From atoms to nuclei, quarks and bejond...

Latest Results for Few-Body Systems

03 December 2024

• Folding Procedure for $$\Omega $$ - $$\alpha $$ Potential

  Abstract

  Using the folding procedure, we investigate the bound state of the \(\Omega \) + \(\alpha \) system. Previous theoretical analyses have indicated the existence of a deeply bound ground state, which is attributed to the strong \(\Omega \) -nucleon interaction. By employing well-established parameterizations of nucleon density within the alpha particle, we performed numerical calculations for the folding \(\Omega \) - \(\alpha \) potential. Our results show that the \(V_{\Omega \alpha }(r)\) potential can be accurately fitted using a Woods-Saxon function, with a phenomenological parameter \(R = 1.1A^{1/3} \approx 1.74\) fm ( \(A=4\) ) in the asymptotic region where \(2< r < 3\) fm. We provide a thorough description of the corresponding numerical procedure. Our evaluation of the binding energy of the \(\Omega \) + \(\alpha \) system within the cluster model is consistent with both previous and recent reported findings. To further validate the folding procedure, we also calculated the \(\Xi \) - \(\alpha \) folding potential based on a simulation of the ESC08c Y-N Nijmegen model. A comprehensive comparison between the \(\Xi \) - \(\alpha \) folding and \(\Xi \) - \( \alpha \) phenomenological potentials is presented and discussed.

• An Experimental Platform for Studying the Heteronuclear Efimov Effect with an Ultracold Mixture of $$^\textbf{6}$$ Li and $$^\textbf{133}$$ Cs Atoms

  Abstract

  We present the experimental apparatus enabling the observation of the heteronuclear Efimov effect in an optically trapped ultracold mixture of \(^6\) Li- \(^{133}\) 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 \({1\times 10^{4}}\) Cs atoms and \({7\times 10^{3}}\) 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.

• The Steepest Slope toward a Quantum Few-Body Solution: Gradient Variational Methods for the Quantum Few-Body Problem

  Abstract

  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.