Generalized on-shell renormalization of heavy quarks

A generalized on-shell (GOS) renormalization scheme of QCD is developed to evaluate the renormalization of heavy quark wave functions and currents. All large logarithms arising from the physical range of quark masses and momentum transferq ² can be absorbed into wave function and vertex renormalization. Our results are more general than those of the heavy quark effective theory and agree with the latter only at zero recoil. The proposed GOS scheme is very suitable for the /m _Q expansion. As an application we discuss the renormalization of the flavour changing currentsb-c, t-b andt-c.Supported by Bundesministerium für Forschung und Technologie (BMFT)     

On the theory of atomic ionization following alpha decay

The -decay of a nucleus may cause atomic ionization. One of the basic assumptions of Migdal's original paper, which is the prototype of all later calculations for this process, is to treat the -particle outside the nuclear region classically as a point charge moving along a definite trajectory. In contrast to this picture, in the standard quantum-mechanical model of the -decay, the -particle is represented by a wave function that, after tunneling through the Coulomb barrier at the nuclear surface, propagates outwards as a spherical wave. We compare these two pictures within a three-body model, clarify the conditions under which the full quantum-mechanical calculation and its semiclassical counterpart give similar results and also point out the origin of their possible discrepancies.This paper is dedicated to the memory of A. B. Migdal. His bright physical intuition, which guided him in his pioneering work on this subject—as in many cases later on-, proved to be essentially correct     

Interferometric phase measurements of average field cubeE ω 2 E 2ω *

The method of interferometric measurements of the field cube evolutionE ² E ₂ ^* due to propagation in air and other media was investigated experimentally by the use of a pair of nonlinear crystals. A gas cell with variable pressure turned out to be the most convenient among different methods of changing the phase of the field cube. The phase shift by rad of the field cube in passing through the focus was demonstrated experimentally.     

Magnetoresistivity of bismuth films in magnetic fields to 19 Tesla

The longitudinal and transverse magnetoresistance to fields of 19 Tesla and 4.2 K has been measured for bismuth films ranging in thickness from 0.01 to 2 m. We have observed a pronounced maximum in the longitudinal magnetoresistance which is thickness dependent. We compare these results with classical size effect theories for the longitudinal magnetoresistance in terms of magnetic-field-dependent electron scattering at grain and film boundaries. Measurements of the longitudinal magnetoresistance to 38 Tesla show a quenching of the classical size effect in the high field limit. This result strongly supports our analysis.Work supported by NSF grant #DMR 8113456Supported by the National Science Foundation     

Mixed insoluble acidic salts of tetravalent metals

Mixed amorphous glassy type hafnium-titanium phosphates have been prepared. The composition and ion exchange capacity of the samples were investigated before and after -irradiation. In addition, the effect of temperature on the ion exchange capacity of the samples was determined. Based on the data obtained, neither the composition nor the ion exchange behavior of the investigated materials was altered by the irradiation. An increased drying temperature led to a decrease in the ion exchange capacity of the samples.     

Problème inverse de la théorie du potentiel logarithmique pour les lemniscates

The paper is related to the question of uniqueness in the inverse logarithmic potential problem. This question is to find the conditions on which two domains D ₁ and D ₂ producing the same external potential must coincide. Assuming the general hypothesis of regularity and an additional condition of connectivity of (D₁D₂)_c, we prove a theorem of uniqueness in the case when one of the domains is a lemniscate. The main tool is one lemma for Cauchy's potential due to M. Sakai. We give a simple proof of its extension to Newtonian potential.

     

Gap-Free Set Partitions

A set partition is called “gap-free” if its block sizes form an interval. In other words, there is at least one block of each size between the smallest and largest block sizes. Let B(n) and G(n), respectively, denote the number of partitions and the number of gap-free partitions of the set [n]. We prove that