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.     

Novel simulated moving-bed adsorber for the fractionation of gas mixtures

The separation of propylene-propane mixture is an energy intensive operation commercially practiced using cryogenic distillation. The separation by pressure swing adsorption has been studied as an alternative. A fixed-bed pressure swing adsorption yields the heavy component as a pure product. The product recovery and the productivity are not high. In a moving-bed process, because of the counter-current solid-gas contact, the separation achieved is similar to that of the fractionation by distillation. Although the moving-bed operation offers the upper limit for the performance of a cyclic adsorptive process, due to mechanical complexities in the handling of solids the 'simulated' moving-bed is preferred. By moving the inlet and outlet ports of streams located along the length of the bed, a moving-bed process can be realized in a fixed bed. We describe here a 'moving-port' system which permits injection or withdrawal of the fluid along the axial direction in a fixed bed. A fixed bed embedded with the moving-port systems emulates a simulated moving-bed adsorber. The proposed adsorber can fractionate a binary gas mixture into two product streams with high purities. It is similar to the Sorbex process of UOP but does not have the eluent as an additional separating agent. A parametric study indicates that high purity products and a higher productivity by an order of magnitude can be achieved with simulated moving-beds compared to the fixed beds.     

Fast oxygen ion migration in Cu–In–oxide bulk and its utilization for effective CO2 conversion at lower temperature

Efficient activation of CO₂ at low temperature was achieved by reverse water–gas shift via chemical looping (RWGS-CL) by virtue of fast oxygen ion migration in a Cu–In structured oxide, even at lower temperatures. Results show that a novel Cu–In₂O₃ structured oxide can show a remarkably higher CO₂ splitting rate than ever reported. Various analyses revealed that RWGS-CL on Cu–In₂O₃ is derived from redox between Cu–In₂O₃ and Cu–In alloy. Key factors for high CO₂ splitting rate were fast migration of oxide ions in the alloy and the preferential oxidation of the interface of alloy–In₂O₃ in the bulk of the particles. The findings reported herein can open up new avenues to achieve effective CO₂ conversion at lower temperatures.

Efficient activation of CO₂ at low temperature was achieved by reverse water–gas shift via chemical looping (RWGS-CL) by virtue of fast oxygen ion migration in a Cu–In structured oxide, even at lower temperatures.     

A convergent approach for the total synthesis of the α-glucosidase inhibitor (−)-panaxjapyne-C

The stereoselective total synthesis of (?)-panaxjapyne-C was accomplished in a convergent fashion. The synthesis utilizes the readily available enantiomers l-(+)-diethyltartrate and d-(?)-diethyltartrate and involves a Cadiot–Chodkiewicz coupling reaction, and an Ohira–Bestmann reaction as the key steps.     

Multispectroscopic DNA interaction and Docking studies

Two new water soluble oxovanadium(IV) complexes with formulae Na[VO(his)(met)SO₄] (1) and Na[VO(gly)(met)SO₄] (2), (gly=glycine his=histidine, and met=metformin) were synthesized and characterized by LCMS, UV‐Visible absorption, infrared spectra, magnetic moment, elemental analysis, thermal analysis and electronic spectral studies. The metal center was found in an octahedral geometry. DNA binding interaction of these complexes with CT DNA has been explored by UV‐Visible absorption, fluorescence, viscosity measurements and cleavage studies. Finally the binding of the complexes with CT‐DNA could be surface binding, mainly in the groove binding. The complexes were docked in to B‐DNA sequence, 5’(D*AP*CP*CP*GP*AP*CP*GP*TP*CP*GP*GP*T)‐3’ retrieved from protein data bank (PDB ID: 423D), using Discovery Studio 2.1 software.     

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.