Heavy Positive Ions Research Articles

Evidence of heavy positive ions at the summer Arctic mesopause from the EISCAT UHF incoherent scatter radar

A confined layer characterised by narrow incoherent scatter spectra has been observed between 86 and 88 km altitude in the high latitude summertime D‐region with the EISCAT radar. Properties of the background plasma inferred from spectral measurements outside the layer are in close agreement with model predictions, but the localised minima in spectral width imply much heavier positive ions within the layer. This feature is interpreted as being due to the presence of large clustered ions with mass of the order of 500 amu, which are possibly hydrated protons with a mean hydration index of almost 30.

Evidence for Chain Molecules Enriched in Carbon, Hydrogen, and Oxygen in Comet Halley

In situ measurements of the composition and spatial distribution of heavy thermal positive ions in the coma of comet Halley were made with the heavy-ion analyzer RPA2-PICCA aboard the Giotto spacecraft. Above 50 atomic mass units an ordered series of mass peaks centered at 61, 75, 91, and 105 atomic mass units were observed. Each peak appears to be composed of three or more closely spaced masses. The abundances decrease and the dissociation rates increase smoothly with increasing mass. These observations suggest the presence of chain molecules that are enriched in carbon, oxygen, and hydrogen, such as polyoxymethylene (polymerized formaldehyde), in comet Halley.

Total binding energy of heavy positive ions including density treatment of Darwin and Breit corrections

Previous work on the relativistic Thomas-Fermi treatment of total energies of neutral atoms is generalised to heavy positive ions. To facilitate quantitative contact with the numerical predictions of Dirac-Fock theory, Darwin and Breit corrections are expressed in terms of electron density, and computed using input again from relativistic Thomas-Fermi theory. These corrections significantly improve the agreement between the two seemingly very different theories.

Dimensionality dependence of energy of heavy positive ions and the 1/Z expansion.

With interactions chosen to satisfy Poisson's equation in d dimensions, the form of the total energy E(Z,N,d) of an atomic ion having nuclear charge Ze and N electrons is considered for large Z within the context of the 1/Z expansion. In particular, the form of the coefficients of this expansion is displayed at large N, the nth order coefficient being shown to be proportional to ${N}^{n+\ensuremath{\alpha}}$ where \ensuremath{\alpha} is given explicitly and depends solely on dimensionality. The singular point is at d=4, in contrast to the situation when the 1/r Coulomb interaction is directly taken over into d dimensions.

Analytic properties of the relativistic Thomas-Fermi equation and the total energy of atomic ions.

The analytic properties of solutions of the relativistic Thomas-Fermi equation which tend to zero at infinity are first examined, the neutral-atom solution being a member of this class. A new length is shown to enter the theory, proportional to the square root of the fine-structure constant. This information is used to develop a perturbation expansion around the neutral-atom solution, corresponding to positive atomic ions with finite but large radii. The limiting law relating ionic radius to the degree of ionization is thereby displayed in functional form, and solved explicitly to lowest order in the fine-structure constant. To embrace this knowledge of heavy positive ions, as well as results from the one-electron Dirac equation, a proposal is then advanced as to the analytic form of the relativistic total energy E(Z,N) of an atomic ion with nuclear charge Ze and total number, N, of electrons. The fact that, for Ng1, the nucleus is known only to bind Z+n electrons, where n is 1 or 2, indicates nonanalyticity in the complex Z plane, represented by a circle of radius Z\ensuremath{\sim}N. Such nonanalyticity is also a property of the nonrelativistic energy derived from the many-electron Schr\odinger equation. The relativistic theory, however, must also embody a second type of nonanalyticity associated with the known property for N=1 that the Dirac equation predicts electron-positron pair production when the electronic binding energy becomes equal to twice the electron rest mass energy. This corresponds to a second circle of nonanalyticity in E(Z,N), and hence to a Taylor-Laurent expansion of this quantity in the atomic number Z. The relation of this expansion to the Layzer-Bahcall series is finally discussed.

Heavy ionospheric ions in the formation process of noctilucent clouds

Results from a multinational rocket experiment in noctilucent cloud (NLC) conditions are presented. Weak NLC was detected at 83 km by visible photometry. Two separate ion mass spectrometer experiments both detected a narrow layer of very heavy positive ions at 90 km. The mass distribution of the large ions showed an increase of “most abundant mass” with height up to 90 km, indicating a temperature decrease up to that altitude. At 90 km the ion size approached the critical size at which nucleation of ice particles can start. If water ice particles would be formed in such a layer, they would continue to grow, as long as the ambient temperature is low enough and the water supply sufficient. While sedimenting through the atmosphere, they would add to the existing population of aerosol particles and thereby increase the total surface area of particles. Such an increased surface area of small particles would increase the loss rate for electrons and cause a deficiency of electrons at heights below the nucleation layer. A pronounced deficiency of electrons below 90 km was found in the measurements. With a theoretically modeled mesospheric H2O concentration, ice particle growth at 90 km is impossible. This situation may, however, change completely under the influence of an upwelling in the mesosphere. In addition to lowering the sink rate of the particles, such an upwelling would increase the concentration of H2O by vertical transport, and lower the gas temperature, which would also enhance the probability of particle growth. The upwelling would have to terminate in a horizontal motion above 90 km. At this height the rocket measurements show marked changes in the atomic oxygen concentration, electron/positive ion ratio and inferred concentrations of nitric oxide and negatively charged aerosol particles in addition to abrupt changes in positive ion composition.

The 1/Z expansion for heavy positive atomic ions

The 1/Z expansion of the total energy E(Z,N) is compared with a recent result giving the total energy of heavy positive atomic ions in the weak ionization limit N/Z near to unity. The leading term in the asymptotic limit of the high order coefficients of the 1/Z expansion for large N is thereby determined precisely. The results are finally compared and contrasted with the treatment by Stillinger of the He-like series with N=2.

Relativistic total energy of heavy atomic ions: Dimensionality dependent scaling

AbstractThe scaling property of the relativistic total energy E (Z, N) established by Marconi and the writer for heavy positive ions with N electrons and atomic number Z is demonstrated, by setting up the self‐consistent relativistic Thomas–Fermi equation in d dimensions, to be a special case of the scaling property α being the fine structure constant.

Scaling properties of total energy of heavy positive ions in d-dimensions

Using density functional theory in the asymptotic limit of very heavy positive ions, it is demonstrated that the well-known scaling property of the total energy E3(Z, N) of an ion with N electrons and atomic number Z is a special case of the d-dimensional result Ed(Z, N)=Z(4+4d−d2)/d(4−d)fd (N/Z):d≠4.

Relativistic total energy and chemical potential of heavy atoms and positive ions

The relativistic Thomas-Fermi theory, with a finite nucleus, is used to study the variation of the chemical potential mu with atomic number Z and number of electrons N(N<or=Z). This is done by solving a suitable dimensionless form of the differential equation for the self-consistent field for the semiclassical radius of the positive ions. Integrating the relation mu =( delta E/ delta N)Z the difference between the total energy of positive ions and that of the corresponding neutral atom has been obtained. The scaling predictions of Marconi and one of the authors are confirmed by their numerical calculations, since the dependence on the nuclear radius for any reasonable variation of this quantity is of negligible consequence. Finally, attention is given to bringing the first principles calculation of the relativistic Thomas-Fermi total energy of neutral atoms which they have carried out into contact with the Dirac-Fock results of Desclaux. To do so, it proves necessary to correct the energy contributions of the K- and L-shell electrons by means of the Sommerfeld formula, thereby generalising the non-relativistic boundary correction of Scott.

Energy relations in the density functional theory of d-dimensional heavy positive ions

By means of the virial theorem, the total energy E, eigenvalue sum E s and chemical potential μ are related in a heavy positive ion in d dimensions. The scaling properties of these quantities in two dimensions are thereby established.

Chemical potential and total energy of heavy positive ions in extremely strong magnetic fields, near the weak ionisation limit

The Thomas-Fermi equations for heavy positive ions in the limit of extremely strong magnetic fields H is solved analytically by perturbation theory about the neutral atom solution. This is useful for an ion, with atomic number Z and N(<or=Z) electrons, with small ionisation number, i.e. when q (=1-N/Z) is small.

Total energy of heavy positive ions especially near the weak ionization limit

Results, both analytical and numerical, for the total energy of heavy positive ions are presented. The q dependence of various energy-related quantities near the weak ionization limit (q → 0) is studied, q being 1−N/Z for N electrons and nuclear charge Ze.

Chemical potential and total energy of heavy positive atomic ions in the weak ionization limit

The chemical potential μ (Z,N) of a heavy positive ion with nuclear charge Ze and N electrons is obtained from the Thomas–Fermi theory near the weak ionization limit specified by q = 1−(N/Z) small as where c = 1/2 (731/2−7). The corresponding form of the total energy E(Z,N) is obtained in terms of the neutral atom energy E(Z,Z) as

Relativistic theory of binding energies of heavy positive ions

AbstractThe self‐consistent relativistic Thomas–Fermi theory of heavy positive ions with N electrons and nuclear charge Ze is shown to lead to a chemical potential μ which has the scaling property with ϵ = α2Z2, α being the fine structure constant. Combining this with the Layzer–Bahcall expansion for the total energy E(Z, N), namely, it is proved that the coefficients Enm (N) at large N have the asymptotic behavior Nn–2m/3#1/3. The corresponding result for the scaling of the relativistic Thomas–Fermi energy is Scaling properties of the higher order terms in Enm (N) and E(Z, N) are also proposed.

Energy of heavy positive ions related to eigenvalue sum and chemical potential

It is shown that for heavy positive ions, the relation that the total energy is 3/2 times the sum of the eigenvalues is modified by a contribution from the chemical potential. This additional term vanishes in the limit of a neutral atom.

Ion Detection Using a Continuous Channel Electron Multiplier

A spiral type continuous channel multiplier was used for pulse counting heavy positive ions. The shape of the output pulses was studied. The pulse risetime was found to be very long and composed of numerous after-pulsing as revealed by the ``staircase'' appearance of the pulse. As a consequence, the count rate capability is greatly hampered. Detection of the positive ions by a catcher foil and collection of the secondary electrons lead to a smooth pulse clean of any after-pulsing and to a greatly improved count rate capability.

Spectroscopic and thermal temperatures in the return stroke of lightning

Two different models of the temperature and state of ionization in the return stroke of a cloud-ground lightning stroke are in use in the literature. In the model that has been adopted for interpretation of the spectroscopic data on lightning, the mechanism of capture of free electrons to form negative oxygen ions is disregarded, the ionization being assumed to exist in the form of free electrons and heavy positive ions. In this case the thermalization time of the channel is expected to be short, so that the optical and thermal temperatures are effectively equal. In the model that accepts negative ion formation as a fundamental process, the ionization behind the tip of the return stroke is considered to be rapidly interchangeable between free electrons and heavy atomic and molecular oxygen ions. It is expected on this model that there exists a distinct time lag of the thermal temperature behind the optical temperature.

Ray tracing in the ionosphere at VLF—I

Booker's method of ray tracing in a horizontally stratified magneto-ionic medium is extended to deal with frequencies so low that the effect of heavy positive ions is important. Some rays are traced in a suitable model of the topside ionosphere.

Sporadic E Theory. I. Collision-Geomagnetic Equilibrium

Abstract A simple equilibrium theory of ionization transport in the ionosphere is described which predicts a tendency for thin layers of overdense ionization (sporadic E layers) to form in the E-region. Such layers can be produced by the dominance of any of five mechanisms of ionization convergence. Three of these mechanisms involve the neutral wind shear and two involve the neutral wind. The theory assumes that ambipolar diffusion of the electrons and heavy positive ions takes place under the influence of the forces due to neutral collisions and the geomagnetic field. The layer formation tendency is strongest for the principal part of the wind shear convergence mechanism in the lower E-region at those altitudes where the neutral vorticity is antiparallel to the geomagnetic field, land in the upper E-region where the neutral vorticity is perpendicular to the geomagnetic field in the westward (eastward) sense in the northern (southern) geomagnetic hemisphere. The layer formation tendency is strongest for t...