|  j >} are considered. With these values, the convergence of the total and binding energies of the ground-state of H H molecule has been studied when n is steadily increasing. Elaborate calculations have shown that the molecule is bound, and its binding energy can be lowered using 25 components to - 0.7476 eV. This result shows that H H is stable against dissociation into antihydrogen and hydrogen atoms. (The details of the theoretical analyses and numerical investigations are ignored due to the limited space available). Further investigations of the effect of adding components depending on u to the set of 25 basis functions have shown that a single component could considerably lower the binding energies of Hydrogen-Antihydrogen molecule to -0.9325. (This large contribution is attributed to the large number of components of the trial wavefunctions (depending on s1, s2, t1, t2, etc.) covered by this term only and added to previous 25 components; a matter which is connected with drastic increase in the computer time of the variational energies).The same basis set leads, within the framework of the virial theory, to -0.9335 eV.

The preceding results encouraged us to search for other four-body systems supported by case II, eqs. (5), i.e. searching for an exotic molecule composed of a positronium (Ps) and protonium (Pn) quasi atoms. (The sum of the binding energies of the positronium and protonium is equal to -12492.28 eV). The system is bound if its total energy calculated by the variational method is lower than this sum. As a matter of fact very careful elaborate calculations have shown that the total energy is equal to. -12493.217 eV, i.e. the parameter ω (σ) = 0.000075, which means that the Ps-Pn system is bound. Both information about H H and Ps-Pn systems, support strongly the argument that a HydrogenAntihydrogen system could be formed in nature. It is bound and stable against dissociation of any kind. This

7

comprehensive information about H H emphasizes, for the first time, experimental trials to build up this molecule in Laboratory. Clearly the formation of these molecules has two advantages: (i) it increases the preannihilation time of Hydrogen and antihydrogen, and (ii) it provides us with a powerful fuel for space engines, (see the introduction). We would expect that a frozen H H could be formed. This would provide us with a strong alternative to a frozen H2 which possesses frizzing point at -259 deg. C and density 0.0855/cc), and planned to be used by NASA/Marshal Center as fuel for space engines[29].

4. COLD FUSION The possible formation of Hydrogen-Antihydrogen molecules allows us to propose the following scenario for implementation in cold fusion which is alternative to a suggestion made by M. Fleischmann and S. Pons [30]. In our case we argue that if a thermalized beam of antihydrogens passes through a palladium sheet in which hydrogen atoms are localized, a bound-state (or exotic molecule) could be formed. Thus, if the antihydrogen enters the Coulomb barrier of the localized atom, the system could collapse in two different channels, namely the annihilation and fusion channels. Both channels would lead to tremendous amount of energy, (much larger than nuclear fusion energy), with the advantage that (i) it is based on a cold fusion, (ii) it is controllable.

CONCLUSIONS The most interesting conclusions of the present work can be summarized in the following points: a) Hydrogen-Antihydrogen exotic molecules are bound and stable against dissociation of any kind. (b) Hydrogen-Antihydrogen exotic molecules provide us with ultimate source of energy for space engines which is light and possesses the highest possible efficiency in comparison with all other sources based on LOX/Hydrogen burning, nuclear fission or nuclear fusion. (c) The possible existence of a Hydrogen-Antihydrogen channel in the interaction between Hydrogen and Antihydrogen opens the gate to the realization of cold fusion based on matter antimatter annihilation.

REFERENCES [1] Albert Einstein, Annalen der Physik 18: pp 639, 1905. [2] O. Hahn and F. Strassmann, Naturwiss. 26, pp757, 1938; ibid 27, pp11, 1939. [3] Ch. Seife, "Sun in a Bottle: The Strange History of Fusion and the Science of Wishful Thinking", Viking Books, 2008. [4] A. Eddington "The Internal Constitution of Stars" , Cambridge University Press, 1926. [5] H. A, Bethe, Phys. Rev.55, pp 436, 1939. [6] K. Niu and K. Sugiura, "Nuclear Fusion", Cambridge University Press, 2009. [7] G. McCracken and P. Stott, "Fusion - The Energy of the Universe", Academic Press, 2005. [8] C M Braams et al, "Nuclear Fusion: half a century of magnetic confinement research", Plasma Phys. Control. Fusion 44, pp 1767, 2002. [9] A. A. Harms, K. F. Schoepf, G. H. Miley and D. R. Kingdon, "Principles of Fusion Energy: An Introduction to Fusion Energy for Students of Science and Engineering", (Paperback), World Scientific, 2000. [10] M. A. Abdel-Raouf, "Possibility of Producing an Intensive Beam of Antihydrogens and its Consequences", 12th International Conference on Few Body Problems in Physics, Vancouver (Canada), pp A17, 1989; "Coexistence of Hydrogen and Antihydrogen: Possible Application to C old Fusion", Positron Positronium Chem., Proceeding of 3 rd Int. Workshop (1990), pp 299, 1990; see also www.newenergytimes.com/v2/archives/fic/all.shtml 1993. [11] M. A. Abdel-Raouf, Cold Fusion Based on Matter-Antimatter Interaction, Verhandlungen der Deutschen Physikalischen Geselschaft, Fruehjahrstagung, Freiburg 1991. [12] P. A. M. Dirac, Proc. R. Soc. A 126, pp 360, 1930. [13] P. A. M. Dirac, Proc. R. Soc. A 133, pp 60, 1931. [14] C. D. Anderson, Phys. Rev. 43, pp 491, 1933. [15] M. Deutsch, et al. Phys. Rev, 82. pp 455, 1951. [16] O. Chamberlain, E. Segrѐ, C. Wiegand and T. Ypsilantis, Phys. Rev.100, pp 947, 1955. [17] G. Baur, et al, Phys. Lett. B 368, pp 251, (1996). [18] G. Blanford, et al, Phys. Rev. Lett.80, pp 3037, (1998).

8

[19] M. Amoretti, et al. Nature 419, pp 456, (2002). [20] N. Zurlo, et al, Phys. Rev. Lett. 97, pp 153401, (2006). [21] S. J. Brodsky and R. F. Lebed, Phys. Rev. Lett. 102, pp 213401 (2009). [22] M. Hori et al., Phys Rev Lett 96 (24), pp 243401, 2006. [23] G. A. Smith, G. Gaidos, R. A. Lewis, K. Meyer, and T. Schmid, Acta Astronautica, 44, pp 183,1999. [24] J. M. Horack, Reaching For The Stars: Scientists Examine Using Antimatter And Fusion To Propel Future Spacecraft, www.eurekalert.org/pub_releases/1999-04/NSFC-RFTS-120499.php - Cached, 1999. [25] M. M. Nieto, M. H., Holzscheiter and S. G. Turyshev, arXiv-astrophy.-0410511, 2004. [26] M. L. Shmatov, JBIS 58, pp74, 2005. [27] L. J. Perkins, C.D. Orth, M. Tabak, , UCRL-ID-TR-200850, 2003. [28] C. Deutsch, www.dtic.mil/cgibin/GetTRDoc?AD=ADA446638&Location=U2&doc=GetTRDoc.pdf, 2005. [29] L. C. Cadwallader and J. S. Herring, www.inl.gov/hydrogenfuels/projects/docs/h2safetyreport.pdf, 1990 [30] M. Fleischmann and S. Pons, J Electroanal. Chem. 216, pp301, (1989).

9