Microscopic-macroscopic approach for binding energies with the Wigner-Kirkwood method. II. Deformed nuclei

The binding energies of deformed even-even nuclei have been analyzed within the framework of a recently proposed microscopic-macroscopic model. We have used the semiclassical Wigner-Kirkwood ̄h expansion up to fourth order, instead of the usual Strutinsky averaging scheme, to compute the shell corrections in a deformed Woods-Saxon potential including the spin-orbit contribution. For a large set of 561 even-even nuclei with Z 8 and N 8, we find an rms deviation from the experiment of 610 keV in binding energies, comparable to the one found for the same set of nuclei using the finite range droplet model of Moller and Nix (656 keV). As applications of our model, we explore its predictive power near the proton and neutron drip lines as well as in the superheavy mass region. Next, we systematically explore the fourth-order Wigner-Kirkwood corrections to the smooth part of the energy. It is found that the ratio of the fourth-order to the second-order corrections behaves in a very regular manner as a function of the asymmetry parameter I=(N−Z)/A. This allows us to absorb the fourth-order corrections into the second-order contributions to the binding energy, which enables us us to simplify and speed up the calculation of deformed nuclei.

Microscopic-macroscopic approach for binding energies with the Wigner-Kirkwood method

The semiclassical Wigner-Kirkwood ̄h expansion method is used to calculate shell corrections for spherical and deformed nuclei. The expansion is carried out up to fourth order in ̄h. A systematic study of Wigner-Kirkwood averaged energies is presented as a function of the deformation degrees of freedom. The shell corrections, along with the pairing energies obtained by using the Lipkin-Nogami scheme, are used in the microscopic-macroscopic approach to calculate binding energies. The macroscopic part is obtained from a liquid drop formula with six adjustable parameters. Considering a set of 367 spherical nuclei, the liquid drop parameters are adjusted to reproduce the experimental binding energies, which yields a root mean square (rms) deviation of 630 keV. It is shown that the proposed approach is indeed promising for the prediction of nuclear masses.

Relativistic deformed mean-field calculation of binding energy differences of mirror nuclei

Binding energy differences of mirror nuclei for A = 15, 17, 27, 29, 31, 33, 39 and 41 are calculated in the framework of relativistic deformed mean-field theory. To fully include the effects of the polarization of the nuclear core due to the extra particle or hole, the spatial components of the vector meson fields and the photon are taken into account in a self-consistent manner. The calculated binding energy differences are systematically smaller than the experimental values and lend support to the existency of the Okamoto-Nolen-Schiffer anomaly found decades ago in nonrelativistic calculations, For the majority of the nuclei studied, however, the results are such that the anomaly is significantly smaller than the one obtained within state-of-the-art nonrelativistic calculations.

Thomas-Fermi theory for atomic nuclei revisited

The recently developed semiclassical variational Wigner-Kirkwood (VWK) approach is applied to finite nuclei using external potentials and self-consistent mean fields derived from Skyrme inter-actions and from relativistic mean field theory. VWK consist s of the Thomas-Fermi part plus a pure, perturbative h 2 correction. In external potentials, VWK passes through the average of the quantal values of the accumulated level density and total en energy as a function of the Fermi energy. However, there is a problem of overbinding when the energy per particle is displayed as a function of the particle number. The situation is analyzed comparing spherical and deformed harmonic oscillator potentials. In the self-consistent case, we show for Skyrme forces that VWK binding energies are very close to those obtained from extended Thomas-Fermi functionals of h 4 order, pointing to the rapid convergence of the VWK theory. This satisfying result, however, does not cure the overbinding problem, i.e., the semiclassical energies show more binding than they should. This feature is more pronounced in the case of Skyrme forces than with the relativistic mean field approach. However, even in the latter case the shell correction energy for e.g.208 Pb turns out to be only ∼ −6 MeV what is about a factor two or three off the generally accepted value. As an adhoc remedy, increasing the kinetic energy by 2.5%, leads to shell correction energies well acceptable throughout the periodic table. The general importance of the present studies for other finite Fermi systems, self-bound or in external potentials, is pointed out.

Fundamental fermion masses from deformed SUq(2) triplets

A spectrum-generating q-algebra, within the framework of SUq(2), as firstly suggested by Iachello, is studied in order to describe the mass spectrum of three generations of quarks and leptons. The SUq(2) quantum group is a q-deformed extension of SU(2), where q = e(alpha) (with alpha real) is the deformation parameter. In this work, the essential use of inequivalent representations of SUq(2) is introduced. The inequivalent representations are labelled by (j, nu(0)), where j = 0, 1/2, 1, ... and nu(0) is a positive real number. A formula for the fermion masses M-m(j, nu(0)), with -j less than or equal to m less than or equal to j is derived. As an example, a possible scheme which corresponds to two triplets (j = 1) associated to up and down quarks is presented here in some detail. They are associated to different values of the deformation parameter, indicating a dependence of the charge Q on the parameter alpha. The masses of the charged leptons are treated in a similar way. The current results show that some mass relations for quarks and leptons found in the literature can be considered as approximations of the equations obtained in the j = 1 representations. The breaking of SUq(2) necessary to describe the Cabibbo-Kobayashi-Maskawa (CKM) flavor mixing is briefly discussed.

Cloud condensation nuclei in pristine tropical rainforest air of Amazonia: size-resolved measurements and modeling of atmospheric aerosol composition and CCN activity

Atmospheric aerosol particles serving as cloud condensation nuclei (CCN) are key elements of the hydrological cycle and climate. We have measured and characterized CCN at water vapor supersaturations in the range of S=0.10-0.82% in pristine tropical rainforest air during the AMAZE-08 campaign in central Amazonia. The effective hygroscopicity parameters describing the influence of chemical composition on the CCN activity of aerosol particles varied in the range of kappa approximate to 0.1-0.4 (0.16+/-0.06 arithmetic mean and standard deviation). The overall median value of kappa approximate to 0.15 was by a factor of two lower than the values typically observed for continental aerosols in other regions of the world. Aitken mode particles were less hygroscopic than accumulation mode particles (kappa approximate to 0.1 at D approximate to 50 nm; kappa approximate to 0.2 at D approximate to 200 nm), which is in agreement with earlier hygroscopicity tandem differential mobility analyzer (H-TDMA) studies. The CCN measurement results are consistent with aerosol mass spectrometry (AMS) data, showing that the organic mass fraction (f(org)) was on average as high as similar to 90% in the Aitken mode (D <= 100 nm) and decreased with increasing particle diameter in the accumulation mode (similar to 80% at D approximate to 200 nm). The kappa values exhibited a negative linear correlation with f(org) (R(2)=0.81), and extrapolation yielded the following effective hygroscopicity parameters for organic and inorganic particle components: kappa(org)approximate to 0.1 which can be regarded as the effective hygroscopicity of biogenic secondary organic aerosol (SOA) and kappa(inorg)approximate to 0.6 which is characteristic for ammonium sulfate and related salts. Both the size dependence and the temporal variability of effective particle hygroscopicity could be parameterized as a function of AMS-based organic and inorganic mass fractions (kappa(p)=kappa(org) x f(org)+kappa(inorg) x f(inorg)). The CCN number concentrations predicted with kappa(p) were in fair agreement with the measurement results (similar to 20% average deviation). The median CCN number concentrations at S=0.1-0.82% ranged from N(CCN,0.10)approximate to 35 cm(-3) to N(CCN,0.82)approximate to 160 cm(-3), the median concentration of aerosol particles larger than 30 nm was N(CN,30)approximate to 200 cm(-3), and the corresponding integral CCN efficiencies were in the range of N(CCN,0.10/NCN,30)approximate to 0.1 to N(CCN,0.82/NCN,30)approximate to 0.8. Although the number concentrations and hygroscopicity parameters were much lower in pristine rainforest air, the integral CCN efficiencies observed were similar to those in highly polluted megacity air. Moreover, model calculations of N(CCN,S) assuming an approximate global average value of kappa approximate to 0.3 for continental aerosols led to systematic overpredictions, but the average deviations exceeded similar to 50% only at low water vapor supersaturation (0.1%) and low particle number concentrations (<= 100 cm(-3)). Model calculations assuming aconstant aerosol size distribution led to higher average deviations at all investigated levels of supersaturation: similar to 60% for the campaign average distribution and similar to 1600% for a generic remote continental size distribution. These findings confirm earlier studies suggesting that aerosol particle number and size are the major predictors for the variability of the CCN concentration in continental boundary layer air, followed by particle composition and hygroscopicity as relatively minor modulators. Depending on the required and applicable level of detail, the information and parameterizations presented in this paper should enable efficient description of the CCN properties of pristine tropical rainforest aerosols of Amazonia in detailed process models as well as in large-scale atmospheric and climate models.

Deformed Gaussian-orthogonal-ensemble description of small-world networks

The study of spectral behavior of networks has gained enthusiasm over the last few years. In particular, random matrix theory (RMT) concepts have proven to be useful. In discussing transition from regular behavior to fully chaotic behavior it has been found that an extrapolation formula of the Brody type can be used. In the present paper we analyze the regular to chaotic behavior of small world (SW) networks using an extension of the Gaussian orthogonal ensemble. This RMT ensemble, coined the deformed Gaussian orthogonal ensemble (DGOE), supplies a natural foundation of the Brody formula. SW networks follow GOE statistics until a certain range of eigenvalue correlations depending upon the strength of random connections. We show that for these regimes of SW networks where spectral correlations do not follow GOE beyond a certain range, DGOE statistics models the correlations very well. The analysis performed in this paper proves the utility of the DGOE in network physics, as much as it has been useful in other physical systems.

g factors of coexisting isomeric states in (188)Pb

The g factors of the 12(+), 11(-), and 8(-) isomeric states in (188)Pb were measured using the time-differential perturbed angular distribution method as g(12(+)) = -0.179(6), g(11(-)) = +1.03(3), and g(8(-)) = -0.037(7). The g factor of the 12(+) state follows the observed slight down-sloping evolution of the g factors of the i(13/2)(2) neutron spherical states with decreasing N. The g factors of the 11(-) and 8(-) isomers proposed as oblate and prolate deformed states, respectively, were interpreted within the rotational model, using calculated and empirical g factor values for the involved single-particle orbitals.

Structure of (46)Ti at low excitation energy

The nucleus (46)Ti has been studied with the reaction (42)Ca((7)Li,p2n)(46)Ti at a bombarding energy of 31 MeV. Thin target foils backed with a thick Au layer were used. Five new levels of negative parity were observed. Several lifetimes have been determined with the Doppler shift attenuation method. Low-lying experimental negative-parity levels are assigned to three bands with K(pi) = 3, 0, and 4, which are interpreted in terms of the large-scale shell model, considering particle-hole excitations from d(3/2) and s(1/2) orbitals. Shell model calculations were performed using a few effective interactions. However, good agreement was not achieved in the description of either negative- or positive-parity low-lying levels.

EBSD characterization of an ECAP deformed Nb single crystal

A niobium single crystal was subjected to equal channel angular pressing (ECAP) at room temperature after orienting the crystal such that [1 -1 -1] ayen ND, [0 1 -1] ayen ED, and [-2 -1 -1] ayen TD. Electron backscatter diffraction (EBSD) was used to characterize the microstructures both on the transverse and the longitudinal sections of the deformed sample. After one pass of ECAP the single crystal exhibits a group of homogeneously distributed large misorientation sheets and a well formed cell structure in the matrix. The traces of the large misorientation sheets match very well with the most favorably oriented slip plane and one of the slip directions is macroscopically aligned with the simple shear plane. The lattice rotation during deformation was quantitatively estimated through comparison of the orientations parallel to three macroscopic axes before and after deformation. An effort has been made to link the microstructure with the initial crystal orientation. Collinear slip systems are believed to be activated during deformation. The full constraints Taylor model was used to simulate the orientation evolution during ECAP. The result matched only partially with the experimental observation.

An In-Depth Study of the Barkhausen Emission Signal Properties of the Plastically Deformed Fe-2%Si Alloy

This paper presents the results of the in-depth study of the Barkhausen effect signal properties for the plastically deformed Fe-2%Si samples. The investigated samples have been deformed by cold rolling up to plastic strain epsilon(p) = 8%. The first approach consisted of time-domain-resolved pulse and frequency analysis of the Barkhausen noise signals whereas the complementary study consisted of the time-resolved pulse count analysis as well as a total pulse count. The latter included determination of time distribution of pulses for different threshold voltage levels as well as the total pulse count as a function of both the amplitude and the duration time of the pulses. The obtained results suggest that the observed increase in the Barkhausen noise signal intensity as a function of deformation level is mainly due to the increase in the number of bigger pulses.

Integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons

A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is applicable to all boundary lattice systems where an invertible R-matrix exists. As an application, the integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons are investigated. The diagonal boundary K-matrices are found and a class of integrable boundary terms are determined. The boundary system is solved by means of the coordinate space Bethe ansatz technique and the Bethe ansatz equations are derived. As a sideline, it is shown that all R-matrices associated with a quantum affine superalgebra enjoy the crossing-unitarity property. (C) 1998 Elsevier Science B.V.

New integrable boundary conditions for the q-deformed supersymmetric U model and Bethe ansatz equations

New classes of integrable boundary conditions for the q-deformed (or two-parameter) supersymmetric U model are presented. The boundary systems are solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are derived. (C) 1998 Elsevier Science B.V.

Integrable Kondo impurity in one-dimensional q-deformed t-J models

Integrable Kondo impurities in two cases of one-dimensional q-deformed t-J models are studied by means of the boundary Z(2)-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realizations of the reflection equation algebras in an impurity Hilbert space. Furthermore, these models are solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained.

The q-deformed supersymmetric t-J model with a boundary

The q-deformed supersymmetric t-J model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the quantum affine superalgebra U-q[sl(2\1)]. We. give the bosonization of the boundary states. We give an integral expression for the correlation functions of the boundary model, and derive the difference equations which they satisfy.