Few-Body SystemsPub Date : 2024-11-30DOI: 10.1007/s00601-024-01973-7
I. Filikhin, R. Ya. Kezerashvili, B. Vlahovic
{"title":"Folding Procedure for (Omega )-(alpha ) Potential","authors":"I. Filikhin, R. Ya. Kezerashvili, B. Vlahovic","doi":"10.1007/s00601-024-01973-7","DOIUrl":"10.1007/s00601-024-01973-7","url":null,"abstract":"<div><p>Using the folding procedure, we investigate the bound state of the <span>(Omega )</span>+<span>(alpha )</span> system. Previous theoretical analyses have indicated the existence of a deeply bound ground state, which is attributed to the strong <span>(Omega )</span>-nucleon interaction. By employing well-established parameterizations of nucleon density within the alpha particle, we performed numerical calculations for the folding <span>(Omega )</span>-<span>(alpha )</span> potential. Our results show that the <span>(V_{Omega alpha }(r))</span> potential can be accurately fitted using a Woods-Saxon function, with a phenomenological parameter <span>(R = 1.1A^{1/3} approx 1.74)</span> fm (<span>(A=4)</span>) in the asymptotic region where <span>(2< r < 3)</span> fm. We provide a thorough description of the corresponding numerical procedure. Our evaluation of the binding energy of the <span>(Omega )</span>+<span>(alpha )</span> system within the cluster model is consistent with both previous and recent reported findings. To further validate the folding procedure, we also calculated the <span>(Xi )</span>-<span>(alpha )</span> folding potential based on a simulation of the ESC08c <i>Y</i>-<i>N</i> Nijmegen model. A comprehensive comparison between the <span>(Xi )</span>-<span>(alpha )</span> folding and <span>(Xi )</span>-<span>( alpha )</span> phenomenological potentials is presented and discussed.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"66 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142754225","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 : 2024-11-29DOI: 10.1007/s00601-024-01971-9
Eleonora Lippi, Manuel Gerken, Stephan Häfner, Marc Repp, Rico Pires, Michael Rautenberg, Tobias Krom, Eva D. Kuhnle, Binh Tran, Juris Ulmanis, Bing Zhu, Lauriane Chomaz, Matthias Weidemüller
{"title":"An Experimental Platform for Studying the Heteronuclear Efimov Effect with an Ultracold Mixture of (^textbf{6})Li and (^textbf{133})Cs Atoms","authors":"Eleonora Lippi, Manuel Gerken, Stephan Häfner, Marc Repp, Rico Pires, Michael Rautenberg, Tobias Krom, Eva D. Kuhnle, Binh Tran, Juris Ulmanis, Bing Zhu, Lauriane Chomaz, Matthias Weidemüller","doi":"10.1007/s00601-024-01971-9","DOIUrl":"10.1007/s00601-024-01971-9","url":null,"abstract":"<div><p>We present the experimental apparatus enabling the observation of the heteronuclear Efimov effect in an optically trapped ultracold mixture of <span>(^6)</span>Li-<span>(^{133})</span>Cs with high-resolution control of the interactions. A compact double-species Zeeman slower consisting of four interleaving helical coils allows for a fast-switching between two optimized configurations for either Li or Cs and provides an efficient sequential loading into their respective MOTs. By means of a bichromatic optical trapping scheme based on species-selective trapping we prepare mixtures down to 100 nK of <span>({1times 10^{4}})</span> Cs atoms and <span>({7times 10^{3}})</span> Li atoms. Highly stable magnetic fields allow high-resolution atom-loss spectroscopy and enable to resolve splitting in the loss feature of a few tens of milligauss. These features allowed for a detailed study of the Efimov effect.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"66 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00601-024-01971-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142737153","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 : 2024-11-19DOI: 10.1007/s00601-024-01965-7
Paolo Recchia, Debabrota Basu, Mario Gattobigio, Christian Miniatura, Stéphane Bressan
{"title":"The Steepest Slope toward a Quantum Few-Body Solution: Gradient Variational Methods for the Quantum Few-Body Problem","authors":"Paolo Recchia, Debabrota Basu, Mario Gattobigio, Christian Miniatura, Stéphane Bressan","doi":"10.1007/s00601-024-01965-7","DOIUrl":"10.1007/s00601-024-01965-7","url":null,"abstract":"<div><p>Quantum few-body systems are deceptively simple. Indeed, with the notable exception of a few special cases, their associated Schrödinger equation cannot be solved analytically for more than two particles. One has to resort to approximation methods to tackle quantum few-body problems. In particular, variational methods have been proposed to ease numerical calculations and obtain precise solutions. One such method is the Stochastic Variational Method, which employs a stochastic search to determine the number and parameters of correlated Gaussian basis functions used to construct an ansatz of the wave function. Stochastic methods, however, face numerical and optimization challenges as the number of particles increases.We introduce a family of gradient variational methods that replace stochastic search with gradient optimization. We comparatively and empirically evaluate the performance of the baseline Stochastic Variational Method, several instances of the gradient variational method family, and some hybrid methods for selected few-body problems. We show that gradient and hybrid methods can be more efficient and effective than the Stochastic Variational Method. We discuss the role of singularities, oscillations, and gradient optimization strategies in the performance of the respective methods.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"65 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142672391","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 : 2024-11-17DOI: 10.1007/s00601-024-01966-6
Faizuddin Ahmed, Abdelmalek Bouzenada
{"title":"Rainbow Gravity Effects on Relativistic Quantum Oscillator Field in a Topological Defect Cosmological Space-Time","authors":"Faizuddin Ahmed, Abdelmalek Bouzenada","doi":"10.1007/s00601-024-01966-6","DOIUrl":"10.1007/s00601-024-01966-6","url":null,"abstract":"<div><p>In this paper, we investigate the quantum dynamics of scalar and oscillator fields in a topological defect space-time background under the influence of rainbow gravity’s. The rainbow gravity’s are introduced into the considered cosmological space-time geometry by replacing the temporal part <span>(dt rightarrow frac{dt}{mathcal {F}(chi )})</span> and the spatial part <span>(dx^i rightarrow frac{dx^i}{mathcal {H} (chi )})</span>, where <span>(mathcal {F}, mathcal {H})</span> are the rainbow functions and <span>(0 le chi =|E|/E_p <1)</span> is the dimensionless parameter. We derived the radial equation of the Klein–Gordon equation and its oscillator equation under rainbow gravity’s in topological space-time. To obtain eigenvalue of the quantum systems under investigations, we set the rainbow functions <span>(mathcal {F}(chi )=1)</span> and <span>(mathcal {H}(chi )=sqrt{1-beta ,chi ^p})</span>, where <span>(p=1,2)</span>. We solve the radial equations through special functions using these rainbow functions and analyze the results. In fact, it is shown that the presence of cosmological constant, the topological defect parameter <span>(alpha )</span>, and the rainbow parameter <span>(beta )</span> modified the energy spectrum of scalar and oscillator fields in comparison to the results obtained in flat space.\u0000</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"65 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142664434","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 : 2024-11-15DOI: 10.1007/s00601-024-01972-8
K. Bakke
{"title":"On a Repulsive Short-Range Potential Influence on the Harmonic Oscillator","authors":"K. Bakke","doi":"10.1007/s00601-024-01972-8","DOIUrl":"10.1007/s00601-024-01972-8","url":null,"abstract":"<div><p>We study the influence of a symmetrically spherical potential on the harmonic oscillator. The symmetrically spherical potential consists of a repulsive short-range potential inspired by the power-exponential potential. By dealing with <i>s</i>-wave in the region where the repulsive short-range potential is significant, we show how the energy levels of the three-dimensional harmonic oscillator are modified by the short-range potential influence. Furthermore, we show that a non-null revival time with regard to the <i>s</i>-state exists.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"65 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636747","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 : 2024-11-12DOI: 10.1007/s00601-024-01968-4
Chetan Lodha, Ajay Kumar Rai
{"title":"Investigation of Mass and Decay Characteristics of the All-light Tetraquark","authors":"Chetan Lodha, Ajay Kumar Rai","doi":"10.1007/s00601-024-01968-4","DOIUrl":"10.1007/s00601-024-01968-4","url":null,"abstract":"<div><p>We investigate the mass spectra and decay properties of pions and all light tetraquarks using both semi-relativistic and non-relativistic frameworks. By applying a Cornell-like potential and a spin-dependent potential, we generate the mass spectra. The decay properties of tetraquarks are evaluated using the annihilation model and the spectator model. Potential tetraquark candidates are interpreted for quantum numbers <span>(J^{PC} = 0^{{+}{+}}, 0^{{-}{+}}, 1^{{-}{+}}, 1^{{+}{-}}, 1^{{-}{-}}, 2^{{+}{-}}, 2^{{-}{+}},)</span> and <span>(2^{{-}{-}})</span>. Additionally, we compare our results with existing experimental data and theoretical predictions to validate our findings. This study aims to enhance the understanding of tetraquarks in the light-light sector. \u0000</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"65 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142600612","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 : 2024-11-03DOI: 10.1007/s00601-024-01970-w
Ruijie Du
{"title":"Analytical Solutions of the Schrödinger Equation for Two Confined Particles with the van der Waals Interaction","authors":"Ruijie Du","doi":"10.1007/s00601-024-01970-w","DOIUrl":"10.1007/s00601-024-01970-w","url":null,"abstract":"<div><p>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 <span>(rrightarrow 0)</span> and <span>(rrightarrow infty )</span> are also elucidated. These results are obtained through the approach we recently developed [arXiv: 2207.09377]. Using our results, we further calculate the <i>s</i>-wave and <i>p</i>-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 <i>s</i>-wave scattering length <span>(a_s)</span> or <i>p</i>-wave scattering volume <span>(V_p)</span>. It is shown that the results of ZRP approaches with energy-dependent <span>(a_s)</span> or <span>(V_p)</span> consist well with our exact ones, when the length scale <span>(beta _6)</span> of the vdW potential equals to or less than the length scale <span>(a_h)</span> of the confinement potential. Furthermore, when <span>(beta _6gg a_h)</span> (e.g., <span>(beta _6=10a_h)</span>) all the ZRP approaches fail. Our results are helpful for the research of confined ultracold atoms or molecules with strong vdW interactions.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"65 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142565830","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 : 2024-10-28DOI: 10.1007/s00601-024-01964-8
Y. Suzuki
{"title":"Calculable Microscopic Theory for (^textbf{12})C((alpha ), (gamma ))(^textbf{16})O Cross Section near Gamow Window II","authors":"Y. Suzuki","doi":"10.1007/s00601-024-01964-8","DOIUrl":"10.1007/s00601-024-01964-8","url":null,"abstract":"<div><p>A microscopic approach to the <span>(^{12})</span>C<span>((alpha , gamma )^{16})</span>O radiative-capture reaction near the Gamow window has been proposed by Y. Suzuki, Few-Body Syst. <b>62</b>, 2 (2021). The important ingredients of the approach include the following: (1) The states of <span>(^{12})</span>C and <span>(^{16})</span>O relevant to the reaction are described by fully microscopic 3 <span>(alpha )</span>-particle and 4 <span>(alpha )</span>-particle configurations. (2) The isovector electric dipole transition is accounted for through the isospin impurity of the constituent <span>(alpha )</span>-particles. (3) The relative motion among the <span>(alpha )</span>-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 <span>(^{12})</span>C consisting of 3 <span>(alpha )</span>-particles and the orbital angular momentum for <span>(^{12})</span>C<span>(-alpha )</span> 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.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"65 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518667","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 : 2024-10-27DOI: 10.1007/s00601-024-01962-w
M. Salazar-Ramírez, D. Ojeda-Guillén, J. A. Martínez-Nuño, R. I. Ramírez-Espinoza
{"title":"Algebraic Approach and Coherent States for the Modified Dirac Oscillator in Curved Spacetime with Spin and Pseudospin Symmetries","authors":"M. Salazar-Ramírez, D. Ojeda-Guillén, J. A. Martínez-Nuño, R. I. Ramírez-Espinoza","doi":"10.1007/s00601-024-01962-w","DOIUrl":"10.1007/s00601-024-01962-w","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"65 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518825","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 : 2024-10-26DOI: 10.1007/s00601-024-01969-3
B. P. Carter, Z. Papp
{"title":"Integral Equation Approach for a Hydrogen Atom in a Strong Magnetic Field","authors":"B. P. Carter, Z. Papp","doi":"10.1007/s00601-024-01969-3","DOIUrl":"10.1007/s00601-024-01969-3","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"65 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518962","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}