Sensitivity of approximate formulas for determining optical constants of thin films

The sensitivity of approximate formulas for determining the optical constants of thin films using measurement of reflectancesR and transmittancesT at normal incidence have been investigated theoretically. The ranges of refractive indexn, absorption indexk,2nk (=₂) andn ²–k ²(=₁) within relative errors of 5%, 10%, and 20% may be obtained. Selected signs of (₁)⁺ or (₁)^– have been determined. Validity of the condition n₀ A=n _s A has been also evaluated (A=1–R –T andA=1–R–T).     

The inverses-wave scattering problem for a class of potentials depending on energy

The inverse scattering problem is considered for the radials-wave Schrödinger equation with the energy-dependent potentialV ⁺(E,x)=U(x)+2 Q(x). (Note that this problem is closely related to the inverse problem for the radials-wave Klein-Gordon equation of zero mass with a static potential.) Some authors have already studied it by extending the method given by Gel'fand and Levitan in the caseQ=0. Here, a more direct approach generalizing the Marchenko method is used. First, the Jost solutionf ⁺(E,x) is shown to be generated by two functionsF ⁺(x) andA ⁺(x,t). After introducing the potentialV ^–(E,x)=U(x)–2 Q(x) and the corresponding functionsF ^–(x) andA ^–(x,t), fundamental integral equations are derived connectingF ⁺(x),F ^–(x),A ⁺(x,t) andA ^–(x,t) with two functionsz ⁺(x) andz ^–(x);z ⁺(x) andz ^–(x) are themselves easily connected with the binding energiesE _n ⁺ and the scattering matrixS ⁺(E),E>0 (the input data of the inverse problem). The inverse problem is then reduced to the solution of these fundamental integral equations. Some specific examples are given. Derivation of more elaborate results in the case of real potentials, and applications of this work to other inverse problems in physics will be the object of further studies.Physique Mathématique et Théorique, Equipe de recherche associée au C.N.R.S.     

The oscillator representation and the stability of three-body Coulomb systems

Within nonrelativistic quantum mechanics the Wick-ordering method, called the oscillator representation, is suggested for calculating the energy spectrum for a wide class of potentials allowing the existence of a bound state. As test cases, anharmonic (V(r)=r ²) and screened Coulomb potentials are considered. In particular, the method is applied to three-body Coulomb systems to obtain the dependence of the bound-state energy on the masses and charges of the particles. The calculations of the bound-state energies for the moleculesH ^–=(pee),H ₂ ⁺ =(ppe), (e ^–e^–e⁺) and (pp), (dd), (dt) prove the accuracy of the zeroth approximation to be better than one per cent. For the three-body Coulomb system with charges +, –, – and arbitrary masses the region of stability is determined. For the systems (pe ^–C⁺), (A ⁺e^–e⁺), and (pB ^–e^–) the critical masses are calculated to beM _c=1.945m_e,M _A=4.350m_e andM _B=1.575m_e. It turns out that the system (pe ^–e⁺) is unstable.     

The temperatures of protons andπ − mesons in central nucleus-nucleus interactions at a momentum of 4.5 GeV/c per incident nucleon

An estimate of the temperature of protons and ^– mesons in central He–Li, He–C, C–C, C–Ne, C–Cu, C–Pb, O–Pb, Mg–Mg interactions is presented. The results indicate an increase of the proton temperature with increasing mass numbers of projectile and target nuclei (A _p ,A _T ) fromT _p =(118±3) MeV for He–Li toT _p =(141±2) MeV for C–Pb. The temperature of ^– mesons does not depend onA _P ,A _T andT 95 MeV. A satisfactory fit for ^– mesons in C–Cu, C–Pb, O–Pb, Mg–Mg collisions can be achieved by using a form involving two temperatures,T ₁ andT ₂. The relative yield of the high temperature component (T ₂) is 24% for C–Cu, C–Pb, and Mg–Mg interactions. The observed results forT _P in C–Ne, C–Cu and C–Pb collisions are consistent with the prediction of the thermodynamic hagedorn model.     

New inequalities from local realism

The probabilistic formulation of local realism is shown to imply the existence of physically meaningful limits for arbitrary linear combinations of joint probabilities. The set of the so generated inequalities (setA) is wider than the previously known set of inequalities for linear combinations of correlation functions (setB). One particular inequality of the setA is shown to be violated by the probabilities of the Garg-Mermin model. The same model satisfies instead all the inequalities of the setB. As a consequence, the Garg-Mermin model is nonlocal and the setA provides physical restrictions not contained in the setB. 1. In the adopted formalism it is implicitly assumed that physical properties of the type are not created in the act of measurement. IfB(b) is measured on the systems, the setT is split into two parts,T(b _±), corresponding to the resultsB(b) = ±1, respectively. AlsoS is split intoS(b _±) from the existing correlation between and systems. If it is possible to predict that a measurement ofA(a) on the's of, say,S(b ₊) will give the results ±1 with respective probabilitiesP _±, then, on the basis of the probabilistic criterion of reality, we can attribute a physical property ₊ toS(b ₊) such that p(a ₊, ₊) is the probability ofA(a) = +1 inS(b ₊), p(a _–, ₊) is the probability ofA(a) = –1 inS(b ₊).It is natural to assume that ₊ belongs toS(b ₊) also ifA(a) isnot measured. In so doing, we exclude that future measurements create, with a retroaction in time, the physical properties of the statistical ensembles on which these measurements are performed.     

q-analog ofA m−1 ⊕A n−1 ⊂A mn−1

A natural embeddingA _m–1 A _n–1 A _mn–1 for the corresponding quantum algebras is constructed through the appropriate comultiplication on the generators of each of theA _m–1 andA _n–1 algebras. The above embedding is proved in theq-boson realization by means of the isomorphism between theA _q ^– (mn ~ ⁿ A _q ^– (m) ~ ^m A _q ^– (n)algebras.     

On the scalar-tetradic theories of gravitation: Cosmology and gravitational radiation

The so-called scalar-tetradic theoriesA andB generalize Møller's theory of gravitation. In this work, some results previously obtained in Møller's theory are extended to the theoriesA andB. When the parametersW and ^*. of the theoryA are not too small (or large), the losses of energy and angular momentum of a nongravitationally bound system are proved to be the same as in general relativity. The basic equations of cosmology are derived and some topics are treated. In particular, any density of energy ₀ (10^–29 g cm^–3 ₀ 10^–31 g cm^–3) appears to be compatible with the observational values ofH ₀ (Hubble constant) andqo (deceleration parameter) in the theory A; thus, no intergalactic energy assumption is necessary.     

Branching rules for conformal embeddings

We give explicit formulas for the branching rules of the conformal embeddingssu(n(n+1)/2)₁su(n) _n+2,su(n(n–1)/2)₁su(n) _n–2,sp(n)₁so(n)₄su(2) _n , andso(m+n)₁so(m)₁ so(n)₁ withm andn odd.This research was supported in part by CONICET, CONICOR and SECYT.     

Two singular integrals containing a partial wave of the two-body coulomb T-matrix

The operatorsT _C,l E+i0)[–G ₀(E+i0)]^1–i andT _C,l(E+i)G ₀[–iG ₀(E+i)]ⁱ acting on spaces of Hölder continuous, differentiable and analytic functions are investigated. The results of their action are expressed in terms of explicit singular factors and terms and Hölder (differentiable, analytic) functions. The most singular part of these operators is shown to be determined by a simple functional.     

Self-gravitating radiation in anti-de sitter space

Equilibrium configurations of self-gravitating massless thermal radiation inside spherical boxes of radiusR in asymptotically anti-de Sitter space (A = -3/b ₂) are constructed numerically for a range of central densities. For each box radius considered (R/b = 0, 1/2, 1, 2, 4, ), there is a unique configuration with maximal total mass and entropy, and another (at a lower central density) with maximum asymptotic red-shifted temperature. With the box removed toR=, the maximum total mass and entropy of self-gravitating thermal radiation areM _max 0.4598b0.7964(–A)^–1/2 andS _max1.3560a ^1/4 b ^3/2 3.0910a ^1/4(–A)^–3/4, and the maximum red-shifted temperature is     

Argon ion laser-induced BaS BΣ-AΣ, A′Π, aΠ, and XΣ fluorescence spectra: Analysis of A A′, A a, and A′ a perturbations

The 333.6-, 351.1-, and 363.8-nm lines of a cw argon ion laser are found to coincide with the BaS B¹Σ⁺-X¹Σ⁺ (12, 0) R(17), (6, 0) P(35), and (3, 0) R(125) transitions, respectively. Fluorescence transitions from the laser-prepared upper levels terminating in X¹Σ⁺ V = 0–28, A¹Σ⁺ V = 1–3, A′¹Π V = 1–13, and a³Π₁ V = 3–12 are assigned. These results are combined with a previous analysis of the extensively perturbed BaS A¹Σ⁺-X¹Σ⁺ system [R. F. Barrow, W. G. Burton, and P. A. Jones, Trans. Farad. Soc.67, 902–906 (1971)]. Every observed perturbation of the BaS A¹Σ⁺ state is electronically and vibrationally assigned. The levels a³Π₀ V = 10–13, a³Π₁ V = 12–14, a³Π₂ V = 15, and A′¹Π V = 10–13 are sampled via their perturbations of A¹Σ⁺ V = 0–2. Although the mutual interactions of the a³Π, A′¹Π, and A¹Σ⁺ states approach Hund's case (c) limit, a complete deperturbation is performed from a case (a) starting point. Of the five lowest energy electronic states of BaS, only b³Σ⁺ remains uncharacterized. Principal deperturbed molecular constants are (in cm⁻¹, 1σ uncertainties in parentheses):

Full-size image

     

Gas-phase vibrational spectroscopy and ab initio calculations of Rb(H2O)n and Rb(H2O)nAr cluster ions

The competition between ion–water electrostatic interactions and water–water hydrogen bonding in cluster ions depends on several factors, including charge density of the ion and temperature of the system. Infrared photodissociation spectra of Rb⁺(H₂O)_n=2–5 and Rb⁺(H₂O)_n=1–5Ar are presented here and compared to previous experiments involving potassium and cesium. The temperature, or internal energy, of hydrated rubidium cluster ions is controlled by varying the evaporative path available for cluster formation. Warmer clusters (with effective temperatures of 250–500 K) are formed by the evaporation of water, while colder clusters (40–120 K) can be formed by argon evaporation. Colder cluster ions tend to favor conformers with more hydrogen bonds compared to those cluster ions at warmer temperatures. Previous work from this laboratory has shown significant and dramatic differences between the spectra of hydrated potassium and cesium ions. With a charge density intermediate between that of K⁺ and Cs⁺, Rb⁺ plays an important role in bridging the gap in our previous studies.     

Beta-decay asymmetries in polarized12B and12N and theG-parity non-conservation

The decay asymmetries (A) in polarized¹²B and¹²N have been measured as a function of -ray energies (E). The coefficients _± inA = ±P(p/E) (1+_± E) have been determined to be _–(¹²B) =+(0.31±0.06)%/MeV and ₊(¹²N) = –(0.21±0.07)%/MeV. The experimental value, _––₊=(0.52±0.09)%/MeV, is larger than the prediction according to conservation of vector current which includes no second-class current, _––_{+ CVC}0.27%/MeV, and indicates the existence of the second-class induced-tensor current.This work has been done in collaboration with I. Tanihata and J. Göring.     

Molecular magnetism of a linear Fe(III)-Mn(II)-Fe(III) complex. Influence of long-range exchange interaction

The magnetic properties of [L-Fe(III)-dmg₃Mn(II)-Fe(III)-L] (ClO₄)₂ have been characterized by magnetic susceptibility, EPR, and Mössbauer studies. L represents 1,4,7-trimethyl-, 1,4,7-triazacyclononane and dmg represents dimethylglyoxime. X-ray diffraction measurements yield that the arrangement of the three metal centers is strictly linear with atomic distancesd _Fe-Mn=0.35 nm andd _Fe-Fe=0.7 nm. Magnetic susceptibility measurements (3–295 K) were analyzed in the framework of the spin-Hamiltonian formalism considering Heisenberg exchange and Zeeman interaction:=J _Fe-Mn(S _Fe1+S _Fe2)S _Mn +J _Fe-Fe(S _Fe1 S _Fe2) +g_B S _total B. The spinsS _Fe1=S _Fe2 =S _Mn=5/2 of the complex are antiferromagnetically coupled, yielding a total spin ofS _total=5/2 with exchange coupling constantsF _Fe-Mn=13.4 cm^–1 andJ _Fe-Fe= 4.5 cm^–1. Magnetically split Mössbauer spectra were recorded at 1.5 K under various applied fields (20 mT, 170 mT, 4T). The spin-Hamiltonian analysis of these spectra yields isotropic magnetic hyperfine coupling withA _total/(g _{N N})=–18.5 T. The corresponding local componentA _Fe is related toA _total via spin-projection:A _total=(6/7)A_Fe. The resultingA _Fe/(g _NN)=–21.6 T is in agreement with standard values of ferric high-spin complexes. Spin-Hamiltonian parameters as obtained from Mössbauer studies and exchange coupling constants as derived from susceptibility measurements are corroborated by temperature-dependent EPR studies.     

Quelques nouvelles propriétés de régularité de l'opérateur de Gribov

In this work, we establish new regularity properties for Gribov's operator:H=A ^* A ₊ iA ^*(A+A ^*)A;(,)², whereA ^* andA are the creation and annihilation operators. Particularly, we prove that for all >0,H ^–1 is in the class of Carleman's operatorl ₁₊.     

Laser- and gamma-ray induced crystallization of IR-transmitting calcium gallate glass

Ar⁺-laser (=488 nm) irradiation of calcium gallate (CG) glass with the composition of 60CaO·39Ga₂O₃·Fe₂O₃ resulted in a distinct decrease in the IR transmittance (T) due to the formation of crystalline CaGa₂O₄ and CaGa₄O₉ phases. The Mössbauer spectrum of non-irradiated glass comprised a broad doublet due to distorted Fe³⁺(T_d) with, , and of 0.20, 1.33, and 1.00 mm s^–1, respectively. An additional doublet due to Fe³⁺(T_d) was observed in the Ar⁺-irradiated glass and, , and were 0.17, 1.32, and 0.75 mm s^–1, respectively. A decrease inT was also observed after the⁶⁰Co -ray irradiation with doses 10⁵Gy, and the precipitation of CaO, Ga₂O₃, and CaGa₄O₇ phases was confirmed by X-ray diffraction.     

Elementary particle states based on the Clifford algebraC 7

The lepton isodoublet (e ^–,v _e ), the bare nucleon isodoublet (n,p), and their antiparticles are shown to constitute a basis of the irreducible representation of the Clifford algebraC ₇. The excited states of these doublets, i.e., ( ^–, ), ( ^–, ),..., and (s ⁰,c ⁺),(b⁰,t⁺) are generated by the products (e ^–,v _e )a and (n,p)a, wherea2^–1/2(e ^– e ⁺+v _e v _e ) has the same quantum numbers as the photon state. The bare baryonss, c, b, t carry the strangeness, charm, bottom, and top quantum numbers. These lepton and bare baryon states are in one-to-one correspondence with the integrally charged colored Han-Nambu quarks, and generate all the observedsu(3) andsu(4) hadron multiplets.     

Estimates of general Mayer graphs. IV. On the computation of Gaussian integrals by the star-mesh transformation

We point out that, to compute by hand a Gaussian integral exp · (– _LL y _l r _ij ² d r _n+1 ...d r _n+k , where the sum runs over all linesL = (i,j) of a graph andr _ij = ¦r _i –r _j ¦, the simplest way is to use the star-mesh transformation, well known in electrical network theory. We apply this to test, on a relatively complicatedn-graph, the accuracy of an estimation method that we proposed elsewhere [Phys. Lett. 62A:295 (1977)].     

Pitfalls in the Use of Common Luminescent Probes for Oxidative and Nitrosative Stress

Lucigenin (LC²⁺, bis-N-methylacridinium) and 2,7-dichlorofluorescin (DCFH₂) are widely used as chemiluminescent or fluorescent probes for cellular oxidative stress, to reflect levels of superoxide (O₂ ^·–) and hydrogen peroxide, respectively. We report mechanistic studies that add to the growing evidence for the unsuitability of either probe except in very well-defined circumstances. The ability for lucigenin to generate superoxide via reduction of LC²⁺ to LC^·+ and redox cycling with oxygen depends on the reduction potential of the LC²⁺/LC^·+ couple. Redox equilibrium between LC^·+ and the redox indicator benzyl viologen is established in microseconds after generation of the radicals by pulse radiolysis and indicated E(LC²⁺/LC^·+) –0.28 V vs. NHE. Reaction of LC^·+ with O₂ to generate O₂ ^·– was also observed directly similarly, occurring in milliseconds, with a rate constant k 3 × 10⁶ M ^–1 s^–1. Quinones act as redox mediators in LC^·+/O₂ redox cycling. Oxidation of DCFH₂ to fluorescent DCF is not achieved by O₂ ^·– or H₂O₂, but NO₂ ^·) reacts rapidly: k 1 × 10⁷ M ^–1 s^–1. Oxidation by H₂O₂ requires a catalyst: cytochrome c (released into the cytosol in apoptosis) is very effective (even 10 nM). Fluorescence reflects catalyst level as much as O₂ ^·–) production.     

Effect of vibrational kinetics of He2 + ions on the afterglow of a discharge in helium

A decaying weakly ionized helium plasma [n_e=(0.2–1.1)·10¹¹ cm^–3, p=(40–70) mm Hg] was studied experimentally. It is shown that the experimental time dependences of the intensities of atomic lines and molecular bands in the afterglow phase can be explained if the vibrational kinetics of He₂ ⁺ ions is included in the analysis. Analysis of the measurements shows that for n_e 10¹¹ cm^–3 and N_a 10¹⁸ cm^–3 deexcitation of He₂ ⁺ ions occurs primarily as a result of inelastic collisions with helium atoms. Based on the experimental data, an approximate value was obtained for the rate constants of the vibrational relaxation of molecular helium ions 10^–16 cm³/sec. These results are used for making a qualitative analysis of the distribution of He₂ ⁺ ions over the vibrational states in the discharge phase.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 88–96, November, 1986.