Investigation of continental drift, phase 1 effort Progress report, 1 Apr. - 30 Sep. 1968

Feasibility of using ultrashort pulse laser ranging and independent clock radio interferometry distance measurement methods to test for existence of continental drif

Mass Profile of the Infall Region of the Abell 2199 Supercluster

Using a redshift survey of 1323 galaxies (1092 new or remeasured) in a region of 95 square degrees centered on the nearby galaxy cluster Abell 2199, we analyze the supercluster containing A2199, A2197, and an X-ray group. The caustic technique accurately reproduces the true mass profiles of simulated simple superclusters (i.e., superclusters where the virial mass of one cluster is 2-10 times the virial mass of all other clusters in the supercluster). We calculate the masses of the two main components of A2197 (A2197W and A2197E) using archival X-ray observations and demonstrate that the A2199 supercluster is simple and thus that the caustic technique should yield an accurate mass profile. The mass profile is uncertain by ~30% within 3 Mpc/h and by a factor of two within 8 Mpc/h and is one of only a few for a supercluster on such large scales. Independent X-ray mass estimates agree with our results at all radii where they overlap. The mass profile strongly disagrees with an isothermal sphere profile but agrees with profiles suggested by simulations. We discuss the interplay of the supercluster dynamics and the dynamics of the bound subclusters. The agreement between the infall mass profile and other techniques shows that the caustic technique is surprisingly robust for simple superclusters (abridged).Comment: 49 pages, 20 figures, to appear in The Astronomical Journal, version containing high-resolution figures available at http://cfa-www.harvard.edu/~krines/a2199mp.p

Lamb Shift of 3P and 4P states and the determination of α\alpha

The fine structure interval of P states in hydrogenlike systems can be determined theoretically with high precision, because the energy levels of P states are only slightly influenced by the structure of the nucleus. Therefore a measurement of the fine structure may serve as an excellent test of QED in bound systems or alternatively as a means of determining the fine structure constant $\alpha$ with very high precision. In this paper an improved analytic calculation of higher-order binding corrections to the one-loop self energy of 3P and 4P states in hydrogen-like systems with low nuclear charge number $Z$ is presented. A comparison of the analytic results to the extrapolated numerical data for high $Z$ ions serves as an independent test of the analytic evaluation. New theoretical values for the Lamb shift of the P states and for the fine structure splittings are given.Comment: 33 pages, LaTeX, 4 tables, 4 figure

Coordinate-space approach to the bound-electron self-energy: Self-Energy screening calculation

The self-energy screening correction is evaluated in a model in which the effect of the screening electron is represented as a first-order perturbation of the self energy by an effective potential. The effective potential is the Coulomb potential of the spherically averaged charge density of the screening electron. We evaluate the energy shift due to a $1s_{1/2}$, $2s_{1/2}$, $2p_{1/2}$, or $2p_{3/2}$ electron screening a $1s_{1/2}$, $2s_{1/2}$, $2p_{1/2}$, or $2p_{3/2}$ electron, for nuclear charge Z in the range $5 \le Z\le 92$. A detailed comparison with other calculations is made.Comment: 54 pages, 10 figures, 4 table

Two-Loop Bethe Logarithms

We calculate the two-loop Bethe logarithm correction to atomic energy levels in hydrogen-like systems. The two-loop Bethe logarithm is a low-energy quantum electrodynamic (QED) effect involving multiple summations over virtual excited atomic states. Although much smaller in absolute magnitude than the well-known one-loop Bethe logarithm, the two-loop analog is quite significant when compared to the current experimental accuracy of the 1S-2S transition: it contributes -8.19 and -0.84 kHz for the 1S and the 2S state, respectively. The two-loop Bethe logarithm has been the largest unknown correction to the hydrogen Lamb shift to date. Together with the ongoing measurement of the proton charge radius at the Paul Scherrer Institute its calculation will bring theoretical and experimental accuracy for the Lamb shift in atomic hydrogen to the level of 10^(-7).Comment: 4 pages, RevTe

QED self-energy contribution to highly-excited atomic states

We present numerical values for the self-energy shifts predicted by QED (Quantum Electrodynamics) for hydrogenlike ions (nuclear charge $60 \le Z \le 110$) with an electron in an $n=3$, 4 or 5 level with high angular momentum ($5/2\le j \le 9/2$). Applications include predictions of precision transition energies and studies of the outer-shell structure of atoms and ions.Comment: 20 pages, 5 figure

Effective 3D Geometry Extraction and Reverse CAD Modeling

The goal of this work is to develop and implement a technology capability for providing cost-effective and rapid geometry evaluation of parts and processes. We were motivated by the new availability of fully three dimensional nondestructive CT scanning for a variety of manufactured parts and assemblies on a rapid and cost-effective basis, with resolutions commensurate with the tolerances required for a variety of manufacturing processes. High-speed, high-quality three dimensional scanning can be accomplished on a overnight service basis for a variety of objects, for costs ranging from a few hundreds to a few thousands of dollars. The resulting images contain quantitative information relating the local x-ray density of scanned objects at every voxel in a three dimensional raster space. There have been significant advances in methods for quantitative volumetric processing and information extraction from these images. However, for many manufacturing process verification applications, the resulting three dimensional images contain more information than can be effectively handled by many end users, particularly when the size of the 3D image data files (often larger than 1 Gbyte) is considered

Convergence Acceleration Techniques

This work describes numerical methods that are useful in many areas: examples include statistical modelling (bioinformatics, computational biology), theoretical physics, and even pure mathematics. The methods are primarily useful for the acceleration of slowly convergent and the summation of divergent series that are ubiquitous in relevant applications. The computing time is reduced in many cases by orders of magnitude.Comment: 6 pages, LaTeX; provides an easy-to-understand introduction to the field of convergence acceleratio

Higher-order binding corrections to the Lamb shift of 2P states

We present an improved calculation of higher-order corrections to the one-loop self energy of 2P states in hydrogen-like systems with small nuclear charge Z. The method is based on a division of the integration with respect to the photon energy into a high- and a low-energy part. The high-energy part is calculated by an expansion of the electron propagator in powers of the Coulomb field. The low-energy part is simplified by the application of a Foldy-Wouthuysen transformation. This transformation leads to a clear separation of the leading contribution from the relativistic corrections and removes higher order terms. The method is applied to the 2P_{1/2} and 2P_{3/2} states in atomic hydrogen. The results lead to new theoretical values for the Lamb shifts and the fine structure splitting.Comment: 18 pages, LaTeX. In comparison to the journal version, it contains an added note (2000) which reflects the current status of Lamb shift calculation

The X-ray Size-Temperature Relation for Intermediate Redshift Galaxy Clusters

We present the first measurements of the X-ray size-temperature (ST) relation in intermediate redshift (z~0.30) galaxy clusters. We interpret the local ST relation (z~0.06) in terms of underlying scaling relations in the cluster dark matter properties, and then we use standard models for the redshift evolution of those dark matter properties to show that the ST relation does not evolve with redshift. We then use ROSAT HRI observations of 11 clusters to examine the intermediate redshift ST relation; for currently favored cosmological parameters, the intermediate redshift ST relation is consistent with that of local clusters. Finally, we use the ST relation and our evolution model to measure angular diameter distances; with these 11 distances we evaluate constraints on Omega_M and Omega_L which are consistent with those derived from studies of Type Ia supernovae. The data rule out a model with Omega_M=1 and Omega_L=0 with 2.5 sigma confidence. When limited to models where Omega_M+Omega_L=1, these data are inconsistent with Omega_M=1 with 3 sigma confidence.Comment: ApJ: submitted April 7, accepted June 28, to appear Dec 1 (vol 544