Spectral distributions in nuclei: General principles and applications

The subject of spectral distribution methods where one derives and applies the locally smoothed forms of observables in nuclei is briefly reviewed. It is well understood that the local forms (with respect to energy) of the level density function, expectation values and strength densities are Gaussian, linear (or ratio of Gaussians) and a bivariate Gaussian respectively. To accomodate symmetries in the above forms, one has to deal with multivariate distributions in general; for example the angular-momentum (J) decomposition leads to a bivariate Gaussian form for the level density. These results extend to indefinitely large spaces by method of partitioning and they generate convolution forms. The origin of these remarkable spectral properties is discussed and shell model examples are given to substantiate their applicability to nuclear systems. Spectral distribution theory is a practical, usable theory because the smoothed forms are defined in terms of traces of low particle-rank operators, and the trace information propagates. Finally we discuss the application of the spectral methods for a wide range of nuclear problems; these include binding energies, orbit occupancies, electromagnetic andβ-decay sum rule quantities, analysis of operators, symmetry breaking, numerical level densities, and determination of bounds on time-reversal non-invariant part of nucleon-nucleon interaction.     

Synthesis and characterization of Ti–Ni shape memory alloy thin films by pulsed laser deposition

Shape-memory alloys are crucial in various industrial fields. However, a high-quality film synthesis method has not been established yet. Here we examine optimum conditions for synthesis of thin films by pulsed laser deposition of Ti–Ni alloy target in vacuum. We investigated surface morphologies and chemical compositions of the films which were obtained under various conditions. We found that the suitable Ti/Ni ratio was obtained by adjusting the distance between the target and the substrate in vacuum. In parallel, we analyzed plasma plume by optical emission spectroscopy and time-of-flight mass spectrometry. We discuss the basic behavior of ablated particles in vacuum.     

Random matrix theory for transition strength densities in finite quantum systems: Results from embedded unitary ensembles

Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless fermion (or boson) systems, with say m$m$ fermions (or bosons) in N$N$ single particle states and interacting via k$k$-body interactions, we have EGUE(k$k$) [embedded GUE of k$k$-body interactions] with GUE embedding and the embedding algebra is U(N)$U\left(N\right)$. A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (then the initial and final systems are same), nuclear beta and double beta decay (then the initial and final systems are different), particle addition to or removal from a given system and so on. Towards developing a complete statistical theory for transition strength densities (transition strengths multiplied by the density of states at the initial and final energies), we have derived formulas for the lower order bivariate moments of the strength densities generated by a variety of transition operators. Firstly, for a spinless fermion system, using EGUE(k$k$) representation for a Hamiltonian that is k$k$-body and an independent EGUE(t$t$) representation for a transition operator that is t$t$-body and employing the embedding U(N)$U\left(N\right)$ algebra, finite-N$N$ formulas for moments up to order four are derived, for the first time, for the transition strength densities. Secondly, formulas for the moments up to order four are also derived for systems with two types of spinless fermions and a transition operator similar to beta decay and neutrinoless beta decay operators. In addition, moments formulas are also derived for a transition operator that removes k₀$k_0$ number of particles from a system of m$m$ spinless fermions. In the dilute limit, these formulas are shown to reduce to those for the EGOE version derived using the asymptotic limit theory of Mon and French (1975). Numerical results obtained using the exact formulas for two-body (k=2$k=2$) Hamiltonians (in some examples for k=3$k=3$ and 4$4$) and the asymptotic formulas clearly establish that in general the smoothed (with respect to energy) form of the bivariate transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extensions of these results to bosonic systems and EGUE ensembles with further symmetries are discussed.     

Asymmetric α‐Hydroxylation of Tetralone‐Derived β‐Ketoesters by Using a Guanidine–Urea Bifunctional Organocatalyst in the Presence of Cumene Hydroperoxide

Highly enantioselective catalytic oxidation of 1‐tetralone‐derived β‐keto esters was achieved by using a guanidine–urea bifunctional organocatalyst in the presence of cumene hydroperoxide (CHP), a safe, commercially available oxidant. The α‐hydroxylation products were obtained in 99 % yield with up to 95 % enantiomeric excess (ee). The present oxidation was successfully applied to synthesize a key intermediate of the anti‐cancer agent daunorubicin ( 2 ).     

On p-class groups of relative cyclic p-extensions

Archiv der Mathematik - We prove a general stability theorem for p-class groups of number fields along relative cyclic extensions of degree $$p^2$$ , which is a generalization of a finite-extension...     

ZnS/Fe2O3/Ag Ternary Nanocomposite Photocatalyst for the Degradation of Dyes Under Visible Light

Russian Journal of Physical Chemistry A - Recently the researchers have shown great interest on photocatalysis, especially in dyes degradation by nanocomposites under visible light. In this work,...     

Electron interactions and the electrical resistivity of alkali metals at low temperatures

The contribution of the electron-electron umklapp scattering processes to the electrical resistivity of sodium, potassium, rubidium and cesium at low temperatures has been evaluated using a simplified spherical Fermi-surface model with an isotropic transition probability. Our values of the electrical resistivity so obtained compare fairly well with the recent experimental values for sodium, potassium and rubidium. Our theoretical results have also been compared with the other available data in the literature due to Lawrence and Wilkins and MacDonald and Geldart.     

Magnetism of fcc/fcc, hcp/hcp twin and fcc/hcp twin-like boundaries in cobalt

The magnetic moments of the fcc/fcc, hcp/hcp twin and fcc/hcp twin-like boundaries in cobalt were investigated by first-principles calculations based on density functional theory. The magnetic moments in fcc/fcc were larger than those of the bulk fcc, while the variations in the magnetic moment were complicated in hcp/hcp and fcc/hcp. The magnetovolume effect on the magnetic moment at the twin(-like) boundaries was investigated in terms of the local average atomic distance and the average deviation from equilibrium; however, the complicated variations in the magnetic moment could not be explained from the magnetovolume effect. Next, the narrowing (or broadening) of the partial density of states (PDOS) width of 3d orbitals, the number of occupied states for the spin-down channel, and the PDOS around the Fermi level were investigated. The entire variation in the magnetic moment at the twin(-like) boundaries could be understood in terms of these factors. Charge transfer occurred in hcp/hcp. In this case, the contributions of 4s and 4p electrons to the variation in the magnetic moment were relatively large.