Compact and accurate variational wave functions of three-electron atomic systems constructed from semi-exponential radial basis functions

The semi-exponential basis set of radial functions [A.M. Frolov, Phys. Lett. A 374, 2361 (2010)] is used for variational computations of bound states in three-electron atomic systems. It appears that the semi-exponential basis set has a substantially greater potential for accurate variational computations of bound states in three-electron atomic systems than was originally anticipated. In particular, the 40-term Larson’s wave function improved with the use of semi-exponential radial basis functions now produces the total energy –7.4780581457 a.u. for the ground 1²S-state in the ^￥Li^\infty{\rm Li} atom (only one spin function c₁\chi_1 = aba\alpha\beta\alpha - baa\beta\alpha\alpha was used in these calculations). This variational energy is very close to the exact ground state energy of the ^￥Li^\infty{\rm Li} atom and is substantially lower than the total energy obtained with the original Larson’s 40-term wave function (–7.477944869 a.u.).     

Coexistence of “ $ \alpha$ + 208Pb ” cluster structures and single-particle excitations in 212 84Po128

Excited states in ²¹²Po have been populated by a \alpha transfer using the ²⁰⁸Pb(¹⁸O,¹⁴C) reaction at 85MeV beam energy and studied with the EUROBALL IV g \gamma multi-detector array. The level scheme has been extended up to ∼ 3.2 MeV excitation energy from the triple-g \gamma coincidence data. Spin and parity values of most of the observed states have been assigned from the g \gamma angular distributions and g \gamma -g \gamma angular correlations. Several g \gamma -lines with E _γ < 1 MeV have been found to be shifted by the Doppler effect, allowing for the measurements of the associated lifetimes by the DSAM method. The values, found in the range [0.1-0.6]ps, lead to very enhanced E1 transitions. All the emitting states, which have non-natural parity values, are discussed in terms of a \alpha - ²⁰⁸Pb structure. They are in the same excitation-energy range as the states issued from shell-model configurations.     

DN interaction from meson exchange

A model of the DN interaction is presented which is developed in close analogy to the meson-exchange [`(K)] \bar{{K}} N potential of the Jülich group utilizing SU(4) symmetry constraints. The main ingredients of the interaction are provided by vector meson (r \rho , w \omega exchange and higher-order box diagrams involving D <sup>*</sup> N , D D \Delta , and D <sup>*</sup> D \Delta intermediate states. The coupling of DN to the p \pi L<sub>c</sub> \Lambda_{c}^{} and p \pi S<sub>c</sub> \Sigma_{c}^{} channels is taken into account. The interaction model generates the L<sub>c</sub> \Lambda_{c}^{}(2595) -resonance dynamically as a DN quasi-bound state. Results for DN total and differential cross sections are presented and compared with predictions of two interaction models that are based on the leading-order Weinberg-Tomozawa term. Some features of the L<sub>c</sub> \Lambda_{c}^{}(2595) -resonance are discussed and the role of the near-by p \pi S<sub>c</sub> \Sigma_{c}^{} threshold is emphasized. Selected predictions of the orginal [`(K)] \bar{{K}} N model are reported too. Specifically, it is pointed out that the model generates two poles in the partial wave corresponding to the L \Lambda(1405) -resonance.     

Bound-state solutions of the Dirac-Rosen-Morse potential with spin and pseudospin symmetry<Superscript>⋆</Superscript>

The energy spectra and the corresponding two-component spinor wave functions of the Dirac equation for the Rosen-Morse potential with spin and pseudospin symmetry are obtained. The s -wave ( k \kappa = 0 state) solutions for this problem are obtained by using the basic concept of the supersymmetric quantum mechanics approach and function analysis (standard approach) in the calculations. Under the spin symmetry and pseudospin symmetry, the energy equation and the corresponding two-component spinor wave functions for this potential and other special types of this potential are obtained. The extension of this result to the k \kappa 1 \neq 0 state is suggested.     

Critical Rotational Speeds in the Gross-Pitaevskii Theory on a Disc with Dirichlet Boundary Conditions

We study the two-dimensional Gross-Pitaevskii theory of a rotating Bose gas in a disc-shaped trap with Dirichlet boundary conditions, generalizing and extending previous results that were obtained under Neumann boundary conditions. The focus is on the energy asymptotics, vorticity and qualitative properties of the minimizers in the parameter range |log ε|≪Ω≲ε ⁻²|log ε|⁻¹ where Ω is the rotational velocity and the coupling parameter is written as ε ⁻² with ε≪1. Three critical speeds can be identified. At \varOmega = \varOmega_c1 ~ |loge|\varOmega=\varOmega_{\mathrm{c_{1}}}\sim |\log\varepsilon| vortices start to appear and for |loge| << \varOmega < \varOmega_c2 ~ e^-1|\log\varepsilon|\ll\varOmega< \varOmega_{\mathrm{c_{2}}}\sim \varepsilon^{-1} the vorticity is uniformly distributed over the disc. For \varOmega 3 \varOmega _c2\varOmega\geq\varOmega _{\mathrm{c_{2}}} the centrifugal forces create a hole around the center with strongly depleted density. For Ω≪ε ⁻²|log ε|⁻¹ vorticity is still uniformly distributed in an annulus containing the bulk of the density, but at \varOmega = \varOmega_c3 ~ e^-2|loge|^-1\varOmega=\varOmega_{\mathrm {c_{3}}}\sim\varepsilon ^{-2}|\log\varepsilon |^{-1} there is a transition to a giant vortex state where the vorticity disappears from the bulk. The energy is then well approximated by a trial function that is an eigenfunction of angular momentum but one of our results is that the true minimizers break rotational symmetry in the whole parameter range, including the giant vortex phase.     

Analysis of the X(1835) and related baryonium states with Bethe-Salpeter equation

In this article, we study the mass spectrum of the baryon-antibaryon bound states p [`(p)] \bar{{p}} , S \Sigma [`(S)] \bar{{\Sigma}} , X \Xi [`(X)] \bar{{\Xi}} , L \Lambda [`(L)] \bar{{\Lambda}} , p [`(N)] \bar{{N}}(1440) , S \Sigma [`(S)] \bar{{\Sigma}}(1660) , X \Xi [`(X)]<sup>￠</sup> \bar{{\Xi}}^{{\prime}}_{} and L \Lambda [`(L)] \bar{{\Lambda}}(1600) with the Bethe-Salpeter equation. The numerical results indicate that the p [`(p)] \bar{{p}} , S \Sigma [`(S)] \bar{{\Sigma}} , X \Xi [`(X)] \bar{{\Xi}} , p [`(N)] \bar{{N}}(1440) , S \Sigma [`(S)] \bar{{\Sigma}}(1660) , X \Xi [`(X)]^￠ \bar{{\Xi}}^{{\prime}}_{} bound states maybe exist, and the new resonances X(1835) and X(2370) can be tentatively identified as the p [`(p)] \bar{{p}} and p [`(N)] \bar{{N}}(1440) (or N(1400)[`(p)] \bar{{p}} bound states, respectively, with some gluon constituents, and the new resonance X(2120) may be a pseudoscalar glueball. On the other hand, the Regge trajectory favors identifying the X(1835) , X(2120) and X(2370) as the excited h^￠ \eta^{{\prime}}_{}(958) mesons with the radial quantum numbers n = 3 , 4 and 5, respectively.     

Assignment of levels in <Superscript>208</Superscript>Fr and 10<Superscript>-</Superscript> isomers in the odd-odd isotones <Superscript>206</Superscript>At and <Superscript>208</Superscript>Fr

Excited states in ²⁰⁸Fr have been identified using the ¹⁹⁷Au(¹⁶O, 5n)²⁰⁸Fr reaction and a variety of time-correlated g \gamma -ray and conversion electron spectroscopic techniques. Transitions above and below a t \tau = 623(16) ns 10^- isomer are placed in the level scheme. This isomer is analogous to that observed in the odd-odd isotone ²⁰⁶At for which additional spectroscopic information is also obtained, including a precise lifetime of t \tau = 1173(30) ns. The g \gamma -rays assigned to ²⁰⁸Fr are the same as the main transitions erroneously assigned to ²⁰⁹Fr in previous work.     

Theory of microphase separation in crosslinked polymer blends immersed in a $ \theta$ -solvent

The aim of this work is a theoretical study of the effects of the solvent quality on the microphase separation in crosslinked polymer blends, from a static and kinetics point of view. More precisely, we assume that the crosslinked mixture is trapped in a q \theta -solvent. The static microphase properties are studied through the static structure factor. The latter is computed using an extended blob model, where the crosslinked unlike chains can be viewed as sequences of blobs. We demonstrate that the presence of the q \theta -solvent simply leads to a multiplicative renormalization of these properties, and the renormalization factors are powers of the overall monomer volume fraction. Second, we investigate the early kinetics of the microphase separation, via the relaxation rate, t_q \tau_{q}^{} , which is a function of the wave number q (at fixed temperature and monomer volume fraction). We first show that the kinetics is entirely controlled by local motions of Rouse type, since the slow motions are frozen out by the presence of crosslinks. Using the blob model, we find an explicit form for the growth rate W \Omega(q) = t_q^-1 \tau_{q}^{{-1}} , which depends, in addition to the wave number q , on the overall monomer volume fraction, F \Phi . Also, we discuss the effect of initial entanglements that are trapped when the system is crosslinked. In fact, these play the role of true reticulation points, and then, they quantitatively contribute to the microseparation phenomenon. Finally, the results are compared to their homologous relatively to the molten state and to the good solvent case. The main conclusion is that the quality of the solvent induces drastic changes of the microphase properties.     

Viscous compressible hydrodynamics at planes,spheres and cylinders with finite surface slip

We consider the linearized time-dependent Navier-Stokes equation including finite compressibility and viscosity. We first constitute the Green's function, from which we derive the flow profiles and response functions for a plane, a sphere and a cylinder for arbitrary surface slip length. For high driving frequency the flow pattern is dominated by the diffusion of vorticity and compression, for low frequency compression propagates in the form of sound waves which are exponentially damped at a screening length larger than the sound wave length. The crossover between the diffusive and propagative compression regimes occurs at the fluid's intrinsic frequency w \omega ∼ c ² r₀ \rho_{0}^{}/h \eta , with c the speed of sound, r₀ \rho_{0}^{} the fluid density and h \eta the viscosity. In the propagative regime the hydrodynamic response function of spheres and cylinders exhibits a high-frequency resonance when the particle size is of the order of the sound wave length. A distinct low-frequency resonance occurs at the boundary between the propagative and diffusive regimes. Those resonant features should be detectable experimentally by tracking the diffusion of particles, as well as by measuring the fluctuation spectrum or the response spectrum of trapped particles. Since the response function depends sensitively on the slip length, in principle the slip length can be deduced from an experimentally measured response function.     

Quenching of the E1 strength in <Superscript>149</Superscript>Nd

Lifetime measurements of excited states in ¹⁴⁹Nd have been performed using the advanced time-delayed b \beta g \gamma g \gamma(t) method. Half-lives of 14 excited states in ¹⁴⁹Nd have been determined for the first time or measured with higher precision. Twelve new g \gamma -lines and 5 new levels have been introduced into the decay scheme of ¹⁴⁹Pr based on results of the g \gamma g \gamma coincidence measurements. Reduced transition probabilities have been determined for 40 g \gamma -transitions in ¹⁴⁹Nd . Configuration assignments for 6 rotational bands in ¹⁴⁹Nd are proposed. Enhanced E1 transitions indicate that the ground-state band and the band built on the 332.9keV level constitute a pair of the K^p = 5/2^±\ensuremath K^{\pi} = 5/2^{\pm} parity doublet bands. Potential energy surfaces on the (b₂,b₃)\ensuremath (\beta_{2},\beta_{3}) -plane have been calculated for the lowest single quasi-particle configurations in ¹⁴⁹Nd using the Strutinski method and the axially deformed Woods-Saxon potential. The predicted occurrence of the octupole-deformed K = 5/2 configuration is in agreement with experiment. Unexpectedly low |D₀|\ensuremath \vert D_0\vert values obtained for the K^p = 5/2^±\ensuremath K^{\pi} = 5/2^{\pm} parity doublet bands may result from cancellation between the proton and neutron shell correction contributions to |D₀|\ensuremath \vert D_0\vert .     

Calculation of radiative parameters for the $$ {A^1}\sum\nolimits_u^{+} {{X^1}} \sum\nolimits_g^{+} {} $$-transition of cesium dimer

Radiative parameters for vibrational bands (0 ≤ v′ ≤ 30, 0 ≤ v′′ ≤ 59) of the A¹?_u⁺ X¹ ?_g⁺ {A^1}\sum\nolimits_u^{+} {{X^1}} \sum\nolimits_g^{+} {} -electronic transition of a cesium dimer are calculated. These include vibronic band wavenumbers, Franck–Condon factors, Einstein coefficients for spontaneous emission, absorption band oscillator strengths, and radiative lifetimes for vibrational levels of the excited electronic state. Vibrational energies and wave functions for the ground and excited electronic states were found by a numerical solution of the radial wave equation based on potential curves plotted during the course of the study.     

The value of the cosmological constant

We make the cosmological constant, Λ, into a field and restrict the variations of the action with respect to it by causality. This creates an additional Einstein constraint equation. It restricts the solutions of the standard Einstein equations and is the requirement that the cosmological wave function possess a classical limit. When applied to the Friedmann metric it requires that the cosmological constant measured today, t _U , be L ~ t_U^-2 ~ 10^-122{\Lambda \sim t_{U}^{-2} \sim 10^{-122}} , as observed. This is the classical value of Λ that dominates the wave function of the universe. Our new field equation determines Λ in terms of other astronomically measurable quantities. Specifically, it predicts that the spatial curvature parameter of the universe is W_k0 o -k/a₀²H²=-0.0055{\Omega _{\mathrm{k0}} \equiv -k/a_{0}^{2}H^{2}=-0.0055} , which will be tested by Planck Satellite data. Our theory also creates a new picture of self-consistent quantum cosmological history.     

Boundary Concentration for Eigenvalue Problems Related to the Onset of Superconductivity

We examine the asymptotic behavior of the eigenvalue w(h) and corresponding eigenfunction associated with the variational problem m(h) o inf_{y ? H¹(W;C )} \fracò_W \abs(i?+hA)y² dx dy ò_W\absy² dx dy \mu(h)\equiv\inf_{\psi\in H^{1}(\Omega;{\bf C} )} \frac{\int_{\Omega } \abs{(i\nabla+h{\bf A})\psi}^{2}\,dx\,dy} {\int_{\Omega }\abs{\psi}^{2}\,dx\,dy} in the regime h>>1. Here A is any vector field with curl equal to 1. The problem arises within the Ginzburg-Landau model for superconductivity with the function w(h) yielding the relationship between the critical temperature vs. applied magnetic field strength in the transition from normal to superconducting state in a thin mesoscopic sample with cross-section W ì \R²\Omega\subset\R^{2}. We first carry out a rigorous analysis of the associated problem on a half-plane and then rigorously justify some of the formal arguments of [BS], obtaining an expansion for w while also proving that the first eigenfunction decays to zero somewhere along the sample boundary ?W\partial \Omega when z is not a disc. For interior decay, we demonstrate that the rate is exponential.     

Light meson mass dependence of the positive-parity heavy-strange mesons

We calculate the masses of the resonances D_s0^*(2317)\ensuremath D_{s0}^{\ast}(2317) and D_s1(2460)\ensuremath D_{s1}(2460) as well as their bottom partners as bound states of a kaon and a D^(*)\ensuremath D^{(\ast)} - and B^(*)\ensuremath B^{(\ast)} -meson, respectively, in unitarized chiral perturbation theory at next-to-leading order. After fixing the parameters in the D_s0^*(2317)\ensuremath D_{s0}^{\ast}(2317) channel, the calculated mass for the D_s1(2460)\ensuremath D_{s1}(2460) is found in excellent agreement with experiment. The masses for the analogous states with a bottom quark are predicted to be M_B^*s0=(5696±40)\ensuremath M_{B^{\ast}_{s0}}=(5696\pm 40) MeV and M_Bs1=(5742±40)\ensuremath M_{B_{s1}}=(5742\pm 40) MeV in reasonable agreement with previous analyses. In particular, we predict M_Bs1-M_Bs0^*=46±1\ensuremath M_{B_{s1}}{-}M_{B_{s0}^{\ast}}=46\pm 1 MeV. We also explore the dependence of the states on the pion and kaon masses. We argue that the kaon mass dependence of a kaonic bound state should be almost linear with slope about unity. Such a dependence is specific to the assumed molecular nature of the states. We suggest to extract the kaon mass dependence of these states from lattice QCD calculations.     

Controlling on Entangled Decoherence by the Interaction Model Between Qubit and Environment

The entangling evolution of the coupled qubits interacting with non-Markov environment is investigated in terms of concurrence. The results show that the entanglement of quantum systems depends on not only the initial state of system but also the coupling ways between qubit and environment. It shows that: (1) when the system is initially in ( | 00 ?±| 11 ?)/?2( | 00 \rangle\pm| 11 \rangle)/\sqrt{2} state or in the mixed state which is produced by the state, if we can control the coupling between the qubits and the environment in a asymmetrical state, we can make the quantum system always in the entangled state. (2) For an initial state ( | 01 ?±| 10 ?)/?2( | 01 \rangle\pm| 10 \rangle)/\sqrt{2} or in its mixed state, in contrast, there will not be entangled death under the symmetric coupling. We also find that, in ( | 01 ?±| 10?)/?2( | 01 \rangle\pm| 10\rangle)/\sqrt{2} or in its mixed state, the stronger the interaction between qubits is, the better to struggle against entanglement sudden death is.     

Entangled Husimi Distribution and Complex Wavelet Transformation

Similar in spirit to the preceding work (Int. J. Theor. Phys. 48:1539, 2009) where the relationship between wavelet transformation and Husimi distribution function is revealed, we study this kind of relationship to the entangled case. We find that the optical complex wavelet transformation can be used to study the entangled Husimi distribution function in phase space theory of quantum optics. We prove that, up to a Gaussian function, the entangled Husimi distribution function of a two-mode quantum state |ψ〉 is just the modulus square of the complex wavelet transform of e^-|h|2/2e^{-\vert \eta \vert ^{2}/2} with ψ(η) being the mother wavelet.     

Continuum theory of lipid bilayer electrostatics

In order to address the concerns about the applicability of the continuum theory of lipid bilayers, we generalize it by including a film with uniaxial dielectric properties representing the polar head groups of the lipid molecules. As a function of the in-plane dielectric constant k_|| \kappa_{{\Vert}}^{} of this film, we encounter a sequence of different phases. For low values of k_|| \kappa_{{\Vert}}^{} , transmembrane pores have aqueous cores, ions are repelled by the bilayer, and the ion permeability of the bilayer is independent of the ion radius as in the existing theory. For increasing k_|| \kappa_{{\Vert}}^{} , a threshold is reached --of the order of the dielectric constant of water-- beyond which ions are attracted to the lipid bilayer by generic polarization attraction, transmembrane pores collapse, and the ion permeability becomes sensitively dependent on the ion radius, results that are more consistent with experimental and numerical studies of the interaction of ions with neutral lipid bilayers. At even higher values of k_|| \kappa_{{\Vert}}^{} , the ion/pore complexes are predicted to condense in the form of extended arrays. The generalized continuum theory can be tested quantitatively by studies of the ion permeability as a function of salt concentration and co-surfactant concentration.     

Plasticity and dynamical heterogeneity in driven glassy materials

Many amorphous glassy materials exhibit complex spatio-temporal mechanical response and rheology, characterized by an intermittent stress strain response and a fluctuating velocity profile. Under quasistatic and athermal deformation protocols this heterogeneous plastic flow was shown to be composed of plastic events of various sizes, ranging from local quadrupolar plastic rearrangements to system spanning shear bands. In this paper, through numerical study of a 2D Lennard-Jones amorphous solid, we generalize the study of the heterogeneous dynamics of glassy materials to the finite shear rate ( [(g)\dot] \dot{{\gamma}} 1 \neq 0 and temperature case (T 1 \neq 0 . In practice, we choose an effectively athermal limit (T ∼ 0 and focus on the influence of shear rate on the rheology of the glass. In line with previous works we find that the model Lennard-Jones glass follows the rheological behavior of a yield stress fluid with a Herschel-Bulkley response of the form, s \sigma = s_Y \sigma_{{Y}}^{} + c ₁ [(g)\dot]^b \dot{{\gamma}}^{{\beta}}_{} . The global mechanical response obtained through the use of Molecular Dynamics is shown to converge in the limit [(g)\dot] \dot{{\gamma}} ? \rightarrow 0 to the quasistatic limit obtained with an energy minimization protocol. The detailed analysis of the plastic deformation at different shear rates shows that the glass follows different flow regimes. At sufficiently low shear rates the mechanical response reaches a shear-rate-independent regime that exhibits all the characteristics of the quasistatic response (finite-size effects, cascades of plastic rearrangements, yield stress, ...). At intermediate shear rates the rheological properties are determined by the externally applied shear rate and the response deviates from the quasistatic limit. Finally at higher shear the system reaches a shear-rate-independent homogeneous regime. The existence of these three regimes is also confirmed by the detailed analysis of the atomic motion. The computation of the four-point correlation function shows that the transition from the shear-rate-dominated to the quasistatic regime is accompanied by the growth of a dynamical cooperativity length scale x \xi that is shown to diverge with shear rate as x \xi μ \propto [(g)\dot]^-n \dot{{\gamma}}^{{-\nu}}_{} , with n \nu ∼ 0.2 -0.3. This scaling is compared with the prediction of a simple model that assumes the diffusive propagation of plastic events.     

Analysis of the $ {\frac{{1}}{{2}}}$+ doubly heavy baryon states with QCD sum rules

In this paper, we study the \frac12 {\frac{{1}}{{2}}} ⁺ doubly heavy baryon states W_QQ \Omega_{{QQ}}^{} and X_QQ \Xi_{{QQ}}^{} by subtracting the contributions from the corresponding \frac12 {\frac{{1}}{{2}}} ^- doubly heavy baryon states with QCD sum rules, and make reasonable predictions for their masses. Those doubly heavy baryon states may be observed at Tevatron, LHCb and PANDA.     

Single flexible and semiflexible polymers at high shear: Non-monotonic and non-universal stretching response

Using Brownian hydrodynamic simulation techniques, we study single polymers in shear. We investigate the effects of hydrodynamic interactions, excluded volume, chain extensibility, chain length and semiflexibility. The well-known stretching behavior with increasing shear rate [(g)\dot] \dot{{\gamma}} is only observed for low shear [(g)\dot] \dot{{\gamma}} < [(g)\dot]^max \dot{{\gamma}}^{{\max}}_{} , where [(g)\dot]^max \dot{{\gamma}}^{{\max}}_{} is the shear rate at maximum polymer extension. For intermediate shear rates [(g)\dot]^max \dot{{\gamma}}^{{\max}}_{} < [(g)\dot] \dot{{\gamma}} < [(g)\dot]^min \dot{{\gamma}}^{{\min}}_{} the radius of gyration decreases with increasing shear with minimum chain extension at [(g)\dot]^min \dot{{\gamma}}^{{\min}}_{} . For even higher shear [(g)\dot]^min \dot{{\gamma}}^{{\min}}_{} < [(g)\dot] \dot{{\gamma}} the chain exhibits again shear stretching. This non-monotonic stretching behavior is obtained in the presence of excluded-volume and hydrodynamic interactions for sufficiently long and inextensible flexible polymers, while it is completely absent for Gaussian extensible chains. We establish the heuristic scaling laws [(g)\dot]^max \dot{{\gamma}}^{{\max}}_{} ∼ N ^-1.4 and [(g)\dot]^min \dot{{\gamma}}^{{\min}}_{} ∼ N ^0.7 as a function of chain length N , which implies that the regime of shear-induced chain compression widens with increasing chain length. These scaling laws also imply that the chain response at high shear rates is not a universal function of the Weissenberg number Wi = [(g)\dot] \dot{{\gamma}} t \tau anymore, where t \tau is the equilibrium relaxation time. For semiflexible polymers a similar non-monotonic stretching response is obtained. By extrapolating the simulation results to lengths corresponding to experimentally studied DNA molecules, we find that the shear rate [(g)\dot]^max \dot{{\gamma}}^{{\max}}_{} to reach the compression regime is experimentally realizable.