Few-Body SystemsPub Date : 2026-06-09DOI: 10.1007/s00601-026-02061-8
Hakon Volkmann, Alejandro Saenz
{"title":"A Distorted Single-Center Approach to Two-Center Coulomb Scattering","authors":"Hakon Volkmann, Alejandro Saenz","doi":"10.1007/s00601-026-02061-8","DOIUrl":"10.1007/s00601-026-02061-8","url":null,"abstract":"<div><p>The two-center Coulomb scattering problem is revisited. It is shown that the scattering wavefunction can be interpreted in terms of distorted single-center Coulomb scattering solutions. The two-center properties are shown to manifest themselves merely in a non-integer quasi-angular momentum and an infinite series of short-range potentials decaying faster than <span>(r^{-2})</span>. Employing this distorted-wave ansatz, two-center Coulomb scattering phase shifts are determined numerically at the challenging low-energy regime with unprecedented accuracy.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"67 3","pages":""},"PeriodicalIF":1.8,"publicationDate":"2026-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148202898","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 : 2026-05-29DOI: 10.1007/s00601-026-02056-5
Ziqi Jin, Paolo Recchia, Mario Gattobigio
{"title":"Advancing Machine Learning Applications in Quantum Few-Body Systems","authors":"Ziqi Jin, Paolo Recchia, Mario Gattobigio","doi":"10.1007/s00601-026-02056-5","DOIUrl":"10.1007/s00601-026-02056-5","url":null,"abstract":"<div><p>This paper presents a general neural network framework for solving quantum few-body systems, extending prior methods to handle diverse particle masses, interaction types, and system configurations. Our architecture, which combines an adaptive step size with the Metropolis-Adjusted Langevin Algorithm for Monte Carlo sampling, accurately approximates the ground-state wave functions of systems featuring harmonic confinement, Gaussian two-body interactions, and including three-body forces. In ten-particle systems, it achieves lower relative energy errors (with respect to the reference values) than previous machine-learning methods. Leveraging GPU-accelerated computation, the method scales favorably with system size while maintaining robust convergence, reduced hyperparameter sensitivity, and stable training. Beyond accurate energy estimation, the model captures spatial distributions and correlation structures, offering physical insights about inter-particle structure. By unifying applicability across identical and nonidentical particles, the proposed approach establishes a versatile computational tool for exploring complex few-body quantum systems, with significant implications for advancing computational models in few-body quantum systems.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"67 2","pages":""},"PeriodicalIF":1.8,"publicationDate":"2026-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148173550","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 : 2026-05-26DOI: 10.1007/s00601-026-02048-5
Jhomel R. Panogao, Denny Lane B. Sombillo
{"title":"Understanding the (T_{cbar{c}1}(3900)) through Machine Learning Techniques","authors":"Jhomel R. Panogao, Denny Lane B. Sombillo","doi":"10.1007/s00601-026-02048-5","DOIUrl":"10.1007/s00601-026-02048-5","url":null,"abstract":"<div><p>In this study, we analyze the nature of the <span>(T_{cbar{c}1}(3900))</span> state using a uniformization approach, with a particular focus on different pole configurations. The <span>(T_{cbar{c}1}(3900))</span> was observed in the <span>(J/psi pi ^pm )</span> invariant mass spectrum near the <span>(Dbar{D}^*)</span> threshold, suggesting its possible interpretation as a <span>(Dbar{D}^*)</span> hadronic molecule. We investigate this structure by modeling the coupled-channel interaction between <span>(J/psi pi )</span> and <span>(Dbar{D}^*)</span> using a fitting function where the pole-based interpretation is embedded. With this, we are able to generate arbitrary pole structures and extract physical insight from the resulting line shapes. These synthetic line shapes are then used to generate a training dataset for a machine learning model. Since the signal appears above the <span>(Dbar{D}^*)</span> threshold, our analysis primarily focuses on pole configurations with at least one pole on the third Riemann Sheet. Once the machine has been trained on a synthetic dataset and has demonstrated good generalization capabilities, an inference will be done on the BESIII dataset. With this method, our technique was able to infer that the signal observed by the BESIII collaboration has a pole-shadow pair configuration, which implies the presence of a large non-molecular component.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"67 2","pages":""},"PeriodicalIF":1.8,"publicationDate":"2026-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148010106","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 : 2026-05-22DOI: 10.1007/s00601-026-02058-3
Netai Das, Arijit Ghoshal, Yew Kam Ho
{"title":"Doubly Excited Singlet S States of Positronium Negative Ion Embedded in Dense Semi-Classical Plasma","authors":"Netai Das, Arijit Ghoshal, Yew Kam Ho","doi":"10.1007/s00601-026-02058-3","DOIUrl":"10.1007/s00601-026-02058-3","url":null,"abstract":"<div><p>Quantum mechanical effect of diffraction of a semi-classical plasma on the doubly excited singlet S states of positronium negative ion (<span>(hbox {Ps}^-)</span>) are investigated. A pseudopotential containing two adjustable parameters is used to model the effective interaction potential in semi-classical plasmas. The screening parameter <span>(kappa )</span> represents the collective screening effect, whereas the parameter <span>(lambda )</span> pertaining to the de Broglie wavelength of the pair of interacting particles corresponds to the quantum mechanical effect of diffraction at short distances. Doubly excited states (DES) of <span>(hbox {Ps}^-)</span> have been identified within the framework of the stabilization method by employing an extensive highly-correlated Hylleraas-type wavefunction containing 715 square integrable functions and a scaling parameter. The energies and the widths characterizing the DESs are then determined by fitting the density of the resonant states with the Lorentzian function. Convergence of the energy and width of each identified DES is examined by expanding the size of the employed wavefunction. For the plasma-free case, it has been possible to identify the existence of four DESs in <span>(hbox {Ps}^-)</span> lying below the Ps(n=3) excitation threshold. The energies and widths of those states are found to be in excellent agreement with some reliable results in the literature. A comprehensive study is then carried out on the changes in the energies and widths of these states due to the variation of <span>(kappa )</span> and <span>(lambda )</span>. Our findings prove that the energies of the DESs increase with increasing <span>(lambda )</span> at a given <span>(kappa )</span>. However, variation of the width with respect to <span>(lambda )</span> at a given <span>(kappa )</span> is distinctive.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"67 2","pages":""},"PeriodicalIF":1.8,"publicationDate":"2026-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148009568","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 : 2026-05-19DOI: 10.1007/s00601-026-02055-6
Nguyen Tri Toan Phuc, Nguyen Hoang Phuc, Dao T. Khoa
{"title":"Nuclear Rainbow of Core-Symmetric Systems","authors":"Nguyen Tri Toan Phuc, Nguyen Hoang Phuc, Dao T. Khoa","doi":"10.1007/s00601-026-02055-6","DOIUrl":"10.1007/s00601-026-02055-6","url":null,"abstract":"<div><p>The nearside-farside (NF) decomposition method developed originally by Fuller for elastic scattering of a nonidentical nucleus-nucleus system was generalized to study the nuclear rainbow pattern in a symmetric or core-symmetric dinuclear system. It has been shown that the projectile-target identity of an identical system implies a symmetric interchange of the nearside and farside components of elastic scattering amplitude around <span>(theta _{mathrm{c.m.}}=90^circ )</span>. A similar interchange appears also in a nonidentical core-symmetric system due to elastic transfer of cluster or nucleon between two identical cores. The analysis of the <span>(^{12}textrm{C}+^{12}textrm{C})</span>, <span>(^{16}textrm{O}+^{12}textrm{C})</span>, and <span>(^{13}textrm{C}+^{12}textrm{C})</span> systems shows how the generalized NF decomposition method reveals the nuclear rainbow pattern in these systems, which can be helpful in probing the real optical potential and nuclear clustering.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"67 2","pages":""},"PeriodicalIF":1.8,"publicationDate":"2026-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148008896","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 : 2026-05-13DOI: 10.1007/s00601-026-02043-w
for the A1 hypernuclear collaboration, Ryoko Kino, Patrick Achenbach, Sho Nagao, Satoshi N. Nakamura, Kotaro Nishi, Pascal Klag, Josef Pochodzalla, Tianhao Shao
{"title":"Spectrometer Momentum Calibration for a Precise Hypertriton Mass Measurement with Decay Pion Spectroscopy","authors":"for the A1 hypernuclear collaboration, Ryoko Kino, Patrick Achenbach, Sho Nagao, Satoshi N. Nakamura, Kotaro Nishi, Pascal Klag, Josef Pochodzalla, Tianhao Shao","doi":"10.1007/s00601-026-02043-w","DOIUrl":"10.1007/s00601-026-02043-w","url":null,"abstract":"<div><p>Decay pion spectroscopy provides a direct and model-independent approach to the precise mass measurement of light hypernuclei, such as the hypertriton (<span>(^3_Lambda )</span>H), through the monochromatic momentum of pions emitted in two-body weak decays. In this experiment at the Mainz Microtron (MAMI), decay pions from stopped hypernuclei produced in the <span>(p(e,e'K^+)Lambda )</span> reaction on a natural lithium target were measured with a high-resolution magnetic spectrometer, Spectrometer A (SpecA). Since the achievable precision of the hypertriton mass is directly determined by the accuracy of the pion momentum, this contribution focuses on the momentum calibration essential for decay pion spectroscopy. A comprehensive calibration based on elastic electron scattering was performed using <span>(^{181})</span>Ta and <span>(^{12})</span>C targets. The reconstructed scattering angle, momentum linearity over the full spectrometer acceptance, and the dependence on the reaction point along the beam axis were systematically evaluated and corrected. These procedures constrained the systematic uncertainty of the elastic-scattering-based momentum calibration to below 10 keV, excluding the beam-energy contribution. The established calibration procedure provides the foundation for a high-precision determination of the hypertriton mass relying on decay pion spectroscopy.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"67 2","pages":""},"PeriodicalIF":1.8,"publicationDate":"2026-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147937977","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 : 2026-05-12DOI: 10.1007/s00601-026-02045-8
Fidele J. Twagirayezu
{"title":"Flavor-Dependent Entanglement Entropy in the Veneziano Limit from Light-Front Holographic QCD","authors":"Fidele J. Twagirayezu","doi":"10.1007/s00601-026-02045-8","DOIUrl":"10.1007/s00601-026-02045-8","url":null,"abstract":"<div><p>We develop a wavefunction-based framework to compute flavor-resolved quantum-information measures in light-front holographic QCD (LFHQCD). A Veneziano-inspired control parameter <span>(lambda equiv N_f/N_c)</span> is used to modulate the strength of a phenomenological flavor-sector deformation of the light-front effective potential while keeping the universal soft-wall background fixed. Flavor dependence is encoded through bulk scalar profiles <span>(X_f(z))</span> dual to <span>(langle bar{q}_f q_frangle ,)</span> whose quadratic invariant contributes an additional local term in the light-front potential. Entanglement diagnostics are defined directly from normalized light-front wavefunctions by constructing reduced density matrices on a discretized transverse/holographic lattice and evaluating von Neumann and Rényi entropies, as well as mutual information between disjoint transverse regions. We implement and compare a factorized-spin baseline and a correlated spin-improved construction to quantify the impact of tracing over spin degrees of freedom. The resulting setup provides a transparent bridge between LFHQCD wavefunctions, flavor-dependent deformations motivated by Veneziano scaling, and quantum-information observables at finite temperature <i>T</i> and chemical potential <span>(mu )</span> through phenomenological crossover functions.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"67 2","pages":""},"PeriodicalIF":1.8,"publicationDate":"2026-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147938245","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 : 2026-05-08DOI: 10.1007/s00601-026-02051-w
Wolfgang Schadow
{"title":"Numerical Study of the Two-Boson Bound-State Problem with and Without Partial-Wave Decomposition","authors":"Wolfgang Schadow","doi":"10.1007/s00601-026-02051-w","DOIUrl":"10.1007/s00601-026-02051-w","url":null,"abstract":"<div><p>The validation of numerical methods is a prerequisite for reliable few-body calculations, particularly when moving beyond standard partial-wave decompositions. In this work, we present a precision benchmark for the two-boson bound-state problem, solving it using two complementary formulations: the standard one-dimensional partial-wave Lippmann–Schwinger equation and a two-dimensional formulation based directly on vector variables. While the partial-wave approach is computationally efficient for low-energy bound states, the vector-variable formulation becomes essential for scattering applications at higher energies where the partial-wave expansion converges slowly. We demonstrate the high-precision numerical equivalence of both methods using rank-one separable Yamaguchi potentials and non-separable Malfliet–Tjon interactions. Furthermore, for the Yamaguchi potential, we derive exact analytical expressions quantifying the systematic errors introduced by finite momentum- and coordinate-space cut-offs. These analytical bounds provide a rigorous tool for disentangling discretization errors from truncation effects in few-body codes. The results establish a highly controlled methodological benchmark that provides a detailed baseline for vector-variable algorithms intended for more complex three- and four-body calculations.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"67 2","pages":""},"PeriodicalIF":1.8,"publicationDate":"2026-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829875","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 : 2026-05-07DOI: 10.1007/s00601-026-02054-7
Satoshi Ohya
{"title":"Scale Invariance Breaking and Discrete Phase Invariance in Few-Body Problems","authors":"Satoshi Ohya","doi":"10.1007/s00601-026-02054-7","DOIUrl":"10.1007/s00601-026-02054-7","url":null,"abstract":"<div><p>Scale invariance in quantum mechanics can be broken in several ways. A well-known example is the breakdown of continuous scale invariance to discrete scale invariance, whose typical realization is the Efimov effect of three-body problems. Here we discuss yet another discrete symmetry to which continuous scale invariance can be broken: <i>discrete phase invariance</i>. We first revisit the one-body problem on the half line in the presence of an inverse-square potential—the simplest example of nontrivial scale-invariant quantum mechanics—and show that continuous scale invariance can be broken to discrete phase invariance in a small window of coupling constant. We also show that discrete phase invariance manifests itself as circularly distributed simple poles on Riemann sheets of the S-matrix. We then present three examples of few-body problems that exhibit discrete phase invariance. These examples are the one-body Aharonov-Bohm problem, a two-body problem of nonidentical particles in two dimensions, and a three-body problem of nonidentical particles in one dimension, all of which contain a codimension-two “magnetic” flux in configuration spaces.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"67 2","pages":""},"PeriodicalIF":1.8,"publicationDate":"2026-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829511","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 : 2026-05-07DOI: 10.1007/s00601-026-02057-4
Othmane Cherroud, Sid-Ahmed Yahiaoui
{"title":"Phase Space Representation for the Inversely Quadratic Hellmann-Kratzer Potential","authors":"Othmane Cherroud, Sid-Ahmed Yahiaoui","doi":"10.1007/s00601-026-02057-4","DOIUrl":"10.1007/s00601-026-02057-4","url":null,"abstract":"<div><p>In this work, we develop a phase space formulation of quantum mechanics to investigate the inversely quadratic Hellmann-Kratzer (IQHK) potential, with the aim of simultaneously constructing the Wigner distribution and the corresponding characteristic functions. By employing Weyl transformations, we establish two independent computational approaches, each yielding explicit and generalized analytical expressions for higher-order moments and momentum. In addition, we derive a generalized analytical formulation of the momentum operator and establish a corresponding generalized expression of Heisenberg’s uncertainty principle, explicitly dependent on the quantum numbers <i>n</i> and <i>L</i>. This constitutes a novel and complementary contribution to the study of the IQHK potential. Furthermore, the key transformation employed in phase space enabled us to derive a generalized analytical expression for the energy levels <span>(E_{n,L})</span>. These energy levels are numerically evaluated and exhibit excellent agreement with previously published results for all special cases of the IQHK potential across various diatomic molecular systems. Furthermore, we verify that our results are consistent with the canonical Heisenberg-Born-Jordan-Dirac commutation relations and Heisenberg’s uncertainty principle, thereby confirming the robustness and reliability of the proposed methodology within this framework.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"67 2","pages":""},"PeriodicalIF":1.8,"publicationDate":"2026-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147830116","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}