Stochastic theory for rate constants of chemical reactions in liquid solution

The stochastic model of irreversible processes is developed in a fashion that yields expressions for the magnitudes and temperature dependences of chemical reaction rate constants. The model is sufficiently abstract to encompass reactions in liquids as well as those in gases. For liquid reactions both the general point of view and one feature of the results (the “frequency factor”) are apparently new. For gas reactions the viewpoints and the results are compatible with (though not as detailed as) those of well-established collision theory. An approximation (to the effect that nonreactive but energy-redistributing transitions are much more frequent than reactive ones) may limit the quantitative, though not the schematic, application of this development to reactions in the presence of an excess of inert diluent. The traditional assumption to the effect that reactants are in equilibrium with “activated complexes” (whether or not such exist in the sense of possessing well-defined microstates) is avoided. As in previous discussion of sufficient conditions for an Arrhenius rate law, in which certain complicating features (treated here) of the case of chemical reactions were ignored, the method used here involves taking explicit account of the role of those (rapidly equilibrating via frequent nonreactive transitions) degrees of freedom that serve as the activation-energy-supplying (and temperature defining) “reservoir” by use of an especially detailed form of stochastic master equation. A concise form for the master equation facilitates (1) the appropriate extension of the previously described steady state treatment of the case in which a “transition state” lasts sufficiently long to be internally equilibrated and (2) the treatment of the probably more realistic case in which reactants undergo transitions directly to products without a definable intermediate and in which “transition state” can only be defined in terms of an energy threshold in the reaction transition probability. The latter case is a generalization to arbitrary density of that originally treated by Ross and Mazur within the framework of collision theory for bimoleculear dilute gas reactions. The familiar exponential dependence on “free energy of activation” is obtained for both cases, but the physical basis for it is different (in both cases) from that provided by the classical version of transition state theory. The “frequency factor” is not in either case simplykT/h but rather is dependent on the fundamental couplings within the system. It is also dependent on an effective “number of states” of reactants, products, and reservoir. A brief discussion of the possible significance of this latter feature in both enzymatic catalysis and heterogeneous catalysis is presented.     

掺镨(Pr3+)和铥(Tm3+)氟化镓铟玻璃标准的和改进后的贾德-奥菲尔特理论研究

贾德-奥菲尔特(Judd-Ofelt,J-O)理论是半定量地研究稀土离子掺杂基质中4f能级间跃迁光学性质的经典理论,但标准的贾德-奥菲尔特理论表达式本身含有一定的简化近似和假设,应用于Pr3 等具有特殊能级的稀土离子时会产生异常结果。制备了掺Pr3 和Tm3 的氟化镓铟玻璃,研究了玻璃的吸收光谱。应用标准的和改进后的贾德-奥菲尔特理论分别拟合得到了不同的贾德-奥菲尔特强度参量和跃迁振子强度。通过分析对比可知,“超敏感跃迁”是产生异常贾德-奥菲尔特理论计算的重要因素;当加入了“超敏感跃迁”所对应奇数项约化矩阵元后,运用改进的贾德-奥菲尔特理论可计算出氟化镓铟玻璃中Pr3 较合理的贾德-奥菲尔特强度参量,并可对Tm3 的振子强度参量进行更好的拟合。     

The spin dynamics of an anisotropic fermi supefluid (3He?)

In this paper we develop a general theory of the spin dynamics of anisotropic Fermi superfluids of the generalized BCS type, under conditions which should be realistic for any such phase of liquid ³He occurring below 3 mK. No restrictions are placed on the nature of the pairing configuration. The system is described in terms of the total spin vector S, and a vector T(n) which describes the amplitude and spin quantization axes of the pairs forming at a given point n on the Fermi surface; the kinematic relations between these quantities are emphasized. An approximation of the Born-Oppenheimer type is used to derive the general equations of motion of S and T; it is pointed out that relaxation of T due to collisions is inhibited by the coherent nature of the superfluid state. The equations of motion are solved for the particular case of unsaturated c.w. resonance, and it is shown that the nature of the transverse (usual) resonance spectrum is a strong function of the kind of configuration occurring; in particular, either one or two finite-frequency resonances may occur, depending on the configuration. A resonance is also predicted to occur when the r.f. field is polarized along the static external field. Specific predictions of the form of the transverse and “longitudinal” spectra are made for all the unitary l = 1 states, and it is shown that these predictions are unaffected by renormalization effects. The “Balian-Werthamer” state is predicted to show a longitudinal resonance but no transverse shift. The theory is compared with other approaches to the problem and its relevance to the anomalous low-temperature phases of liquid ³He is discussed.     

Spatial and angular distribution of the heavy ion charge under channeling in crystals

A kinetic theory of passage of multiply charged heavy ions through crystals is developed that allows for diffusion in the transverse momentum space and ion-crystal charge exchange. The theory provides an adequate explanation for the observed angular distributions of heavy ions passing through oriented crystals, makes it possible to calculate the partial angular distributions of different charge states, and treats the discovered effects of “cooling” and “heating” of channeled ion beams in physical terms. The angular and spatial distribution of channeled ions with different energies is calculated. Whether a channeled beam of multiply charged heavy ions will be cooled or heated is related to the dependence of the electron capture and loss probabilities on the impact parameter when the ions interact with atomic chains. This interaction governs the run of the angular and spatial distribution of the channeled ion charge.     

Phase transitions in random Potts systems and the community detection problem: spin-glass type and dynamic perspectives

Phase transitions in spin-glass type systems and, more recently, in related computational problems have gained broad interest in disparate arenas. In the current work, we focus on the “community detection” problem when cast in terms of a general Potts spin-glass type problem. As such, our results apply to rather broad Potts spin-glass type systems. Community detection describes the general problem of partitioning a complex system involving many elements into optimally decoupled “communities” of such elements. We report on phase transitions between solvable and unsolvable regimes. A solvable region may further split into “easy” and “hard” phases. Spin-glass type phase transitions appear at both low and high temperatures (or noise). Low-temperature transitions correspond to an “order by disorder” type effect wherein fluctuations render the system ordered or solvable. Separate transitions appear at higher temperatures into a disordered (or an unsolvable) phase. Different sorts of randomness lead to disparate behaviors. We illustrate the spin glass character of both transitions and report on memory effects. We further relate Potts type spin systems to mechanical analogs and suggest how chaotic-type behavior in general thermodynamic systems can indeed naturally arise in hard computational problems and spin glasses. The correspondence between the two types of transitions (spin glass and dynamic) is likely to extend across a larger spectrum of spin-glass type systems and hard computational problems. We briefly discuss potential implications of these transitions in complex many-body physical systems.     

Plasma Sources in Analytical Mass Spectrometry

Abstract

The recent interest in gas discharge ion sources for analytical mass spectrometry illustrates the often cyclic nature of scientific progress. The ion source capabilities of a gas discharge were discovered by Goldstein [1] in 1886 and such discharges were used by the pioneer mass spectroscopists (Thomson, Aston, and Bainbridge) as a convenient source of ions. The simplicity of design (see Fig. 1) and the high output ion currents were decisive factors in such applications. Alternative ion sources then replaced the gas discharge, to the point where the production of ions by gaseous discharge was suggested, correctly, to be of “more historical than contemporary interest” [2]. Nevertheless, new requirements and developments, as described in this paper, have once again drawn attention to the plasma ion source as having possible specialized and valuable analytical applications.     

Statistical and dynamic intensities of atomic spectral lines in plasma

Based on the quasi-classical approach, we solve the problem of a radiative cascade between Rydberg states in the space of parabolic quantum numbers that correspond to atom (or ion) quantization in a plasma microfield. We consider the level population source associated with the dielectronic recombination of electrons on ions with the cores in an external electric field. We determine the populations of states and the intensities of transitions between levels with a small change in principal quantum number. These “dynamic” intensities are compared with the “ statistical” intensities that correspond to an equidistribution in Stark sublevels. An appreciable discrepancy was found between the two types of intensities in plasma of low density that corresponds to the dominance of radiative transitions over collisional transitions.     

Ionization loss of relativistic structural heavy ions in collisions with atoms

A nonperturbative theory of energy loss in collisions between structural, highly charged heavy ions moving at relativistic velocities and atoms is developed. A simple formula for effective deceleration is derived. By structural ions are meant ions containing partially filled electron shells. It is such ions characterized, as a rule, by a significant charge (for example, partially “stripped” uranium ions) that are used in numerous experiments involving the use of modern heavy-ion accelerators.     

Influence of the inverse sheath on divertor plasma performance in tokamak edge plasma simulations

Recently, it was shown that strong electron thermionic emission from material walls could result in the formation of an “inverse sheath,” which prevents the flow of cold ions to the wall.^[1–3] Such regimes look very favourably from the point of view of plasma–material interactions at the edge of magnetic fusion devices, where the problem of the erosion of plasma-facing components under ion irradiation is one of the key issues for the development of future magnetic fusion reactors. However, it is not clear whether such regimes are compatible with edge plasma parameters and heat removal requirements in fusion reactors. To address the issue of practicality of the “inverse sheath” regime for edge tokamak plasma conditions, we perform a set of numerical simulations with 2D edge plasma transport code UEDGE^[4] for a DIII-D-like geometry and magnetic configuration. To describe both “standard” and “inverse sheath” conditions within the framework of the UEDGE code (which does not consider the sheath region per se), at the material surfaces, we apply effective boundary conditions that emulate both “standard” and “inverse sheath” regimes. We demonstrate that, for the same input parameters, spatial distributions of edge plasma parameters corresponding to detached divertor and “inverse sheath” regimes are similar, with only a few minor differences. We discuss the compatibility of “inverse sheath” regimes with core plasma parameters.     

“Nonmagnetic” (antiferromagnetic) magnetic polaron

It is shown that, within deep narrow quantum potential wells in systems based on semimagnetic semiconductors containing Mn²⁺ ions, both magnitude and sign of the exchange interaction between electrons in the conduction band and in the d-shell of a magnetic ion depend significantly on the spatial position of this ion. This situation allows magnetic polarons with zero magnetic moment to appear, for which the localized-electron-induced spatial distribution of polarization of the surrounding magnetic ions exhibits an antiferromagnetic character. The possibility of experimental detection of these “nonmagnetic” magnetic polarons is considered.     

Temperature quenching of intracenter luminescence of Mn<Superscript>2+</Superscript> ions in diluted magnetic semiconductors

The Spectr-W³ database was developed in 2001–2013 and is available online (http://spectrw3. snz.ru). The database contains information on various spectroscopic constants of atoms and ions such as the wavelengths and probabilities of radiative transitions, energy levels of atoms and ions, ionization potentials, autoionization rates, and the parameters of analytical approximation of cross sections and rates of collisional transitions in atoms and ions. Spectr-W³ presently contains around 450 thousand records and is the world’s largest factual database on spectral properties of multicharged ions. A new stage of development of Spectr-W³, which involves adding a new section titled “Emission Spectrograms” to the database, commenced in 2014. In contrast to the already existing sections that contain tabulated data, this new section provides graphical data (with necessary explanatory notes) on the spectrograms of emission of atoms and ions excited in various plasma sources. The structure of sections of the Spectr-W³ database is characterized, and examples of queries and the corresponding search results are given.     

Sputtering of solids by heavy ions and temperature effects in electronic and lattice subsystems

The results of sputtering coefficient measurements for pure metals, alloys, amorphous alloys, semiconductors, and highly oriented pyrolytic graphite under irradiation by high energy ions are considered. The possible mechanisms of strong sputtering of materials with high defect concentrations are discussed. The three-dimensional thermal spike model (“hot ion track”) with the temperature dependence of thermodynamic parameters (specific heat thermal conductivity) is formulated for single-layer mono-and polycrystals and multilayer systems (materials). The results of a numerical solution to the introduced system of partial differential equations are considered for the lattice and electronic subsystem temperatures around and along the fast heavy ion trajectory as a function of the time t, as well as radial r and longitudinal z coordinates, taking into account possible phase transitions such as melting and evaporation. The results obtained are discussed.     

The Theory of the Rise of Sap in Trees: Some Historical and Conceptual Remarks

The ability of trees to suck water from roots to leaves, sometimes to heights of over a hundred meters, is remarkable given the absence of any mechanical pump. In this study I deal with a number of issues, of both a historical and conceptual nature, in the orthodox Cohesion-Tension (CT) theory of the ascent of sap in trees. The theory relies chiefly on the exceptional cohesive and adhesive properties of water, the structural properties of trees, and the role of evaporation (“transpiration”) from leaves. But it is not the whole story. Plant scientists have been aware since the inception of the theory in the late 19^th century that further processes are at work in order to “prime” the trees, the main such process – growth itself – being so obvious to them that it is often omitted from the story. Other factors depend largely on the type of tree, and are not always fully understood. For physicists, in particular, it may be helpful to see the fuller picture, which is what I attempt to provide in nontechnical terms.     

Statistical characteristics of the motion of a pair of heavy ions in non-convex cavities of complicated geometry with fixed crosspieces and charges

Using the method of classical trajectories, the motion of a pair of ions Cs⁺ and Cl^– in three non-convex closed cavities of complicated geometry containing neutral cylindrical “crosspieces” and charged spherical “nuclei” is simulated. The collisions of the ions with the cavity boundary, crosspieces, and nuclei are supposed to be inelastic. The signs of the charges of the nuclei are varied. In each cavity, in one of the calculation series, the nuclei are assumed to be shielded (to carry charges smaller than 1 a.u. in absolute value), whereas in another calculation series, the possibility of the mutual neutralization of an ion and an oppositely charged nucleus at their encounter is taken into account. The statistics of various events, such as the “stickings” of ions to nuclei, neutralizations of ions and nuclei, collisions of ions with obstacles, recombinations of ions, and dissociations of the CsCl ionic-bond molecule are analyzed.     

A class of exactly soluble many-body Hamiltonians with the interaction of substance and boson field

A general class of model systems of quantum statistical mechanics representing substance coupled to a discrete spectrum of a quantized boson field is studied on the basis of the “approximating (trial) Hamiltonian” method. Proof is presented that the models under investigation are exactly soluble in the thermodynamical limit. Besides, some characteristic features of the phase transitions in such systems are under consideration. Some concrete models are treated as an illustration.     

Dynamical aspects of nucleus-nucleus collisions

This is an extension of the macroscopic theory of nucleus-nucleus reactions described by Swiatecki. The fusion or reseparation of two colliding nuclei is treated according to a schematic model based on the “chaotic regime dynamics” (liquid-drop potential energy plus one-body dissipation). Attention is focused on three hurdles or “milestone configurations” that a colliding system may be faced with: the touching configuration, the conditional saddle-point configuration at frozen mass asymmetry, and the unconditional saddle-point configuration. Semi-empirical formulae are derived for the “extra push” (the extra energy needed in some situations to carry the system from the first to the second hurdle) and for the “extra-extra push” (the energy needed to carry the system from the first to the third hurdle). The theoretical formulae are confronted with measurements of fusion and evaporation-residue cross sections. A discussion of the implications for super-heavy-element reactions is given, using the production of element 107 in the bombardment of ²⁰⁹Bi with ⁵⁴Cr as a calibrating reaction.     

Structural phase transitions in ionic molecular solids

An overview is presented of our studies on the nature of structural instabilities in relatively complex ionic solids. These are based on parameter-free interionic potentials based on the Gordon-Kim modified electron gas formalism extended to molecular ions.

We describe the manner in which there emerge from these studies quite general concepts of “size” and “shape” as structural determinants. In particular, we discuss how these, and the approximate symmetries that they can produce, can provide a relatively simple structure-based explanation of the origins of incommensurate phases in these systems. However, we also emphasize that the existence of such symmetries does not guarantee an incommensurate phase. This can only be realized if long-range correlations are sufficiently strong to overcome random local disordering. Thus, either the molecular units are partially linked and/or there exist long-range Coulomb interactions between individual units.     

Influence of the surface electric field in ion-beam-surface interaction at grazing incidence

We have measured the polarization of light emitted after ion surface scattering at small angle of incidence. The measurements are carried out with H⁺-, H ₂ ⁺ - and He⁺-ions under UHV-conditions with mono- and polycrystalline targets. We explain the typical variation of the polarization as “post collision Stark interaction” (PCSI) in the surface electric field, which can force transitions between nearly degenerate terms. The electric field is composed of two different contributions, a strong but short range surface field which is “seen” by atomsand ions and a long range but weak field due to the image charge which is “seen” to first orderonly by ions. The influence of the electric field on H-Balmer radiation is negligible at typical survival distances r_s≧0.35nm. But in contrast to H-atoms He⁺-ions feel the additional influence of the image field leading to a strong alteration of the polarization of the emitted light. The polarization of the Balmer-radiation stemming from Coulomb exploding H ₂ ⁺ -beams is observed to be modified by the electric field of the “spectator proton”.     

An alternative to quantum theory

In a recent paper we have shown that continuous sets of resonances (as expressed by the nonvanishing of the kinetic collision operator) result in divergences in the traditional unitary transformation theory in addition to the usual ultraviolet divergences. Therefore, relaxation processes and lifetimes cannot be eliminated by unitary transformations diagonalizing the Hamiltonian. For this reason, we introduce a more general transformation theory based on nonfactorizable superoperators which “block diagonalize” the Hamiltonian superoperator and eliminate the divergence of the unitary transformation. This leads to a new concept of “observables” which are represented in general by operators which are both noncommuting and nondistributive. For example, to a single energy level we now associate a set of numbers corresponding to a probability distribution whose width is determined by the lifetime of the state. This new approach incorporates dissipation into the frame of quantum mechanics. It leads directly to a number of predictions such as the existence of a new anomalous Lamb shift dependent on lifetime as well as the appearance of a broken “time symmetry” in the structure of the energy spectrum. As this symmetry breaking depends on the arrow of time (thermodynamic equilibrium is approached in our future and not in our past) which is a property of our universe as a whole, we may call this new effect the “cosmological” Lamb shift. Of course subsequent experiments will have to explore the existence of this effect. Other consequences of this approach are briefly mentioned and will be developed in subsequent papers.