On quantum matrix algebras satisfying the Cayley-Hamilton-Newton identities

The Cayley-Hamilton-Newton identities which generalize both the characteristic identity and the Newton relations have been recently obtained for the algebras of the RTT-type. We extend this result to a wider class of algebras M(R,F) defined by a pair of compatible solutions of the Yang-Baxter equation. This class includes the RTT-algebras as well as the Reflection equation algebras

On R-matrix representations of Birman-Murakami-Wenzl algebras

We show that to every local representation of the Birman-Murakami-Wenzl algebra defined by a skew-invertible R-matrix $R\in Aut(V\otimes V)$ one can associate pairings $V\otimes V\to C$ and $V^*\otimes V^*\to C$, where V is the representation space. Further, we investigate conditions under which the corresponding quantum group is of SO or Sp type.Comment: 9 page

Modified Affine Hecke Algebras and Drinfeldians of Type A

We introduce a modified affine Hecke algebra \h{H}^{+}_{q\eta}({l}) (\h{H}_{q\eta}({l})) which depends on two deformation parameters $q$ and $\eta$. When the parameter $\eta$ is equal to zero the algebra \h{H}_{q\eta=0}(l) coincides with the usual affine Hecke algebra \h{H}_{q}(l) of type $A_{l-1}$, if the parameter q goes to 1 the algebra \h{H}^{+}_{q=1\eta}(l) is isomorphic to the degenerate affine Hecke algebra \Lm_{\eta}(l) introduced by Drinfeld. We construct a functor from a category of representations of $H_{q\eta}^{+}(l)$ into a category of representations of Drinfeldian $D_{q\eta}(sl(n+1))$ which has been introduced by the first author.Comment: 11 pages, LATEX. Contribution to Proceedings "Quantum Theory and Symmetries" (Goslar, July 18-22, 1999) (World Scientific, 2000

Local energy-density functional approach to many-body nuclear systems with s-wave pairing

The ground-state properties of superfluid nuclear systems with ^1S_0 pairing are studied within a local energy-density functional (LEDF) approach. A new form of the LEDF is proposed with a volume part which fits the Friedman- Pandharipande and Wiringa-Fiks-Fabrocini equation of state at low and moderate densities and allows an extrapolation to higher densities preserving causality. For inhomogeneous systems, a surface term with two free parameters is added. In addition to the Coulomb direct and exchange interaction energy, an effective density-dependent Coulomb-nuclear correlation term is included with one more free parameter, giving a contribution of the same order of magnitude as the Nolen-Schiffer anomaly in Coulomb displacement energy. The root-mean-square deviations from experimental masses and radii with the proposed LEDF come out about a factor of two smaller than those obtained with the conventional functionals based on the Skyrme or finite-range Gogny force, or on the relativistic mean-field theory. The generalized variational principle is formulated leading to the self-consistent Gor'kov equations which are solved exactly, with physical boundary conditions both for the bound and scattering states. With a zero-range density-dependent cutoff pairing interaction incorporating a density-gradient term, the evolution of differential observables such as odd-even mass differences and staggering in charge radii, is reproduced reasonably well, including kinks at magic neutron numbers. An extrapolation to infinite nuclear matter is discussed. We study also the dilute limit in both the weak and strong coupling regime.Comment: 19 pages, 8 figures. LaTeX, with modified cls file supplied. To be published in vol. 3 of the series "Advances in Quantum Many-Body Theory", World Scientific (Proceedings of the MBX Conference, Seattle, September 10-15, 1999

The beta-delayed neutron emission in 78Ni region

A systematic study of the total $\beta$-decay half-lives and $\beta$-delayed neutron emission probabilities is performed. The $\beta$-strength function is treated within the self-consistent density-functional + continuum-QRPA framework including the Gamow-Teller and first-forbidden transitions. The experimental total $\beta$-decay half-lives for the Ni isotopes with $A\leq$76 are described satisfactorily. The half-lives predicted from $A$=70 up to $A$=86 reveal fairly regular $A$-behaviour which results from simultaneous account for the Gamow-Teller and first-forbidden transitions. For $Z\approx$ 28 nuclei, a suppression of the delayed neutron emission probability is found when the $N$=50 neutron closed shell is crossed. The effect originates from the high-energy first-forbidden transitions to the states outside the $Q_{\beta} - S_n$-window in the daughter nuclei. PACS numbers: 23.40.Bw,21.60.Jz,25.30.Pt,26.30.+kComment: LaTeX, 13 pages, 5 figure

Semi-microscopic description of the backbending phenomena in some deformed even-even nuclei

The mechanism of backbending is semi-phenomenologically investigated based on the hybridization of two rotational bands. These bands are defined by treating a model Hamiltonian describing two interacting subsystems: a set of particles moving in a deformed mean field and interacting among themselves through an effective pairing force and a phenomenological deformed core whose intrinsic ground state is an axially symmetric coherent boson state. The two components interact with each other by a quadrupole-quadrupole and a spin-spin interaction. The total Hamiltonian is considered in the space of states with good angular momentum, projected from a quadrupole deformed product function. The single-particle factor function defines the nature of the rotational bands, one corresponding to the ground band in which all particles are paired and another one built upon a $i_{13/2}$ neutron broken pair. The formalism is applied to six deformed even-even nuclei, known as being good backbenders. Agreement between theory and experiment is fairly good.Comment: 37 pages, 9 figure