In 1921, Otto Stern conceived the idea for an experiment that would decide between a classical and a quantum description of atomic behavior, as epitomized by the Bohr–Sommerfeld–Debye model of the atom. This model entailed not only the quantization of the magnitude of the orbital electronic angular momentum but also of the projection of the angular momentum on an external magnetic field – the so‐called space quantization. Stern recognized that space quantization would have observable consequences: namely, that the magnetic dipole moment due to the orbital angular momentum would be space quantized as well, taking two opposite values for atoms whose only unpaired electron has just one quantum of orbital angular momentum. When acted upon by a suitable inhomogeneous magnetic field, a beam of such atoms would be split into two beams consisting of deflected atoms with opposite projections of the orbital angular momentum on the magnetic field. In contradistinction, if atoms behaved classically, the atomic beam would only broaden along the field gradient and have maximum intensity at zero deflection, i. e., where there would be a minimum or no intensity for a beam split due to space quantization. Stern anticipated that, although simple in principle, the experiment would be difficult to carry out – and invited Walther Gerlach to team up with him. Gerlach's realism and experimental skills together with his sometimes stubborn determination to make things work proved invaluable for the success of the Stern–Gerlach experiment (SGE). After a long struggle, Gerlach finally saw, on 8 February 1922, the splitting of a beam of silver atoms in a magnetic field. The absence of the concept of electron spin confused and confounded the interpretation of the SGE, as the silver atoms were, in fact, in a2S state, with zero orbital and
Relativistic aspects of orbital and magnetic anisotropies in the chemical bonding and structure of lanthanide molecules
Abstract The electronic structure of magnetic lanthanide atoms is fascinating from a fundamental perspective. They have electrons in a submerged open 4f shell lying beneath a filled 6s shell with strong relativistic correlations leading to a large magnetic moment and large electronic orbital angular momentum. This large angular momentum leads to strong anisotropies, i. e. orientation dependencies, in their mutual interactions. The long-ranged molecular anisotropies are crucial for proposals to use ultracold lanthanide atoms in spin-based quantum computers, the realization of exotic states in correlated matter, and the simulation of orbitronics found in magnetic technologies. Short-ranged interactions and bond formation among these atomic species have thus far not been well characterized. Efficient relativistic computations are required. Here, for the first time we theoretically determine the electronic and ro-vibrational states of heavy homonuclear lanthanide Er 2 and Tm 2 molecules by applying state-of-the-art relativistic methods. In spite of the complexity of their internal structure, we were able to obtain reliable spin–orbit and correlation-induced splittings between the 91 Er 2 and 36 Tm 2 electronic potentials dissociating to two ground-state atoms. A tensor analysis allows us to expand the potentials between the atoms in terms of a sum of seven spin–spin tensor operators simplifying future research. The strengths of the tensor operators as functions of atom separation are presented and relationships among the strengths, derived from the dispersive long-range interactions, are explained. Finally, low-lying spectroscopically relevant ro-vibrational energy levels are computed with coupled-channels calculations and analyzed.
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- Award ID(s):
- 1908634
- NSF-PAR ID:
- 10331541
- Date Published:
- Journal Name:
- New Journal of Physics
- Volume:
- 23
- Issue:
- 8
- ISSN:
- 1367-2630
- Page Range / eLocation ID:
- 085007
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract spin angular momentum. However, a key quantum feature whose existence the SGE was designed to test – namely space quantization of electronic angular momentum – was robust enough to transpire independent of whether the electronic angular momentum was orbital or due to spin. The SGE entails other key aspects of quantum mechanics such as quantum measurement, state preparation, coherence, and entanglement. Confronted with the outcome of the SGE, Stern noted: “I still have objections to the idea of beauty of quantum mechanics. But she is correct.” -
Ion time-of-flight velocity-map imaging was used to measure the kinetic-energy distributions of the I2 ion-pair fragments formed after photoexcitation of Ar⋯I2 complexes to intermolecular vibrational levels bound within the Ar + I2 (E, vE = 0–2) potential energy surfaces. The kinetic-energy distributions of the I2 products indicate that complexes in the Ar⋯I2 (E, vE) levels preferentially dissociate into I2 in the D and β ion-pair states with no change in I2 vibrational excitation. The energetics of the levels prepared suggest that there is a non-adiabatic coupling of the initially prepared levels with the continuum of states lying above the Ar + I2 (D, vD = vE) and Ar + I2 (β, vβ = vE) dissociation limits. The angular anisotropies of the I2 product signals collected for many of the Ar⋯I2 (E, vE) levels have maxima parallel to the laser polarization axis. This contradicts expectations for the prompt dissociation of complexes with T-shaped geometries, which would result in images with maxima perpendicular to the polarization axis. These anisotropies suggest that there is a perturbation of the transition moment in these clusters or there are additional intermolecular interactions, likely those sampled while traversing above the attractive wells of the lower-energy potentials during dissociation. I2 (D′, vD′) products are also identified when preparing several of the low-lying levels localized in the T-shaped well of the Ar + I2 (E, vE = 0–2) potentials, and they are formed in multiple νD′ vibrational levels spanning energy ranges up to 500 cm−1.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1088/1367-2630/ac1a9a
