Michał Gryziński

Not to be confused with politician and military leader Michał Grażyński.

Michał Gryziński
Born	(1930-09-29)September 29, 1930
Died	June 1, 2004(2004-06-01) (aged 73)
Known for	Free fall atomic model
Scientific career
Fields	Plasma physics
Institutions	Warsaw Institute of Experimental Physics Institute for Nuclear Research, Swierk (Otwock)

Michał Gryziński (29 September 1930 - 1 June 2004) was a Polish nuclear physicist specialized in plasma physics. He is developed the free-fall atomic model, a semiclassical approximation of the electron motion in the atom, averaging over trajectories to reproduce the results of quantum mechanics. His model provided a partial explanation for the Ramsauer effect.

Work

Electron scattering

Michał Gryziński worked in a hot plasma group on an 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 1957 to emphasize the importance of the orbital motion of electrons of a medium for stopping of slow charged particles. This work led him to a series of articles in 1965 about the problem of scattering with classical approximation of dynamics of the electrons.

The first three papers in 1965 developed a model electron scattering from atoms based on an empirical form for the velocity of electrons in the atom. These results where widely used for computing cross sections. For plasma research the inelastic scattering cross-section for electrons from atoms is needed to understand plasma energy loss mechanisms. The Born approximation cross sections work for energies above 200 eV; the Gryziński model has been shown match experiment better below 40eV. Similarly, using exact analytic calculations for hydrogen atoms, the classical Gryzinski model works well at low energy but fails for higher energies. Numerous extensions of Gryziński's model have been applied to atom-electron impact ionization.

The fourth paper in 1965 replaced the empirical velocity distribution with a model based on radial motion of a classical electron. Gryziński's later work all focused on this model.

Free-fall atomic model

This classical approximation of the 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), what 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.

In 2002 Gryzinski published a book length description of his atomic theory along with related topics. Gryzinski found the Bohr model unsatisfactory, presenting arguments against it,, especially for agreement with various scattering scenarios, to focus on nearly zero angular momentum trajectories: with electrons traveling through nearly radial trajectories. Attracted by the Coulomb field they free-fall to the nucleus, then increase the distance up to some turning point and so on.

The free-fall atomic model focuses on Kepler-like orbits for very low angular momentum. They are not exactly ellipses due to adding the magnetic dipole moment of the electron (electron magnetic moment) into considerations, which results in a Lorentz force proportional to $v/r^{3}$ and perpendicular to the velocity and spin of the electron. This spin–orbit interaction is nearly negligible unless the electron passes very close to the nucleus (small distance $r\approx 10^{-13}\mathrm {m}$, large speed $v$). This force bends the trajectory of the electron, preventing any collision with the nucleus.

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 - this is called 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 dynamics of a single electron in these models is:

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

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).

David Bates and R. Snyder examined the free-fall model and found it unsatisfactory (disagreeing with other models, not experimental data).

Bibliography

• M. Gryzinski (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. Gryzinski (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. Gryzinski (1965). "Radially Oscillating Electron-the Basis of the Classical Model of the Atom". Physical Review Letters. 14 (26): 1059. Bibcode:1965PhRvL..14.1059G. doi:10.1103/PhysRevLett.14.1059.
• M. Gryzinski (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. Gryzinski; J. Kunc; M. Zgorzelski (1972). "Ionization of atomic hydrogen by electron impact. Numerical calculations for the "free-fall" atomic model". Physics Letters A. 38 (1): 35–36. Bibcode:1972PhLA...38...35G. doi:10.1016/0375-9601(72)90964-4.
• M. Gryzinski; J. Kunc; M. Zgorzelski (1973). "Three-body analysis of electron-hydrogen atom collisions". Journal of Physics B. 6 (11): 2292–2302. Bibcode:1973JPhB....6.2292G. doi:10.1088/0022-3700/6/11/022.
• M. Gryzinski (1975). "Classical theory of atomic collisions. II. Low energy scattering". Journal of Chemical Physics. 62 (7): 2620–2628. Bibcode:1975JChPh..62.2620G. doi:10.1063/1.430846.
• M. Gryzinski (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. S2CID 121003387.
• M. Gryzinski (1987). "Diamagnetism of matter and structure of the atom". Journal of Magnetism and Magnetic Materials. 71 (1): 53–62. Bibcode:1987JMMM...71...53G. doi:10.1016/0304-8853(87)90333-7.
• M. Gryzinski (27 April 1989). "Cold fusion: what's going on?". Nature. 338 (6218): 712. Bibcode:1989Natur.338..712G. doi:10.1038/338712a0. S2CID 4363542.
• M. Gryzinski (1994). "Dynamical model of the molecular bond". Chemical Physics Letters. 217 (5–6): 481–485. Bibcode:1994CPL...217..481G. doi:10.1016/0009-2614(93)E1417-F.
• M. Gryzinski, J. A. Kunc (1999). "Double ionization of atoms by electrons". Journal of Physics B. 32 (24): 5789–5804. Bibcode:1999JPhB...32.5789G. doi:10.1088/0953-4075/32/24/314. S2CID 250874368.