Publications

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods). Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numerical complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange) part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. This technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

We spectroscopically measure multiple hydrogen Balmer line profiles from laboratory plasmas to investigate the theoretical line profiles used in white dwarf (WD) atmosphere models. X-ray radiation produced at the Z Pulsed Power Facility at Sandia National Laboratories initiates plasma formation in a hydrogen-filled gas cell, replicating WD photospheric conditions. We also present time-resolved measurements of Hβ and fit this line using different theoretical line profiles to diagnose electron density, n_e, and n = 2 level population, n₂. Aided by synthetic tests, we characterize the validity of our diagnostic method for this experimental platform. During a single experiment, we infer a continuous range of electron densities increasing from n_e ~ 4 to ~30 × 10¹⁶ cm^-3 throughout a 120-ns evolution of our plasma. Also, we observe n₂ to be initially elevated with respect to local thermodynamic equilibrium (LTE); it then equilibrates within ~55 ns to become consistent with LTE. This also supports our electron-temperature determination of T_e ~ 1.3 eV (~15,000 K) after this time. At n_e≲ 10¹⁷ cm^-3, we find that computer-simulation-based line-profile calculations provide better fits (lower reduced χ²) than the line profiles currently used in the WD astronomy community. The inferred conditions, however, are in good quantitative agreement. Lastly, this work establishes an experimental foundation for the future investigation of relative shapes and strengths between different hydrogen Balmer lines.