Opacities and spectra of hydrogen atmospheres of moderately magnetized neutron stars

There is observational evidence that central compact objects (CCOs) in supernova remnants have moderately strong magnetic fields $B\sim10^{11}$ G. Meanwhile, available models of partially ionized hydrogen atmospheres of neutron stars with strong magnetic fields are restricted to $B\gtrsim10^{12}$ G. We extend the equation of state and radiative opacities, presented in previous papers for 10^{12}\mbox{ G}\lesssim B \lesssim 10^{15} G, to weaker fields. An equation of state and radiative opacities for a partially ionized hydrogen plasma are obtained at magnetic fields $B$, temperatures $T$, and densities $\rho$ typical for atmospheres of CCOs and other isolated neutron stars with moderately strong magnetic fields. The first- and second-order thermodynamic functions, monochromatic radiative opacities, and Rosseland mean opacities are calculated and tabulated, taking account of partial ionization, for 3\times10^{10}\mbox{ G}\lesssim B\lesssim 10^{12} G, $10^5$ K $\lesssim T\lesssim 10^7$ K, and a wide range of densities. Atmosphere models and spectra are calculated to verify the applicability of the results and to determine the range of magnetic fields and effective temperatures where the incomplete ionization of the hydrogen plasma is important.Comment: 11 pages, 7 figures, accepted for publication in A&

Analytical calculation of pressure for confined atomic and molecular systems using the eXtreme-Pressure Polarizable Continuum Model

We show that the pressure acting on atoms and molecular systems within the compression cavity of the eXtreme-Pressure Polarizable Continuum method can be expressed in terms of the electron density of the systems and of the Pauli-repulsion confining potential. The analytical expression holds for spherical cavities as well as for cavities constructed from van der Waals spheres of the constituting atoms of the molecular systems

Tensor Numerical Methods in Quantum Chemistry: from Hartree-Fock Energy to Excited States

We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, led to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in $O(n\log n)$ complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D $n\times n\times n$ Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D ``density fitting`` scheme. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excited states, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is related to the recent attempts to develop a tensor-based Hartree-Fock numerical scheme for finite lattice-structured systems, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a $L\times L\times L$ lattice manifests the linear in $L$ computational work, $O(L)$, instead of the usual $O(L^3 \log L)$ scaling by the Ewald-type approaches

Modeling surface roughness scattering in metallic nanowires

Ando's model provides a rigorous quantum-mechanical framework for electron-surface roughness scattering, based on the detailed roughness structure. We apply this method to metallic nanowires and improve the model introducing surface roughness distribution functions on a finite domain with analytical expressions for the average surface roughness matrix elements. This approach is valid for any roughness size and extends beyond the commonly used Prange-Nee approximation. The resistivity scaling is obtained from the self-consistent relaxation time solution of the Boltzmann transport equation and is compared to Prange-Nee's approach and other known methods. The results show that a substantial drop in resistivity can be obtained for certain diameters by achieving a large momentum gap between Fermi level states with positive and negative momentum in the transport direction.Comment: 25 pages, 11 figure

Finite nuclear size effect on Lamb shift of s1/2, p1/2, and p3/2 atomic states

We consider one-loop self-energy and vacuum polarization radiative corrections to the shift of atomic energy level due to finite nuclear size. Analytic expressions for vacuum polarization corrections are derived. For the self-energy of p1/2 and p3/2 states in addition to already known terms we derive next-to-leading nonlogarithmic Z\alpha-terms. Together with contributions obtained earlier the terms derived in the present work give explicit analytic expressions for s1/2 and p1/2 corrections which agree with results of previous numerical calculations up to Z=100 (Z is the nuclear charge number). We also show that the finite nuclear size radiative correction for a p3/2 state is not small compared to the similar correction for a p1/2 state at least for small Z.Comment: 12 pages, 7 figure