Michał Gryziński

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Michał Gryziński (29 September 1930 - 1 June 2004) was a Polish nuclear physicist, plasma physics specialist and the founder of the free-fall atomic model, an alternative theoretical formulation, a classical approximation asking for trajectories of electron averaging to probability densities described by quantum mechanics.


Michał Gryziński was working in group of hot plasma of Polish Academy of Sciences 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 1957 "Stopping Power of a Medium for Heavy, Charged Particles" Phys. Rev. article emphasizing importance of orbital motion of electrons of a medium for stopping of slow charged particles. This work has received great interest and have 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), 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.

Free-fall atomic model[edit]

In Bohr model electrons are imagined as traveling in circular orbits, which leads to many disagreements with experimental results. For example in observed electron capture process the nucleus captures electron from an orbital, what needs this electron to get to a distance of the range of nuclear forces (femtometers), which is many orders of magnitude smaller than in Bohr model. Another fundamental disagreement for circulating electron is created magnetic field, not observed for hydrogen. In contrast, angular momentum of electron in quantum ground state of hydrogen is zero.

Gryzinski presents many other argument, especially for agreement with various scattering scenarios, to focus on nearly zero angular momentum trajectories: with electrons traveling through nearly radial trajectories. They free-fall to the nucleus, then increase the distance up to some turning point and so on.

Free-fall atomic model focuses on Kepler-like orbits for very low angular momentum. They are not exactly ellipses due to adding magnetic dipole moment of electron (electron magnetic moment) into considerations, which results in Lorentz force proportional to and perpendicular to velocity and spin of electron. This spin-orbit interaction is nearly negligible unless the electron passes very close to the nucleus (small , large ). This force bends the trajectory of electron, preventing 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 - 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:

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

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