Modified Rydberg formula:
En = -Ry / (n - δl)²
n* = n - δl: effective quantum number
Ry = 13.6 eV (H), Z²·Ry (Z-core)
Quantum defect origin:
δl = -(∂φ/∂E)|_{E=0}
phase shift from core scattering
En = -Ry / (n - δl)²
n* = n - δl: effective quantum number
Ry = 13.6 eV (H), Z²·Ry (Z-core)
Quantum defect origin:
δl = -(∂φ/∂E)|_{E=0}
phase shift from core scattering
The quantum defect parameterizes how much the outer electron "sees" the non-Coulomb core. Large δ for s-states (deep core penetration), small δ for d-states (centrifugal barrier keeps electron out).