Few-Body SystemsPub Date : 2025-08-05DOI: 10.1007/s00601-025-02003-w
D. V. Fedorov, A. M. Pedersen
{"title":"Calculation of low-energy scattering parameters using artificial oscillator trap","authors":"D. V. Fedorov, A. M. Pedersen","doi":"10.1007/s00601-025-02003-w","DOIUrl":"10.1007/s00601-025-02003-w","url":null,"abstract":"<div><p>We introduce a recipe to estimate the low-energy scattering parameters of a quantum few-body system — scattering length, effective range, and shape parameter — by using only <i>discrete</i> state calculations. We place the system in an artificial oscillator trap of varying size and calculate the energies of the resulting discrete states close to the threshold of the system as function of the trap size. The low-energy scattering parameters are then extracted — using a simple analytic formula — from the functional dependence of these energies upon the trap size. We first test the recipe against a simple model problem and then apply it to low-energy nucleon-nucleon scattering within the nuclear Model with Explicit Mesons in one sigma-meson approximation.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"66 3","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00601-025-02003-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162048","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}
Few-Body SystemsPub Date : 2025-07-11DOI: 10.1007/s00601-025-02001-y
A. N. Mendoza-Tavera, H. Olivares-Pilón, M. Rodríguez-Arcos, A. M. Escobar-Ruiz
{"title":"Cylindrically Confined Hydrogen Atom in Magnetic Field: Variational Cut-Off Factor","authors":"A. N. Mendoza-Tavera, H. Olivares-Pilón, M. Rodríguez-Arcos, A. M. Escobar-Ruiz","doi":"10.1007/s00601-025-02001-y","DOIUrl":"10.1007/s00601-025-02001-y","url":null,"abstract":"<div><p>In the present study, we consider the hydrogen atom confined within an impenetrable infinite cylindrical cavity of radius <span>(rho _{0})</span> in the presence of a constant magnetic field <span>(textbf{B} = B,hat{textbf{z}})</span> oriented along the main cylinder’s axis. In the Born-Oppenheimer approximation, anchoring the nucleus to the geometric center of the cylinder, a physically meaningful 3-parametric trial function is used to determine the ground state energy <i>E</i> of the system. This trial function incorporates the exact symmetries and key limiting behaviors of the problem explicitly. In particular, it does not treat the Coulomb potential nor the magnetic interaction as a <i>perturbation</i>. The novel inclusion of a variational cut-off factor <span>(big (1 - big (frac{rho }{rho _0}big )^nu big ))</span>, <span>(nu ge 1)</span>, appears to represent a significant improvement compared to the non-variational cut-off factors commonly employed in the literature. The dependence of the total energy <span>(E=E(rho _0,,B))</span> and the binding energy <span>(E_b=E_b(rho _0,,B))</span> on the cavity radius <span>(rho _0 in [0.8,,5] ,)</span>a.u. and the magnetic field strength <span>(Bin [0.0,,1.0],)</span>a.u. is presented in detail. The expectation values <span>(langle rho rangle )</span> and <span>(langle |z| rangle )</span>, and the Shannon entropy in position space are computed to provide additional insights into the system’s localization. A brief discussion is provided comparing the 2D and 3D cases as well.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"66 3","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00601-025-02001-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164537","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}
Few-Body SystemsPub Date : 2025-07-11DOI: 10.1007/s00601-025-02002-x
A. R. P. Rau
{"title":"Phase-amplitude separation of wave function as local gauge transformation","authors":"A. R. P. Rau","doi":"10.1007/s00601-025-02002-x","DOIUrl":"10.1007/s00601-025-02002-x","url":null,"abstract":"<div><p>A quantum-mechanical wave function is complex, but all observations are real, expressible through expectation values and transition matrix elements that involve the wave functions. It can be useful to separate at the outset the amplitude and phase as real quantities that together carry the same information that is contained in the complex wave function. Two main avenues for doing so go way back in the history of the subject and have been used both for scattering and bound states. A connection is made here to gauge transformations of electrodynamics where the advent of quantum mechanics and later quantum field theory showed the central role that local gauge transformations play in physics.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"66 3","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00601-025-02002-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164540","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}
Few-Body SystemsPub Date : 2025-07-05DOI: 10.1007/s00601-025-01998-6
N. Rouabhia, M. Merad, B. Hamil, T. Birkandan
{"title":"Relativistic oscillators in the context of energy-dependent noncommutative phase space","authors":"N. Rouabhia, M. Merad, B. Hamil, T. Birkandan","doi":"10.1007/s00601-025-01998-6","DOIUrl":"10.1007/s00601-025-01998-6","url":null,"abstract":"<div><p>In this work, we investigate the Klein-Gordon and Dirac oscillators in (2+1) dimensions under the influence of a constant magnetic field, within the framework of energy-dependent noncommutative phase space. This space is characterized by two energy-dependent deformation parameters, <span>(theta (E))</span> and <span>(eta (E))</span>, which modify the standard phase-space algebra through generalized commutation relations. By applying the Bopp shift method and using polar coordinates, we derive exact analytical solutions for both relativistic oscillators. The relativistic energy equations and corresponding wave functions are obtained explicitly in terms of confluent hypergeometric functions for the Klein-Gordon case and associated Laguerre functions for the Dirac case. We also analyze various limiting cases, including the commutative limit, the energy-independent NC case, and the non-relativistic regime. Our results show that the energy dependence of the noncommutative parameters leads to significant modifications in the spectral structure, potentially shedding light on quantum gravitational effects at high energies.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"66 3","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162249","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}
Few-Body SystemsPub Date : 2025-07-04DOI: 10.1007/s00601-025-02000-z
Faizuddin Ahmed
{"title":"Modified Quantum Oscillator Field in 4D Wormhole With a Cosmic String","authors":"Faizuddin Ahmed","doi":"10.1007/s00601-025-02000-z","DOIUrl":"10.1007/s00601-025-02000-z","url":null,"abstract":"<div><p>In this paper, we explore quantum dynamics of relativistic quantum oscillator field within the framework of generalized Klein-Gordon oscillator in the context of four-dimensional wormhole with a cosmic string. The considered space-time is an example of Morris-Thorne-type traversable wormhole with topological defect. We derive a radial second-order differential equation of the generalized Klein-Gordon oscillator equation and obtain analytical solution through special functions by choosing different potential functions. In this study, we consider two distinct functions: a Coulomb- and Cornell-like potential form and solve the differential equation. As particular case, we presented the ground state energy level and the corresponding wave function of quantum oscillator fields. In fact, it is shown that the wormhole throat radius and cosmic string influences the eigenvalue solution compared to flat space results. The presence of topological defect of cosmic string breaks the degeneracy of the spectra of energy.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"66 3","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161424","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}
Few-Body SystemsPub Date : 2025-06-27DOI: 10.1007/s00601-025-01999-5
B. Hamil, B. C. Lütfüoğlu, A. N. Ikot, U. S. Okorie
{"title":"Spectral and Thermal Analysis of the Morse Potential within the Dunkl Formalism: Analytical Approximations and Applications","authors":"B. Hamil, B. C. Lütfüoğlu, A. N. Ikot, U. S. Okorie","doi":"10.1007/s00601-025-01999-5","DOIUrl":"10.1007/s00601-025-01999-5","url":null,"abstract":"<div><p>In this work, we investigate the quantum dynamics of a particle subject to the Morse potential within the framework of Dunkl quantum mechanics. By employing the Dunkl derivative operator–which introduces reflection symmetry–we construct a deformed Schrödinger equation and obtain exact analytical solutions using the Pekeris approximation. The resulting energy spectrum and wavefunctions reveal how Dunkl parameters alter the effective potential and vibrational states. The model is applied to several diatomic molecules, including <span>(hbox {H}_2)</span>, HCl, and <span>(hbox {I}_2)</span>, illustrating the impact of symmetry deformation on energy spectra. We also compute thermodynamic functions including the partition function, free energy, internal energy, entropy, and specific heat. The analysis shows that the Dunkl deformation induces distinct thermal behavior and offers a tunable approach to molecular modeling. These results highlight the potential of the Dunkl formalism as a useful tool for extending conventional quantum models and for exploring symmetry-deformed systems in molecular physics and quantum thermodynamics.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"66 3","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170339","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}
Few-Body SystemsPub Date : 2025-06-11DOI: 10.1007/s00601-025-01996-8
Zhongqi Liang, Jesús Pérez-Ríos
{"title":"Classical Grand Angular Momentum in N-Body Problems","authors":"Zhongqi Liang, Jesús Pérez-Ríos","doi":"10.1007/s00601-025-01996-8","DOIUrl":"10.1007/s00601-025-01996-8","url":null,"abstract":"<div><p>The concept of grand angular momentum is widely used in the study of N-body problems quantum mechanically. Here, we applied it to a classical analysis of N-body problems. Utilizing the tree representation for Jacobi and hyperspherical coordinates, we found a decomposition of its magnitude into magnitudes of one-body angular momenta in three dimensions. We generalized some results from the two-body case and derived a general expression for the scattering angle in N-body problems.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"66 2","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164293","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}
Few-Body SystemsPub Date : 2025-06-11DOI: 10.1007/s00601-025-01997-7
Abbad Moussa, Houcine Aounallah, Sebastián Valladares, Clara Rojas
{"title":"A Relativistic Position–Dependent Mass System of Bosonic Field in Cosmic String Space–Time Background","authors":"Abbad Moussa, Houcine Aounallah, Sebastián Valladares, Clara Rojas","doi":"10.1007/s00601-025-01997-7","DOIUrl":"10.1007/s00601-025-01997-7","url":null,"abstract":"<div><p>In this work, we investigate the relativistic quantum motion of spin–zero scalar bosons via the Duffin–Kemmer–Petiau (DKP) equation with a position–dependent mass (PDM) system in the background of the topological defect space–time produced by a cosmic string. We determine the radial wave equation and obtain the exact analytical solutions of the wave equation for the linear and Cornell–type potential through the Bi–Confluent Heun differential equation. In fact, we have obtained the ground state energy for both potentials.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"66 2","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164292","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}
Few-Body SystemsPub Date : 2025-06-04DOI: 10.1007/s00601-025-01991-z
Egorov Mikhail
{"title":"Three-Dimensional Integral Faddeev Equations without a Certain Symmetry","authors":"Egorov Mikhail","doi":"10.1007/s00601-025-01991-z","DOIUrl":"10.1007/s00601-025-01991-z","url":null,"abstract":"<div><p>A method for the direct integration of the three-dimensional Faddeev equations with respect to the breakup T-matrix in momentum space for three-body systems with differing masses is presented. The Faddeev equations are explicitly formulated without imposing symmetry or antisymmetry requirements on the two-body t-matrices, thus accounting for mass differences between the three interacting particles. An algorithm for the algebraic determination of non-relativistic wave functions for three-body systems with arbitrary masses is given. Furthermore, it is directly demonstrated how the domain of logarithmic singularities in the integral kernels of the Faddeev equations is significantly altered by varying the masses of the interacting particles. The developed method for traversing logarithmic singularities is tested using the example of calculating the total cross sections for elastic neutron-deuteron scattering and breakup reaction.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"66 2","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161633","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}
Few-Body SystemsPub Date : 2025-06-02DOI: 10.1007/s00601-025-01995-9
Chandan Sarma, Praveen C. Srivastava
{"title":"Ab initio no-core shell-model study of (^{20-23})Na isotopes","authors":"Chandan Sarma, Praveen C. Srivastava","doi":"10.1007/s00601-025-01995-9","DOIUrl":"10.1007/s00601-025-01995-9","url":null,"abstract":"<div><p>We have done a systematic no-core shell-model study of <span>(^{20-23})</span>Na isotopes. The low-energy spectra of these sodium isotopes consisting of natural and un-natural parity states were reported, considering three realistic interactions: inside nonlocal outside Yukawa (INOY), charge-dependent Bonn 2000 (CDB2K), and the chiral next-to-next-to-next-to-leading order (N<span>(^3)</span>LO). We also present the mirror energy differences in the low-energy spectra of <span>(|T_z|)</span> = 1/2 mirror pair (<span>(^{21})</span>Na - <span>(^{21})</span>Ne). Apart from the energy spectra, we have also reported the electromagnetic transition strengths and moments. Finally, considering all three realistic interactions, we report the point-proton radii and neutron skin thicknesses.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"66 2","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161295","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}