Exact solution for quantum scattering from noncentral rational scatterers for ultracold molecules to quantum dots

Authors

Marvin A. Maulion ⋅ PH Physics Department, Western Mindanao State University and Department of Physics, University of San Carlos
M. Victoria Carpio-Bernido† ⋅ PH Research Center for Theoretical Physics, Central Visayan Institute Foundation and Department of Physics, University of San Carlos
Christopher C. Bernido ⋅ PH Research Center for Theoretical Physics, Central Visayan Institute Foundation and Department of Physics, University of San Carlos

Abstract

The double ring-shaped oscillator (DRO) was first introduced in 1989 where an exact solution was presented in a couple of articles, first using the Feynman path integral [Phys. Lett. A 134, 395 (1989)] followed by an algebraic approach [Phys. Lett. A 137, 1 (1989)]. Since then, interest has grown in the anisotropic DRO potential because of its widespread application from ultracold molecule collisions to ring-shaped molecules and double ring-shaped quantum dots, which all lack spherical symmetry [Nat. Phys. 13, 35 (2017), J. Low Temp. Phys. 190, 200 (2018)]. The quantum scattering from this potential has also been treated using the Feynman path integral formulation of the S-matrix [Phys. Lett. A 264, 45 (1999)]. In this talk, we generalize the DRO to a novel set of rational trigonometric forms of anisotropic potentials given by

V_n(r,θ) = αf(r) + A[4r²cos²ⁿ(θ/2)]⁻¹ + B[4r²sin²ⁿ(θ/2)]⁻¹

The case n = 1, is akin to the DRO introduced earlier. We solve the quantum problem for this potential using the Jacobi partial waves in contrast to the spherical harmonics normally used in partial wave analysis. An exact quantum scattering solution for this set of noncentral rational scatterers is then presented where we obtain the scattering amplitude and the total scattering cross-section.

About the Speaker

Christopher C. Bernido, Research Center for Theoretical Physics, Central Visayan Institute Foundation and Department of Physics, University of San Carlos

Christopher Bernido obtained his Ph.D. and M.S. Physics degrees from the State University of New York at Albany, and B.S. Physics degree from the University of the Philippines Diliman (UPD). He was a Research Fellow of the Alexander von Humboldt Foundation (Germany) from 1987 to 1989. From 1996 to 2001, he was a Senior Associate Member of the International Centre for Theoretical Physics in Trieste, Italy. Chris was the Director of the National Institute of Physics in UPD from 1983 to 1986 and served as President of the Samahang Pisika ng Pilipinas (SPP) from 1984 to 1987. He is the founding Director of the Research Center for Theoretical Physics, Central Visayan Institute Foundation, which organizes international workshops with Proceedings published by the American Institute of Physics and World Scientific. He was elected member of the National Academy of Science and Technology in 2007 and elected Fellow of the SPP in 2016.

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Issue

2022: Proceedings of the 40th Samahang Pisika ng Pilipinas Physics Conference

Article ID

SPP-2022-INV-2B-05

Section

Invited Presentations

Published

2022-10-02

How to Cite

[1]

MA Maulion, MV Carpio-Bernido†, and CC Bernido, Exact solution for quantum scattering from noncentral rational scatterers for ultracold molecules to quantum dots, Proceedings of the Samahang Pisika ng Pilipinas 40, SPP-2022-INV-2B-05 (2022). URL: https://proceedings.spp-online.org/article/view/SPP-2022-INV-2B-05.