Z-dependence of the level intervals in 2s 2 2p 2, 2s 2 2p 3 and 2s 2 2p 4

Values of the level intervals in the ground configurations 2s ² 2p ², 2s ² 2p ³ and 2s ² 2p ⁴ have been critically compiled from laboratory observations and from observations of nebular and coronal forbidden transitions. The data are represented within experimental errors by means of semi-empirical extrapolation formulae which contain from 3 to 5 adjusted parameters. The results provide means for checking laboratory and astrophysical identifications and measurements. Tables of best level values are given for the configurations concerned.     

Wavelength predictions for the 1s2 2p - 1s2p3p satellite transitions

The energy differences between 1s ²2p 1s2p3p transitions and the corresponding 1s ² 1s3p resonances are expressed by means of a polynomial function of the atomic number. The agreement with experimental data from lithium to potassium is very good. Interpolated values for nitrogen to sodium and argon as well as extrapolation for calcium are reported.     

Wavelength predictions for the 1s 22s-1s2s3p satellite transitions

The experimentally known energies of the 1s ²2s 1s2s(¹ S, ³ S)3p transitions are considered for lithium to calcium. Their differences from the corresponding He-like resonances are fitted to the atomic number by means of a polynomial function and, through interpolation, the wavelengths for nitrogen to sodium are calculated.     

Line intensity ratios of transitions within the 1s 22s 22p 2 ground configuration of Mgvii

Using theR-matrix approach new calculations have been made for the electron impact excitation of the fine structure transitions within the 1s ²2s ²2p ² ground configuration of Mgvii. The computations have been made at a large number of energies in order to account for the contribution of resonances. All partial waves withL 9 are included in the calculations which are considered to be sufficient for the convergence of collision strengths in the energy range below 65 Ry. From this collision strength data, excitation rate coefficients have been calculated at a series of electron temperatures which are employed in the computation of population of the five lowest levels of Mgvii. The line intensity ratios for the transitions³ P ₁ ¹ D ₂ and³ P ₂ ¹ D ₂ to³ P ₁ ¹ S ₀ are then calculated in the temperature range of 10⁵ to 10⁷ K at electron densities in the range 10⁶ to 10¹⁰ cm^–3. The calculated values are in good agreement with the earlier available results.     

On the number of central configurations in the N-body problem

Central configurations are critical points of the potential function of the n-body problem restricted to the topological sphere where the moment of inertia is equal to constant. For a given set of positive masses m ₁,..., m _n we denote by N(m ₁, ..., m _n, k) the number of central configurations' of the n-body problem in ^k modulus dilatations and rotations. If m _{n 1},..., m _n, k) is finite, then we give a bound of N(m ₁,..., m _n, k) which only depends of n and k.     

A comparison of theoretical line strengths for the 2s 22p 2 − 2s2p 3 transitions in Ne v with solar data

Results are presented for several theoretical line ratios in Nev involving transitions between multiplets in the 2s ²2p ² and 2s2p ³ configurations. A comparison of these with solar data from the S082A and S-055 instruments on board Skylab reveals generally good agreement between theory and experiment, especially in the case of the high-resolution (S082A) observations. However the 2s ²2p ^{2 1} D – 2s2p ^{3 1} P (365.6 Å) and 2s ²2p ^{2 3}P – 2s2p ^{3 3} S (359 Å) lines appear to be blended, possibly with transitions in Fex and Fexi/Fexiii, respectively. We note that the intensity ratio I(365.6 Å)/I(416.2 Å) should be a valuable calibration check for a high-resolution extreme ultraviolet instrument in the spectral range 360–420 Å.     

Maximum temperatures for radiation from plasma waves

We derive upper limits to the radiation temperaturesT ^t(k) for emission near the fundamental and second harmonic of the electron plasma frequency in terms of the effective temperature for plasma wavesT ^l(k). We findT ^t(k)(c/(3)^1/2 V _e)³ T ^l(k) for emission near the fundamental which differs from the result of Melrose (1970b) by the factor in parentheses. This factor can exceed 4×10⁴ in some plasmas. The conditions under which this limit could be reached are delinated. For emission near the second harmonicT ^t(k)T ^l(k) since the absorption coefficient in this case can only be positive.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Some applications of Jacobi dynamics to the stellar evolution

The stars in the Main Sequence are seen as a hierarchy of objects with different massesM and effective dynamical radiiR _eff=R/ given by the stellar radii and the coefficients for the inner structure of the stars.As seen in a previous work (Paper I), during the lifetime in the Main SequenceR _eff(t) remains a near invariant when compared to the variation in the time ofR(t) and (t).With such an effectiveR _eff one obtains the amounts of actionA _c(M), the effective densities _eff(M)=(M)³(M), the densities of action and of energy (or mean presures in the stellar interior)a _c(M),e _c(M), and the potential energiesE _p(M).The amounts of action areA _cM ^k withk1.87 for the M stars,k5/3 for the KGF stars, andk1.83 for the A and earlier stars, representing very simples conditions for the other dynamical parameters. For instancek5/3 means a near invariant effective density _eff for the KGF stars, while for such stars the mean densities and coefficients present the strongest variations with masses (M)M ^–1.81, (M)M^0.6.The cases for the M stars (e _c(M)M ^–1) and for the A and earlier stars (betweena _c(M)=constant and _eff(M)M ^–1) and also discussed. These conditions for the earlier stars also represent reasonable mean values for the whole stellar hierarchy in the range of masses 0.2M M25M .With all this, one can build dynamical HR diagrams withA _c(M), E_p(M), _eff M ^–p , etc., whose characteristics are analogous to these in the photometrical HR diagram. A comparison is made betweenA _c(M) from the models here and the HR diagram with the best known stars of luminosity classes IV, V, and white dwarfs.The comparison of the potential energiesE _p(M)M ^–p according to the stellar models used here and the observed frequency function (MM _–q (number of stars in a given interval of masses) from different authors suggests the possibility that the productE _p(M)(M) is a constant, but this must be confirmed with further studies of the function (M) and its fine structure.There are analogies between the formulation used here for the stellar hierarchy and other physical processes, for instance, in modified forms of the Kolmogorov law of turbulence and in the formulation used for the hierarchy of molecular clouds in gravitational equilibrium. Besides, the function of actionA _c(M) for the stars has analogous properties to the relations of angular momenta and massesJ(M) for different types of objects. The cosmological implications of all this are discussed.     

Expected intensities of solar neon-like ions

A study of the expected intensities of the stronger solar neon-like ion emission lines, some not yet observed, is carried out to compare with the observational situation. The potential usefulness of the 2p ⁵ 3s(³ P ₂) - 2p ⁶ forbidden line as a density diagnostic is discussed and new electric quadrupole lines in the soft X-ray range are noted. Observability diagrams are presented as a convenient overview of the known and unobserved lines. The S vii resonance lines appear to have anomalous intensities.     

Observation of possible Fe xvii 2p 53p(1S0)-2p 53s(1 P 1, 3 P 1) transitions in spectra of a solar active region and flare

Expected wavelengths and relative intensities are obtained, from calculations of other workers, for the hitherto unobserved transitions 2p ⁵3p(¹ S ₀)-2p ⁵3s(¹ P ₁, ³ P ₁) in Fe xvii. A candidate pair of lines at 197.05 Å and 242.09 Å was found in laboratory spectra and appears to be present in the spectra of a solar active region observed by the OSO-7 Goddard spectroheliograph, and in the spectrum of a Skylab-observed solar flare.     

Extreme Ultraviolet Emission Lines of ca xv in Solar and Laboratory Spectra

New R-matrix calculations of electron impact excitation rates in Caxv are used to derive theoretical electron density diagnostic emission line intensity ratios involving 2s ²2p ²–2s2p ³ transitions, specifically R ₁=I(208.70 Å)/I(200.98 Å), R ₂=I(181.91 Å)/I(200.98 Å), and R ₃=I(215.38 Å)/I(200.98 Å), for a range of electron temperatures (T _e=10^6.4–10^6.8 K) and densities (N _e=10⁹–10¹³ cm^–3) appropriate to solar coronal plasmas. Electron densities deduced from the observed values of R ₁, R ₂, and R ₃ for several solar flares, measured from spectra obtained with the Naval Research Laboratory's S082A spectrograph on board Skylab, are found to be consistent. In addition, the derived electron densities are in excellent agreement with those determined from line ratios in Caxvi, which is formed at a similar electron temperature to Caxv. These results provide some experimental verification for the accuracy of the line ratio calculations, and hence the atomic data on which they are based. A set of eight theoretical Caxv line ratios involving 2s ²2p ²–2s2p ³ transitions in the wavelength range 140–216 Å are also found to be in good agreement with those measured from spectra of the TEXT tokamak plasma, for which the electron temperature and density have been independently determined. This provides additional support for the accuracy of the theoretical line ratios and atomic data.     

Period distributions in pulsating and binary stars

We analyze the hypothesis of quantization in bands for the angular momenta of binary systems and for the maount of actionA _c in stable and pulsating stars. This parameter isA _c=Mv _eff R _eff, where the effective velocity corresponds to the kinetic energy in the stellar interior and the effective radius corresponds to the potential energyGM ²/R _eff. Analogous parameters can be defined for a pulsating star withm=M where is the rate of the massm participating in the oscillation to the total massM andv _osc,R _osc the effective velocity and oscillation radius.From an elementary dimensional analysis one has thetA _c (energy x time) (period)^1/3 independently ifA _c corresponds to the angular momentum in a binary system, or to the oscillation in a pulsating star or the inner energy and its time-scaleP _eff in a stable star.From evolving stellar models one has that P _effP _eff(solar)1.22 hr a near-invariant for the Main Sequence and for the range of masses 0.6M <M<1.6M .With this one can give scalesn _k=kn ₁ withk integers andn ₁=(P/P ₁)^1/3 withP ₁=P _eff1.22 hr. In these scales proportional toA _c, one sees that the periods in binary and pulsating stars are clustered in discrete unitsn ₁,n ₂,n ₃, etc.This can be seen in pulsating Scuti, Cephei, RR Lyrae, W Virginis, Cephei, semi-regular variables, and Miras and in binary stars as cataclysmic binaries, W Ursa Majoris, Algols, and Lyrae with the corresponding subgroups in all these materials. Phase functions (n _k) in RR Lyrae and Cephei are also associated with discrete levelsn _k.the suggested scenario is that the potential energies and the amounts of actionE _p(t), A_c(t) are indeed time-dependent, but the stars remain more time in determinated most proble states. The Main Sequence itself is an example of this. These most probable states in binary systems, or pulsating or stable stars, must be associated with velocities sub-multiplesc/ _F , given by the velocity of light and the fine structure constant.Additional tests for such a hypothesis are suggested when the sufficient amount of observational data are available. They can made with oscillation velocities in pulsating stars and velocity differences of pairs of galaxies.     

Density dependence of forbidden transitions within 3s 23p 53d of the coronal ion Fe IX

The relative populations of metastable levels within the configuration 3s ²3p ⁵3d of the ion Fe ix have been calculated as a function of electron density N _e . The results are used to derive emissivities of the most intense lines originating from these levels. Comparison with observations confirms the proposed identifications. The density dependence of some line ratios may be used to determine N _e .     

Resistive ballooning modes in line-tied coronal fields

The stability of coronal arcades to localized resistive interchange modes in the ballooning ordering, including photospheric line tying, is investigated. It is found that the anchoring of magnetic footpoints in the photosphere is not sufficient to stabilise ballooning modes, once resistivity is taken into account. All configurations with a pressure profile decreasing from the arcade axis at some point are unstable, a purely growing mode being excited. The dependence of the growth rate on the parameter Rm ^–1 k ² , where is the resistivity and k the wavenumber in a direction perpendicular to the equilibrium field, can be described by a power law with varying index: for small values of k ² and an ideally stable field one finds Rm ^–1. As k ² is increased or marginal stability is approached one finds Rm^–1/3. T implications of these localised instabilities to the temporal evolution and overall energy balance of arcade structures in the solar corona is discussed.     

General integral transform of the exponential integrals

General integral transform of the exponential integralsE _n is considered and will be denoted asB _(k) ⁿ (). Different expressions and the equations satisfied byB _(k) ⁿ are developed. Two-term recurrence formula forB _(k) ⁿ (0) and three-term recurrence formula forB _(k) ⁿ (); 0 will be established for a givenk1 andn=2,3, ...,N. The computational algorithms based on these formulae are also constructed for the casesk=1,2,3, andn2. Finally the numerical results fork=2,3 andn=2(1)25 are presented to 15-digit accuracy     

A model cosmology based on gravity-electromagnetism unification

In this article the GEM (Brandenburg, 1992; Brandenburg, 1988) theory is applied to the problem of the cosmos in which most of the matter is hydrogen, spacetime is flat, and a Cosmic Background Radiation CBR field exists. Using the two postulates of the GEM theory: 1. That gravity fields are equivalent to an array ofE ×B drifts or a spacially varying Poynting field, such that spacetime is determined by EM fields so that the stress tensor of ultrastrong fields is self-canceling; 2. That EM and gravity fields and protons and electrons are unified at the Planck scale of lengths and energies and split apart to form distinct fields and separate particles at the Mesoscale of normal particle rest energies and classical radii. A new derivation is made of the formula forG found previously:G =e ²/(m _p m _e ) exp(-2R ^1/2) = 6.668 × 10^–8 dynes cm² g^–2wherem _p andm _e are the proton and electron masses respectively,R =m _p /m _e and is the fine structure constant, shows that quantum processes may occur which make the vacuum unstable to appearance of hydrogen thus allowing matter creation and a steady state universe to occur. The value for the Hubble Time calculated from this model isT _o = (3/((2)(R ^1/2)⁴))^1/3(r _e /c)(e ²/Gm _p m _e )= 19 Gyr wherer _e =e ² / (m _e c ²)and follows the form first hypothesized by Dirac(1937). The CBR is traced to this process of matter creation and its temperature is calculated as beingT _CBR = ((3/4)Gm _e ² c/( ² _o ))^1/4 = 2.66K where is the Thomson cross section of the electron and _o is the Stefan-Boltzman constant.     

Electron heating in superhigh mach number shocks

Fluid and MHD models, as well as direct extrapolation of the Earth's bow shock measurements in the high Mach number (HMN) range (3M _F 12) to the superhigh Mach number (SHMN) range (M _F >30–40) predict that the downstream electron pressurep _e2 is only a negligible fraction of the Rankine-Hugoniot downstream pressurep ₂, i.e.,p _e2/p₂(M _F ² )^–1. However, the interpretation of X-ray supernovae emissions, due to SHMN shock heating requiresp _e2/p₂0(1). Following Alfvén we have used plasma physics experimental-theoretical data combined with magnetospheric observations to probe the physics of the SHMN shocks. It is shown below that inclusion of proper plasma physics considerations in the interaction of the reflected and transmitted ions and the electrons at the foot of the shock leads to the surprising result that electron heating can dominate in the SHNM range. A stationary model of the shock structure is derived and shown to be the result of extrapolation of the high Mach number shock physics with incorporation of collective interactions at the foot.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

The existence of a chaotic region due to the overlap of secular resonances ν5 and ν6

A nonlinear theory of secular resonances is developed. Both terms corresponding to secular resonances ₅ and ₆ are taken into account in the Hamiltonian. The simple overlap criterion is applied and the condition for the overlap of these resonances is found. It is shown that in given approximation the value p = (1 - e²)^1/2(1 - cosI) is an integral of motion, where the mean eccentricity e and mean inclination I are obtained by eliminating short-period perturbations as well as the nonresonant terms from the planets. The overlap criterion yields a critical value of parameter p depending on the semi-major axis a of the asteroid. For p greater than the critical value, resonance overlap occurs and chaotic motion has to be expected. A mapping is presented for fast calculation of the trajectories. The results are illustrated by level curves in surfaces of section method.     

Solar particle propagation from 1 to 5 AU

A statistical analysis of solar particle events, observed by the GSFC-UNH charged particle detector on board Pioneer 10 and Pioneer 11 from March 1972 to December 1974 (from 1 to 5 AU for each spacecraft), is carried out with the goal of experimentally determining the statistical average interplanetary propagation conditions from 3 to 30 MeV. A numerical propagation model is developed that includes diffusion with a diffusion coefficient of the form k _r =k _o r , convection, adiabatic deceleration, and a variable coronal injection profile. The statistical analysis is carried out by individually analyzing each of five parameters (t _max, (t_max), t ₅, ) that are uniquely defined in a solar particle event. Each of the five parameter data sets were analyzed in terms of both a spacecraft-solar flare connection longitude 50°, and a numerical model that employed a variable exponential decaying coronal injection profile.The five individual parameter analyses are combined with the results that the statistical average radial interplanetary diffusion coefficient from 1 to 5 AU is given by k _r = (1.2 ± 0.4) × 10²¹ cm² s^-1 with = 0.0± 0.3 for 3.4 to 5.2 MeV protons and k _r = (2.6 ± 0.6) × 10²¹ cm² s^-1 with () = 0.0± 0.3 for 24 to 30 MeV protons. Using the classical relationship for the radial scattering mean free path _r, i.e. k _r = _r/3, we obtain _r = 0.09 ± 0.03 AU and 0.075 ± 0.020 AU for the low and high energy data, respectively. These results show, from 1 to 5 AU and from 3 to 30 MeV, that _r is both independent of radial distance and approximately independent of rigidity (for _r~P , where P = rigidity, = -0.15 ± 0.20).The above diffusion coefficients are inconsistent With both the predictions of the diffusion coefficient from present theoretical transport models and with the diffusion coefficient used in modulation studies at low energies.     

Magnetic and thermal pressures in the solar wind

Explorer 34 solar wind data for the period June to December, 1967 show that(a) The magnetic pressure, P _BB ²/8, and thermal pressure,P _kn _p kTp+n kT+n _e kTe,are variable and positively correlated on a scale of 2 days, but (b) changes in P _b and P _k are anticorrelated on a scale 1 hr (0.01 AU). Thus, dynamical hydromagnetic processes (dv/dto) must occur on the mesoscale, but the solar wind tends to be in equilibrium(P _B+P _Kconstant) on a smaller scale, the microscale. The 3-hr averages show that the most probable value of P _{k/P B} is =1.0±0.1, which implies that the most probable state of the solar wind at 1 AU is not one of equipartition between the thermal energy and magnetic energy. The average total pressure for a given bulk speed(P(V)=P ^k+P _k+P _B) is essentially independent of V, implying that P is not determined by the heating or acceleration mechanisms of the solar wind; the average pressure is P=(2.9±1.5)×10^-10dyne/cm².