In the realm of energy and material sciences, understanding the fundamental interactions within atoms is crucial. Two prominent researchers, Gordon Baym from the University of Illinois at Urbana-Champaign and Glennys Farrar from New York University, have delved into the intricacies of hyperfine interactions in atoms, particularly hydrogen and positronium. Their work, published in the journal Physical Review A, offers insights that could have implications for various fields, including energy research.
The hyperfine interaction in the ground state of a hydrogen atom is inversely proportional to the cube of its radius. This raises a puzzling question: why doesn’t this interaction cause the hydrogen atom to collapse? Baym and Farrar approached this problem using a minimax variational calculation based on the exact Gordon solution of the Dirac equation for the hydrogen atom’s ground state.
Their findings reveal that in an assumed variational state of size R, when R minimizes the total energy, the magnetic moment of the electron assumes its usual value. However, when the atom’s size is smaller than the Compton wavelength of the electron (R < ħ/mc), the effective electron magnetic moment becomes essentially eR/2. This softens the hyperfine interaction and eliminates an energy minimum at small R, preventing the atom from collapsing. The magnetic moment of the proton is similarly suppressed, ensuring the stability of the atom. The researchers extended their variational calculation to positronium, finding simple results for the ground state energy and hyperfine interaction. They further generalized this calculation to Coulombic atoms of two fermions of arbitrary masses. Additionally, their work lays out a framework for treating diquarks as relativistic Coulombic systems in the presence of color electric and magnetic interactions. While the immediate practical applications to the energy sector may not be apparent, understanding the stability of atomic and subatomic systems is foundational to various energy technologies. For instance, advances in nuclear fusion research, which aims to replicate the sun's energy-producing process, rely on a deep understanding of atomic and subatomic interactions. Similarly, developments in quantum technologies, which could revolutionize energy storage and transmission, also benefit from such fundamental research. In conclusion, Baym and Farrar's work provides a deeper understanding of the hyperfine interactions in atoms, ensuring their stability and offering a framework for treating more complex systems. This research, published in Physical Review A, contributes to the broader scientific knowledge base that underpins technological advancements in the energy sector. This article is based on research available at arXiv.