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Mapped Grid Methods Applied to the Slow Variable Discretization--Enhanced Renormalized Numerov Approach.

Juan Blandon1,2, Gregory A Parker2, Christopher Madrid1

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We developed a new hyperspherical coordinate mapping for atom-dimer scattering calculations. This method improves accuracy and cost-effectiveness for cold and ultracold atom interactions.

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Area of Science:

  • Atomic and Molecular Physics
  • Quantum Chemistry
  • Scattering Theory

Background:

  • Accurate calculations of atom-dimer scattering are crucial for understanding cold and ultracold atomic systems.
  • Existing numerical methods can be computationally expensive and limited in accuracy for complex potentials.

Purpose of the Study:

  • To introduce a novel hyperspherical coordinate mapping procedure for the slow variable discretization-enhanced renormalized Numerov method.
  • To enhance the accuracy and cost-effectiveness of calculating cold and ultracold atom-dimer scattering.
  • To optimize numerical grid point spacing based on interaction potential characteristics.

Main Methods:

  • Implementation of a hyperspherical coordinate mapping within the slow variable discretization-enhanced renormalized Numerov method.
  • Optimization of numerical grid point spacing tailored to the interaction potential's shape.
  • Application to elastic scattering calculations for the HeH2 system.

Main Results:

  • Demonstrated improved accuracy and computational efficiency for atom-dimer scattering.
  • Successfully adapted the numerical grid to the specific interaction potential.
  • Achieved comparable or improved results to established methods like MOLSCAT.

Conclusions:

  • The hyperspherical coordinate mapping procedure offers a more accurate and efficient approach to atom-dimer scattering.
  • This method provides a flexible way to optimize calculations for various interaction potentials.
  • The technique is validated by successful application to the HeH2 system.