Condensed Matter Nuclear Science

Condensed Matter Nuclear Science

Condensed Matter Nuclear Science

--- Correlation between Deuterium Flux and Excess Heat ---

Xing Z. Li, Xian Z. Ren, Bin Liu

Department of Physics, Tsinghua University, Beijing CHINA

ABSTRACT

An emerging nuclear energy is proposed based on the new development of nuclear science in condensed matter; i. e. selective resonant tunneling model, and the concept of “super-radiation” in crystal lattice. The experiment for proof of principle has been described. The preliminary result seems promising.

INTRODUCTION

The beam-target interaction in nuclear physics has been prevailing without careful consideration of the interaction between the charged projectiles and the crystal lattice. When the energy of the projectiles become lower and lower, the de’ Broglie wave length of the projectiles are comparable with the constant of the crystal lattice. It is expected that the interaction between the charged projectiles and the crystal lattice should play more important role. However, the experimental data become scarce when the energy of the charged projectile is getting lower and lower. Mostly, the Coulomb barrier would reduce the cross-section exponentially; thus the poor statistics makes the experiment very difficult. The other difficulty comes from the mistake in conception. The most of nuclear physicists intended to identify a nuclear reaction in terms of neutron or gamma radiations. Indeed the selective resonant tunneling model reveals that when Coulomb barrier is penetrated due to resonant tunneling at low energy, we should expect the energetic charged particles as the products of nuclear reaction instead of the neutron or gamma radiation. If we are able to correct this misconception in nuclear physics; then, it is possible to recognize a series of low energy nuclear reactions in the condensed matter, which makes an emerging safe and clean nuclear energy.

Fig.1 Super-absorption and deuterium flux

Figure 1 illustrates the interaction between projectiles and the crystal lattice of target. Usually when the deuteron beam interacts with the deuterons in the titanium target, only the 2-body interactions are considered, and the product of p+T Å n+3He are expected (Fig. 1 a). However, Some abnormal nuclear products (Fig. 1 b) were observed if the titanium target was cooled down to 5~15oC to reduce the heating effect of the injected beam, and if the loading ratio of deuteron to titanium was as high as 1.4. Takahashi observed abnormally large yield of (d+d+d) 3-body nuclear reaction after careful experimental study for more than 7 years [1]. Usually, the (d+d+d) 3-body nuclear reaction is scarcely observed because for every 1030 (d+d) 2-body interactions there was only one chance for (d+d+d) 3-body nuclear reaction; nevertheless, Takahashi group has observed one (d+d+d) 3-body nuclear reaction for every 105 (d+d) 2-body nuclear reaction if the titanium target with high loading ratio was kept cool during the bombardment. Because the energy of nuclear products (4.75+4.75 MeV), the charge number (1+2) and the mass number (3+3) are only possible for (d+d+d) 3-body nuclear reaction. This is a clear evidence that the nuclear interaction might be affected by the condensed matter physics.

Now we make one more step towards the effect of the crystal lattice. It is apparent that the deuteron beam in Fig. 1b just plays the role of a probe. It just reveals the fact that there are a lot of (d+d) compoud states inside the titanium target, which will greatly enhance the probability of having (d+d+d) 3-body interactions. Now the question is that if we do not use the probe (the deuteron beam); then, what will happen to these (d+d) compound states inside the titanium target? We anticipate that these (d+d) compound states would undergo a nuclear reaction, because they are in the range of nuclear interactions. Selective resonant tunneling model has predicted that the nuclear products for this interaction must not be neutron or gamma ray, because the strong nuclear force or electromagnetic force is too strong to form this long lifetime (d+d) compound states inside the titanium target [2,3,4]. Hence, it is not suggested to detect these (d+d) compound states inside the titanium target in terms of neutron or gamma detection. Instead, the heat of nuclear reaction is preferred as an object of detection. Fig.1c shows a possible scheme to detect the heat of the nuclear reaction when the deuterium gas is permeating through the thin wall of a palladium tube.

CALORIMETRIC EXPERIMENT FOR HEAT OF NUCLEAR REACTION

If every nuclear reaction produces 10 MeV; then,1012 nuclear reactions would produce 1.6 Joules. If the lifetime of above-mentioned (d+d) compoud state is 104 seconds; then, for every 1010 (d+d) compound states we may expect a heat flow of 1 microwatt. Hence, if the sensitivity of the calorimeter is in the order of microwatt, a Pd tube of 100 mg is enough to produce measurable heat of nuclear reaction. (Fig. 2b).

A Calvet calorimeter(C-80D, Setaram, France) has been used as an independent calorimeter to detect this heat of nuclear reaction. A series of 3500 thermal couples measure the heat flow through the surface which enclosed the reaction cell. It is based on the Seebeck effect. It does not depend on the heat transfer coefficient of the D/Pd system, and it does not require a thermal equilibrium of D/Pd system. A thin wall Pd tube is inserted in to the reaction cell. One end of the Pd tube is sealed, and the other end is connected to a deuterium gas bottle. At room temperature when we pump out the gas in the reaction cell, the deuterium gas permeating through the thin-wall of Pd tube is negligible. When we enhance the temperature of Pd tube; then, stop the heating and let it cooling down gradually, there will be a flux through the thin-wall of Pd tube at certain temperature (Fig. 2a blue zigzag line). The gas pressure inside the Pd tube decreases quickly, and the pressure outside the Pd tube increases quickly even if the vacuum pumping is working continuously to pump out the gas in the reaction cell. In the meanwhile a heat flow is detected by this Calvet calorimeter. The precision of this Calvet calorimeter is 20 microwatts; however, the heat flow detected is in the order of 4 milliwatts (Fig. 2a red smooth line). The deuterium flux may decrease and increase again when the temperature of D/Pd system is decreasing, and the heat flow will decrease and increase correspondingly. It is evident that the higher deuterium flux corresponds to the higher heat flow, and the peak position of the heat flow is a little delayed with respect to the peak of deuterium flux due to the time constant of C-80D (100-250 seconds). This heat flow experiment has been repeated 16 times. It is backed up by the nitrogen gas experiment (no flux and no heat flow), and the calibration with a standard electrical heater (error bar is less than 20 mW).

Fig. 2 Schematics of Calvet calorimeter and the curves showing correlation between deuterium flux and heat flow

WHAT IS THE ORIGIN OF THIS HEAT FLOW?

Was it the energy of solution? No, because it was a flux, the energy of solution must be balanced with the energy of dissolution. Was it the Joule-Thomson effect? No, because the J-T effect is very small. It is detectable only if the pressure difference is in the order of several hundred atm. In our experiments, the pressure difference across the thin wall of Pd tube is less than 2 atm. The J-T effect is in the order of microwatt. In order to find the nuclear nature of the heat flow, TLD (Thermoluminescence detector) was placed inside the reaction cell just next to the Pd tube. It will record any nuclear radiation inside the reaction cell during the whole process. It was found that the recorded radiation in foreground was always a little higher than the background.[5] Since TLD is only sensitive to the radiation with energy greater than 20 keV. It is an evidence of the nuclear nature of this heat flow.

THE NATURE OF THE DEUTERIUM FLUX IS NOT DIFFUSIVE ONLY.

For a long time we believe that the permeation of deuterium gas through the palladium is a diffusion process in nature [6]. Usually the diffusion coefficient decreases quickly when the temperature is decreasing; however, it is clearly shown that the flux might be enhanced when the temperature of Pd is decreasing (Fig. 2a). This part of flux is apparently not related to a diffusion process, possibly it is related to a kind of resonant process. It implies that a single deuteron wave function might be applied to the whole D/Pd system as suggested by Professor M. Fleischmann [7] who has searched this multi-body feature in condensed phase for more than 4 decades. Indeed this is the basic assumption in the following calculation for “super-absorption” process in a crystal lattice. It explains why a heat flow is correlated with a flux in the crystal lattice.

SUPER-ABSORPTION IN CRYSTAL LATTICE

FROM SUPER-RADIATION TO SUPER-ABSORPTION

It is easier to introduce the concept of super-absorption in terms of the comparison with super-radiation in optics. In optics, super-radiation[8] due to the coherence between several optical sources has been proved in experiment (Fig. 3a). The total intensity of the light is proportional to ½4´Amplitude of single light½2 instead of 4´½Amplitude of single light½2 for the case of super-radiation. In converse, we might ask what happens if there is coherence between several optical absorbers (Fig. 3b) because any nuclear reaction may be considered as an absorption of the injected wave. When the injected wave hit on several absorbers in the lattice, there will be the scattered wave and absorbed wave, the phases of the scattered waves may be in coherence which might result in constructive interference or destructive interference. The constructive interference will enhance the amplitude of the scattered wave inside the lattice; then, it will enhance the absorption when the scattered wave hit on the next absorber. The destructive interference will be important when it reduce the amplitude of the total reflected wave because the total reflected wave outside the crystal is the superposition of all reflected waves from all absorbers. This will be illustrated by a 1-dimensional model as follows.

SUPER-ABSORPTION IN ONE-DIMENSIONAL MODEL

A series of potential wells and barriers in one dimension are used to illustrate this coherent effect (Fig. 4). The narrow-deep well represents the absorber, and the wide-shallow well represents the space between absorbers. When the injected wave is coming from the left, we may calculate how much is absorbed, how much is reflected, and how much penetrates this array of lattice well and barrier. Using quantum mechanics [9], for a single cell of barrier-well-barrier array we may calculate the matrix, M(1), which connects the outgoing wave function, Yout(1) , and the incoming wave function, Yin(1) as:

(1)

This matrix is written in the plane—wave representation. For example in the case of outgoing wave only (see right-hand-side of Fig.4),

(2)

then, the incoming wave should be

(3)

When the array is increased to a set of N cells of barrier-well-barrier (Fig. 4a), the matrix equation should be written as

(4)

An Array of Coherent Absorbers inside the Lattice

If we keep the outgoing wave function same as before; then,

(5)

Since,

(6)

we have

(7)

Based on matrix algebra, it can been proved that

(8)

(9)

(10)

The reflection rate, R, penetration rate, T, and the absorption rate, A, may be written as the function of the elements of the connection matrix:

(11)

(12)

(13)

The similar definition is valid for an array of N set of barrier-well-barrier

(14)

(15)

(16)

CORRELATION BETWEEN HEAT FLOW AND DEUTERIUM FLUX

An important conclusion may be drawn from this very general relationship between M(N)21 and M(1)21 (equation (9)): when the reflection rate for single cell is not zero; the total reflection rate for N cell might be zero as long as

(17)

In physics, this is the result of destructive interference among all the reflected waves. At the same time R(N)=0 implies T(N)®1 when there is no absorption(Fig. 4b). It means a constructive interference among all the propagating waves inside the array of barrier-well-barrier region which enhances the penetration rate greatly. The conservation of the probability guarantees the eventual penetration after all the reflection and penetration in each cell.

Now we may find another important conclusion from this relationship: when a small imaginary potential is introduced in the well region of the absorbers; then, there will be an absorption rate (Fig. 4c):

(18)

It is proportional to the product of imaginary part of the potential and the square of the amplitude of the wave function, Im(U1)´½Y1(N)½2, which has been greatly enhanced due to the constructive interference among all the propagating waves inside the array of cells. It is a kind of resonant tunneling. Here, Im(U1) is the imaginary part of the potential in the absorber region; ½Y1(N)½ is the average amplitude of the wave function in that region. This resonant tunneling predicts that the peak of the penetration rate(T(N)) will be accompanied with a peak of the absorption peak(A(N)). i. e. the correlation between the flux and the reaction rate, or a heat flow is related to a deuterium flux.

NUCLEAR ENERGY WITHOUT STRONG NUCLEAR RADIATION

When we are sure this flux is related to a resonance in nature; then, it is possible to apply the selective resonant tunneling model[2,3,4]. We may anticipate that the imaginary potential can not be too large or too small. It is evident that the absorption rate A(N)®0 if this imaginary potential Im(U1) ®0. On the other hand if this imaginary potential is too large; then, it will damp the resonance such that the product of Im(U1)´½Y1(N)½2®0. Thus there must be a maximum for a certain value of Im(U1) in between. This selectivity will explain why only certain channel of reaction is open to the resonant tunneling. In other words, the absorption peak will reach its maximum when the imaginary part of the potential reaches a certain intermediate value. Indeed, it implies that only the nuclear reaction without strong neutron and gamma radiation would be selected by this resonant tunneling mechanism.

ACKNOWLEDGEMENTS

This work is supported by Ministry of Science and Technology, Natural Science Foundation of China (No. ), and Tsinghua University Fundamental Research Fund.

REFERENCES

[1] A. Takahashi, et al., "Anomalous Enhancement of Three-Body Deuteron Fusion in Titanium-deuteride under Low-Energy D+ Bean Implantation", Fusion Technology

[2] Xing. Z. Li, J. Tian, M. Y. Mei and C. X. Li, “Sub-barrier Fusion and Selective Resonant Tunneling,” Phys. Rev. ,C 61, 024

[3] Xing. Z.Li, "Nuclear Physics for Nuclear Fusion." Fusion Science and Technology, 41,

[4] Xing Z. Li, et al., "Study Of Nuclear Physics For Nuclear Fusion," Journal of Fusion Energy ,19,

[5] Jian Tian, Xing Z. Li, et al., "Reproducible Heat and Correlation with Deuterium Flux in a D/Pd Gas-loading System", Presentation in ICCF9 (2002).

[6]Y. Fukai, “The Metal-Hydrogen System,” Springer-Verlag, Berlin Heidelberg (1993), p.214.

[7]M. Fleischmann, “Searching for the Consequences of Many-Body Effects in Condensed Phase Systems,” Presentation in ICCF9 (2002).

[8] R. H. Dicke, “Coherence in Spontaneous Radiation Processes,” Phys. Rev. 93,

[9] Xing Z. Li, et al., “Super-Absorption—The Effect of Crystal Lattice on Enhancement of Nuclear Reaction—”, Proceedings of 2001 Chinese Physical Society Fall Meeting, Sept. 20-23, 2001, Shanghai, China. P.98.(in Chinese)