Does Cold Fusion Exist and is it Measurable?

Abstract

The dynamical nature of the cold fusion problem is considered. A general model of two slow charged particles interacting in a metal crystal is developed. It is shown that there exists a resonance state of this system. The value of the positive real resonance energy depends on the properties of the metal crystal. An estimate of the probability of cold nuclear fusion in condensed matter is given.Recently, the d + d nuclear fusion in Pd-D (i.e., Pd metal crystal with absorbed deuterium atoms) at room temperature has received much attention. Various experimental papers were published in which this effect was studied, however with contradictory results [1][2][3].From the theoretical point of view, cold nuclear fusion was considered in [4][5][6]. It was shown in [4] that this process possibly may take place without production of neutrons, if one considers the Pd-D crystal as a cold plasma. In [5], estimates of the screening effects of the electrons on the nuclear Coulomb barrier were given, and in [6], a calculation based on the effective potential of two interacting deuterons in a palladium lattice was presented.In the present paper, the dynamical nature of the cold fusion is considered. Attempting to clarify this problem, we have developed a general model of two slow charged quantum particles interacting in a metal crystal. We have proven that there exists a resonance state of this system and that the value of the positive real resonance energy depends on the properties of the metal crystal. So we probably have found a dynamical pairing of the positively charged particles in a metal crystal. This result made it possible to estimate the probability of cold nuclear fusion in condensed matter.In developing this general model, we made some special assumptions, since the system under consideration has special features due to the type of the interaction potential of two slow positively charged particles in a metal crystal, i.e., in the electron gas of the metal. Taking one particle with the charge Z^ as a center fixed in the electron cloud of density p(r), where r(x, y, z) is the distance from the center, we treat now the problem as a scattering of the other incoming particle (with the charge Z 2 ) in a field obtained as the superposition of the two potential fields. One potential, of the Coulomb point central field, is given byZy ' Z,and the second potential, which is due to the charge of the electron cloud with density g 0 , is given by the potential functionwhereand r s is the Wigner-Seitz radius for an electron in atomic units (r o = 0.5 • 10" 8 cm), e the electron charge and e 0 the dielectric constant. It is easy to see that, whereas the Coulomb central potential is decreasing with the distance as r -1 , the potential of the electron cloud increases with growing distances as r 2 . Because of this fact, the interaction between the two charged particles takes place effectively only for a distance smaller than R 0 Kr s , which can be found from the relation V C (R 0 )= -V tl (R 0 ). To describe the interaction of two ...