Relativistic and QED corrections for the beryllium atom

Area of Science:

• Atomic Physics
• Quantum Electrodynamics
• Relativistic Quantum Mechanics

Background:

• Accurate theoretical calculations are crucial for understanding atomic structure and spectra.
• Beryllium (Be) and its ions are fundamental systems for testing quantum theories.
• Previous calculations lacked comprehensive relativistic and quantum electrodynamics (QED) corrections.

Purpose of the Study:

• To compute complete relativistic and QED corrections of order alpha(2) Ry and alpha(3) Ry for the ground state of beryllium and its positive ion.
• To provide high-precision theoretical predictions for atomic energy levels and ionization potentials.
• To validate theoretical methods by comparing with experimental data.

Main Methods:

• Utilized a basis set of correlated Gaussian functions.
• Optimized Gaussian function exponents against nonrelativistic binding energies.
• Performed calculations including complete relativistic and QED corrections.

Main Results:

• Calculated Bethe logarithms for Be: ln(k(0)(Be)) = 5.750 34(3).
• Calculated Bethe logarithms for Be+: ln(k(0)(Be+)) = 5.751 67(3).
• Determined a recommended ionization potential for Be: 75 192.514(80) cm(-1).

Conclusions:

• The high precision of the calculated Bethe logarithms demonstrates the capability for accurate theoretical predictions of energy levels in light atoms and ions.
• The agreement between the calculated ionization potential and experimental values validates the employed theoretical approach.
• This work provides benchmark data for the beryllium atom and its ion, advancing the field of atomic physics.