9. Atoms V and Atoms in External Fields I

The professor begins the lecture by discussing the importance of MIT OpenCourseWare and transitions into the topic of atoms, particularly the effects of external magnetic fields on them. The lecture wraps up the discussion on atoms without an external field and introduces the concept of isotope shifts, providing specific examples with lithium and rubidium atoms. The isotope shift is explained in terms of mass and volume effects, and the precision of modern experiments allows for the calculation of these effects and the extraction of information about atomic nuclei sizes.

The lecture continues by addressing a question from the previous class regarding the minimum angular momentum required to observe a deformation of a nucleus or any anisotropic shape. The professor explains the concepts of lab frame versus body-fixed frame and how different angular momenta (I=0, 1/2, 1) can reveal information about the object's shape, such as dipole and quadrupole moments. The discussion also explores the philosophical implications of measurement and existence regarding deformation in the lab frame versus the body-fixed frame.

This section delves into the nuances of spectroscopic observations and the implications for understanding the deformation of objects like molecules or nuclei. The professor discusses the conditions under which angular momentum can be added without altering the internal structure and how this affects the interpretation of deformation. Examples are provided to illustrate the points, including the case of a weakly bound molecule that cannot withstand angular momentum without disintegrating, as opposed to a stable molecule or a nucleus with excited states that can exhibit deformation.

The professor provides a historical overview of the development of hydrogen spectroscopy, highlighting key discoveries such as the Lamb shift and the associated QED corrections. The discussion includes the evolution of technology and experimental techniques that have allowed for increasingly precise measurements, as well as the theoretical advancements that have kept pace with these improvements. The lecture touches on the historical papers that led to the understanding of the need for QED corrections and the technological milestones that enabled their measurement.

The lecture continues with an exploration of the advances in hydrogen spectroscopy, focusing on the increasing precision of measurements and the implications for fundamental physics. The discovery of the Lamb shift and its subsequent measurements with higher accuracy are discussed, leading to the introduction of the proton radius puzzle. This puzzle arose from a discrepancy between the proton size determined from hydrogen spectroscopy and that from scattering measurements, which remains an unresolved issue in physics.

The professor shifts the focus to the behavior of atoms in external magnetic fields, specifically discussing the fine structure and the lambda g-factor. The lecture explains how the introduction of an external magnetic field adds a new vector to the atomic system, leading to the Zeeman effect. The discussion covers the different g-factors for spin and orbital angular momentum and how they contribute to the magnetic moment of the atom in the presence of a magnetic field.

This section delves into the vector model and the Zeeman Hamiltonian to understand the behavior of atoms in weak magnetic fields. The professor explains how the projections of L and S on the J-axis are essential for calculating the Zeeman energies and derives the lambda g-factor using both the vector model and matrix elements. The lecture also touches on the internal magnetic field within an atom due to fine structure and the assumption of the weak field limit for the discussion.

The lecture continues with the topic of hyperfine structure in the presence of magnetic fields. The professor introduces the additional vector of nuclear angular momentum and discusses how it interacts with the electronic angular momentum and the external magnetic field. The weak field and strong field limits are explored, along with the derivation of the g-factor for hyperfine structure and the implications for the energy levels of the atom.

The professor concludes the lecture by examining the high field limit for atoms with hyperfine structure. The discussion focuses on how the electronic Zeeman energy dominates over the hyperfine coupling, leading to a different quantization of angular momentum along the magnetic field. The lecture explains the avoided crossings that occur during the transition from weak to strong field limits and how these can be understood through the diagonalization of the Hamiltonian. The sodium and rubidium 87 atoms serve as examples to illustrate the concepts.