Few-Body Systems最新文献

We consider the three-dimensional stationary Schrödinger equation deformed by Dunkl operators, and constrained to the surface of a torus. After separation of variables in toroidal coordinates, it is shown that the Schrödinger equation admits solutions in terms of Heun functions, provided the potential has a certain form. As an application, elementary solutions of bound-state type are constructed that are expressed through Heun polynomials.

The Jost function is defined as the coefficient function connecting the regular and irregular solutions of the fundamental differential equations. It is known that the zeros of the Jost function on the complex energy plane correspond to the poles of the S-matrix, which represent the complex eigenvalues of bound and resonant states. This paper reviews our recent extensions of the Jost function method to nuclear multichannel systems, specifically within the frameworks of the Hartree-Fock-Bogoliubov (HFB) theory and the Random Phase Approximation (RPA) theory (Jost-RPA method). A unitary S-matrix is derived using these extended Jost functions. By focusing on the poles of the S-matrix, we attempt to analyze and classify the resonances. We discuss three key applications: (1) the extraction of Fano parameters to analyze asymmetric line shapes in neutron scattering within the HFB framework, (2) the decomposition of the RPA strength function using eigenphase shifts, and (3) the application of the Mittag-Leffler theorem to decompose the RPA response into contributions from individual resonance poles.

We study the effects of rotation on the Landau quantization of a charged spin-1/2 particle in the presence of a spiral dislocation using the Pauli equation. The coupling between spin, magnetic field, topological defect, and rotation makes the spinor components distinct, each with its own effective angular momentum and principal quantum number. The eigenenergies contain terms related to the spin–magnetic field, topological defect, and rotation interactions, and in a limiting case, we recover the spinless result. We show that, for quantized angular velocities, the eigenenergies can become independent of spin orientation. Graphical analysis reveals that eigenenergies for the spin((-1/2)) state are higher than for spin((+1/2)), especially at stronger magnetic fields and higher angular velocities. Moreover, the magnetic field and the rotation of the reference frame produce a similar effect on the particle dynamics, shifting the radial probability density toward regions closer to the origin. This suggests that the rotational effect in this case can be regarded as a quantum analogue of the Coriolis effect. Finally, increasing the magnetic field or spiral dislocation parameter reduces the effective angular velocity magnitude while raising the eigenenergy values in the spin-orientation-independent case.

We investigate the backward-angle oscillations in elastic (^{16})O+(^{12})C scattering at (E_textrm{lab}=100) MeV by contrasting a minimal two-channel CRC model (true elastic (oplus ) elastic (alpha ) transfer) with a single-channel optical model augmented by a parity-dependent (Majorana) term. Using a joint near/far (NF) and barrier/internal (BI) decomposition together with Fourier-transform-based imaging of the decomposed amplitudes, we show how the (theta leftrightarrow pi -theta ) mixing from elastic transfer maps onto a parity-dependent elastic (S_L) and yields the backward pattern. A fixed-geometry Wigner baseline reproduces the data at forward and medium angles; the remaining backward strength is recovered either by a compact surface-peaked Majorana term in one channel or by a baseline-dependent effective elastic-transfer normalization (S_alpha ) in CRC, both enhancing the same internal–farside (I–F) branch at large angles.

We report on our new models for photoproduction and electroproduction of kaons off the proton and neutron target, focusing first on the (K^+Lambda ) channel and then extending the analysis to (Sigma ) photoproduction channels. For the proper treatment of the exchanges of higher-spin resonances, we opted for the so-called consistent formalism and in order to partially account for the unitarity corrections at the tree level, we introduced energy-dependent widths of nucleon resonances. For selecting the appropriate set of resonances, we used regularization methods known from machine learning, the Least Absolute Shrinkage Selection Operator and Ridge regression.

This study examines the dynamics of the third body in an elliptic restricted three-body problem (ERTBP) framework, taking into account perturbations from radiation pressure, oblateness, and elongation of the primary bodies, as well as disk-like structures. The objectives are to determine the positions and stability of the equilibrium points, assess how these points shift under the influence of perturbations, and evaluate the dependence of their stability on the orbital eccentricity and perturbation parameters. The ERTBP model is modified to include a radiating, oblate primary body and an elongated secondary body modeled as a finite straight segment, alongside perturbations from a surrounding disk. The system’s equations of motion are numerically solved using parameters from perturbed and classical cases. Equilibrium positions are computed over a range of eccentricities and perturbation values, and stability is analyzed using linearized equations and eigenvalue methods. In all cases, we have found three collinear ((L_1), (L_2), (L_3)) and two non-collinear ((L_4), (L_5)) equilibrium points solutions. The inclusion of radiation, oblateness, elongation using a finite straight segment, and disk perturbation systematically displaces each equilibrium point from its classical location, with the magnitude and direction of the displacement varying with the perturbation parameter. Stability analysis confirms that the collinear points remain linearly unstable under all tested conditions. Meanwhile, non-collinear points are stable under a specific condition. We investigate the stability boundary of these points as a function of orbital eccentricity and we found there is a critical range of eccentricity values within which stability is preserved.

Few-atom systems play an important role in understanding the transition from few- to many-body quantum behaviors. This work introduces a new approach for determining the energy spectra and eigenstates of small harmonically trapped single-component Bose and Fermi gases with additive two-body zero-range interactions in one spatial dimension. The interactions for bosons are the usual (delta )-function interactions while those for fermions are (delta )-function interactions that contain derivative operators. Details of the derivation and benchmarks of the numerical scheme are presented. Extensions to other systems are discussed.

We have treated the collision between two hydrogen atoms in the ground states using atomic-orbital close-coupling calculations within the impact parameter method. The cross sections for projectile excitation to 2s and 2p, (hbox {H}^-) formation in the projectile, and projectile ionization are calculated with a larger basis set than previous calculations in the energy range of 1 to 30 keV. The excitation results do not agree with experimental data. The (hbox {H}^-) formation results agree well with experimental data, and the ionization results are also acceptable.

Few-body scattering and loosely bound states in the vicinity of an isolated narrow Feshbach resonance are well described by a conceptually simple contact interaction two-channel model, where an open atomic continuum channel is coupled to a closed molecular channel. However, real systems are often characterized by the multiplicity of both continuum and molecular channels. Here we develop a systematic framework to deal with multi-channel problems within a contact interaction approximation. We demonstrate the differences and similarities of adding a molecular or atomic channel to the two-channel model. By means of direct comparison, we show that while an additional atomic channel makes loosely bound states shallower, an additional molecular channel makes them more deeply bound. This approach facilitates the study of the influence of multi-channel environments on few-body physics in a systematic manner by gradually increasing the level of complexity. Furthermore, we account for real atomic systems whose understanding can benefit from this study.

In this paper, we present the Sakata-Taketani equation within the framework of conformable derivatives. We propose conformable Lagrangian and Hamiltonian densities that incorporate both temporal and spatial conformable derivatives, we have obtained exact analytical solutions for several important physical scenarios: the free Sakata-Taketani equation in both purely temporal conformable and full space-time conformable cases, the confined Sakata-Taketani particle in an infinite potential well with conformable spatial derivatives, and systems subject to power-law external potentials. The solutions reveal how conformable derivatives modify energy spectra, alter wavefunction distributions.