Analytical theory of charge-exchange-caused dips in spectral lines of He-like ions from laser-produced plasmas

Abstract

Previously we discovered a way for producing not-yet-available fundamental data on charge exchange between multicharged ions, virtually inaccessible by other experimental methods. It was based on the formation of dips (called x-dips) in spectral lines of hydrogen-like ions from laser-produced plasmas. At that time the x-dip phenomenon was considered to be possible only in spectral lines of hydrogenic systems: due to the existence of exact algebraic (higher than geometrical) symmetries relevant only to hydrogenic systems and to the corresponding two-Coulomb-centre systems (dicentres) having one electron. In the present paper, by engaging the concept of an approximate algebraic symmetry of two-electron dicentres (and of helium-like ions), we opened up the way to significantly broaden the scope of experimental studies of the x-dip phenomenon-to studies of possible x-dips in spectral line profiles emitted by He-like ions in laser-produced plasmas. We identified three prospective two-electron dicentres and calculated analytically theoretical positions of the x-dips in the corresponding He-like spectral lines (though future experimental and theoretical studies should not be limited to these three two-electron dicentres). Since future experimental and theoretical studies should not be limited to these three two-electron dicentres, we presented also a table containing 15 prospective He-like spectral lines and 10 corresponding solid targets for observing x-dips in laser-produced plasmas. For completeness we presented also a similar table for H-like lines. It presented 16 prospective H-like spectral lines and 11 corresponding solid targets for observing x-dips in laser-produced plasmas. From the shape of experimental x-dips it is possible to determine the rate coefficient of charge exchange in the corresponding dicentre, as demonstrated previously. Therefore the results of the present paper should very significantly extend the range of fundamental data on charge exchange between multicharged ions that can be obtained via the x-dip phenomenon, but not by any other method.

Mathematics Behind the Heisenberg Uncertainty Principle

“…This contrast to the quantum world, since atoms and subatomic particles have very small masses, the effect increasing of the accuracy of their positions will be accompanied by increasing uncertainty related with their velocities. It can be stated that one of fundamental principles in quantum physics is Heisenberg uncertainty since this principle reveal a fundamental aspect of the behavior of matter and energy at the quantum level (Dalimier et al, 2014), and it has important implications for our understanding of the fundamental nature of the universe. There are several applications of Heisenberg uncertainty that will discuss briefly in the following: (1) The uncertainty principle proves a limitation measurement on the precision with which certain physical quantities, such as position and momentum, also energy and time.…”

Review of Langmuir-Wave-Caused Dips and Charge-Exchange-Caused Dips in Spectral Lines from Plasmas and their Applications

“…The reason is the existence of an additional conserved quantity for the corresponding two-center Coulomb system with one bound electron. Recently we showed that X-dip phenomena are possible in spectral lines of helium-like ions from laser-produced plasmas [24,25]. The reason is the existence of an approximate additional conserved quantity for the corresponding two-center Coulomb system with two bound electrons [26].…”