Quantum defects at the critical charge

Area of Science:

• Atomic Physics
• Quantum Mechanics
• Spectroscopy

Background:

• The quantum defect is an empirical concept for spectral data interpolation and extrapolation.
• It provides insights into atomic isoelectronic sequences and electron scattering phase shifts.

Purpose of the Study:

• To examine a conjecture about the extrapolated quantum defect along isoelectronic sequences.
• To determine if the quantum defect is an integer when the outermost electron's binding energy vanishes in a singly negative ion.

Main Methods:

• Analysis of spectral data along isoelectronic sequences.
• Electronic structure calculations to determine asymptotic orbital behavior.
• Examination of the relationship between binding energy and quantum defect.

Main Results:

• The conjecture was examined for various atomic systems.
• In cases where binding energy vanishes, the asymptotic quantum defect is often an integer.
• This integer value correlates with the number of occupied electron shells of the same angular momentum.

Conclusions:

• The study supports the conjecture linking vanishing binding energy to integer quantum defects.
• Asymptotic behavior of the outermost electron orbital is hydrogen-like.
• Spectral analysis is a key method for determining these atomic properties.