On the Nuclear Mechanisms Underlying the Heat Production by the “E-Cat” Norman D. Cook1 and Andrea Rossi2 1. Department of Informatics, Kansai University, Osaka, 1095-569, Japan 2. Leonardo Corporation, Miami Beach, Florida, 33139, USA We discuss the isotopic abundances found in the E-Cat reactor with regard to the nuclear mechanisms responsible for “excess” heat. We argue that a major source of energy is a reaction between the first excited-state of 7Li4 and a proton, followed by the breakdown of 8Be4 into two alphas with high kinetic energy, but without gamma radiation. The unusual property of the 7Li4 isotope that allows this reaction is similar to the property that underlies the Mössbauer effect: the presence of unusually low-lying excited states in stable, odd-Z and/or odd-N nuclei. We use the lattice version of the independent-particle model (IPM) of nuclear theory to show how the geometrical structure of isotopes indicate nuclear reactions that are not predicted in the conventional version of the IPM. Finally, we speculate on similar mechanisms that may be involved in other low-energy nuclear reactions (LENR). PACS numbers: 21. Nuclear structure 27.40.+z Properties of specific nuclei 1<A<64 1 Introduction month was found [3]. For technological exploitation, it may be sufficient to mimic the materials and protocols that have made that The checkered history of low-energy nuclear possible (e.g., Parkhomov [4]), but the huge reaction (LENR) research remains highly con- diversity of conditions that have been reported troversial. It includes disputed claims of both in the “cold fusion” literature for 26 years experimental successes and failures in both suggest that there may exist general LENR Nickel and Palladium systems. Reported mechanisms that have not yet been identified. results and theoretical models are far too Although progress has been made in defining diverse to allow definitive conclusions to be the solid-state, chemical and electromagnetic drawn, but Storms [1, 2] has summarized the field properties of the nuclear active overwhelming consensus that nuclear effects environment (NAE), the specifically nuclear have been obtained in experimental set-ups aspects of the NAE have not generally been where conventional theory predicts the total addressed. Here, we argue that femtometer- absence of nuclear involvement. While further level LENR can occur in isotopes with low- empirical work remains a high priority, a lying excited-states, provided that an appro- remaining theoretical task is to demonstrate priate, Angstrom-level molecular environment how the published data on heat production has been created. and isotopic transmutations are consistent In the present study, we focus on recent with the major themes of nuclear physics, as findings of nuclear transmutations concerning established over the past century. Lithium isotopes [3] in light of the lattice In the latest empirical test of Andrea version [5] of the independent-particle model Rossi’s invention, known as the E-Cat, (IPM) of the nucleus. Specifically, after brief significant excess heat (a ratio of output/input review of the well-established IPM, we energy in excess of 3.0) over the course of one consider details of the substructure of the 7Li4 1 and 8Be4 isotopes that allow for the generation inventors of the shell model shared the Nobel of alpha particles at kinetic energies well Prize in Physics in 1963, and their combined beyond what could be produced solely insights gave nuclear structure theory a through chemical reactions. coherent quantum mechanical basis. The bold assumption of the shell model was that there 2 Methods occurs a coupling between quantum numbers, l and s, to produce an observable total angular momentum, j (=l+s). Inherent to that 2.1 Theory: The Independent-Particle assumption, however, was the highly Structure of Nuclei unrealistic notion that “point” nucleons “orbit” freely in the nuclear interior and do For more than six decades, it has been known not interact with other nucleons (in first that many nuclear properties can be described approximation) orbiting within the nuclear in terms of the simple summation of the potential well. Similar assumptions had also properties of the constituent protons and been made in the still earlier Fermi gas model neutrons. In the 1930s, this theoretical of the nucleus, but were eventually rejected perspective was rejected by Niels Bohr, who because of the theoretical successes of the favored a “collective” view of nuclei, but the liquid-drop model (LDM) concerning nuclear shell model assumption of spin-orbit coupling binding energies, radii, fission phenomena, in the early 1950s proved to be a major etc. The LDM, in turn, was based upon theoretical success that established the realistic assumptions about the nuclear “independent-particle” approach as the central interior: electrostatic and magnetic RMS radii paradigm of nuclear structure theory. of protons and neutrons of about 0.85 fm [9], Most importantly, the IPM description of a nuclear core density of 0.17 nucleons/fm3 nuclear states allowed for a coherent (implying a nearest-neighbor internucleon explanation of experimentally observed spins distance of only 2.0 fm) and the non-orbiting and parities (Jπ) (and, more approximately, of nucleons – all of which argued strongly magnetic moments, µ) as the simple against a diffuse nuclear “gas” and for a summation of the jπ and µ of any unpaired dense nuclear “liquid”. protons and neutrons. Subsequently, the The inherent contradictions between the ground-state spin and parity of more than gaseous-phase IPM and the liquid-phase LDM 2800 relatively-stable nuclear isotopes and, are of course summarized in most nuclear most impressively, the nearly half-million textbooks, but an interesting blend of those excited-states of those isotopes, as tabulated two competing models was first developed in in the Firestone Table of Isotopes (1996) [6], the 1970s in the form of a lattice model of have been classified in the IPM. Arguably, it nuclear structure (the history of which is is this overwhelming success of the IPM that discussed in ref. [5]). The lattice model (a has led many nuclear physicists to conclude “frozen liquid-drop”) has most of the that LENR phenomena are unlikely to be real, properties of the traditional LDM, but, when insofar as they are not consistent with the nuclei are built around a central tetrahedron of established principles of nuclear theory. As four nucleons, the lattice shows the discussed below, we have found that the remarkable property of reproducing the theoretical framework provided by the IPM is, correct sequence and occupancy of all of the paradoxically, essential for explaining the n-shells of the shell model as triaxially- transmutations reported to occur in the E-Cat. symmetrical (spherical) lattice structures. The early mathematical development of Moreover, the j-subshells of the shell model the IPM was undertaken by Eugene Wigner emerge as cylindrical structures and the m- [7] in the 1930s, but the IPM did not become subshells of the shell model arise as conical the dominant model of nuclear structure until substructures – all in the same sequence and the early 1950s, with the emergence of the with the same occupancy of protons and shell model [8]. In fact, Wigner and the 2 neutrons as known from the conventional parity (Jπ) values based upon very different IPM. assumptions concerning the “point” or “space- Although various aspects of the mathe- occupying” structure of the nucleons them- matical identity between the shell and lattice selves. Here, we consider the lattice IPM to be models have frequently been published in the a realistic alternative to the gaseous-phase physics literature, the lattice model itself has IPM, and elaborate on its implications in been dismissed as a “lucky” reproduction of relation to LENR phenomena. the symmetries of the shell model and has had The quantal properties in the lattice little impact on nuclear theorizing, in general. model are defined in Eqs. (1-6), and are The fact remains, however, that the lattice and illustrated in Figure 1. Related theoretical gaseous-phase versions of the IPM reproduce arguments have been published since the the same patterns of observable spin and 1970s, and full details are available online [5]. n = (|x| + |y| + |z| - 3) / 2 (Eq. 1) l = (|x| + |y|) / 2 (Eq. 2) j = (|x| + |y| -1) / 2 (Eq. 3) m =|y| *(-1)^((x-1)/2)/ 2 (Eq. 4) s = (-1)^((x-1)/2)/ 2 (Eq. 5) i = (-1)^((z-1)/2) (Eq. 6) The significance of the “quantal identical to that produced in the conventional geometry” (Eqs. 1-6) (Figure 1) can be simply IPM. Conversely, knowing the quantum stated: every unique grid site in the lattice characteristics of individual nucleons, their corresponds to a unique set of nucleon positions (Cartesian coordinates) in the lattice quantum numbers, the sum of which is can be calculated, as shown in Eqs. (7-9). x = |2m|(-1)^(m-1/2) (Eq. 7) y = (2j+1-|x|)(-1)^(i/2+j+m+1/2) (Eq. 8) z = (2n-3+|x|-|y|)(-1)^(i/2+n+j+1) (Eq. 9) Figure 1: The geometry of nuclear quantum numbers in the lattice representation of the IPM. A simple example of the identity conventional tabulation of IPM states in between IPM quantal features and lattice relation to the quantum numbers. On the symmetries is illustrated in Figure 2 for the right is shown the corresponding lattice ground-state of 15Ni8. On the left is shown structure for those 15 nucleons. Note that the the build-up of protons and neutrons in a geometrical configuration of neutrons (blue) 3 and protons (yellow) is given explicitly by of nucleons in the lattice IPM is determined the lattice definitions of the quantum explicitly by the quantum characteristics of numbers.