Proton radii of 4,6,8He isotopes from high-precision nucleon-nucleon interactions

Recently, precision laser spectroscopy on 6He atoms determined accurately the isotope shift between 4He and 6He and, consequently, the charge radius of 6He. A similar experiment for 8He is under way. We have performed large-scale ab initio calculations for 4,6,8He isotopes using high-precision nucleon-nucleon (NN) interactions within the no-core shell model (NCSM) approach. With the CD-Bonn 2000 NN potential we found point-proton root-mean-square (rms) radii of 4He and 6He 1.45(1) fm and 1.89(4), respectively, in agreement with experiment and predict the 8He point proton rms radius to be 1.88(6) fm. At the same time, our calculations show that the recently developed nonlocal INOY NN potential gives binding energies closer to experiment, but underestimates the charge radii.Comment: 5 pages, 9 figure

All-Electron Path Integral Monte Carlo Simulations of Warm Dense Matter: Application to Water and Carbon Plasmas

We develop an all-electron path integral Monte Carlo (PIMC) method with free-particle nodes for warm dense matter and apply it to water and carbon plasmas. We thereby extend PIMC studies beyond hydrogen and helium to elements with core electrons. PIMC pressures, internal energies, and pair-correlation functions compare well with density functional theory molecular dynamics (DFT-MD) at temperatures of (2.5-7.5)$\times10^5$ K and both methods together form a coherent equation of state (EOS) over a density-temperature range of 3--12 g/cm$^3$ and 10$^4$--10$^9$ K

Host-Parasite Co-evolution and Optimal Mutation Rates for Semi-conservative Quasispecies

In this paper, we extend a model of host-parasite co-evolution to incorporate the semi-conservative nature of DNA replication for both the host and the parasite. We find that the optimal mutation rate for the semi-conservative and conservative hosts converge for realistic genome lengths, thus maintaining the admirable agreement between theory and experiment found previously for the conservative model and justifying the conservative approximation in some cases. We demonstrate that, while the optimal mutation rate for a conservative and semi-conservative parasite interacting with a given immune system is similar to that of a conservative parasite, the properties away from this optimum differ significantly. We suspect that this difference, coupled with the requirement that a parasite optimize survival in a range of viable hosts, may help explain why semi-conservative viruses are known to have significantly lower mutation rates than their conservative counterparts

Energies and Z-expansion coefficients for the D states in the helium sequence

Non-relativistic variational energies for the 1s3d(1,3D) states of the helium isoelectronic sequence are calculated with a 50-term correlated basis set for Z=2-10, where Z is the nuclear charge, and the corresponding Z-expansion coefficients found through sixth order by fitting the energies to a series in Z-1. A variational-perturbation calculation of these coefficients through eleventh order (with the same basis set) is presented for comparison, and agreement is satisfactory. The 3d energies obtained by summing the Z-expansion perturbation series are found to yield excellent approximations to the variational values. The calculations are extended to the 1s4d( 1,3D) states to furnish variational energies for neutral helium and perturbation energies for the higher sequence members. All of these results are the most accurate yet reported

An explanation of the Newman-Janis Algorithm

After the original discovery of the Kerr metric, Newman and Janis showed that this solution could be ``derived'' by making an elementary complex transformation to the Schwarzschild solution. The same method was then used to obtain a new stationary axisymmetric solution to Einstein's field equations now known as the Kerr-newman metric, representing a rotating massive charged black hole. However no clear reason has ever been given as to why the Newman-Janis algorithm works, many physicist considering it to be an ad hoc procedure or ``fluke'' and not worthy of further investigation. Contrary to this belief this paper shows why the Newman-Janis algorithm is successful in obtaining the Kerr-Newman metric by removing some of the ambiguities present in the original derivation. Finally we show that the only perfect fluid generated by the Newman-Janis algorithm is the (vacuum) Kerr metric and that the only Petrov typed D solution to the Einstein-Maxwell equations is the Kerr-Newman metric.Comment: 14 pages, no figures, submitted to Class. Quantum Gra

Two-photon E1M1 decay of 2 3P0 states in heavy heliumlike ions

Two-photon E1M1 transition rates are evaluated for heliumlike ions with nuclear charges in the range Z = 50-94. The two-photon rates modify previously published lifetimes/transition rates of 2 3P0 states. For isotopes with nuclear spin I not equal 0, where hyperfine quenching dominates the 2 3P0 decay, two-photon contributions are significant; for example, in heliumlike 187 Os the two-photon correction is 3% of the total rate. For isotopes with I= 0, where the 2 3P0 decay is unquenched, the E1M1 corrections are even more important reaching 60% for Z=94. Therefore, to aid in the interpretation of experiments on hyperfine quenching in heliumlike ions and to provide a more complete database for unquenched transitions, a knowledge of E1M1 rates is important.Comment: 6 pages, 3 figures, 3 table

Application of discrete-basis-set methods to the Dirac equation

Variational solutions to the Dirac equation in a discrete L2 basis set are investigated. Numerical calculations indicate that for a Coulomb potential, the basis set can be chosen in such a way that the variational eigenvalues satisfy a generalized Hylleraas-Undheim theorem. A number of relativistic sum rules are calculated to demonstrate that the variational solutions form a discrete representation of the complete Dirac spectrum including both positive-and negative-energy states. The results suggest that widely used methods for constructing L2 representations of the nonrelativistic electron Green\u27s function can be extended to the Dirac equation. As an example, the relativistic basis sets are used to calculate electric dipole oscillator strength sums from the ground state, and dipole polarizabilities. © 1981 The American Physical Society

Relativistic two-photon decay rates of 2s12 hydrogenic ions

Rates are calculated for the decay of metastable 2s12 ions to the ground state by the simultaneous emission of two photons. The calculation includes all relativistic and retardation effects, and all combinations of photon multipoles which make significant contributions up to Z=100. Summations over intermediate states are performed by constructing a finite-basis-set representation of the Dirac Green\u27s function. The estimated accuracy of the results is 10 ppm for all Z up to 100. The decay rates are about 20 (Z)2% larger than an earlier calculation by Johnson owing to the inclusion of higher-order retardation effects. The general question of gauge invariance in two-photon transitions is discussed. © 1981 The American Physical Society