Recurrence Formulas for Fully Exponentially Correlated Four-Body Wavefunctions

Formulas are presented for the recursive generation of four-body integrals in which the integrand consists of arbitrary integer powers (>= -1) of all the interparticle distances r_ij, multiplied by an exponential containing an arbitrary linear combination of all the r_ij. These integrals are generalizations of those encountered using Hylleraas basis functions, and include all that are needed to make energy computations on the Li atom and other four-body systems with a fully exponentially correlated Slater-type basis of arbitrary quantum numbers. The only quantities needed to start the recursion are the basic four-body integral first evaluated by Fromm and Hill, plus some easily evaluated three-body "boundary" integrals. The computational labor in constructing integral sets for practical computations is less than when the integrals are generated using explicit formulas obtained by differentiating the basic integral with respect to its parameters. Computations are facilitated by using a symbolic algebra program (MAPLE) to compute array index pointers and present syntactically correct FORTRAN source code as output; in this way it is possible to obtain error-free high-speed evaluations with minimal effort. The work can be checked by verifying sum rules the integrals must satisfy.Comment: 10 pages, no figures, accepted by Phys. Rev. A (January 2009

A new readily processable polyimide

As part of an effort to develop tough solvent resistance thermoplastics for potential use as structural resins on aerospace vehicles, a new processable polyimide was evaluated. The synthesis involved the reaction of a new diamine, 1,3-bis 2-(3-aminophenoxy)ethyl ether, with 3,3',4,4'-benzophenonetetracarboxylic dianhydride to form the polyamic acid and subsequent conversion of it to the polyimide. Various physical properties such as thermal stability, solvent resistance, glass transition temperature, crystalline melt temperature, melt viscosity and mechanical properties such as fracture toughness, adhesive, film and composite properties are reported. Of particular interest is the extremely high titanium to titanium tensile shear strength obtained for this polyimide

Supersonic aircraft Patent

Design of supersonic aircraft with novel fixed, swept wing planfor