Calcul des probabilités de transition pour divers états excités du Fe XII

Résumé On a calculé les probabilités de transition pour les raies interdites ou permises entre les états (3p²3d-3p³), (3p²4s-3p³), (3s3p⁴-3s²3p³), (3p²4d-3P³) du FeXII. Les niveaux d'énergie ²D_3/2, ²D_5/2, ²P_1/2, ²P_3/2 ont été obtenus par extrapolation le long de la séquence isoélectronique P1. On discute brièvement les effets d'un écart aux conditions de couplage L-S dus aux interactions spin-orbite et de configuration.

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Transition probabilities have been computed for forbidden or permitted lines within the (3p²3d-3p³), (3p²4s-3p³), (3s3p⁴-3s²3p³), (3p²4d-3p³) configurations in FeXII. Energy levels ²D_3/2, ²D_5/2, ²P_1/2, ²P_3/2 have been predicted by extrapolation along the isoelectronic sequence P1. The effects of departures from L-S coupling due to spin-orbit and configuration interaction are briefly discussed.

     

Non-integrability of Hénon-Heiles system

We show that the Hénon-Heiles system with Hamiltonian H=\frac12(y₁²+y₂²)+\frac12(ax₁²+bx₂²)+\frac13dx₂³+cx₁²x₂{H=\frac12(y_1^2+y_2^2)+\frac12(ax_1^2+bx_2^2)+\frac13dx_2^3+cx_1^2x_2} is integrable in Liouvillian sense (i.e., the existence of an additional first integral) if and only if c = 0; or \frac dc=1, a=b; or \frac dc=6, a, b{\frac dc=1, a=b; {\rm or}\, \frac dc=6, a, b} arbitrary; or \frac dc=16, b=16a{\frac dc=16, b=16a}. Therefore, we get a complete classification of the Hénon-Heiles system in sense of integrability and non-integrability.     

Normal form,Lie-Poisson structure and reduction for the Henon-Heiles system

The reduced Henon-Heiles system is investigated as a Hamiltonian dynamical system obtained by applying the normalization of the HamiltonianH=1/2(p ₁ ² +p ₂ ² +q ₁ ² +q ₂ ² )+1/3q ₁ ³ –q ₁ q ₂ ² to fourth-degree terms. The related equations of motion are bi-Hamiltonian and possess the Lie-Poisson structure. Each Lie-Poisson structure possesses an associated Casimir function. When reduced to level sets of these functions, the equations of motion take various symplectic forms. The various reductions give different coordinate representations of the solutions. These coordinate representations are used to seek the simplest representation of the solutions.     

A note on the correspondence between Mathieu's transformations and redundant variables in lagrangian mechanics

It is shown that, to any change of variables:q _i=q_i(r, t) (i=1,..., n; =1,...,n+m; mn) increasing the number of variables, it is possible to associate a Mathieu's transformation and conversely. The results are applied to the theory of the osculating plane of motion.

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Resumé On montre qu'à toute transformation:q _i=q_i(r, t)(i=1,..., n; =1,...,n+m; mn) augmentant le nombre de variables, on peut associer une transformation de Mathieu et réciproquement. Les résultats sont appliqués à la théorie du plan osculateur du mouvement.

     

Drift in toroidal configurations

It is found that charged particles of positive energiesE, when constrained on axisymmetric isoflux surfaces , execute sinusoidal motions with typical frequencies =(2E/m)^1/2). In general, it was found that under equilibrium condition p=J ^B/cthe particles develop a non-ambipolar drift velocityv _d =(cµ/eb)[1+q ² +2(q/)²]p.     

The mass-ratio distribution of spectroscopic binary stars

In order to determine the mass-ratio distribution of spectroscopic binary stars, the selection effects that govern the observations of this class of binary systems are investigated. The selection effects are modelled numerically and analytically. The results of the models are compared to the data inThe Eighth Catalogue of the Orbital Elements of Spectroscopic Binary Stars (DAO8) compiled by Battenet al. (1989). The investigations involve binary systems with Main-Sequence primary components only, in order to avoid confusion of evolutionary and selection effects.For single-lined spectroscopic binaries (SBI) it is found that the mass ratios (q=M _sec/M _prim) in general adhere to a distribution _q q ^-2 forq>q ₀, withq ₀=0.3. The observations are consistent with a distribution that is flat forq<q ₀. The turn-over value varies fromq ₀=0.3 for systems with B-type primaries, toq ₀=0.55 for systems with K-type primaries. The semi-major axesa ₁ are distributed according to _a (a ₁)a ₁ ^-a with an average value of _a =1.3. The power varies from _a =1.7 for systems with B-type primaries to _a =0 for systems with K-type primaries. The eccentricitiese of the orbits of SBI systems are distributed according to _e (e)e ^-1.For double-lined spectroscopic binary stars (SBII) it is found that the shape of theq-distribution, as derived from observations, is almost entirely determined by selection effects. It is shown that the distribution is compatible with theq-distribution found for SBI systems. A sub-sample, consisting of the SBII systems from DAO8 with magnitudesm _V 5 ^m , is less hampered by selection effects, and shows the same shape of theq-distribution as the SBI systems, at theq-interval (0.67, 1).It is estimated that 19–45% of the stars in the solar neighbourhood are spectroscopic binary systems.     

Kaitianite,Ti3+2Ti4+O5, a new titanium oxide mineral from Allende

Kaitianite, Ti³⁺₂Ti⁴⁺O₅, is a new titanium oxide mineral discovered in the Allende CV3 carbonaceous chondrite. The type grain coexists with tistarite (Ti₂O₃) and rutile. Corundum, xifengite, mullite, osbornite, and a new Ti,Al,Zr‐oxide mineral are also present, although not in contact. The chemical composition of type kaitianite is (wt%) Ti₂O₃ 56.55, TiO₂ 39.29, Al₂O₃ 1.18, MgO 1.39, FeO 0.59, V₂O₃ 0.08 (sum 99.07), yielding an empirical formula of (Ti³⁺_1.75Al_0.05Ti⁴⁺_0.10Mg_0.08Fe_0.02)(Ti⁴⁺_1.00)O₅, with Ti³⁺ and Ti⁴⁺ partitioned, assuming a stoichiometry of three cations and five oxygen anions pfu. The end‐member formula is Ti³⁺₂Ti⁴⁺O₅. Kaitianite is the natural form of γ‐Ti₃O₅ with space group C2/c and cell parameters a = 10.115 Å, b = 5.074 Å, c = 7.182 Å, β = 112°, V = 341.77 Å³, and Z = 4. Both the type kaitianite and associated rutile likely formed as oxidation products of tistarite at temperatures below 1200 K, but this oxidation event could have been in a very reducing environment, even more reducing than a gas of solar composition. Based on experimental data on the solubility of Ti³⁺ in equilibrium with corundum from the literature, the absence of tistarite in or on Ti³⁺‐rich corundum (0.27–1.45 mol% Ti₂O₃) suggests that these grains formed at higher temperatures than the kaitianite (>1579–1696 K, depending on the Ti concentration). The absence of rutile or kaitianite in or on corundum suggests that any exposure to the oxidizing environment producing kaitianite in tistarite was too short to cause the precipitation of Ti‐oxides in or on associated corundum.     

Sur une etude de stabilite par analogie avec la collision triple

Résumé Dans cet article on a adapté les méthodes d'étude de la collision triple et de son voisinage au problème de la stabilité d'une position d'équilibre d'un lagrangienL = (x ² +y ²)/2 +U oùU est un polynôme homogène de degrék, le cask=3 étant tout particulièrement développé. On met en évidence des configurations centrales, des solutions par homothétie d'énergie nulle et on étudiera leur voisinage [3, 4].

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In this paper, we apply the methods of study of the triple collision and its neighbourhood to the problem of stability of the equilibrium ofL = (x ² +y ²)/2 +U, whereU is homogeneous. The case ofU of degree 3 is especially studied. We investigate the central configurations and homothetical solutions with zero energy and we study their neighbourhood.

     

On Szebehely's problem for holonomic systems involving generalized potential functions

We consider the problem of finding the generalized potential function V = U _i(q ¹, q ²,..., q ⁿ)q ⁱ + U(q ¹, q ²,...;q ⁿ) compatible with prescribed dynamical trajectories of a holonomic system. We obtain conditions necessary for the existence of solutions to the problem: these can be cast into a system of n – 1 first order nonlinear partial differential equations in the unknown functions U ₁, U ₂,...;, U _n, U. In particular we study dynamical systems with two degrees of freedom. Using adapted coordinates on the configuration manifold M ₂ we obtain, for potential function U(q ¹, q ²), a classic first kind of Abel ordinary differential equation. Moreover, we show that, in special cases of dynamical interest, such an equation can be solved by quadrature. In particular we establish, for ordinary potential functions, a classical formula obtained in different way by Joukowsky for a particle moving on a surface.Work performed with the support of the Gruppo Nazionale di Fisica Matematica (G.N.F.M.) of the Italian National Research Council.     

Theorie de Weyl et principe de moindre action: Application a l'etude des mouvements

Sommaire Les lois du mouvement dans une variété riemannienneV ₄ peuvent être déduites d'un principe de moindre action. Nous établissons dans cet article l'équivalence des relations ds=0 et dL=-L _k d^k, où ds ²=L ² est une métrique riemannienne et d _k /dt une fonction homogène de degré 1 des variables dx ⁱ/dt qui définit un espace de Weyl. Ce théorème permet de ramener une théorie de jaugen à un principe de moindre action. Il peut être utilisé dans la théorie de la double métrique de Dirac, obtenue en choissant la théorie des grands nombres comme condition de jauge. Une fibration de l'espace physiqueV ₃ basée sur le théorème de Huyghens permet de déduire les propriétés dynamiques des particules des propriétés des photons dansV ₃, et constitue en ce sens une unification des propriétés dynamiques des particules.

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The laws of motion in a RiemannianV ₄ manifold can be deduced from the principle of least action. We state in this work the equivalence between the equations ds=0 and dL=-L _k d^k, where ds ² =L ² is the Riemannian metric and d _k /dt the homogeneous functions of first degree of the dx ⁱ/dt which define a Weylian space. This theorem can then reduce a gauge theory to a principle of least action. It can be used in the double metric theory of Dirac, obtained by means of the Large Number Hypothesis as a gauging condition. A fibration of the physical spaceV ₃ based on Huyghens' theorem allows the deduction of the dynamical properties of particles by means of the properties of photons inV ₃, and constitutes in this way an unification of the dynamical properties of particles.

     

Models of the universe compatible with present observations

It is shown that cosmic radiation almost follows a Planck distribution, because just as matter is formed, its density of energy is negligible in comparison with that of radiation, and that the present age of the Universe does not depend on the particular manner in which the matter is formed.Thus, if the results of the latest observations (which imply a deceleration parameterq=1.6) are combined with the assumption that the present age of the Universe is at least 12×10⁹ yr, they lead to a hyperbolic oscillating universe with a negative cosmological constant (<–1.53×10^–56 cm^–2) and a present mass-density _m of less than 1.2×10^–30 g cm^–3. If the cosmological constant is taken to be zero, a solution is only possible if we are prepared to admit a rate of evolution of galaxies with a deceleration parameterq<0.52. Three types of oscillating universe are then possible, but the heperbolic type is the most probable. If Hubble's constant is greater than 63.4 km s^–1 Mpc^–1, the solutions are only hyperbolic universes with <+0.45×10^–56 cm^–2 and _m <4.8×10^-30g cm^-3.

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Sommaire On montre que le rayonnement cosmique général suit pratiquement une loi de Planck parce que la densité d'énergie de la matière au moment de sa formation est négligeable à côté de celle du rayonnement et que l'âge actuel de l'Univers ne dépend pas du mode de formation de la matière.Dans ces conditions, si l'on combine les derniers résultats d'observations (qui impliquent un paramètre de décélérationq=1.6) avec l'hypothèse que l'âge actuel de l'Univers est au moins de 12×10⁹ années on est conduit à un Univers hyperbolique oscillant à constante cosmologique négative (<–1.53×10^–56 cm^–2) et où l'actuelle densité de matière _m est moindre que 1.2×10^–30 g cm^–3. Si la constante cosmologique est supposée nulle, une solution ne peut être obtenue que si l'on admet un certain taux d'évolution des Galaxies et un paramètre de décélérationq<0.52. Alors, les trois types d'Univers oscillants sont possibles, mains les Univers hyperboliques paraissent plus probables. Enfin, si la constante de Hubble est plus grande que 63.4 km s^–1 Mpc^–1 les solutions ne peuvent être que des Univers hyperboliques avec <+0.45×10^–56 cm^–2 et _m <4.8×10^-30g cm^-3.

     

A deconvolved structure of the nebulosity associated with 3C 206

The published photographic profile of 3C 206 (reported in the low redshift sample of quasars by Wyckoffet al., 1981) has been deconvolved from the PSF by means of an effective restoration procedure. The deconvolved photometric structure of the quasar consists of a central point-like source, containing 68% of the integrated luminosity, an intermediate region of about 10 kpc radius (H ₀=60 km s^–1 Mpc^–1,q ₀=0) and an external region with nearly-linear slope and brightness level of the profile similar to those of the corresponding regions in giant elliptical and cD galaxies. The result confirms the previous findings in 3C 273, PKS 2135+147, and PKS 0812+020 obtained in the same way.     

Formation of the solar system

Prentice (1978a, b), in his modern Laplacian theory of the origin of the solar system, has established a scenario in which he finds the ratio of the orbital radii of successively disposed gaseous rings to be a constant 1.69. In an attempt to understand this law in an alternative way, Rawal (1984a) assumes that during the collapse of the solar nebula the halts at various radii are brought about by the supersonic turbulent convection and arrives at the relation of the formR _p=Ra^p, whereR is the radius of the present Sun anda=1.422, is referred to, here, as the Roche constant. Kepler's third law assumes the form:T _p=T₀(a ^3/2) ^p ,T ₀ being the rotational period of the Sun at the time it attained its present radius.R _p satisfy Laplace's resonance relation without any exception. The present paper investigates inter-relations among the concepts of supersonic turbulent convection, rotational instability, and Roche limit.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

Posterior probability of the deceleration parameter q0 from quasars provided with a luminosity indicator

We have worked out a ’statistical algorithm’ for obtaining the posterior probability density of the deceleration parameter q₀ from quasars where there is a luminosity indicator available. We point out that the role of the luminosity indicator is to provide asecond estimate of individual luminosities after a first estimate has been obtained from measured brightness and redshift together with an assumed q₀. Discrimination of q₀ is to be sought in the statistical properties of the set of differences between the two estimates (the residuals). We show that the variance of the residuals and their correlation with redshifts (further refined to luminosity distances) are two independent test-statistics for q₀, whose known distributions then lead to the probability density sought. We have applied the above algorithm to a sample of flat-spectrum radio quasars with measured CIV, MgII and Ly α lines. A combined Baldwin’s relation was used for all 3 lines. Our result is that log q₀ is normally distributed with a mean value of + 0.270± 0.135 (s.d.), or, q₀ = + 1.86 ± 0.135 dex. This result, we believe, is the sharpest result so far published on q₀.     

Motion of rigid bodies in a set of redundant variables

In this article we study the conditions for obtaining canonical transformationsy=f(x) of the phase space, wherey(y ₁,y ₂,...,y _2n ) andx(x ₁,x ₂,...,x _2m ) in such a way that the number of variables is increased. In particular, this study is applied to the rotational motion in functions of the Eulerian parameters (q ₀,q ₁,q ₂,q ₃) and their conjugate momenta (Q ₀,Q ₁,Q ₂,Q ₃) or in functions of complex variables (z ₁,z ₂,z ₃,z ₄) and their conjugate momenta (Z ₁,Z ₂,Z ₃,Z ₄) defined by means of the previous variables. Finally, our article include some properties on the rotational motion of a rigid body moving about a fixed point.     

Excitation class of nebulae—An evolution criterion?

A principally new, quantitative system of the classification of the spectra of planetary nebulae is proposed. Spectral class of excitation class of the nebulap is determined according to the relative intensities of emission lines (N ₁+N ₂) [OIII]/4686 HeII and (N ₁+N ₂) [OIII]/H (Table I, Figure 1). The excitation classes are obtained for 142 planetary nebulae of all classes—low (p=1–3), middle (p=4–8), and high (p=9–12⁺) (Tables II, III, and IV). An empirical relationship between excitation classp and mean radius of nebulae is discovered (Figure 2). This relationship as well as excitation classp, as an independend parameter, admit an evolutionary interpretation. It is shown that after reaching the highest class of excitationp=12⁺ the nebulae decrease their class of excitation with the further increases of sizes. The diagram of this relationship has two nearly-symmetric branches — rising and descending with the apogee onp=12⁺ (Figure 2).     

Evolution du spectre de la Nova Delphini 1967 en 1971 et 1972

Continued spectroscopic observations of Nova Del 67 during 1971 and 1972 show a general decrease of the nebular and coronal emission with respect to the local continuum. The continuous spectrum exhibits a strong Balmer emission (figure 1). Equivalent widths of Hi, Hei, Heii, Oi, [Oi], Oii, [Oii], Oiii, [Oiii], Niii, [Sii], [Aiii], [Neiii], [Nev], [Fevi], [Fevii], [Fex], [Fexi], [Fexiv], [Nixvi], [Nixv] are listed in tables 1 and 2.Figures 5 to 10 show several line profiles, which can be interpreted in terms of a model proposed by Hutchings (1972). Kinematical properties of the nova envelope do not seem to have changed in the 1968–1972 time interval. However, a study of the [Oiii] (4959 Å) line indicates that the physical conditions in the polar blobs in 1972 (T _e=10 660 K,N _e=5,5×10⁵ cm^–3) are different from those prevailing in equatorial rings (T _e=9×100 K,N _e=7×10⁵ cm^–3).

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Le matérial d'observation utilisé pour cette étude a été obtenu à l'aide de téléscopes de 120 cm, 152 cm et 193 cm de l'Observatoire de Haute-Provence (CNRS).     

Theoretical intensities of Fexiv in the solar EUV spectrum

Equilibrium population of Fexiv levels in coronal conditions was calculated including configurations 3s ²3p, 3s3p ², 3s ²3d, 3p ³, 3s3p3d, 3s ²4s, 3s ²4p, 3s ²4d, 3s ²4f. Relative populations of selected levels are given in Table VII. Figure 1 shows the dependence of relative intensities of the strongest lines on electron density. Certain line ratios can be used for the determination of N _e .E.g., at T=2 × 10⁶ K and with a dilution factor 0.4, the intensity ratio of λ211.3 and λ219.0 changes by a factor of 65 if N _e increases from 10⁷ to 10¹¹ (Table VIII). Cascades from the 3s3p3d and 3p ³ configurations are important in the population of some levels of 3s3p ² (Table VI). A possibility of identification of additional lines in the solar spectrum is indicated. NAS-NRC Resident Research Associate.     

Maohokite,a post‐spinel polymorph of MgFe2O4 in shocked gneiss from the Xiuyan crater in China

Maohokite, a post‐spinel polymorph of MgFe₂O₄, was found in shocked gneiss from the Xiuyan crater in China. Maohokite in shocked gneiss coexists with diamond, reidite, TiO₂‐II, as well as diaplectic glasses of quartz and feldspar. Maohokite occurs as nano‐sized crystallites. The empirical formula is (Mg_0.62Fe_0.35Mn_0.03)²⁺Fe³⁺₂O₄. In situ synchrotron X‐ray microdiffraction established maohokite to be orthorhombic with the CaFe₂O₄‐type structure. The cell parameters are a = 8.907 (1) Å, b = 9.937(8) Å, c = 2.981(1) Å; V = 263.8 (3) ų; space group Pnma. The calculated density of maohokite is 5.33 g cm^?3. Maohokite was formed from subsolidus decomposition of ankerite Ca(Fe²⁺,Mg)(CO₃)₂ via a self‐oxidation‐reduction reaction at impact pressure and temperature of 25–45 GPa and 800–900 °C. The formation of maohokite provides a unique example for decomposition of Fe‐Mg carbonate under shock‐induced high pressure and high temperature. The mineral and its name have been approved by the Commission on New Minerals, Nomenclature and Classification of the International Mineralogical Association (IMA 2017‐047). The mineral was named maohokite after Hokwang Mao, a staff scientist at the Geophysical Laboratory, Carnegie Institution of Washington, for his great contribution to high pressure research.     

Size Distribution of Cometary Dust Particles

We considered two types of size distributions of cometary dust particles, namely, a: f(a) a ^{–( + 1)}(for comet Encke) and (for comet Halley). Using these distributions, expressions for the loss of the comet's absolute brightness per revolution, H ₁₀, are obtained; this quantity depends on the relative volume content of dust in the nucleus, f _v; the granulometric composition of dust ( or A _d, B _d, a _min, anda _max); the nucleus size and density; and the orbital elements P, q, and e. Under reasonable assumptions on the values of the above-mentioned physical parameters, a nucleus radius can be estimated from the value of H ₁₀obtained from observations.