Density-like and Generalized Density Ideals

We show that there exist uncountably many (tall and nontall) pairwise nonisomorphic density-like ideals on which are not generalized density ideals. In addition, they are nonpathological. This answers a question posed by Borodulin-Nadzieja et al. in [this Journal, vol. 80 (2015), pp. 1268-1289]. Lastly, we provide sufficient conditions for a density-like ideal to be necessarily a generalized density ideal

He+ 2p state lifetime by a quenching-asymmetry measurement

An interference asymmetry in the angular distribution of the Ly quenching radiation emitted by He+ ions in the metastable 2s1/2 state is measured to high precision to obtain the lifetime of the 2p1/2 state. The derived lifetime of (0.997 170.000 75)×10-10 s is the most accurate available for a fundamental atomic system. A detailed discussion of systematic corrections is included. The result is in good agreement with theory, thereby confirming the theory of radiative transition probabilities to 0.075%, and indicating that differences between theory and experiment for the alkali metals must be due to either inadequate wave functions or experimental errors. © 1992 The American Physical Society

Measurement of the n=2 Lamb shift in He+ by the anisotropy method

A high-precision measurement of the 2s 2S1/22p 2P1/2 Lamb shift in He+ by the quenching-anisotropy method is reported. The theory and experimental method are described in detail. The measured value of 14042.520.16 MHz (11 parts per million) rivals the accuracy of Lamb-shift measurements in hydrogen by microwave resonance. By subtracting the known low-order terms in the Lamb shift, we interpret the results as a measurement of the order (Z)6mc2 and higher contributions to the electron self-energy GSE(Z). The various contributions to the Lamb shift are discussed, and a revised value for GSE(Z) at low Z is extracted from high-Z calculations. The theoretical value for the Lamb shift is 14042.510.2 MHz, in excellent agreement with experiment. The results provide the most sensitive available determination of GSE(Z) for low Z. Measurements and calculations for hydrogen and other members of the isoelectronic sequence are discussed. © 1991 The American Physical Society

Combinatorics of ideals --- selectivity versus density

summary:This note is devoted to combinatorial properties of ideals on the set of natural numbers. By a result of Mathias, two such properties, selectivity and density, in the case of definable ideals, exclude each other. The purpose of this note is to measure the ``distance'' between them with the help of ultrafilter topologies of Louveau