Statistical mechanics of quantum mechanical particles with hard cores

The definition of the thermodynamic pressure of a quantum mechanical system of hard core particles is considered for a wide variety of boundary conditions and a large class of interactions. It is shown that the pressure can be defined for elastic walls and that in the limit of an infinite system the thermodynamic pressure both exists and is independent of the coefficient of elasticity. Similarly if repulsive wall boundary conditions are used the thermodynamic pressure exists. Unfortunately it has not been possible to demonstrate that the two pressures obtained are identical but a number of their properties and interrelationships are established.     

Numbers of cubic graphs

The numbers of unlabeled cubic graphs on p = 2n points have been found by two different counting methods, the best of which has given values for p ≦ 40.     

Measurement of equilin and estrone in human plasma by capillary gas chromatography-negative ion chemical ionization mass spectrometry

A procedure is described for the analysis of the estrogens equilin and estrone in human plasma following oral administration of conjugated estrogen preparations. After enzymatic hydrolysis of the sulfate conjugates, plasma proteins are precipitated with methanol and the estrogens extracted into ethyl acetate. Derivatization with the reagent flophemesylamine converts equilin and estrone into volatile pentafluorophenyldimethylsilyl ethers ideally suited to capillary gas chromatography-negative ion chemical ionization mass spectrometry. Using a 15 meter dimethyl silicone bonded phase fused silica capillary column separation of the estrone and equilin derivatives is achieved within 9 minutes. Selected ion monitoring of the intense negative molecular ions enables levels of 1 ng.ml^?1 to be measured with coefficients of variation of 9.3 % and 14.2 % for estrone and equilin respectively. Plasma levels of the compounds are reported in two male volunteers up to 24 hours after dosing with 5 milligrams of Premarin?. (? Ayerst Laboratories Inc., New York, USA.).     

Population of high spin states in 22Na by means of the 10B(16O, α) reaction

Strong selectivity has been observed in the population of states in ²²Na up to high excitation energies. Angular distributions were measured, and a comparison with Hauser-Feshbach calculations allow us to select strong candidates for the high-spin members of the K^π = 3⁺, T = 0 and K^π = 0⁺, T = 0 bands in ²²Na.     

Anisotropy of electron-phonon interactions in alkali metals

Electron-phonon scattering in the solid alkalis is distinguished from that in most other metals by a combination of three circumstances: The phonon spectra and structure factors are very anisotropic, the Fermi surface in the reduced zone is simply connected and virtually spherical and important large momentum transfers (0.7<(q/2k _F)<1.0) fall within the first large peaks of the phonon structure factors. Anisotropy of microscopic contributions to the macroscopic coefficients is controlled by and is quite sensitive to values of electron-ion matrix elements at large momentum transfer, and can be explored by a realistic yet relatively simple theoretical calculation. A brief summary is presented of such calculations, for the all alkalies, of mean free paths, thermoelectric powers, and electron-phonon mass enhancements. The results show marked anisotropy only for lithium, are consonant with experimental low field Hall coefficients and in addition indicate strong anisotropy in the mass enhancement for lithium.     

Asymptotically abelian systems

We study pairs { , } for which is aC*-algebra and is a homomorphism of a locally compact, non-compact groupG into the group of *-automorphisms of . We examine, especially, those systems { , } which are (weakly) asymptotically abelian with respect to their invariant states (i.e. |A _g (B) — _g (B)A 0 asg for those states such that ( _g (A)) = (A) for allg inG andA in ). For concrete systems (those with -acting on a Hilbert space andg _g implemented by a unitary representationg U _g on this space) we prove, among other results, that the operators commuting with and {U _g } form a commuting family when there is a vector cyclic under and invariant under {U _g }. We characterize the extremal invariant states, in this case, in terms of weak clustering properties and also in terms of factor and irreducibility properties of { ,U _g }. Specializing to amenable groups, we describe operator means arising from invariant group means; and we study systems which are asymptotically abelian in mean. Our interest in these structures resides in their appearance in the infinite system approach to quantum statistical mechanics.