Identification of the new isotope 241Bk

A new neutron-deficient berkelium isotope ²⁴¹Bk produced in the ²³⁹Pu(⁶Li, 4n) reaction has been identified using a gas-jet coupled on-line isotope separator. Cm K and L X-rays associated with the EC decay of ²⁴¹Bk were observed in the mass-241 fraction, and three γ transitions were attributed to the EC decay of ²⁴¹Bk through X-γ coincidences. The half-life of ²⁴¹Bk was determined to be 4.6±0.4 min which is 1/2-1/4 of that of theoretical predictions. The half-life value and the observed γ transitions can be consistently explained as a consequence of the allowed EC transition of π7/2⁺[633] → ν7/2⁺[624]. Received: 14 October 2002 / Accepted: 6 November 2002 / Published online: 17 January 2003 RID="a" ID="a"e-mail: asai@tandem.tokai.jaeri.go.jp Communicated by J. ?yst?     

Anharmonic resonances in the vibrational spectra of pyrazine

The quartic force field of pyrazine has been calculated in the B3LYP/6-31G(d) hybrid density-functional approximation. Based on the results of this calculation, the total IR (250–3800 cm^–1) and Raman (400–3200 cm^–1) spectra of pyrazine have been interpreted with consideration for the Fermi and Darling-Dennison resonances and their spectral manifestations. A precision method is proposed for anharmonic analysis of the vibrational states of polyatomic molecules on the basis of consideration of their theoretical anharmonicity constants in combination with the corresponding experimental frequencies. The method of linear scaling of frequencies has been theoretically substantiated.__________Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 1, pp. 13–22, January–February, 2005.     

Canonical Ensemble with Temperature Limitation

Ideal Bose and Fermi systems are studied on the basis of a canonical ensemble, subject to the condition that their temperature is less than a given temperature T_max. A single new parameter (the tau-parameter, τ) is needed to keep account of the new constraint. The parameter τ is shown to be the exponential of a pseudo-chemical potential that is linearly dependent on temperature. The inclusion of the τ- parameter leads to generalizations of usual thermodynamic quantities (internal energy, heat capacity and entropy) and various particular cases are discussed. The heat capacity of a Bose system can exhibit a maximum at a temperature less than the maximum temperature T_max. The number of micro-states in the canonical ensemble is found to increase with τ. The heat capacity c_V of a Fermi system of non-interacting spins exhibits a Schottky anomaly. The peak depends on τ, and for some cases c_V/k can significantly exceed unity. The influence of τ on the entropy of the Fermi system and on the number of micro-states in the canonical ensemble is significant but not spectacular.     

Levels in <Superscript>127</Superscript>La fed by the <Superscript>127</Superscript>Ce beta-decay

The low-lying levels in ¹²⁷La have been studied through the -decay of ¹²⁷Ce ( T_1/2 = 29s) produced by bombarding a ^natMo target with a 185-MeV ³⁵Cl beam. Reaction products were on-line mass-separated, and -ray singles and - coincidence measurements were performed. Conversion electrons were also measured and multipolarities of transitions have been derived. The half-life of the 210.9-keV level was determined to be (1.9±0.3)ns by the - delayed coincidence technique. The level scheme obtained has been compared with calculations based on the Nilsson model.     

Unified properties of a weakly interacting Fermi gas in a weak magnetic field

When the orbital motion and the spin motion of particles were considered simultaneously, the thermodynamic potential function of a weakly interacting Fermi gas in a weak magnetic field was derived using the thermodynamics method. Based on the derived expression, the analytical expressions of energy, heat capacity, chemical potential, susceptibility and stability conditions of the system were given, and the effects of the interparticle interactions as well as the magnetic field on the properties of the system were analyzed. It was shown that the magnetic field always causes energy and stability to decrease, while the chemical potential of the system to increase. The repulsive (attractive) interactions always increase (decrease) energy and stability, but decrease (increase) the chemical potential and paramagnetism. The repulsive (attractive) interactions decrease (increase) heat capacity of the system at high temperatures but increase (decrease) it at low temperatures.     

Annihilating a subspace of with the sign of a continuous function

Let be a -finite, nonatomic, Baire measure space. Let be a finite dimensional subspace of . There is a bounded, continuous function, , defined on , such that

(1) for all , and (2) almost everywhere.

     

An abnormal phenomenon in the saturated absorption spectrum of ^87Rb

A polarization-type saturated absorption spectrum set-up for {}^{87}Rb atom laser cooling and trapping has been established in our laboratory. By changing the polarization components and optical power, enhanced absorption of the transition 5S_{1/2} F=2→5P_{3/2}F′=3 was observed with other transitions and cross-over resonance staying unvaried.     

Function cones and interpolation

We consider interpolation of operators acting on functions that belong to a given cone Q with the so‐called decomposition property. The set of all positive functions whose level sets are the level sets of a given function is the main example, and the cone of all decreasing functions is a particular case. As applications, we obtain conditions for the identity (E₀ ∩ Q,E₁ ∩ Q)_θ,p = (E₀,E₁)_θ,p ∩ Q and interpolation results for operators which are bounded when restricted to a given family of characteristic funcions. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Generalized descent for global optimization

This paper introduces a new method for the global unconstrained minimization of a differentiable objective function. The method is based on search trajectories, which are defined by a differential equation and exhibit certain similarities to the trajectories of steepest descent. The trajectories depend explicitly on the value of the objective function and aim at attaining a given target level, while rejecting all larger local minima. Convergence to the gloal minimum can be proven for a certain class of functions and appropriate setting of two parameters.The author wishes to thank Professor R. P. Brent for making helpful suggestions and acknowledges the financial support of an Australian National University Postgraduate Scholarship.