Momentum-Space Probability Density of $${}^6$$ 6 He in Halo Effective Field Theory Abstract We compute the momentum-space probability density of \({}^6\) He at leading order in Halo EFT. In this framework, the \({}^6\) He nucleus is treated as a three-body problem with a \({}^4\) He core ( \(c\) ) and two valence neutrons ( \(n\) ). This requires the \(nn\) and \(n c\) t-matrices as well as a \(cnn\) force as input in the Faddeev equations. Since the \(n c\) t-matrix corresponds to an energy-dependent potential, we consider the consequent modifications to the standard normalization and orthogonality conditions. We find that these are small for momenta within the domain of validity of Halo EFT. In this regime, the \({}^6\) He probability density is regulator independent, provided the cutoff is significantly above the EFT breakdown scale.

Electromagnetic Transition Form Factor of the Nucleon $$\Delta $$ Δ (1232) in The Nonrelativistic Constituent Quark Model Abstract The study of nucleon electromagnetic form factors has long been identified as a singular source of information for conception strong interactions in the extent of quark confinement. We have performed a calculation of the helicity amplitudes and the electromagnetic transition form factors of the electromagnetic excitation in \(\Delta \) (1232) resonances. In this paper, the electromagnetic interaction for N \((938)\rightarrow \Delta (1232)\) transitions at four-momenta transfer \(0 \le \hbox {Q2}(\hbox {GeV}^\mathrm{{2}}) \le 8\) in the nonrelativistic constituent quark model calculated. In comparison with present experimental, relativistic and non-relativistic data, our results are in good agreement with the experimental and the other theoretical results, in particular of the medium-high \(\hbox {Q}^{2}\) behavior.

Exact Energy of the Two and Three-Body Interactions in the Trigonometric Three-Body Problem via Jack Polynomials Abstract The Hamiltonian of the three-body problem with two and three-body interactions of Calogero–Sutherland type written in an appropriate set of variables is shown to be a differential operator of Laplace–Beltrami \(H_{LB}\) type. Its eigenfunction is expressed then in terms of Jack Polynomials. In the case of identical distinguishable fermions, the only possible partition and its corresponding occupation state in Fock space is exhibited. In the co-moving frame with the center of mass, the exact explicit excitation energy due to interactions is given in terms of the parameters of the problem. The excitation energy due to interactions is expressed in such a way that it is possible to distinguish the excitation energy due to the pairwise interactions neglecting the three-body interaction as well as the excitation energy due to the pure three-body interactions neglecting the pairwise interactions. Different possible levels of excitation energy due to different type of interactions are explicitly written.

The Regge Trajectories and Leptonic Widths of the Vector $$\varvec{s}\bar{\varvec{s}}$$ s s ¯ Mesons Abstract The spectrum of the \(s\bar{s}\) mesons is studied performing a phenomenological analysis of the Regge trajectories defined for the excitation energies. For the \(\phi (3\,^3S_1)\) state the mass \(M(\phi (3S))=2100(20)\)  MeV and the leptonic width \(\varGamma _{ee}(\phi (3S))=0.27(2)\)  keV are obtained, while the mass of the \(2\,^3D_1\) state, \(M(\phi (2\,^3D_1))=2180(5)\)  MeV, appears to be in agreement with the mass of the \(\phi (2170)\) resonance, and its leptonic width, \(\varGamma _{ee}(2\,^3D_1)=0.20\pm 0.10\)  keV, has a large theoretical uncertainty, depending on the parameters of the flattened confining potential.

Study the Nuclear Form Factors of Low-Lying Excited States in $${}^{7}\hbox {Li}$$ 7 Li Nucleus Using the Shell Model with Skyrme Effective Interaction Abstract In the present work, the Skyrme interaction with the core polarization calculations has been used and implemented to study the inelastic electroexcitation form factor for low-lying excited states in \({}^{7}\hbox {Li}\) . In particular, the \(1/2^{-}\) (0.478 MeV) and \(7/2^{-}\) (4.630 MeV) states have been analyzed within the \(0\hbar \omega \) shell model including core-polarization effect. The present results reveal that the core-polarization calculation incorporating Skyrme type interaction for the single-particle states reproduces the longitudinal electron scattering data and predicts the diffraction minimum correctly and describes the high momentum data that has not been reported before. The measured \(B(C2{\uparrow })\) value for the \(1/2^{-}\) transition is very well described. The result of the \(7/2^{-}\) transition is close to the measured value. Transverse form factors are better described by the single-particle wave functions obtained from Hartree–Fock with Skyrme type interaction, rather than by the harmonic-oscillator wave functions.

Experimental Approach to Three-Nucleon Forces via Few-Nucleon Scattering Abstract Few-nucleon scattering offers a good opportunities to study dynamical aspects of three-nucleon forces that are momentum, spin and iso-spin dependent. In this paper experimental results of deuteron–proton elastic scattering are presented. The data are compared with state-of-the art theoretical predictions based on realistic bare nuclear potentials. Recently, our experimental study has been extended to proton– \(^3\mathrm{He}\) scattering in which the isospin \(T=3/2\) channel in 3NFs could be investigated.

Correlated Gaussians and Low-Discrepancy Sequences Abstract Within the Correlated Gaussian Method the parameters of the Gaussian basis functions are often chosen stochastically using pseudo-random sequences. We show that alternative low-discrepancy sequences, also known as quasi-random sequences, provide bases of better quality.

NSTAR 2017

Bosonic Oscillator on the de Sitter and the Anti-de Sitter Spaces Abstract In this work, we present the exact solution of the bosonic oscillator subjected to the interaction of an uniform electric field on the de Sitter and anti de Sitter spaces. In both cases, we extract the energy spectrum and the associated wave functions. For de Sitter case, the wave functions are expressed according to the Jacobi polynomial and for anti de Sitter case, the wave functions are expressed according to Romanovski’s polynomial. Finally the limiting cases are studied.

Few-Body Systems in Condensed Matter Physics Abstract This review focuses on the studies and computations of few-body systems of electrons and holes in condensed matter physics. We analyze and illustrate the application of a variety of methods for description of two- three- and four-body excitonic complexes such as an exciton, trion and biexciton in three-, two- and one-dimensional configuration spaces in various types of materials. We discuss and analyze the contributions made over the years to understanding how the reduction of dimensionality affects the binding energy of excitons, trions and biexcitons in bulk and low-dimensional semiconductors and address the challenges that still remain.