Detection of Close-In Extrasolar Giant Planets Using the Fourier-Kelvin Stellar Interferometer

We evaluate the direct detection of extrasolar giant planets with a two-aperture nulling infrared interferometer, working at angles ${\theta}<{\lambda}/2B$, and using a new `ratio-of-two-wavelengths' technique. Simple arguments suggest that interferometric detection and characterization should be quite possible for planets much closer than the conventional inner working angle, or angular resolution limit. We show that the peak signal from a nulling infrared interferometer of baseline ($\lesssim 40$ meters) will often occur `inside the null', and that the signal variations from path-difference fluctuations will cancel to first order in the ratio of two wavelengths. Using a new interferometer simulation code, we evaluate the detectability of all the known extrasolar planets as observed using this two-color method with the proposed {\it Fourier Kelvin Stellar Interferometer (FKSI)}. In its minimum configuration {\it FKSI} uses two 0.5-meter apertures on a 12.5-meter baseline, and a $\pm 20^{\circ}$ field-of-regard. We predict that $\sim 7$ known extrasolar planets are directly detectable using {\it FKSI}, with low-resolution spectroscopy ($R \sim 20$) being possible in the most favorable cases. Spaceborne direct detection of extrasolar giant planets is possible with $\sim 12$ meter baselines, and does not require the much longer baselines provided by formation flying.Comment: Accepted for publication in ApJ Letter

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

Combined Gamma Ray/neutron Spectroscopy for Mapping Lunar Resources

Some elements in the Moon can be resources, such as hydrogen and oxygen. Other elements, like Ti or the minerals in which they occur, such as ilmenite, could be used in processing lunar materials. Certain elements can also be used as tracers for other elements or lunar processes, such as hydrogen for mature regoliths with other solar-wind-implanted elements like helium, carbon, and nitrogen. A complete knowledge of the elemental composition of a lunar region is desirable both in identifying lunar resources and in lunar geochemical studies, which also helps in identifying and using lunar resources. The use of gamma ray and neutron spectroscopy together to determine abundances of many elements in the top few tens of centimeters of the lunar surface is discussed. To date, very few discussions of elemental mapping of planetary surfaces considered measurements of both gamma rays and the full range of neutron energies. The theories for gamma ray and neutron spectroscopy of the Moon and calculations of leakage fluxes are presented here with emphasis on why combined gamma ray/neutron spectroscopy is much more powerful than measuring either radiation alone

A multiplet table for neutral helium (4He I) with transition rates

This paper combines the precise determination of the energy levels of 4He I from calculations and experiments with theoretical transition probabilities to present multiplet tables and finding lists for the fine structure of the helium atom. The tabulated transition rates and oscillator strengths include corrections for singlet-triplet mixing and spin-orbit coupling, but not the higher order relativistic terms nor the finite nuclear mass, although the latter are tabulated for future use. The results are consistent with laboratory lifetimes and oscillator strengths, but very few measurements are accurate enough to be stringent tests. An Appendix discusses the corrections for finite nuclear mass. © 2007. The American Astronomical Society. All rights reserved

Asymptotic-expansion method for the evaluation of correlated three-electron integrals

An asymptotic-expansion method is presented for the evaluation of correlated three-electron integrals arising in Hylleraas-type variational calculations for lithium and other many-electron atoms. The method proves to be very efficient in accelerating the rate of convergence of an infinite series representation of the integrals. An analytic expression for the terms in the series is derived. © 1995 The American Physical Society

Energies and relativistic corrections for the Rydberg states of helium: Variational results and asymptotic analysis

The results of an extended series of high-precision variational calculations for all states of helium up to n=10 and L=7 (excluding S states above n=2) are presented. Convergence of the nonrelativistic eigenvalues ranges from five parts in 1015 for the 2P states to four parts in 1019 for the 10K states. Relativistic and quantum electrodynamic corrections of order 2, 3, 2/M, 2(/M)2, and 3/M are included and the required matrix elements listed for each state. For the 1s2p 3PJ states, the lowest-order spin-dependent matrix elements of the Breit interaction are determined to an accuracy of three parts in 109, which, together with higher-order corrections, would be sufficient to allow an improved measurement of the fine-structure constant. Methods of asymptotic analysis are extended to provide improved precision for the relativistic and relativistic-recoil corrections. A comparison with the variational results for the high-angular-momentum states shows that the standard-atomic-theory and long-range-interaction pictures discussed by Hessels et al. [Phys. Rev. Lett. 65, 2765 (1990)] come into agreement, thereby resolving what appeared to be a discrepancy. The comparison shows that the asymptotic expansions for the total energies are accurate to better than 100 Hz for L\u3e7, and results are presented for the 9L, 10L, and 10M states (i.e., angular momentum L=8 and 9). Significant discrepancies with experiment persist for transitions among the n=10 states, which cannot be easily accommodated by supposed higher-order corrections or additional terms. Finally, the asymptotic analysis indicates that a revision to the quantum-defect method is required for the analysis of high-precision data. © 1992 The American Physical Society

Lithium transition energies and isotope shifts: QED recoil corrections

The quantum electrodynamic recoil correction for lithium in the 22S1/2, 32S1/2 and 22PJ states was evaluated, and its impact on lithium isotope shifts was examined. The nonrelativistic variational wave functions were constructed from fully correlated basis sets in Hylleraas coordinates. Results for the total transition frequencies were shown to be in good agreement with experiment, but there were discrepancies between theory and experiment for isotope shift in the fine structure splitting for 1s22p2P state

Spin-forbidden radiative decay rates from the 3′,3P 1,2 and 3′,1P 1 states of helium

We have calculated atomic helium spontaneous decay rates and absorption oscillator strengths for the spin-forbidden transitions from 3′,3P 1,2 and 3′,1P 1 to all lower 1S 0 and 3S 1 states. In particular we found A 10=44.33(4)′, s -1 for the E1 transition 3′,3P 1-1′,1S 0 and 0.1147(1) s -1 for the M2 transition 3′,3P 2-1′,1S 0. © 2011 American Physical Society

Lithium isotope shifts as a measure of nuclear size

The isotope shifts for 2 2PJ-2 2S and 3 2S-2 2S transition energies in lithium are calculated variationally in Hylleraas coordinates, including nonrelativistic, relativistic, and QED terms up to O(μ/M), O(μ/M)2, O(α2 μ/M), and O(α3 μ/M) atomic units, and the lowest-order finite nuclear size correction. With high-precision isotope shift measurements, our results can potentially yield a precise determination of the nuclear charge radius for different isotopes of lithium, and especially for the exotic 11Li halo isotope. For the case of 7Li-6Li, using the nuclear charge radii from nuclear scattering data, our calculated isotope shifts for the 2 2P1/2-2 2S, 2 2P3/2-2 2S, and 3 2S-2 2S transitions are 10 534.31(61)(6) MHz, 10 534.70(61)(6) MHz, and 114 54.31(39)(5) MHz, respectively, where the first brackets indicate the uncertainties due to the nuclear charge radii, and the second brackets indicate the computational uncertainties. The experimental isotope shifts are inconsistent with each other and with theory for these transitions