On-shell approximation for the s-wave scattering theory

Anno: 2023

Autori: Lorenzi F., Bardin A., Salasnich L.

Affiliazione autori: Univ Padua, Dipartimento Fis & Astron Galileo Galilei, Via Marzolo 8, I-35131 Padua, Italy; Ist Nazl Fis Nucl INFN, Sez Padova, Via Marzolo 8, I-35131 Padua, Italy; Ist Nazl Ott INO Consiglio Nazl Ric CNR, Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy.

Abstract: We investigate the scattering theory of two particles in a generic D-dimensional space. For the s-wave problem, by adopting an on-shell approximation for the T-matrix equation, we derive analytical formulas which connect the Fourier transform V similar to(k) of the interaction potential to the s-wave phase shift. In this way we obtain explicit expressions of the low-momentum parameters g similar to 0 and g similar to 2 of V similar to(k) = g similar to 0 + g similar to 2k2 + center dot center dot center dot in terms of the s-wave scattering length as and the s-wave effective range rs for D = 3, D = 2, and D = 1. Our results, which are strongly dependent on the spatial dimension D, are a useful benchmark for few-body and many-body calculations. As a specific application, we derive the zero-temperature pressure of a two-dimensional uniform interacting Bose gas with a beyond-mean-field correction which includes both scattering length and effective range.

Giornale/Rivista: PHYSICAL REVIEW A

Volume: 107 (3)      Da Pagina: 33325-1  A: 33325-8

Maggiori informazioni: The authors thank S. K. Adhikari, G. Bertaina, A. Cappellaro, L. Dell’Anna, and A. Tononi for useful comments and suggestions. This work has been partially supported by the Iniziativa Specifica Quantum of INFN, by the BIRD grant Ultracold atoms in curved geometries of the University of Padova, and by the European Union-NextGenerationEU within the National Center for HPC, Big Data and Quantum Computing (Project No. CN00000013, CN1 Spoke 1: Quan-tum Computing).
Parole chiavi: Nonsingular Integral-equation; Effective-field Theory; Renormalization
DOI: 10.1103/PhysRevA.107.033325

Citazioni: 6
dati da “WEB OF SCIENCE” (of Thomson Reuters) aggiornati al: 2025-05-18
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