Showing papers in "Few-body Systems in 2012"

The Infrared Behaviour of the Pure Yang–Mills Green Functions

Abstract: We review the infrared properties of the pure Yang–Mills correlators and discuss recent results concerning the two classes of low-momentum solutions for them reported in literature, i.e. decoupling and scaling solutions. We will mainly focus on the Landau gauge and pay special attention to the results inferred from the analysis of the Dyson–Schwinger equations of the theory and from “quenched” lattice QCD. The results obtained from properly interplaying both approaches are strongly emphasized.

Spectrum of Hadrons with Strangeness

Abstract: We describe a calculation of the spectrum of strange and nonstrange hadrons that simul- taneously correlates the dressed-quark-core masses of meson and baryon ground- and excited-states within a single framework. The foundation for this analysis is a symmetry-preserving Dyson-Schwinger equation treatment of a vector×vector contact interaction. Our results exemplify and highlight the deep impact of dynamical chiral symmetry breaking on the hadron spectrum: an accurate description of the meson spectrum entails a similarly successful prediction of the spectrum of baryons, including those with strangeness. The analysis also provides numerous insights into baryon structure. For exam- ple, that baryon structure is largely flavour-blind, the first radial excitation of ground-state baryons is constituted almost entirely from axial-vector diquark correlations, and DCSB is the foundation for

Quarkonium Physics at a Fixed-Target Experiment using the LHC Beams

Abstract: We outline the many quarkonium-physics opportunities offered by a multi-purpose fixed-target experiment using the p and Pb Large Hadron Collider (LHC) beams extracted by a bent crystal. This provides an integrated luminosity of 0.5 fb−1 per year on a typical 1 cm-long target. Such an extraction mode does not alter the performance of the collider experiments at the LHC. With such a high luminosity, one can analyse quarkonium production in great details in pp, pd and pA collisions at $${\sqrt{s_{NN}}\simeq 115}$$ GeV and at $${\sqrt{s_{NN}}\simeq 72}$$ GeV in PbA collisions. In a typical pp (pA) run, the obtained quarkonium yields per unit of rapidity are 2–3 orders of magnitude larger than those expected at RHIC and about, respectively, 10(70) times larger than for ALICE. In PbA, they are comparable. By instrumenting the target-rapidity region, the large negative-x F domain can be accessed for the first time, greatly extending previous measurements by Hera-B and E866. Such analyses should help resolving the quarkonium-production controversies and clear the way for gluon PDF extraction via quarkonium studies. The nuclear target-species versatility provides a unique opportunity to study nuclear matter and the features of the hot and dense matter formed in PbA collisions. A polarised proton target allows the study of transverse-spin asymmetries in J/ψ and $${\Upsilon}$$ production, providing access to the gluon and charm Sivers functions.

Arbitrary ℓ -State Solutions of the Hyperbolical Potential by the Asymptotic Iteration Method

Abstract: The asymptotic iteration method is employed to calculate the any l-state solutions of the Schrodinger equation with the hyperbolical potential by proper approximation to the centrifugal term. Energy eigenvalues and corresponding eigenfunction are obtain analytically. The energy eigenvalues are computed numerically for some values of l and n. Our results are in good agreement with the findings of other methods for short potential range. A straightforward extension to the s-wave (l = 0) and σ o = 1 cases are also presented.

Solution of the Dirac Equation with Position-Dependent Mass for q-Parameter Modified Pöschl–Teller and Coulomb-like Tensor Potential

Abstract: In this research, we have been obtained the Dirac equation for q-parameter modified Poschl–Teller potential including a Coulomb-like tensor interaction with arbitrary spin-orbit coupling quantum number by choosing a position-dependent mass. The energy eigenvalues equation and the corresponding unnormalized wave functions have been obtained. The Nikiforov-Uvarov method has been used in the calculations.

Spectrum of Dirac Equation Under Deng–Fan Scalar and Vector Potentials and a Coulomb Tensor Interaction by SUSYQM

Abstract: We give the approximate analytic solutions of the Dirac equation for the Deng Fan potential. After a Pekeris-type approximation, we bring the problem into a Schrodinger-like equation and obtain the spectrum of the system via supersymmetry quantum mechanics. Some numerical comments are given on the energy spectrum.

Exact Solutions of the Klein-Gordon Equation with Position-Dependent Mass for Mixed Vector and Scalar Kink-Like Potentials

Abstract: The relativistic problem of spinless particles with position-dependent mass subject to kink-like potentials (~tanh αx) is investigated. By using the basic concepts of the supersymmetric quantum mechanics formalism and the functional analysis method, we solve exactly the position-dependent effective mass Klein–Gordon equation with the vector and scalar kink-like potential coupling, and obtain the bound state solutions in the closed form. It is found that in the presence of position-dependent mass there exists the symmetry that the discrete positive energy spectra and negative energy spectra are symmetric about zero energy for the case of a mixed vector and scalar kink-like potential coupling, and in the presence of constant mass this symmetry only appears for the cases of a pure scalar kink-like potential coupling or massless particles.

Solutions of Dirac Equation for Generalized Hyperbolical Potential Including Coulomb-Like Tensor Potential with Spin Symmetry

Abstract: We solved the Dirac equation for the generalized hyperbolical potential including a Coulomb-like tensor potential under spin symmetry with spin-orbit quantum number k. We used the parametric generalization of the Nikiforov–Uvarov method to obtain the energy eigenvalue and the unnormalized wave function.

Relativistic Morse Potential and Tensor Interaction

Abstract: In this paper, by applying the Pekeris approximation, we present solutions of the Dirac equation for the Morse potential including a Coulomb-like tensor potential with arbitrary spin-orbit coupling number κ under spin and pseudospin symmetry limits. The generalized parametric Nikiforov–Uvarov method is used to obtain energy eigenvalues and corresponding eigenfunctions in their closed forms. We show that tensor interaction removes degeneracies between spin and pseudospin doublets. Some numerical results are given, too.

Centrality, Rapidity, and Transverse-Momentum Dependence of Gluon Shadowing and Antishadowing on J/ψ Production in dAu Collisions at {\sqrt{s} = 200} GeV

Abstract: We have carried out a wide study of shadowing and antishadowing effects on J/ψ production in dAu collisions at $${\sqrt{s_{N N}} = 200}$$ GeV. We have studied the effects of three different gluon nPDF sets, using the exact kinematics for a 2 → 2 process, namely g + g → J/ψ + g as expected from LO pQCD. We have computed the rapidity dependence of R CP and R dAu for the different centrality classes of the PHENIX data. For mid rapidities, we have also computed the transverse-momentum dependence of the nuclear modification factor, which cannot be predicted with the usual 2 → 1 simplified kinematics. All these observables have been compared to the PHENIX data in dAu collisions.

Few-Body Aspects of Hypernuclear Physics

Abstract: Recent development in the study of the structure of light Λ and double Λ hypernuclei is reviewed from the view point of few-body problems and interactions between the constituent particles. In the study the present author and collaborators employed Gaussian expansion method for few-body calculations; the method has been applied to many kinds of few-body systems in the fields of nuclear physics and exotic atomic/molecular physics. We reviewed the following subjects studied using the method: (1) Precise three- and four-body calculations of $${^7_{\Lambda}{\rm He}}$$ , $${^7_{\Lambda}{\rm Li}}$$ , $${^7_{\Lambda}{\rm Be}}$$ , $${^8_{\Lambda}{\rm Li}}$$ , $${^8_{\Lambda}{\rm Be}}$$ , $${^9_{\Lambda}{\rm Be}}$$ , $${^{10}_{\Lambda}{\rm Be}}$$ , $${^{10}_{\Lambda}{\rm B}}$$ and $${^{13}_{\Lambda}{\rm C}}$$ provide important information on the spin structure of the underlying Λ N interaction by comparing the calculated results with the recent experimental data by γ-ray hypernuclear spectroscopy. (2) The Λ-Σ coupling effect was investigated in $${^4_{\Lambda}{\rm H}}$$ and $${^4_{\Lambda}{\rm He}}$$ on the basis of the N + N + N + Λ (Σ) four-body model. (3) A systematic study of double-Λ hypernuclei and the Λ Λ interaction, based on the NAGARA event data ( $${^6_{\Lambda\Lambda}{\rm He}}$$ ), was performed within the α + x + Λ + Λ cluster model (x = n, p, d, t,3He and α) and α + α + n + Λ + Λ cluster model, (4) The Demachi-Yanagi event was interpreted as observation of the 2+ state of $${^{10}_{\Lambda \Lambda}{\rm Be}}$$ , (5) The Hida event was interpreted as observation of the ground state of $${^{11}_{\Lambda \Lambda}{\rm Be}}$$ .

Exact Solutions of the Klein–Gordon Equation for Spherically Asymmetrical Singular Oscillator

Abstract: The relativistic Klein–Gordon equation with equal scalar and vector spherically asymmetrical singular oscillators is solved using the asymptotic iteration method. The energy eigenvalues equation and the corresponding wave functions are obtain explicitly. It was found that the asymptotic iteration method provides the closed-forms for the energy eigenvalues as well as the eigenfunctions. The non-relativistic limit \({c \rightarrow \infty}\) of the energy spectrum, where c is the speed of light, have also been discussed.

Four-Nucleon Scattering with a Correlated Gaussian Basis Method

Abstract: Elastic-scattering phase shifts for four-nucleon systems are studied in an ab-initio type cluster model in order to clarify the role of the tensor force and to investigate cluster distortions in low energy d+d and t+p scattering. In the present method, the description of the cluster wave function is extended from (0s) harmonic-oscillator shell model to a few-body model with a realistic interaction, in which the wave functions of the subsystems are determined with the Stochastic Variational Method. In order to calculate the matrix elements of the four-body system, we have developed a Triple Global Vector Representation method for the correlated Gaussian basis functions. To compare effects of the cluster distortion with realistic and effective interactions, we employ the AV8′ potential + a three nucleon force as a realistic interaction and the Minnesota potential as an effective interaction. Especially for 1 S 0, the calculated phase shifts show that the t+p and h+n channels are strongly coupled to the d+d channel for the case of the realistic interaction. On the contrary, the coupling of these channels plays a relatively minor role for the case of the effective interaction. This difference between both potentials originates from the tensor term in the realistic interaction. Furthermore, the tensor interaction makes the energy splitting of the negative parity states of 4He consistent with experiments. No such splitting is however reproduced with the effective interaction.

Charmonium States in QCD-Inspired Quark Potential Model Using Gaussian Expansion Method

Abstract: We investigate the mass spectrum and electromagnetic processes of charmonium system with the nonperturbative treatment for the spin-dependent potentials, comparing the pure scalar and scalar-vector mixing linear confining potentials. It is revealed that the scalar-vector mixing confinement would be important for reproducing the mass spectrum and decay widths, and therein the vector component is predicted to be around 22 %. With the state wave functions obtained via the full-potential Hamiltonian, the long-standing discrepancy in M1 radiative transitions of J/ψ and ψ′ are alleviated. This work also provides an inspection and suggestion for the possible cc states among the copious higher charmonium-like states. Particularly, the newly observed X(4160) and X(4350) are found in the charmonium family mass spectrum as M(21 D 2) = 4164.9 MeV and M(33 P 2) = 4352.4 MeV, which strongly favor the J PC = 2−+, 2++ assignments respectively. The corresponding radiative transitions, leptonic and two-photon decay widths have been also predicted theoretically for the further experimental search.

Exact Solutions of the Klein-Gordon Equation with Hylleraas Potential

Abstract: We present the exact solution of the Klein–Gordon with Hylleraas Potential using the Nikiforov–Uvarov method. We obtain explicitly the bound state energy eigenvalues and the corresponding eigen function for s-wave. The wave functions obtained are expressed in terms of Jacobi polynomials.

Calculation of the Oscillator Strength for the Klein–Gordon Equation with Tietz Potential

Abstract: The Klein–Gordon equation under equal scalar and vector potentials is solved for the Tietz potential in D-dimensions by using supersymmetric quantum mechanics. The spectrum of the system is numerically calculated and the oscillator strength is determined and discussed in terms of parameters of the system.

Relativistic New Yukawa-Like Potential and Tensor Coupling

Abstract: We approximately solve the Dirac equation for a new suggested generalized inversely quadratic Yukawa potential including a Coulomb-like tensor interaction with arbitrary spin-orbit coupling quantum number \({\kappa}\) . In the framework of the spin and pseudospin (p-spin) symmetry, we obtain the energy eigenvalue equation and the corresponding eigenfunctions, in closed form, by using the parametric Nikiforov–Uvarov method. The numerical results show that the Coulomb-like tensor interaction, −T/r, removes degeneracies between spin and p-spin state doublets. The Dirac solutions in the presence of exact spin symmetry are reduced to Schrodinger solutions for Yukawa and inversely quadratic Yukawa potentials.

Entanglement in Hooke’s Law Atoms: an Effect of the Dimensionality of the Space

Abstract: We study a singlet ground-state of the D-dimensional Hooke’s law model for D = 1, 2, 3. We explore an effect of the dimensionality of the space D on the entanglement in the whole range of the repulsive interaction. Among other features, it is found that there exists a critical interaction strength above which for D = 3 the amount of entanglement contained in the singlet ground-state becomes larger than that for D = 2.

Fermion Flavors in Quaternion Basis and Infrared QCD

Abstract: I analyze the lattice simulation data of the Domain Wall Fermion in quaternion basis. As pointed out by Atiyah and Ward, the minimum action solution for SU(2) Yang–Mills fields in Euclidean 4-space correspond, via Penrose twistor transform, to algebraic bundles on the complex projective 3-space. Assuming dominance of correlation between the fermions on the domain walls via exchange of instantons, I extract parameters necessary for defining gauge fields of Atiyah–Ward ansatz. The QCD effective coupling in the infrared and the relation between the number of flavors and the infrared fixed point is investigated. Consequence of this lepton flavor assignment to phenomenology of baryons is also discussed.

Quantum Correlations of a Few Bosons within a Harmonic Trap

Abstract: We study two one-dimensional atomic models composed of identical bosons trapped in a harmonic trap: one model with a short-range interaction potential and another model with a long-range one, and compare their entanglement features. Properties of the ground-states of two-, three-, and four-particle systems are explored.

Dimers, Effective Interactions, and Pauli Blocking Effects in a Bilayer of Cold Fermionic Polar Molecules

Abstract: We consider a bilayer setup with two parallel planes of cold fermionic polar molecules when the dipole moments are oriented perpendicular to the planes. The binding energy of two-body states with one polar molecule in each layer is determined and compared to various analytic approximation schemes in both coordinate- and momentum-space. The effective interaction of two bound dimers is obtained by integrating out the internal dimer bound state wave function and its robustness under analytical approximations is studied. Furthermore, we consider the effect of the background of other fermions on the dimer state through Pauli blocking, and discuss implications for the zero-temperature many-body phase diagram of this experimentally realizable system.

Approximate Relativistic Bound State Solutions of the Tietz–Hua Rotating Oscillator for Any κ -State

Abstract: Approximate analytical solutions of the Dirac equation with Tietz–Hua (TH) potential are obtained for arbitrary spin–orbit quantum number κ using the Pekeris approximation scheme to deal with the spin–orbit coupling terms κ(κ ± 1)r −2. In the presence of exact spin and pseudo-spin symmetric limitation, the bound state energy eigenvalues and associated two-component wave functions of the Dirac particle moving in the field of attractive and repulsive TH potential are obtained using the parametric generalization of the Nikiforov–Uvarov method. The cases of the Morse potential, the generalized Morse potential and non-relativistic limits are studied.

Erratum to: Testing the Concept of Quark–Hadron Duality with the ALEPH τ Decay Data

Abstract: 0.301262, 0.453421, 0.555401, 0.651373, 0.721687. Equations (45), (47 )a nd (52) of the article now become αs(m 2 )|NLO = 0.337 ± 0.016exp ± 0.032th αs(m 2 )|N2LO = 0.321 ± 0.016exp ± 0.008th αs(m 2 )| N3LO = 0.313 ± 0.014exp ± 0.004th αs(m 2 )|N4LO = 0.308 ± 0.014exp ± 0.002th, (45)

Any J-State Solution of the Duffin–Kemmer–Petiau Equation for a Vector Deformed Woods–Saxon Potential

Abstract: By using the Pekeris approximation, the Duffin–Kemmer–Petiau (DKP) equation is investigated for a vector deformed Woods–Saxon (dWS) potential. The parametric Nikiforov–Uvarov (NU) method is used in calculations. The approximate energy eigenvalue equation and the corresponding wave function spinor components are calculated for any total angular momentum J in closed form. The exact energy equation and wave function spinor components are also given for the J = 0 case. We use a set of parameter values to obtain the numerical values for the energy states with various values of quantum levels (n, J) and potential’s deformation constant q and width R.

Solutions of the Two-Body Salpeter Equation Under an Exponential Potential for Any l State

Abstract: The two-body Salpeter equation is analytically solved for an interaction of exponential form. We see that after using appropriate approximations, the problem appears as the well-known Morse potential whose solutions are already known from the supersymmetry quantum mechanics. The results are useful in some branches of physics and in particular in dealing with heavy quark systems. The solutions are reported for any l.

Analytical Treatment of a Three-Electron-Quantum Dot Under Rashba Spin-Orbit Interaction

Abstract: Bearing in mind the wide applications of quantum dots in modern technology, we theoretically investigate a three-electron-quantum dot in the presence of Rashba spin–orbit interaction by an analytical methodology. Using the Jacobi transformations as well as the hyperspherical coordinates; we separate the Hamiltonian in terms of center of mass and relative terms and thereby calculate the basic ingredients of such systems, i.e. the wavefunction and the energy spectra. We see that in some special cases, the solutions appear in the form of Bessel functions.

Different Methods for the Two-Nucleon T-Matrix in the Operator Form

Abstract: We compare three methods to calculate the nucleon–nucleon t-matrix based on the three-dimensional formulation of Golak et al. (Phys Rev C 81:034006, 2010). In the first place we solve a system of complex linear inhomogeneous equations directly for the t-matrix. Our second method is based on iterations and a variant of the Lanczos algorithm. In the third case we obtain the t-matrix in two steps, solving a system of real linear equations for the k-matrix expansion coefficients and then solving an on-shell equation, which connects the scalar coefficients of the k- and t-matrices. A very good agreement among the three methods is demonstrated for selected nucleon–nucleon scattering observables using a chiral next-to-next-to-leading-order neutron–proton potential. We also apply our three-dimensional framework to the demanding problem of proton–proton scattering, using a corresponding version of the nucleon–nucleon potential and supplementing it with the (screened) Coulomb force, taken also in the three-dimensional form. We show converged results for two different screening functions and find a very good agreement with other methods dealing with proton–proton scattering.

Complex-Scaling Calculations for Doubly Excited Resonances in Ps− Interacting with Screened Coulomb (Yukawa) Potentials

Abstract: We have investigated the effect of screened Coulomb potentials on the high-lying doubly excited resonance states of the positronium negative ion in the framework of complex-scaling method. Highly correlated wave functions in Hylleraas coordinates are used. The resonance parameters below the Ps (2s2S) and Ps (3s2S) thresholds, for various screening parameters, are reported.

Spin symmetry in the relativistic q-deformed morse potential

Abstract: In this paper, we investigate the spin symmetry case of a spin\({-\frac{1}{2}}\) particle governed by a q-deformed Morse potential by presenting an approximate bound-state solutions of the Dirac equation with the spin-orbit coupling term for spin symmetry vector and scalar q-deformed Morse potential within framework of the Pekeris approximation. The relativistic energy levels are obtained using the Nikiforov–Uvarov (NU) method and the two-components spinor wave functions are obtain in terms of the Jacobi polynomials. It is found that there exist only positive-energy for the bound states of some diatomic molecules under spin symmetry.

A short introduction to spallation reactions

Abstract: Spallation reactions, as well as the standard theoretical tool for their study, namely the intra-nuclear cascade (INC) + evaporation model, are briefly introduced. The theoretical foundations and the domain of validity of the INC model are discussed in some detail.