Electron Capture Probabilities in105Ag

TheK-electron capture probabilities for the 1/2^? → 3/2^? and 1/2^? → 1/2⁺ transitions in the decay of¹⁰⁵Ag were measured for the first time using the sum coincidence method. The experimental P_K values were estimated to be 0.824 ± 0.042 and 0.851 ±0.046 for the allowed and first-forbidden beta transitions, respectively in agreement with the theory. The P_L experimental values to these two levels were also computed using the experimental P_L/P_K values reported by earlier authors. These results are also found to be consistent with the theoretical P_L values.     

On Artin's conjecture

Let $\text{F}$ be a family of number fields which are normal and of finite degree over a given number field K. Consider the lattice L(scF) spanned by all the elements of $\text{F}$. The generalized Artin problem is to determine the set of prime ideals of K which do not split completely in any element H of L(scF), H≠K. Assuming the generalized Riemann hypothesis and some mild restrictions on $\text{F}$, we solve this problem by giving an asymptotic formula for the number of such prime ideals below a given norm. The classical Artin conjecture on primitive roots appears as a special case. In another case, if $\text{F}$ is the family of fields obtained by adjoining to $\text{Q}$ the q-division points of an elliptic curve E over $\text{Q}$, the Artin problem determines how often E($\text{F}$_p) is cyclic. If E has complex multiplication, the generalized Riemann hypothesis can be removed by using the analogue of the Bombieri-Vinogradov prime number theorem for number fields.     

Linear programming under uncertainty: A basic property of the optimal solution

Summary We show that if the two-stage linear programming problem under uncertainty has an optimal solution, then it has an optimal solution in which the column vectors corresponding to the positive first stage decision variables are linearly independent. This leads to the result that if an optimal solution exists, then there exists an optimal solution in which not more than m + ¯m of the first stage decision variables are positive. These results extend to the multi-stage case.This research was partially supported by the Office of Naval Research under Contract Nonr-222(83), the National Science Foundation under Contract GP-4593, the Army Research Office under Contract DA-31-124-ARO-D-331 and the University of California. Reproduction in whole or part is permitted for any purpose of the United States Government.     

Die analytische Chemie des Zirkoniums

Ohne Zusammenfassung     

On the interlattice displacement of rhombohedral structure

The expressions for the components of the interlattice displacement to the first order in strain and hence the expressions for the SOE constants are obtained for the rhombohedral lattice using the method of homogeneous deformation. Two and three body interactions are considered up to fourth neighbours in the calculations. The special strains that are generally chosen in explaining the temperature variation of thermal expansion of a uniaxial crystal, which make the interlattice displacement zero, are shown to be dependent [$\text{η}{}_{\mathrm{zz}}\text{= ?}\text{3}\text{2p}{}^2\text{C}\text{D}\text{(η}{}_{\mathrm{xx}}\text{+ η}{}_{\mathrm{yy}}\text{)}$]. The internal displacement factors A, B, C and D are calculated for the metals As, Sb and Bi to get an idea on the magnitude of C/D.     

A search for heavy leptons in cosmic radiation underground

An experiment to search massive long-lived, weakly interacting particles (leptons) in cosmic radiation has been conducted at Kolar Gold Fields at a depth of 7.6 hg cm⁻² (1 hg cm⁻²=100 g cm⁻²) below surface. The apparatus was senstive to sub-relativistic (velocity<0.75 c) charged leptons of mass greater than that of a proton and life times greater than a microsecond. The method consists of selecting charged particles using a scintillator counter telescope and vetoing relativistic particles (velocity >0.75 c) by using a water Čerenkov detector. The range of the particle is observed in arrays of neon flash tubes interspersed with iron absorbers. During 3000 hours of observation 28 events were recorded satisfying the trigger and event selection criteria. Bulk of these events were interpreted as due to recoil protons (low energy) from the inelastic scattering of high energy muons in the overhead absorber. The remaining events were interpreted as either atmospheric stopping protons or stopping muons that failed to generate a Čerenkov signal. The observed events are thus consistent with the background and no heavy leptons were seen. From our observations an upper limit of 2.12×10⁻⁷ (with 90% confidence level) is set on the ratio of the flux of heavy leptons to that of all muons at this depth.     

Structure of 3P size resonance in neutron strength functions

Neutron capture cross sections of 21 nuclei have been determined using the activation technique and an antimony-beryllium photoneutron source. The nuclei have been selected in the mass range 60 < A < 140 so as to cover the 3P size resonance region of neutron strength functions. Using the latest available data on the low energy resonance parameters, the P-wave neutron strength functions of the 21 isotopes are extracted, and found to be in general agreement with similar isotopic values reported in literature. The values of experimental P-wave neutron strength functions in the 3P resonance region (60 < A < 140) are compared on the one hand with the theoretical predictions of Fiedeldey and Frahn and on the other with those of Buck and Perey. The shape and structure of the 3P size resonance, as revealed experimentally, are found to agree better with the predictions of Fiedeldey and Frahn, who assumed twice the normal spin-orbit force in their calculations.