Free-fall atomic model

The free-fall atomic model was introduced in 1965 by Michał Gryziński (1930–2004), a Polish nuclear and plasma physicist, as a result of adding the electron's magnetic moment to Bohr's atomic picture. Gryziński proposed the model as a consequence of his classical scattering theory. In this classical approximation, electrons do not circulate as in the Bohr model, but enter in an almost radial free-fall towards the nucleus. Due to their magnetic moment, the Lorentz force bends the electron trajectories to return them to their initial radius. This model has never been part of mainstream physics. It can be seen as an attempt to answer the question: "what would have happened had quantum mechanics not been invented?".^[1]

Model

For simplicity, most of these considerations neglect small changes of orientation of the spin axis of the electron, assuming that it is firmly oriented in space—it's called the rigid top approximation. The magnetic moment of the nucleus is thousands of times smaller than the electron's, so such hyperfine corrections can be neglected in basic models.

Finally, the basic considered Lagrangian for the dynamics of a single electron in these models is:

$𝐋 = \frac{1}{2} m 𝐯^{2} + \frac{Z e^{2}}{r} + \frac{Z e}{c} [𝐯 \cdot (\frac{μ \times 𝐫}{r^{3}})]$

The last term describes the interaction between the magnetic field of the traveling electron's magnetic moment and the electric field of the nucleus (spin-orbit interaction).

History

Michał Gryziński was working in a hot plasma group at the Polish Academy of Sciences on an approach to nuclear fusion which has later evolved into what is currently known as dense plasma focus. His experimental and theoretical considerations led him to his 1957 "Stopping Power of a Medium for Heavy, Charged Particles" Physical Review article emphasizing the importance of the orbital motion of electrons of a medium for stopping slow charged particles. This work received great interest and led him to a series of articles about the problem of scattering with a classical approximation of electron dynamics; his 1965 articles have received more than 2000 total citations.

The classical approximation of electron dynamics in atoms led him to the free-fall atomic model to improve agreement with scattering experiments compared to the popular Bohr approximation as circular orbits for electrons. This dominant radial dynamics of electrons makes the atom effectively a pulsating electric multipole (dipole, quadrupole), which allowed him to propose an explanation for the Ramsauer effect (1970) and improve agreement for modeling low-energy scattering (1975). His later articles attempt to expand these classical approximations to multielectron atoms and molecules.

Primary sources

M. Gryziński (1957). "Stopping Power of a Medium for Heavy, Charged Particles". Physical Review. 107 (6): 1471–1475. Bibcode:1957PhRv..107.1471G. doi:10.1103/PhysRev.107.1471.
M. Gryziński (1959). "Classical Theory of Electronic and Ionic Inelastic Collisions". Physical Review. 115 (2): 374–383. Bibcode:1959PhRv..115..374G. doi:10.1103/PhysRev.115.374.
M. Gryziński (1965). "Two-Particle Collisions. I. General Relations for Collisions in the Laboratory System". Physical Review A. 138 (2A): 305–321. doi:10.1103/PhysRev.138.A305.
M. Gryziński (1965). "Two-Particle Collisions. II. Coulomb Collisions in the Laboratory System of Coordinates". Physical Review A. 138 (2A): 322–335. doi:10.1103/PhysRev.138.A322.
M. Gryziński (1965). "Classical Theory of Atomic Collisions. I. Theory of Inelastic Collisions". Physical Review A. 138 (2A): 336–358. Bibcode:1965PhRv..138..336G. doi:10.1103/PhysRev.138.A336.
M. Gryziński (1965). "Radially Oscillating Electron—the Basis of the Classical Model of the Atom". Physical Review Letters. 14 (26): 1059–1059. Bibcode:1965PhRvL..14.1059G. doi:10.1103/PhysRevLett.14.1059.
M. Gryziński (1970). "Ramsauer Effect as a Result of the Dynamic Structure of the Atomic Shell". Physical Review Letters. 24 (2): 45–47. Bibcode:1970PhRvL..24...45G. doi:10.1103/PhysRevLett.24.45.
M. Gryziński; J. Kunc; M. Zgorzelski (1972). "Ionization of atomic hydrogen by electron impact. Numerical calculations for the "free-fall" atomic model". Physics Letters A. 38: 35–36. Bibcode:1972PhLA...38...35G. doi:10.1016/0375-9601(72)90964-4.
M. Gryziński (1972). ""Free-fall" solution of the Kepler problem in the presence of the magnetic moment". Physics Letters A. 41: 69–70. doi:10.1016/0375-9601(72)90637-8.
M. Gryziński, J. Kunc, M. Zgorzelski (1973). "Three-body analysis of electron-hydrogen atom collisions". Journal of Physics B. 6 (11): 2292–2302. doi:10.1088/0022-3700/6/11/022.CS1 maint: Multiple names: authors list (link)
M. Gryziński (1975). "Low energy scattering and the "free-fall" atomic model". Journal of Chemical Physics. 62 (7): 26–29. Bibcode:1975JChPh..62.2629G. doi:10.1063/1.430847.
M. Gryziński (1975). "Collisions between systems of Coulomb particles. I. Small‐angle scattering for time‐dependent fields". Journal of Chemical Physics. 62: 2610–2619. doi:10.1063/1.430845.
M. Gryziński (1975). "Classical theory of atomic collisions. II. Low energy scattering". Journal of Chemical Physics. 62: 2620–2628. doi:10.1063/1.430846.
M. Gryziński (1976). "Systematics of spectral lines and classical atom". Physics Letters A. 56 (3): 180–182. doi:10.1016/0375-9601(76)90638-1.
M. Gryziński (1980). "Stationary Kepler orbits of the electron with velocity-dependent perturbations — classical quantization". Physics Letters A. 76 (1): 28–30. doi:10.1016/0375-9601(80)90138-3.
M. Gryziński (1982). "Probabilistic description of the electron motion in the Coulomb field of the nucleus". Journal de Physique Lettres. 43 (12): 425–430. doi:10.1051/jphyslet:019820043012042500.
M. Gryziński, J. A. Kunc (1986). "Collisional ionisation and the atomic model". Journal of Physics B. 19 (16): 2479–2504. doi:10.1088/0022-3700/19/16/009.
M. Gryziński (1987). "Spin-dynamical theory of the wave-corpuscular duality". International Journal of Theoretical Physics. 26 (10): 967–980. Bibcode:1987IJTP...26..967G. doi:10.1007/BF00670821.
M. Gryziński (1987). "Diamagnetism of matter and structure of the atom". Journal of Magnetism and Magnetic Materials. 71 (1): 53–62. doi:10.1016/0304-8853(87)90333-7.
M. Gryziński (1987). "Angular distribution of electrons ejected from helium by protons and the FF atomic model". Journal of Physics B. 20 (18): 4741–4758. doi:10.1088/0022-3700/20/18/014.
M. Gryziński (1987). "Electronic structure of the H+2 molecule". Physics Letters A. 123 (4): 170–174. doi:10.1016/0375-9601(87)90698-0.
M. Gryziński (27 April 1989). "Cold fusion: what's going on?". Nature. 338 (6218): 712. Bibcode:1989Natur.338..712G. doi:10.1038/338712a0.
M. Gryziński, M. Kowalski (1993). "Theory of inner shell ionisation by positrons". Physics Letters A. 183 (2–3): 196–200. doi:10.1016/0375-9601(93)91169-6.
M. Gryziński (1994). "Dynamical model of the molecular bond". Chemical Physics Letters. 217 (5–6): 481–485. doi:10.1016/0009-2614(93)E1417-F.
M. Gryziński, M. Kowalski (1995). "Alignment of hydrogen atoms in e+ and e− ionising collisions". Physics Letters A. 200 (5): 360–364. doi:10.1016/0375-9601(95)00106-D.
M. Gryziński, J. A. Kunc (1999). "Double ionization of atoms by electrons". Journal of Physics B. 32 (24): 5789–5804. doi:10.1088/0953-4075/32/24/314.
M. Gryziński, J. A. Kunc (2000). "Differential scattering of electrons from atoms and molecules: I. General and exact binary-encounter approximation cross sections for three-dimensional transfer of energy and linear momentum from the incident electron to the electrons of the target". Journal of Physics B. 33 (8): 1549–1561. doi:10.1088/0953-4075/33/8/306.

References

↑ Petar V. Grujić, Classical theory of atomic collisions – The first hundred years, 2015.

External links

This article "Free-fall atomic model" is from Wikipedia. The list of its authors can be seen in its historical. Articles copied from Draft Namespace on Wikipedia could be seen on the Draft Namespace of Wikipedia and not main one.

[Grujic-1] Petar V. Grujić, Classical theory of atomic collisions – The first hundred years, 2015.

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v t e Atomic models
Single atoms	Dalton model (Billiard ball model) Lewis model (Cubical atom model) Nagaoka model (Saturnian model) Rutherford model (Planetary model) Bohr model (Rutherford–Bohr model) Bohr–Sommerfeld model (Refined Bohr model) Gryziński model (Free-fall model) Schrodinger model (Electron cloud model) Dirac-Gordon model (Relativistic atomic model) Thomson model (Plum pudding model) Vortex theory of the atom (Knot model)
Atoms in solids	Einstein solid Debye model Drude model Free electron model Nearly free electron model Band structure Density functional theory
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Scientists	Felix Bloch Niels Bohr Satyendra Nath Bose John Dalton Peter Debye Paul Dirac Paul Drude Albert Einstein Walter Gordon Michał Gryziński Irving Langmuir Gilbert N. Lewis Hantaro Nagaoka Isaac Newton Ernest Rutherford Erwin Schrödinger Arnold Sommerfeld J. J. Thomson Johannes Diderik van der Waals
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