Few-Body Systems最新文献

{"title":"Comment on “Modified Quantum Oscillator Field in 4D Wormhole With a Cosmic String”","authors":"Francisco M. Fernández","doi":"10.1007/s00601-026-02078-z","DOIUrl":"10.1007/s00601-026-02078-z","url":null,"abstract":"<div><p>We show that one of the models proposed by Ahmed [Few-Body Syst. <b>66</b>, 28 (2025)] does not support bound states and the eigenfunctions derived by the author are not square integrable. His second example supports bound states but the author failed to truncate the infinite series and consequently he derived functions that are not solutions to the eigenvalue equation. Consequently, the energies reported by Ahmed are in both cases unphysical and of no utility whatsoever.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"67 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Variational Neural-Network Solution of the Two-Body (^{17}textrm{F}) Proton-Halo Problem with a Coulomb–Whittaker Tail","authors":"Lucas A. Souza,&nbsp;Tobias Frederico","doi":"10.1007/s00601-026-02077-0","DOIUrl":"10.1007/s00601-026-02077-0","url":null,"abstract":"<div><p>We present a variational artificial neural-network (VANN) solution of <span>(^{17})</span>F in a two-body <span>(^{16})</span>O<span>(+p)</span> potential model. The calculation uses a standard interaction from the literature as a controlled benchmark for testing whether a neural variational ansatz can reproduce not only bound-state energies and interior wave functions, but also the Coulomb–Whittaker tails that control halo and peripheral-capture observables. The reduced radial wave function is obtained by minimizing the Rayleigh quotient of the radial Schrödinger Hamiltonian with the constraints required by each partial wave. Because the variational energy can converge before the asymptotic normalization is correct, the ansatz combines a neural interior with the charged-particle Coulomb–Whittaker form. In the <span>(s_{1/2})</span> channel, the Pauli-forbidden <span>(0s_{1/2})</span> component is computed and the physical one-node branch is checked independently for forbidden-state contamination. The Coulomb–Whittaker-constrained VANN reproduces independent Numerov benchmarks for the compact <span>(d_{5/2})</span> ground state and the extended <span>(s_{1/2})</span> halo state in energy, nodes, rms radius, and overlap. The compact-state ANC agrees to within one percent, while the halo ANC differs by about <span>(4.2%)</span>, within the larger numerical sensitivity of the asymptotic extraction. The continuum scattering states are obtained by standard Numerov integration with Coulomb matching; only the bound states are represented by the neural ansatz. Combined with these <i>p</i>-wave scattering states, the VANN bound states yield astrophysical <i>S</i> factors consistent with published benchmarks and data within the accuracy of the adopted two-body model. The results demonstrate the usefulness of physically constrained neural wave functions for tail-sensitive nuclear calculations and identify the asymptotic region as the most sensitive part of the calculation.\u0000</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"67 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bound State Solutions of the Relativistic Finite-Difference Equation for the Ring-Shaped Quesne Oscillator Potential","authors":"Sh. M. Nagiyev,&nbsp;Narmin Nasibova,&nbsp;V. A. Tarverdiyeva,&nbsp;G. H. Guliyeva","doi":"10.1007/s00601-026-02075-2","DOIUrl":"10.1007/s00601-026-02075-2","url":null,"abstract":"<div><p>We solve exactly the relativistic finite-difference equation for the quantum three-dimensional ring-shaped Quesne oscillator potential. Our investigation is based on a finite-difference version of relativistic quantum mechanics. The so-called relativistic configurational <span>(textbf{r})</span>-space is a key concept here. We show that the radial wavefunctions and angular wavefunctions are expressed through the continuous dual Hahn polynomials and Jacobi polynomials, respectively. A discrete energy spectrum has been found. The radial wave functions and the energy spectrum possess the correct nonrelativistic limit. We also build a dynamical symmetry group <i>SU</i>(1, 1) for the radial part of the equation of motion, which allows us to find the energy spectrum purely algebraically. The dependence of the effective potential, wave functions, and probability densities of the system on the radial coordinate was studied, and it was determined that the energy spectrum monotonically shifts toward higher energies with the increase of the parameter <span>(alpha )</span>.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"67 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Approximate Bound States for the Dunkl–Schrödinger Equation with Exponential-Cusp Potential","authors":"A. Merad,&nbsp;S. Merad","doi":"10.1007/s00601-026-02076-1","DOIUrl":"10.1007/s00601-026-02076-1","url":null,"abstract":"<div><p>We construct bound state solutions to the one-dimensional Schrödinger equation within the Dunkl formalism for a symmetrized exponential-cusp 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 the limiting case where the Dunkl parameter vanishes, our results reduce to those of the standard Schrödinger equation, in agreement with previous studies in the literature. Scattering states are also discussed.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"67 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hierarchical Fractional N-Body Dynamics: Structural Analogies and Computational Benchmarks Against Classical Gravitational Few-Body Problems","authors":"Farrukh A. Chishtie","doi":"10.1007/s00601-026-02074-3","DOIUrl":"10.1007/s00601-026-02074-3","url":null,"abstract":"<div><p>We present a systematic comparison of the hierarchical fractional <i>N</i>-body framework of Chishtie (Phys. Open 27, 100391, [4]) with three classical benchmarks in gravitational few-body dynamics, establishing structural analogies with the Kepler two-body radial free-fall, Euler’s two-fixed-centre problem, and Hill’s restricted lunar theory, together with quantitative computational benchmarks. The framework derives exact closed-form solutions to hierarchical configurations through Riesz fractional dynamics, yielding the fundamental scaling law <span>(alpha _k = 2 - 2/(N_k+1))</span> connecting the correlation exponent to subsystem particle number. For the hierarchical three-body configuration with <span>(N_k= 2)</span>, the effective radial ODE is <span>(ddot{r} = -(2/N_k)omega ^2 r^{(1-N_k)/N_k})</span> and the parametric solution <span>(r_3(theta ) = a^4sin ^4theta )</span> conserves energy at the double-precision floor (<span>(textrm{std}/E_0 sim 10^{-16})</span>) with Chebyshev cubic inversion residuals below <span>(3times 10^{-15})</span>. The effective potential satisfies the virial relation <span>(langle Trangle /langle Vrangle = 1/(2N_k))</span> exactly over the finite infall interval, providing an independent consistency check on the framework. The parametric structure is closely analogous to that of the Kepler radial free-fall via eccentric anomaly representation and to the Euler two-fixed-centre problem at equal masses and large separation (<span>(r_3 gg c)</span>, quadrupole/monopole ratio <span>(0.49%)</span> at the reference separation); the Hill radius arises naturally as the inner-subsystem scale at hierarchical level <i>k</i>. The universal near-collision velocity exponent <span>(gamma = 1)</span> is confirmed analytically for all <span>(N_kge 1)</span>; the fitted position exponent increases monotonically from 1.02 (<span>(N_k=1)</span>) to 1.22 (<span>(N_k=5)</span>), remaining within the theoretically predicted interval (1, 2) throughout. Computational benchmarks demonstrate speedups of 212–505 times over DOP853 adaptive integration across all tested configurations while maintaining energy conservation at <span>(textrm{std}/E_0 le 1.82times 10^{-16})</span> across 15 parameter combinations.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"67 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Aharonov–Bohm Effect from Exponentially Decreasing Energy Levels of a Non-Hermitian System","authors":"K. Bakke","doi":"10.1007/s00601-026-02073-4","DOIUrl":"10.1007/s00601-026-02073-4","url":null,"abstract":"<div><p>We introduce a non-Hermitian operator which has exponentially decreasing energy levels and study the Aharonov–Bohm effect for bound states. Further, we include the two-dimensional harmonic oscillator in this non-Hermitian quantum system and obtain real energy levels with exponentially decrease. We also show that the Aharonov–Bohm effect for bound states exists in this second case. In both cases, we go further by showing that non-null persistent currents at zero temperature and non-null revival times exist.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"67 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00601-026-02073-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148750944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Probing Kaons as Light-Strange Tetraquarks Through Spectral and Decay Dynamics","authors":"Chetan Lodha,&nbsp;Ajay Kumar Rai","doi":"10.1007/s00601-026-02072-5","DOIUrl":"10.1007/s00601-026-02072-5","url":null,"abstract":"<div><p>Motivated by the discovery of several kaon-like states observed at BESIII and LHCb, this study explores S-wave and P-wave tetraquark states with quark contents <span>( ssbar{s}bar{q} )</span> and <span>( sqbar{q}bar{q} )</span> using potential-based phenomenology. The tetraquarks are modeled as diquark-antidiquark systems in antitriplet-triplet and sextet-antisextet color configurations. The mass spectra are calculated using the Cornell potential, while decay properties are analyzed through Fierz rearrangement. A comparison with experimentally observed states is provided to enhance our understanding of light-light tetraquark systems with non-homogeneous quark compositions.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"67 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148750554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Haar Multiresolution Construction of a Finite-Resolution Scalar Field Hamiltonian","authors":"Murat Buldu,&nbsp;Fatih Bulut","doi":"10.1007/s00601-026-02071-6","DOIUrl":"10.1007/s00601-026-02071-6","url":null,"abstract":"<div><p>In this paper, we study the discretization of free scalar quantum field theory using the Haar wavelet basis. The field operators are expanded in an orthonormal multi-resolution system and the expansion is truncated at finite resolution, with this application a finite-dimensional representation of the Hamiltonian is obtained. These procedures turn the operator in a form of quadratic Hamiltonian that describes a set of coupled harmonic oscillators. This construction provides an explicit realization of ultraviolet and infrared cutoffs within a wavelet framework also the basis functions preserve their orthogonality and spatial localization. The Haar wavelet basis has a property of compact support which allows a transparent implementation of the discretization procedure. Using this property we can create a matrix formulation suitable for numerical diagonalization. We analyze the structure of the discretized Hamiltonian and comment on how locality and symmetry considerations are affected by the Haar approximation, and identify the spectral implications of the nearest-neighbor coupling structure. We use the results to show how multiresolution techniques can be used as a constructive discretization scheme in quantum field theory and clarify both the practical advantages and intrinsic limitations of the Haar basis in this context.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"67 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148750738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Classical Description of Two-Electron Diatomic Molecules and of the Double Charge Exchange","authors":"N. Kryukov,&nbsp;E. Oks","doi":"10.1007/s00601-026-02069-0","DOIUrl":"10.1007/s00601-026-02069-0","url":null,"abstract":"<div><p>Our previous papers provided a classical description of one-electron diatomic molecules and of charge exchange. In the present paper we advanced these studies by providing a classical description of two-electron diatomic molecules, consisting of the two nuclei of charges <i>Z</i> and <span>(Z' ge )</span> <i>Z</i> and two electrons. In particular, in laboratory and astrophysical plasmas, in the process of charge exchange between multicharged ions, there can form <i>transient</i> two-electron diatomic <i>quasi</i>-molecules containing nuclei of <span>(Z' ge Z&gt;&gt; 1)</span>. We analyzed classical two-electron diatomic molecules in two configurations: one where the two electrons rotate in the same circular orbit, being at the opposite ends of the diameter; another where the two electrons rotate in two different quasi-circular orbits. We demonstrated that in the first configuration, the two-electron system is characterized by a lower energy in all cases than the corresponding one-electron system. Besides, we showed that the equilibrium range of the projection of the electrons orbit on the internuclear axis is smaller than in the corresponding one-electron case. We also analyzed the stability of the system against small fluctuations of the parameters of the electrons orbit and gave the ranges of the stability. Most importantly, for the first configuration we described classically the <i>double charge exchange </i>in plasmas. The feasibility of the classical description of the double charge exchange represents a <i>counterintuitive</i> <i>result</i>. For the second configuration, we demonstrated that it is stable when one electron is relatively close to one of the nuclei while the other electron is relatively close to the other nucleus.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"67 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00601-026-02069-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Neural-network solution of subtracted three-body Faddeev integral equations near the Efimov limit","authors":"Lucas A. Souza","doi":"10.1007/s00601-026-02070-7","DOIUrl":"10.1007/s00601-026-02070-7","url":null,"abstract":"<div><p>We apply a deep-neural-network (DNN) ansatz to the symmetrized spectator vector of the subtracted three-body Faddeev integral equation for identical bosons near the Efimov limit. The network is trained by minimizing the residual of the discretized integral equation, while the positive binding scale associated with the three-body energy is treated as a trainable parameter. Deterministic diagonalization of the same discretized kernel is used only as an a posteriori numerical benchmark. As preliminary validation, the neural-solver strategy is tested on the analytically solvable hydrogen radial problem. At unitarity, the DNN reproduces the Efimov ground-state binding scale with a DNN–deterministic deviation of <span>(0.022%)</span>, while the first excited state is recovered to <span>(0.002%)</span>. The deterministic solver recovers the universal Efimov sscaling ratio <span>(e^{2pi /s_0}simeq 515.03)</span>, and the neural method traces the bound-state branches as a function of the inverse scattering length 1/<i>a</i> by continuation from the unitary solution. These results indicate that DNN-based residual minimization can provide a compact and differentiable representation of a renormalized few-body integral-equation solution in a regime governed by discrete scale invariance.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"67 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00601-026-02070-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}