Low-Energy Nuclear Reactions Sourcebook - American Chemical

Chapter 3

An Approach to Nuclear Energy without Strong Nuclear Radiation X. Z. Li, Q. M . Wei, and B. Liu

Downloaded by YORK UNIV on July 1, 2012 | http://pubs.acs.org Publication Date: August 1, 2008 | doi: 10.1021/bk-2008-0998.ch003

Department of Physics, Tsinghua University, Beijing 100084, China

Collaboration between chemists and physicists has been essential in the history of scientific discovery. In order to make the discovery more convincing to mainstream science, we have to have the theoretical prediction verified by the various independent experimental results. The splendid goal of nuclear energy without strong nuclear radiation has been the motivation of this untiring worldwide effort. The next steps are a self-sustaining reactor and the detection of the neutrino emissionfromthe metal-hydrides (deuterides).

Introduction Chemists have been the pioneers of scientific discovery because they are confident about their experimental tools such as calorimeters, chemical analysis, etc. However, they have always faced strong rejection from those physicists who were believers in their own theory without considering the limitations of their theory. The history of nuclear energy is a good example. Early in 1933, the famous physicist, Ernst Rutherford, alleged that any energy source based on nuclear transmutation was just "moonshine" (7). Six years later, in 1939, when Otto Hahn discovered barium after the bombardment of uranium by neutrons, he was so afraid of the physicists that he was always trying to figure out what was wrong with his experiment because barium was incredible (2). Unfortunately, Martin Fleischmann and Stanly Pons faced the same strong objections from physicists again in 1989, because physicists could not find the "commensurable neutron" emission. The physicists alleged that it was impossible to have "thunder without lightning." If they did not see the lightning they would not believe any thunder. Thus the physicists denied the experimental results in terms of their own theory, even if the amount of "excess heat" is greater than that from © 2008 American Chemical Society In Low-Energy Nuclear Reactions Sourcebook; Marwan, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2008.

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any conceivable chemical reactions. To their minds, the neutron was the "lightning" and the thunder was the "nuclear reaction." Indeed the neutron is not a necessary product of any nuclear reaction. After a nuclear reaction between two positively charged nuclei only the charged particle is the necessary product, but not the neutron. Solar energy is an example (5). However, why did so many nuclear physicists try to detect the neutron emission from the electrolytic cell using a palladium cathode in heavy water? They were looking for deuteron-deuteron fusion, of which they had knowledge based on beam-target experiments only. Using accelerators, the physicists established two reactions:

The physicists further inferred from these equations that whenever two deuterons enter in the nuclear force region they will emit neutrons. The physicists unconsciously assumed that the choice of the reaction channel would be independent of the penetration of the Coulomb barrier. They forgot the important effect of the resonance on tunneling, and the selectivity of the resonant tunneling.

Importance of the Resonance on Tunneling Early in the 1990s, a professor at Princeton University wrote a textbook on quantum mechanics (4). There was a special section to discuss "cold fusion." He intended to make some estimate favorable to cold fusion. Eventually he mistakenly proved that there was no way to have any detectable penetration of Coulomb barrier at low energy. He made a great mistake when he assumed that the entire wave of penetrating deuterons would be absorbed by nuclear potential well immediately after its penetration. It looked like an assumption favorable to cold fusion, because there would be no reflected wave inside the nuclear potential well, and the entire deuteron wave entering the nuclear potential well would disappear instantly. Indeed this was the worst assumption for cold fusion because it killed the resonance. Consequently, there would be no resonant tunneling, which was essential to cold fusion. Why is the reflection so important for resonance? Since resonance is essentially the constructive interference phenomenon, there must be two waves—incident wave and the reflected wave—in order to have this constructive interference. When the absorption kills the reflection totally, it kills the resonance too. Without the constructive interference, the amplitude of the deuteron wave function would not be built up inside the nuclear potential well; hence, the

In Low-Energy Nuclear Reactions Sourcebook; Marwan, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2008.

41 tunneling current through the Coulomb barrier becomes negligible (exponentially small). This was just the result of Peebles' calculation (4). In fact, Peebles' calculation just shows how important the resonance is by assuming an infinite absorption. Without resonance, there is no way to penetrate the Coulomb barrier at low energy.


Neutron Emission Should not be Taken as an Indication of Resonance at Low Energy Physicists might argue that all the negative results in neutron detection from the electrolytic cell just showed no resonance for a pair of deuterons at low energy. This was a mistake again because the neutron emission was no longer a good indication of the resonance at low energy due to the selectivity of the resonant tunneling. The selectivity of the resonant tunneling means that the choice of the reaction channel depends on the thickness and the height of the Coulomb barrier. When the Coulomb barrier is very thick and high, the tunneling wave becomes very weak (exponentially small). It requires a lot of bouncing back and forth to build up the amplitude of the wave function in terms of the constructive interference inside the nuclear potential well in order to have a detectable effect of tunneling. This simply requires a long life-time of the probability wave of deuterons inside the nuclear potential well. Thus the resonant tunneling will select the long life-time channel only in the case of a thick and high barrier. The neutron emission channels are short life-time channels because they are induced by the strongest nuclear interaction. Hence, for the neutron emission channel there will be no chance to have any resonant tunneling at low energy. Some physicists believed that the tunneling happens in two independent steps: penetration first, then decay independently. Hence they always asked why two deuterons could not emit neutrons when they stayed together. They forgot that penetration and decay were dependent processes. For the rapid decay channel there was no way to have any detectable tunneling at low energy. This selectivity of resonant tunneling should be true for both cold fusion and "hot fusion"; hence, we may justify this concept first in terms of hot fusion data.

"Hot Fusion" Data Justify Selectivity of Resonant Tunneling Having started from basic quantum mechanics, we may write the general expression of fusion cross-section of S-wave as (5,6):


42

Γ

2

*V +(^-i)

2

r

Here, /: is the wave number of the incoming wave function; W = Cotô, and δ is the phase shift when the incoming wave is scattered by a nuclear potential well. When nuclear fusion happens, there is absorption of the deuteron wave in the nuclear potential well. Hence, the nuclear potential is a complex potential; and this phase shift, δ, is a complex number as well. Thus W = Cotô becomes a complex number, as does W= W + iW This Wjust shows the resonance effect and the selectivity of resonance clearly. When its real part, W , approaches zero, there is a peak of cross-section. However, the height of peak depends on the imaginary part, W If W = 0, it corresponds to the case of elastic scattering, and fusion cross-section a = 0. If W = -oo, it corresponds to the case of strong damping (Peebles' assumption (4)). The strong damping might kill the resonance totally, and the peak height of the fusion cross-section vanishes also. Indeed the peak height of the fusion cross-section reaches its maximum when Wj = -l. This is the selectivity of resonance which selects the matching damping. We successfully applied this concept to the hot fusion data for deuterontriton, for deuteron-helium3, and for deuteron-deuteron. Figure 1 shows the results of calculations based on the selective resonant tunneling model and comparison with the experimental data. The crosses are the experimental data points from the National Nuclear Data Center (NNDC) and the open circles are the results of calculation (6). Their agreements are better than those of the empirical five-parameter formula which has been listed in the Handbook of Plasma Physics for more than 25 years (7). This calculation even corrected an error in old NNDC data in 2002 (8). It further verifies the dependence of the reaction on the penetration using the data of astrophysics factor in 2004 (6). Thus, hot fusion data have justified the selectivity of resonanttunneling. Thisselectivity of the resonant tunneling would be much sharper in the case of confined deuterons in the lattice potential well because the Coulomb barrier would be much higher and thicker there. r

h


r

h

t

r

t

Selectivity of Resonant Tunneling for a Pair of Confined Deuterons The boundary condition plays the key role in wave mechanics. When an inward spherical wave was assumed at the boundary of the nuclear potential well (4), there was no chance for any resonance (Figure 2a) When a matching damping was assumed inside the nuclear potential well (i.e., W = -1), the resonance appeared and there was incoming spherical wave only at the distant edge of the Coulomb potential without any outgoing spherical wave (Figure 2b). The boundary condition for a pair of confined deuterons is very different from that in the beam-target case. An exponentially decaying wave has to be assumed {



D+T Fusion Cross Section (Barn) ο

3 s 3

°

SI! a.

«
1.4) and used a cold finger to cool the titanium target during the beam bombardment (5~15°C) (77) (Figure 5). He found the products of a 3-deuteron fusion reaction, i.e., 2

4


2

31

x

d + d + d-± p + n + a + 2\.62MeV

TiD ,x>1.4 (5 °C~15°C) x

Figure 5. Beam-target experiment tofindthe 3-deuteron fusion reactions.

The products of 3-deuteron fusion are distinct from that of 2-deuteron fusion because 3-deuteron fusion gives more energetic products and they have a


49 continuous energy distribution among three nuclear products. The maximum energy of alpha-particles is 6.5 MeV, and the maximum energy of protons is 17 MeV. There is no way to explain these maximum values of energy in terms of any 2-deuteron reactions. Professor Takahashi of Osaka University confirmed this 3-deuteron reaction in terms of another 3-deuteron reaction channel (12): 3


Low-Energy Nuclear Reactions Sourcebook - American Chemical

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