Few-Body Systems最新文献

We derive exact analytical solutions to the Schrödinger equation featuring a dual-scale potential, namely, a blend of a van der Waals (vdW) potential and an isotropic harmonic potential. The asymptotic behaviors of these solutions as (rrightarrow 0) and (rrightarrow infty ) are also elucidated. These results are obtained through the approach we recently developed [arXiv: 2207.09377]. Using our results, we further calculate the s-wave and p-wave energy spectrums of two particles confined in an isotropic harmonic trap, with vdW inter-particle interaction. We compare our exact results and the ones given by the zero-range pseudopotential (ZRP) approaches, with either energy-dependent or energy-independent s-wave scattering length (a_s) or p-wave scattering volume (V_p). It is shown that the results of ZRP approaches with energy-dependent (a_s) or (V_p) consist well with our exact ones, when the length scale (beta _6) of the vdW potential equals to or less than the length scale (a_h) of the confinement potential. Furthermore, when (beta _6gg a_h) (e.g., (beta _6=10a_h)) all the ZRP approaches fail. Our results are helpful for the research of confined ultracold atoms or molecules with strong vdW interactions.

A microscopic approach to the (^{12})C((alpha , gamma )^{16})O radiative-capture reaction near the Gamow window has been proposed by Y. Suzuki, Few-Body Syst. 62, 2 (2021). The important ingredients of the approach include the following: (1) The states of (^{12})C and (^{16})O relevant to the reaction are described by fully microscopic 3 (alpha )-particle and 4 (alpha )-particle configurations. (2) The isovector electric dipole transition is accounted for through the isospin impurity of the constituent (alpha )-particles. (3) The relative motion among the (alpha )-particles is expanded in terms of correlated-Gaussian basis functions. A calculation of the radiative-capture cross section demands double angular-momentum projections, that is, the angular momentum of (^{12})C consisting of 3 (alpha )-particles and the orbital angular momentum for (^{12})C(-alpha ) relative motion. Advancing the previous formulation based on the single angular-momentum projection, I carry out the double projection and present all the formulas needed for the cross section calculation.

In this paper, we study and exactly solve the modified Dirac oscillator in curved spacetime with spin and pseudospin symmetries using an algebraic approach. Moreover, we focus on the radial part of this problem and apply the Schrödinger factorization method to demonstrate that the system possesses an SU(1, 1) symmetry. From this, we derive the wave functions and their respective energy spectrum. Additionally, we compute the radial coherent states of the modified Dirac oscillator and examine their temporal evolution in the spin and pseudospin limits, respectively.

The problem of a hydrogen atom in a strong magnetic field is a notorious example of a quantum system that has genuinely different asymptotic behaviors in different directions. In the direction perpendicular to the magnetic field the motion is quadratically confined, while in the direction along the field line the motion is a Coulomb-distorted free motion. In this work, we identify the asymptotically relevant parts of the Hamiltonian and cast the problem into a Lippmann-Schwinger form. Then, we approximate the asymptotically irrelevant parts by a discrete Hilbert space basis that allows an exact analytic evaluation of the relevant Green’s operators by continued fractions. The total asymptotic Green’s operator is calculated by a complex contour integral of subsystem Green’s operators. We present a sample of numerical results for a wide range of magnetic field strengths.

This research investigates the complex statistical behavior of fermion-antifermion pairs within a (2+1)-dimensional magnetized Bonnor-Melvin background affected by non-zero cosmological conditions. The Bonnor-Melvin magnetic universe model, known for its cylindrical symmetry, preserves the invariance of quantum field dynamics under Lorentz boosts along the (z)-axis. This framework facilitates the examination of (2+1)-dimensional scenarios, where the corresponding spacetime background is identified as the Bonnor-Melvin magnetic 2+1+0-brane solution within the realm of gravity coupled with nonlinear electrodynamics. Initially, the precise energy spectra of these pairs are summarized using an analytical solution derived from the fully covariant two-body Dirac equation. Subsequently, the statistical properties inherent in these pair formations are investigated. These findings may illuminate the interplay among magnetic fields, spacetime geometry, and the cosmological constant, thereby enhancing our comprehension of the fundamental behaviors of fermions amidst intricate cosmological conditions. It is anticipated that this investigation could offer new insights into the statistical attributes of fermion-antifermion systems. All thermal characteristics, including free energy, total energy, entropy, and specific heat, have been computed. The impact of diverse factors, such as magnetic fields, spacetime geometry, and the cosmological constant, on these characteristics has been scrutinized.

We present a simple model of composite particle tunnelling through a potential barrier in presence of a (pseudo)magnetic field. The exact numerical solution of the problem is provided and the applicability to real physical systems is discussed. When the magnetic field is present some new qualitative features of the transmission spectrum are observed, compared to the previously studied composite particle tunnelling with no magnetic field. Splitting of energy levels in a magnetic field leads to splitting of transmission probability resonances, which are a generic feature of composite particle tunnelling. Magnetic field also induces precession of spin on the Bloch sphere, that can be used as a Larmor clock for measuring tunnelling time.

Nuclear reactions are complex, with a large number of possible channels. Understanding how different channels contribute to a given reaction is investigated by perturbing the continuous spectrum. Tools are developed to investigate reaction mechanisms by identifying the contributions from each reaction channel. Cluster decomposition methods, along with the spectral theory of proper subsystem problems, is used to identify the part of the nuclear Hamiltonian responsible for scattering into each channel. The result is an expression of the nuclear Hamiltonian as a sum over all scattering channels of channel Hamiltonians. Each channel Hamiltonian is constructed from solutions of proper subsystem problems. Retaining any subset of channel Hamiltonians results in a truncated Hamiltonian where the scattering wave functions for the retained channels differ from the wave functions of the full Hamiltonian by N-body correlations. The scattering operator for the truncated Hamiltonian satisfies an optical theorem in the retained channels. Because different channel Hamiltonians do not commute, how they interact determines their contribution to the full dynamics.

Dynamical association of Efimov trimers in thermal gases by means of modulated magnetic fields has proven very fruitful in determining the binding energy of trimers. The latter was extracted from the number of remaining atoms, which featured oscillatory fringes stemming from the superposition of trimers with atom-dimers. Subsequent theoretical investigations utilizing the time-dependent three-body problem revealed additional association mechanisms, manifested as superpositions of the Efimov state with the trap states and the latter with atom-dimers. The three atoms were initialized in a way to emulate a thermal gas with uniform density. Here, this analysis is extended by taking into account the effects of the density profile of a semi-classical thermal gas. The supersposition of the Efimov trimer with the first atom-dimer remains the same, while the frequencies of highly oscillatory fringes shift to lower values. The latter refer to the frequencies of trimers and atom-dimers in free space since the density profile smears out the contribution of trap states.

We construct approximate bound state solutions to the one-dimensional Schrödinger equation within the Dunkl formalism for a symmetrized Hulthén potential. Our method is based on reducing the governing equation to conventional Schrödinger form, such that an approximation to an inverse quadratic term becomes applicable. Conditions for computing stationary energies, as well as for establishing boundedness and normalizability of our solutions are discussed.

In this study, we present a perturbative analysis of the three-gluon vertex for a kinematical symmetric configuration in dimensions (n=4-2epsilon ) and different covariant gauges. Our study can describe the form factors of the three gluon vertex in a wide range of momentum. We employ a momentum subtraction scheme to define the renormalized vertex. We give an in-depth review of three commonly used vector representations for the vertex, and explicitly show the expressions to change from one representation to the other. Although our estimates are valid only in the perturbative regime, we extend our numerical predictions to the infrared domain and show that in (n=4) some nonperturbative properties are qualitatively present already at perturbation theory. In particular, we find a critical gauge above which the leading form factor displays the so-called zero crossing. We contrast our findings to those of other models and observe a fairly good agreement.