Local density approximation for long-range or for short-range energy functionals?

Density functional methods were developed, in which the Coulomb electron-electron interaction is split into a long- and a short-range part. In such methods, one term is calculated using traditional density functional approximations, like the local density approximation. The present paper tries to shed some light upon the best way to do it by comparing the accuracy of the local density approximation with accurate results for the He atom.Comment: 4 pages, 2 figures, to appear in J. Mol. Struct. (Theochem

The Long Range Gravitational Potential Energy Between Strings

We calculate the gravitational potential energy between infinitely long parallel strings with tensions \tau_1 and \tau_2. Classically, it vanishes, but at one loop, we find that the long range gravitational potential energy per unit length is U/L = 24G_N^2\tau_1\tau_2/(5 \pi a^2) + ..., where a is the separation between the strings, G_N is Newton's constant, and we set \hbar = c =1. The ellipses represent terms suppressed by more powers of G_N \tau_i. Typically, massless bulk fields give rise at one loop to a long range potential between p-branes in space-times of dimension p+2+1. The contribution to this potential from bulk scalars is computed for arbitrary p (strings correspond to p=1) and in the case of three-branes its possible relevance for cosmological quintessence is commented on.Comment: 10 pages, 6 figure

Neutrino-nucleus reactions in the energy range 1-100 MeV

We review some salient aspects of calculations of the neutrino-nucleus reaction cross sections in the low energy range (1-100 MeV).Comment: 6 pages:Invited talk at NuInt05 (Fourth International Workshop on Neutrino- Nucleus Interactions in the Few-GeV Region), Okayama, Japan. September 26 - 29, 2005, ver2 corrected typos and reference

Mid-range adiabatic wireless energy transfer via a mediator coil

A technique for efficient mid-range wireless energy transfer between two coils via a mediator coil is proposed. By varying the coil frequencies three resonances are created: emitter-mediator (EM), mediator-receiver (MR) and emitter-receiver (ER). If the frequency sweeps are adiabatic and such that the ER resonance precedes the MR resonance, the energy flows sequentially along the chain emitter-mediator-receiver. If the MR resonance precedes the ER resonance, then the energy flows directly from the emitter to the receiver via the ER resonance; then the losses from the mediator are suppressed. This technique is robust to noise, resonant constraints and external interferences

Long-range asymptotics of exchange energy in the hydrogen molecule

The exchange energy, i.e. the splitting $\Delta E$ between gerade and ungerade states in the hydrogen molecule has proven very difficult in numerical calculation at large internuclear distances $R$, while known results are sparse and highly inaccurate. On the other hand, there are conflicting analytical results in the literature concerning its asymptotics. In this work we develop a flexible and efficient numerical approach using explicitly correlated exponential functions and demonstrate highly accurate exchange energies for internuclear distances as large as 57.5 au. This approach may find further applications in calculations of inter-atomic interactions. In particular, our results support the asymptotics form $\Delta E \sim R^{5/2}e^{-2R}$, but with the leading coefficient being $2\,\sigma$ away from the analytically derived value