I. Bloch Ions

A Bloch ion has periodic symmetry and is distributed in space in a lattice array form. Its spatial density distribution is neutralized within each unit cell by a metal's electrons. The wave function repeats coherently modulo a Bravais lattice vector. Paired Bloch deuterons partitioned over a sufficiently large number of unit cells become superposed and coherently mixed by coordinate exchange. A Hamiltonian describing paired deuterons 2-D+Bloch is presented, and its nuclear self-interaction and coupling with the lattice are described. INTRODUCTION This paper is the first of a group of 3 papers that argues the view that LENR processes share a common physics. Conclusions are summarized at the end of Paper III. Wave function coherence plus a partitioning of nuclear charge appear to be a requirement for LENR, including Fleischmann and Pons (F-P) cold fusion. Bloch ion wave functions1 have the required characteristics. The D+Bloch ion is compared with the D2 molecule in Fig. 1. The deuterons in the molecule have coordinate-exchange-symmetry2 and share a common potential well provided by spin-paired electrons. Drawings compare a D2 molecule trapped in a harmonic well with a 2-D+Bloch wave function trapped in multiple potential wells furnished by a metal lattice. The center of the D2 molecule is distributed as a Gaussian within the harmonic well (not shown). The molecule's double-peaked structure exists in "separation space". It is pictured in Fig. 1a, and is the site of vibration,rotation excitations. The lattice-conforming structure of the 2-D+Bloch wave function exists in "center-of-mass" space, i.e., lattice space, and closely resembles that of the Bloch-state electrons in a metal. Both are characterized by coherent partitioning of charge density over multiple potential wells. Their wave function phases are ordered with respect to position, and can only change in concert. The partitioned coherence of Bloch electrons gives the metal its high conductivity. Both types of Bloch particles are described by periodic symmetry that occurs in response to the periodic order of a hosting metal atom lattice. The 2-D+Bloch wave function also exists in "separation space". In "separation space" it has important resemblance to the spin-paired 2-electron orbital that neutralizes the He nucleus in the atom ground state. Both paired particles are subject to coordinate exchange symmetry, but differ in that the 2-D+Bloch has a local maximum in each of multiple potential wells, whereas the He atom's spin-paired 2-electron density has a single maximum in a single potential well. Both are expressed by 2-particle wave functions describing anti-correlated superposed charged particles, instead of side-by-side charged particles kept separate by a Coulomb barrier.