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 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 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 the QM not been invented?".^[1]

Model[edit]

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

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

$\mathbf {L} ={\frac {1}{2}}m\mathbf {v} ^{2}+{\frac {Ze^{2}}{r}}+{\frac {Ze}{c}}\left[\mathbf {v} \cdot \left({\frac {\mu \times \mathbf {r} }{r^{3}}}\right)\right]$

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

History[edit]

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

Classical approximation of dynamics of electrons in atoms has led him to the free-fall atomic model to improve agreement with scattering experiments comparing 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 of low energy scattering (1975). His later articles try to expand these classical approximations to multielectron atoms and molecules.

Primary sources[edit]

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 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[edit]

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

External links[edit]

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.

[1]

v t e Atomic models
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