Fractal measures and polynomial sampling: I.F.S.–Gaussian integration

Measures generated by Iterated Function Systems can be used in place of atomic measures in Gaussian integration. A stable algorithm for the numerical solution of the related approximation problem – an inverse problem in fractal construction – is proposed. Dedicated to Walter Gautschi.     

Test of a symmetrical four-detector compton polarimeter using low temperature nuclear orientation

A symmetrical four-detector Compton polarimeter was used to measure the linear polarization of gamma-rays emitted from nuclei oriented by the hyperfine interaction at low temperature. Its polarization detection efficiency was determined in the range 0.3–1.4 MeV and compared with some other polarimeters.     

Nuclear structure studies of187Ir via on-line nuclear orientation

A more complete level scheme is presented here for the decay of¹⁸⁷Pt, incorporating many new lines and levels up to 2.4 MeV. Emphasis has been placed on the extraction of multipole mixing ratios from nuclear orientation data. Analysis of that data, however, required a more complete understanding of the level structure (including, in particular, branching ratios, conversion coefficients, and level feedings), prompting the collection of new spectroscopy data. The low-lying, positive-parity levels are described in terms of (odd-proton) single-particle Nilsson states coupled to a triaxial core. Multipole mixing ratios are compared to those calculated in the Particle-Plus-Triaxial-Rotor Model.     

Determination of the magnetic dipole moment of114Sb Via on-line nuclear orientation

The magnetic dipole moment of¹¹⁴Sb has been measured using on-line nuclear orientation (OLNO) at the UNISOR Nuclear Orientation Facility (UNISOR/NOF). The value was determined to be 1.72 (8) nuclear magnetons. The observed anisotropy of the 1299 keV transition was fitted as a function of temperature making allowance for incomplete thermalization of the¹¹⁴Sb nuclei prior to decay. The relaxation constant, C_k, is discussed, as is the ground state structure of¹¹⁴Sb.     

Twisted Lorentzian manifolds: a characterization with torse-forming time-like unit vectors

Robertson–Walker and generalized Robertson–Walker spacetimes may be characterized by the existence of a time-like unit torse-forming vector field, with other constrains. We show that Twisted manifolds may still be characterized by the existence of such (unique) vector field, with no other constrain. Twisted manifolds generalize RW and GRW spacetimes by admitting a scale function that depends both on time and space. We obtain the Ricci tensor, corresponding to the stress–energy tensor of an imperfect fluid.     

Intruder configurations in the A=33 isobars: 33Mg and 33Al

The beta decay of 33Mg (N=21) presented in this Letter reveals intruder configurations in both the parent and the daughter nucleus. The lowest excited states in the N=20 daughter nucleus, 33Al, are found to have nearly 2p-2h intruder configuration, thus extending the "island of inversion" beyond Mg. The allowed direct beta-decay branch to the 5/2{+} ground state of the daughter nucleus 33Al implies positive parity for the ground state of the parent 33Mg, contrary to an earlier suggestion of negative parity from a g-factor measurement. An admixture of 1p-1h and 3p-3h configurations is proposed for the ground state of 33Mg to explain all of the experimental observables.     

UNISOR on-line nuclear orientation facility (UNISOR/NOF)

The UNISOR on-line nuclear orientation facility (UNISOR/NOF) consists of a₃He−₄He dilution refrigerator on line to the isotope separator. Nuclei are implanted directly into a target foil which is soldered to the bottom accessed cold finger of the refrigerator. A 1.5 T superconducting magnet polarizes the ferromagnetic target foils and determines the axis of symmetry. Up to eight gamma detectors can be positioned around the refrigerator, each 9 cm from the target. A unique feature of this system is that the k=4 term in the directional distribution function can be directly and unambigously deduced so that a single solution for the mixing ratio can be found. The first on-line experiment at this facility reported here was a study of the decay of the¹⁹¹Hg and¹⁹³Hg isotopes.     

Distribution of roots of random real generalized polynomials

The average density of zeros for monic generalized polynomials, , with real holomorphic ,f _k and real Gaussian coefficients is expressed in terms of correlation functions of the values of the polynomial and its derivative. We obtain compact expressions for both the regular component (generated by the complex roots) and the singular one (real roots) of the average density of roots. The density of the regular component goes to zero in the vicinity of the real axis like |lmz|. We present the low- and high-disorder asymptotic behaviors. Then we particularize to the large-n limit of the average density of complex roots of monic algebraic polynomials of the form with real independent, identically distributed Gaussian coefficients having zero mean and dispersion . The average density tends to a simple,universal function of =2nlog|z| and in the domain coth(/2)n|sin arg(z)|, where nearly all the roots are located for largen.     

Nuclear structure of neutron-rich nuclei near closed shells from excited-state g-factor measurements

New techniques to measure the g factors of picosecond-lived excited states of neutron-rich nuclei produced as radioactive beams are discussed along with their applications to study nuclear structure near ¹³² ₅₀Sn₈₂ and in the region between N=20 and N=28.