Showing papers in "Few-body Systems in 2014"
TL;DR: In this article, a unified study of nucleon and elastic and transition form factors is presented, and predictions made using a framework built upon a Faddeev equation kernel and interaction vertices that possess QCD-like momentum dependence with results obtained using a symmetry-preserving treatment of a vector vector contact-interaction.
Abstract: We present a unified study of nucleon and $${\Delta}$$
elastic and transition form factors, and compare predictions made using a framework built upon a Faddeev equation kernel and interaction vertices that possess QCD-like momentum dependence with results obtained using a symmetry-preserving treatment of a vector $${\otimes}$$
vector contact-interaction. The comparison emphasises that experiments are sensitive to the momentum dependence of the running couplings and masses in the strong interaction sector of the Standard Model and highlights that the key to describing hadron properties is a veracious expression of dynamical chiral symmetry breaking in the bound-state problem. Amongst the results we describe, the following are of particular interest: $${G_{E}^{p}(Q^{2})/G_{M}^{p}(Q^{2})}$$
possesses a zero at Q
2 = 9.5 GeV2; any change in the interaction which shifts a zero in the proton ratio to larger Q
2 relocates a zero in $${G_{E}^{n}(Q^{2})/G_M^{n}(Q^{2})}$$
to smaller Q
2; there is likely a value of momentum transfer above which $${G_{E}^{n} > G_{E}^{p}}$$
; and the presence of strong diquark correlations within the nucleon is sufficient to understand empirical extractions of the flavour-separated form factors. Regarding the $${\Delta(1232)}$$
-baryon, we find that, inter alia: the electric monopole form factor exhibits a zero; the electric quadrupole form factor is negative, large in magnitude, and sensitive to the nature and strength of correlations in the $${\Delta(1232)}$$
Faddeev amplitude; and the magnetic octupole form factor is negative so long as rest-frame P- and D-wave correlations are included. In connection with the $${N \to \Delta}$$
transition, the momentum-dependence of the magnetic transition form factor, $${G_{M}^{*}}$$
, matches that of $${G_{M}^{n}}$$
once the momentum transfer is high enough to pierce the meson-cloud; and the electric quadrupole ratio is a keen measure of diquark and orbital angular momentum correlations, the zero in which is obscured by meson-cloud effects on the domain currently accessible to experiment. Importantly, within each framework, identical propagators and vertices are sufficient to describe all properties discussed herein. Our analysis and predictions should therefore serve as motivation for measurement of elastic and transition form factors involving the nucleon and its resonances at high photon virtualities using modern electron-beam facilities.
120 citations
TL;DR: In this article, a confining, symmetry-preserving treatment of a vector ⊗ vector contact interaction at leading-order in a widely used truncation of QCD's Dyson-Schwinger equations is presented for Δ and Ω baryon elastic form factors.
Abstract: Predictions obtained with a confining, symmetry-preserving treatment of a vector ⊗ vector contact interaction at leading-order in a widely used truncation of QCD’s Dyson–Schwinger equations are presented for Δ and Ω baryon elastic form factors and the γN → Δ transition form factors. This simple framework produces results that are practically indistinguishable from the best otherwise available, an outcome which highlights that the key to describing many features of baryons and unifying them with the properties of mesons is a veracious expression of dynamical chiral symmetry breaking in the hadron bound-state problem. The following specific results are of particular interest. The Δ elastic form factors are very sensitive to mΔ. Hence, given that the parameters which define extant simulations of lattice-regularised QCD produce Δ-resonance masses that are very large, the form factors obtained therewith are a poor guide to properties of the Δ(1232). Considering the Δ-baryon’s quadrupole moment, whilst all computations produce a negative value, the conflict between theoretical predictions entails that it is currently impossible to reach a sound conclusion on the nature of the Δ-baryon’s deformation in the infinite momentum frame. Results for analogous properties of the Ω baryon are less contentious. In connection with the N → Δ transition, the Ash-convention magnetic transition form factor falls faster than the neutron’s magnetic form factor and nonzero values for the associated quadrupole ratios reveal the impact of quark orbital angular momentum within the nucleon and Δ; and, furthermore, these quadrupole ratios do slowly approach their anticipated asymptotic limits.
56 citations
TL;DR: In this paper, the authors evaluated the valence double parton distribution functions of the nucleon in the framework of a simple model, where the conservation of the longitudinal momentum is taken into account.
Abstract: Valence double parton distribution functions of the nucleon are evaluated in the framework of a simple model, where the conservation of the longitudinal momentum is taken into account. The leading-order DGLAP QCD evolution from the low quark-model scale to higher renormalization scales is carried out via the Mellin moments of the distributions. Results of the valence quark correlation function show that in general the double distributions cannot be approximated as a product of the single-particle distributions.
55 citations
TL;DR: In this paper, a trapped one-dimensional system of multicomponent spinless fermions that interact with a zero-range two-body potential was examined analytically, and it was shown that when the repulsion between particles is very large, the energy spectrum is sixfold degenerate.
Abstract: The paper examines a trapped one-dimensional system of multicomponent spinless fermions that interact with a zero-range two-body potential. We show that when the repulsion between particles is very large the system can be approached analytically. To illustrate this analytical approach we consider a simple system of three distinguishable particles, which can be addressed experimentally. For this system we show that for infinite repulsion the energy spectrum is sixfold degenerate. We also show that this degeneracy is partially lifted for finitely large repulsion for which we find and describe corresponding wave functions.
32 citations
TL;DR: In this article, the bound state solution of the Schrodinger equation with the hyperbolical potential is obtained by using supersymmetric approach by applying proper approximation scheme to deal with the centrifugal barrier.
Abstract: The bound state solution of the Schrodinger equation with the hyperbolical potential is obtained by using supersymmetric approach. By applying proper approximation scheme to deal with the centrifugal barrier, we obtain the energy eigenvalues and the corresponding wave functions are obtained in terms of generalized hypergeometric functions. Comparison of our computed numerical results with the ones obtained by findings of other methods reveals that supersymmetric approach is reliable, efficient and accurate.
32 citations
TL;DR: In this paper, the deuteron analyzing powers in dp- elastic scattering obtained at Nuclotron (JINR, Dubna) are compared with the calculations performed within relativistic multiple scattering model.
Abstract: Recent results on the deuteron analyzing powers in dp- elastic scattering obtained at Nuclotron (JINR, Dubna) are compared with the calculations performed within relativistic multiple scattering model. The data demonstrate strong deviation form the predictions at large angles in the cms. The preliminary data on the energy dependence of the cross section in the dp → ppn reaction at 150–250 MeV/nucleon for different configurations and dp elastic scattering up to 1 GeV obtained at internal target station at Nuclotron are reported. The prospects of the further few-body studies at JINR are discussed.
27 citations
TL;DR: In this paper, the entanglement in the ground states of helium and helium-like ions using an original Hylleraas expansion was examined and the von Neumann and linear entropies of the reduced density matrix were accurately computed by performing the Schmidt decomposition of the S singlet spatial wavefunctions.
Abstract: We examine the entanglement in the ground states of helium and helium-like ions using an original Hylleraas expansion. The von Neumann and linear entropies of the reduced density matrix are accurately computed by performing the Schmidt decomposition of the S singlet spatial wavefunctions. The results presented are more accurate than currently available in published literature.
27 citations
TL;DR: In this article, the spatial entanglement entropies in the helium atom were investigated by using highly correlated Hylleraas functions to represent the S-wave states, and the Schmidt-Slater decomposition method was applied to obtain eigenvalues of the one-particle reduced density matrix, from which the linear entropy and von Neumann entropy can be determined.
Abstract: In this work, we present an investigation on the spatial entanglement entropies in the helium atom by using highly correlated Hylleraas functions to represent the S-wave states. Singlet-spin 1sns
1
S
e states (with n = 1 to 6) and triplet-spin 1sns
3
S
e states (with n = 2 to 6) are investigated. As a measure on the spatial entanglement, von Neumann entropy and linear entropy are calculated. Furthermore, we apply the Schmidt–Slater decomposition method on the two-electron wave functions, and obtain eigenvalues of the one-particle reduced density matrix, from which the linear entropy and von Neumann entropy can be determined.
23 citations
TL;DR: In this paper, the authors review experiments and phenomenology of the near-threshold production of ground-state mesons in the few-body final states as for example: nucleus-meson and nucleon-nucleon bound states, and report on the status of the search of the mesic nuclei.
Abstract: During the last decade large samples of data have been collected on the production of the ground-state pseudoscalar mesons in collisions of proton or deuteron beam with hydrogen or deuterium target. These measurements have been performed in the vicinity of the kinematical threshold for meson production where only a few partial waves in both initial and final state are expected to contribute to the production process. This simplifies significantly the interpretation of the data, yet still appears to be challenging due to the three or four particle final state systems with a complex hadronic potential. We review experiments and phenomenology of the near threshold production of the ground-state mesons in the few-body final states as for example: nucleus-meson and nucleon-nucleon-meson, and report on the status of the search of the mesic-nuclei (a meson-nucleus bound states). Experimental advantages of measurements close to the kinematical threshold are discussed, and general features of the production mechanism of the η and η′ mesons in the nucleon-nucleon collisions are presented emphasising results of measurements of spin and isospin dependence of the production cross sections.
23 citations
TL;DR: An introductory to generalized parton distributions (GDPs) is given in this article, which emphasizes their spectral property and its uses as well as the equivalence of various GDP representations.
Abstract: An introductory to generalized parton distributions (GDPs) is given which emphasizes their spectral property and its uses as well as the equivalence of various GDP representations. Furthermore, the status of the theory and phenomenology of hard exclusive processes is shortly reviewed.
22 citations
TL;DR: In this article, the Stochastic Variational Method with an Explicitly Correlated Gaussian basis was used to calculate the energies of systems comprised of N = 2-8 bosons interacting with various potentials.
Abstract: The energies of systems comprised of N = 2–8 bosons interacting with various potentials are calculated using the Stochastic Variational Method with an Explicitly Correlated Gaussian basis. Besides the energies, particle–particle distances and correlation functions are also calculated and structural properties are discussed.
TL;DR: In this article, a four-body theoretical study of the single charge transfer process in collision of energetic alpha ions with helium atoms in their ground states is presented, which utilizes the Coulomb-Born distorted wave approximation with correct boundary conditions to calculate the single-electron capture differential and integral cross sections.
Abstract: A four-body theoretical study of the single charge transfer process in collision of energetic alpha ions with helium atoms in their ground states is presented. The model utilizes the Coulomb–Born distorted wave approximation with correct boundary conditions to calculate the single-electron capture differential and integral cross sections. The influence of the dynamic and static electron correlations on the capture probability is investigated. The results of the calculations are compared with the recent experimental measurements for differential cross sections and with the other theoretical manipulations. The results for scattering at extreme forward angles are in good agreement with the experimental measurements, but in other scattering angles the agreement is poor. However, the present four-body results for integral cross sections are in excellent agreement with the experimental data.
TL;DR: Navratil et al. as discussed by the authors used a translationally invariant finite harmonic oscillator basis to calculate the lightest Λ hypernuclei and showed that the model can be used for many-body systems with strangeness.
Abstract: We report on a novel ab initio approach for nuclear few- and many-body systems with strangeness. Recently, we developed a relevant no-core shell model technique (Navratil et al. in J Phys G 36:083101, 2009) which we successfully applied in first calculations of the lightest Λ hypernuclei. The use of a translationally invariant finite harmonic oscillator basis allows us to employ large model spaces, compared to traditional shell model calculations, and use realistic nucleon–nucleon and nucleon–hyperon interactions [such as those derived from EFT (Polinder et al. in Nucl Phys A 779:244, 2006)]. We discuss formal aspects of the methodology, show first demonstrative results for Λ3H, Λ4H and 4ΛHe, and give outlook.
TL;DR: In this paper, the authors consider the problem of quantum mechanical few-body systems and suggest possible approaches to this line of research using some simple, yet non-trivial, examples.
Abstract: The study of quantum mechanical few-body systems is a century old pursuit relevant to countless subfields of physics. While the two-body problem is generally considered to be well-understood theoretically and numerically, venturing to three or more bodies brings about complications but also a host of interesting phenomena. In recent years, the cooling and trapping of atoms and molecules has shown great promise to provide a highly controllable environment to study few-body physics. However, as is true for many systems where few-body effects play an important role the few-body states are not isolated from their many-body environment. An interesting question then becomes if or (more precisely) when we should consider few-body states as effectively isolated and when we have to take the coupling to the environment into account. Using some simple, yet non-trivial, examples I will try to suggest possible approaches to this line of research.
TL;DR: In this article, the authors analyze chiral interactions to N2LO in the light of proton-proton and neutronproton scattering data published from 1950 to 2013 and discuss under which conditions the chiral constants can be extracted.
Abstract: We analyze chiral interactions to N2LO in the light of proton–proton and neutron–proton scattering data published from 1950 to 2013 and discuss under which conditions the chiral constants can be extracted.
TL;DR: In this paper, the modified Schrodinger equation with a minimal length is considered under a Cusp potential which includes the exponential interaction, and exact analytical solutions of the problem are reported and thereby the scattering states as well as the corresponding transmission and reflection coefficients are reported.
Abstract: The modified Schrodinger equation with a minimal length is considered under a Cusp potential which includes the exponential interaction. Next, exact analytical solutions of the problem are reported and thereby the scattering states as well as the corresponding transmission and reflection coefficients are reported.
TL;DR: In this paper, the authors apply the supersymmetric model of E. Cartan to the pseudoscalar meson decay into two photons, and show that dark matter is interpreted as matter emitting photons in a different triality sector than that of electromagnetic probes in our world.
Abstract: We apply the supersymmetric model of E. Cartan to the pseudoscalar meson decay into two photons, \({\pi_0\to\gamma\gamma}\), \({\eta\to\gamma\gamma}\) and \({\eta'\to\gamma\gamma}\). In the book of E. Cartan published in 1966, Dirac spinors t(A, B) and t(C, D) and vector fields E and E′ were introduced and five supersymmetric transformations G23, G12, G13, G123 and G132 were considered. The Pauli spinor is treated as a quaternion and the Dirac spinor is treated as an octonion. In the pseudoscalar meson decay, when the two final vector fields belong to the same group (EE or E′E′), we call the diagram rescattering diagram. When they belong to different groups (EE′), the diagram is called twisted diagram. Assuming the triality selection rules of octonions, dark matter is interpreted as matter emitting photons in a different triality sector than that of electromagnetic probes in our world.
TL;DR: In this paper, the expected errors of nuclear matrix elements coming from the uncertainty on the NN interaction were estimated using a coarse-grained interaction fitted to NN scattering data, with several prescriptions for the long part of the interaction.
Abstract: We estimate the expected errors of nuclear matrix elements coming from the uncertainty on the NN interaction. We use a coarse grained interaction fitted to NN scattering data, with several prescriptions for the long-part of the interaction, including one pion exchange and chiral two-pion exchange interactions.
TL;DR: In this paper, the effect and role of sea quarks and gluons, and their contributions to the parton distributions and the structure functions of 3====== He and 3====== H mirror nuclei are analyzed.
Abstract: The valence quark exchange (QE) model for the nuclear system and the constituent quark (CQ) model in which the quarks are assumed to be the complex objects, are used to calculate the parton distributions and the structure functions (SF) of 3
He and 3
H mirror nuclei. The effect and the role of sea quarks and gluons, and their contributions to the SF of 3
He and 3
H nuclei are analyzed. Specifically, for small x regions a more “realistic” result is found with respect to our previous works, in which only the valence quarks have been considered. By using the DGLAP evolution equations, the resulting parton distributions and SF are evolved to the high-energy scales and compared with available data. Finally, the ratios of 3
He to 3
H nuclei SF with the isospin symmetry assumption is compared to the results of the deep inelastic electron experiments on the 3
He and 3
H nuclei, especially, those which have been extracted from the kinematic region of the proposed 11 GeV upgraded beam experiment of Jefferson laboratory, and a reasonable agreement is found.
TL;DR: In this article, the spin dependent generalized parton distributions (GPDs) of 3He nuclei have been analyzed in the context of coherent deeply virtual Compton scattering (DVCS) off 3He.
Abstract: Recently, coherent deeply virtual Compton scattering (DVCS) off 3He nuclei has been proposed to access the neutron generalized parton distributions (GPDs). In impulse approximation (IA) studies, it has been shown, in particular, that the sum of the two leading twist, quark helicity conserving GPDs of 3He, H and E, at low momentum transfer, is dominated by the neutron contribution, so that 3He is very promising for the extraction of the neutron information. Nevertheless, such an extraction could be not trivial. A technique, able to take into account the nuclear effects included in the IA analysis in the extraction procedure, has been therefore developed. In this work, the IA calculation of the spin dependent GPD \({\tilde H}\) of 3He is presented for the first time. This quantity is found to be largely dominated, at low momentum transfer, by the neutron contribution, which could be extracted using arguments similar to the ones previously proposed for the other GPDs. The known forward limit of the IA calculation of \({\tilde H}\), yielding the polarized parton distributions of 3He, is correctly recovered. The knowledge of the GPDs H, E and \({\tilde H}\) of 3He will allow now the evaluation of the cross section asymmetries which are relevant for coherent DVCS off 3He at Jefferson Lab kinematics, an important step towards the planning of possible experiments.
TL;DR: In this article, the leading-twist distribution amplitude for the longitudinal rho-meson was studied using QCD sum rules with nonlocal condensates and a spectral density which includes next-to-leading order radiative corrections.
Abstract: The leading-twist distribution amplitude for the longitudinal rho-meson was studied using QCD Sum Rules with nonlocal condensates and a spectral density which includes next-to-leading order radiative corrections. The obtained profile is compared with results from standard QCD sum rules, lattice QCD, holographic QCD, a light-front quark model, and the instanton liquid model. Preliminary estimates for the first two moments of the transverse ρ-meson distribution amplitude are also given.
TL;DR: In this article, the binding energies of light hypernuclei were predicted based on Faddeev- and Yakubovsky equations in momentum space, and the results for the chiral interactions at next-to-leading order.
Abstract: We present predictions for the binding energies of the light hypernuclei \({^3_\Lambda{\rm H},\, ^4_\Lambda{\rm He}}\) and \({^4_\Lambda{\rm H}}\) based on Faddeev- and Yakubovsky equations in momentum space. We discuss how such results can help to test the existing hyperon–nucleon (Y N) potential models and effective field theory based Y N interactions. Especially, we show results for the chiral interactions at next-to-leading order.
TL;DR: In this paper, the analysis at finite momentum transfers in a Poincare covariant framework is outlined and a generalized eikonal approach to include final state interaction is presented. And the possibility of improving the description of the semi-inclusive deep inelastic electron scattering off polarized 3He, that provides information on the neutron single spin asymmetries, is illustrated.
Abstract: The possibility of improving the description of the semi-inclusive deep inelastic electron scattering off polarized 3He, that provides information on the neutron single spin asymmetries, is illustrated. In particular, the analysis at finite momentum transfers in a Poincare covariant framework is outlined and a generalized eikonal approach to include final state interaction is presented.
TL;DR: The elastic scattering angular distribution of 6He projectile scattered from 6Li target nucleus at incident energy of 17.90 MeV has been analyzed by using microscopic density distributions for both 6He and 6Li.
Abstract: The elastic scattering angular distribution of 6He projectile scattered from 6Li target nucleus at incident energy of 17.90 MeV has been analyzed by using microscopic density distributions for both 6He and 6Li. For the first-time, no-core shell model and no-core full configuration density distributions have simultaneously been used in order to obtain the real potentials of the double folding model. The results have been compared with the findings obtained by using phenomenological approach as well as the experimental data. These comparisons provide information about the similarities and differences of the models used in the calculations.
TL;DR: In this article, nuclear polarization corrections in muonic atoms can be formally connected to inelastic response functions of a nucleus, and the point-nucleon approximation is discussed.
Abstract: We illustrate how nuclear polarization corrections in muonic atoms can be formally connected to inelastic response functions of a nucleus. We first discuss the point-nucleon approximation and then include finite-nucleon-size corrections. As an example, we compare our ab-initio calculation of the third Zemach moment in μ 4He+ to previous phenomenological results.
TL;DR: In this paper, a generalized pseudospectral method was used to obtain improved eigenvalues, eigenfunctions and energy variations with respect to parameters in the hyperbolic potential.
Abstract: Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary n, l quantum states by solving the relevant non-relativistic Schrodinger equation allowing a non-uniform, optimal spatial discretization. Eigenvalues accurate up to tenth decimal place are reported for a large range of potential parameters; thus covering a wide range of interaction. Excellent agreement with available literature results is observed in all occasions. Special attention is paid for higher states. Some new states are given. Energy variations with respect to parameters in the potential are studied in considerable detail for the first time.
TL;DR: In this article, the elastic and π transition form factors of the pion along with its usual static observables are calculated within a light-front field approach to the constituent quark model.
Abstract: The elastic and γ → π transition form factors of the pion along with its usual static observables are calculated within a light-front field approach to the constituent quark model. The focus of this exercise in a simple model is on a unified description of all observables with one singly parametrized light-front wave function to detect possible discrepancies in experimental data, in particular the contentious large momentum-squared data on the transition factor as reported by BaBar and Belle. We also discuss the relation of a small to vanishing pion charge radius with an almost constant pion distribution amplitude and compare our results with those obtained in a holographic light-front model.
TL;DR: In this article, the authors compare three different methods in practical calculations of inelastic cross sections, that is, treating the initial and final states as pure continuum states on the real energy axis, discretizing the continuum states with a box boundary condition, and complex rotation of the hamiltonian (complex scaling method).
Abstract: Bremsstrahlung emission in collisions between charged nuclei is equivalent to nuclear gamma decay between continuum states. The way the continuum spectrum can be treated is not unique, and efficiency and accuracy of cross section calculations depend on the chosen method. In this work we describe, relate, and compare three different methods in practical calculations of inelastic cross sections, that is, by (i) treating the initial and final states as pure continuum states on the real energy axis, (ii) discretizing the continuum states on the real energy axis with a box boundary condition, and (iii) complex rotation of the hamiltonian (complex scaling method). The electric quadrupole transitions, 2+ → 0+ and 4+ → 2+, in α + α scattering are taken as an illustration.
TL;DR: In this paper, the Wigner distribution of unpolarized quarks in a longitudinally polarized nucleon was studied in light-front quark models and the quark orbital angular momentum was calculated using a Fourier transform in the transverse space of the generalized transverse momentum dependent parton distributions.
Abstract: We discuss the quark Wigner distributions which represent the quantum-mechanical analogues of the classical phase-space distributions. These functions can be obtained through a Fourier transform in the transverse space of the generalized transverse momentum dependent parton distributions, which encode the most general one-body information of partons in momentum space. In particular, we present a study within light-front quark models. The quark orbital angular momentum is also obtained from the phase-space average of the orbital angular momentum operator weighted with the Wigner distribution of unpolarized quark in a longitudinally polarized nucleon. The corresponding results calculated within different light-front quark models are compared with alternative definitions of the quark orbital angular momentum as given in terms of generalized parton distributions and transverse momentum dependent parton distributions.
TL;DR: In this article, the authors use an S-wave toy model for the two-nucleon system to show that the implicit renormalization of a contact theory matches the explicit renormalisation through a flow equation which integrates out the high momentum components.
Abstract: We use an S-wave toy model for the two-nucleon system to show that the implicit renormalization of a contact theory matches the explicit renormalization through a flow equation which integrates out the high momentum components. By fitting the low-momentum interaction with a new contact theory, we show that the running of the contact strengths in both original and fitted contact theories match over a wide cutoff range.