Numerical solution of Dalgarno-Lewis equations by a mapped Fourier grid method

Area of Science:

• Computational physics
• Quantum chemistry
• Atomic physics

Background:

• Standard perturbation theory often involves complex radial differential equations.
• Accurate calculation of atomic polarizabilities is crucial for understanding light-matter interactions.

Purpose of the Study:

• To develop and validate a novel numerical approach for solving inhomogeneous radial differential equations.
• To compute static and dynamic dipole polarizabilities for hydrogen and lithium atoms.

Main Methods:

• Utilizing Fourier grid methods combined with a mapping scheme.
• Applying the Dalgarno-Lewis method for polarizability calculations.
• Employing an effective local potential approach with second-order energy correction for lithium.

Main Results:

• The novel algorithm demonstrates high efficiency and accuracy for hydrogen atom states (1s, 2s, 2p).
• Calculated dynamic dipole polarizabilities for hydrogen and lithium show excellent agreement with exact or established theoretical values.
• The method proves variationally stable for complex atomic systems.

Conclusions:

• The proposed Fourier grid method offers an efficient and accurate solution for calculating atomic polarizabilities.
• This technique is applicable to both simple (hydrogen) and more complex (lithium) atomic systems.
• The study validates the numerical approach against known results, confirming its reliability.