Radiative Opacity Research Articles

X-ray scattering by many-particle systems

This paper reviews the treatment of high-frequency Thomson scattering in the non-relativistic and near-relativistic regimes with the primary purpose of understanding the nature of the frequency redistribution correction to the differential cross-section. This correction is generally represented by a factor involving the ratio ωα /ωβ of the scattered (α) to primary (β) frequencies of the radiation. In some formulae given in the literature, the ratio appears squared, in others it does not. In Compton scattering, the frequency change is generally understood to be due to the recoil of the particle as a result of energy and momentum conservation in the photon–electron system. In this case, the Klein–Nishina formula gives the redistribution factor as . In the case of scattering by a many-particle system, however, the frequency and momentum changes are no longer directly interdependent but depend also upon the properties of the medium, which are encoded in the dynamic structure factor. We show that the redistribution factor explicit in the quantum cross-section (that seen by a photon) is ωα /ωβ, which is not squared. Formulae for the many-body cross-section given in the literature, in which the factor is squared, can often be attributed to a different (classical) definition of the cross-section, though not all authors are explicit about which definition they are using. What is shown not to be true is that the structure factor simply gives the ratio of the many-electron to one-electron differential cross-sections, as is sometimes supposed. Mixing up the cross-section definitions can lead to errors when describing x-ray scattering. We illustrate the nature of the discrepancy by deriving the energy-integrated angular distributions, with first-order relativistic corrections, for classical and quantum scattering measurements, as well as the radiative opacity for photon diffusion in a Thomson-scattering medium, which is generally considered to be governed by quantum processes.

Investigations on radiative opacity measurement by the method of direct laser-heating and self-backlighting

A target designed for opacity studies of dense plasmas by laser direct heating and self-backlighting technique was presented and tested. The backlight source and sample plasma were generated by directing a frequency-tripled Nb-glass laser onto an Au/CH/Al/CH multilayer target on the XG-II laser facility, and the absorption of the sample plasma was obtained by measuring the attenuated backlight spectrum of the sample plasma. One-dimensional radiative hydrodynamic code Multi-1D was used to simulate the laser heating of the multilayer target, and the temperature and density profiles in the target were given. Experimental data were compared with the theoretically calculated spectra using the detailed-term-accounting model, which showed a temperature range from 20 eV to 70 eV in the sample plasma, a result in quite good agreement with the Multi-1D simulations.

Cumulative physical uncertainty in modern stellar models

Using our updated stellar evolutionary code, we quantitatively evaluate the effects of the uncertainties in the main physical inputs on the evolutionary characteristics of low mass stars from the main sequence to the zero age horizontal branch (ZAHB). We calculated more than 3000 stellar tracks and isochrones, with updated solar mixture, by changing the following physical inputs within their current range of uncertainty: 1H(p,nu e+)2H, 14N(p,gamma)15O, and triple-alpha reaction rates, radiative and conductive opacities, neutrino energy losses, and microscopic diffusion velocities. We performed a systematic variation on a fixed grid, in a way to obtain a full crossing of the perturbed input values. The effect of the variations of the chosen physical inputs on relevant stellar evolutionary features, such as the turn-off luminosity, the central hydrogen exhaustion time, the red-giant branch (RGB) tip luminosity, the helium core mass, and the ZAHB luminosity in the RR Lyrae region are statistically analyzed. For a 0.9 Msun model, the cumulative uncertainty on the turn-off, the RGB tip, and the ZAHB luminosities accounts for $\pm$ 0.02 dex, $\pm$ 0.03 dex, and $\pm$ 0.045 dex respectively, while the central hydrogen exhaustion time varies of about $\pm$ 0.7 Gyr. The most relevant effect is due to the radiative opacities uncertainty; for the later evolutionary stages the second most important effect is due to the triple-alpha reaction rate uncertainty. For an isochrone of 12 Gyr, we find that the isochrone turn-off log luminosity varies of $\pm$ 0.013 dex, the mass at the isochrone turn-off varies of $\pm$ 0.015 Msun, and the difference between ZAHB and turn-off log-luminosity varies of $\pm$ 0.05 dex. The effect of the physical uncertainty affecting the age inferred from turn-off luminosity and from the vertical method are of $\pm$ 0.375 Gyr and $\pm$ 1.25 Gyr respectively.

Analysis of the influence of the plasma thermodynamic regime in the spectrally resolved and mean radiative opacity calculations of carbon plasmas in a wide range of density and temperature

In this work the spectrally resolved, multigroup and mean radiative opacities of carbon plasmas are calculated for a wide range of plasma conditions which cover situations where corona, local thermodynamic and non-local thermodynamic equilibrium regimes are found. An analysis of the influence of the thermodynamic regime on these magnitudes is also carried out by means of comparisons of the results obtained from collisional-radiative, corona or Saha–Boltzmann equations. All the calculations presented in this work were performed using ABAKO/RAPCAL code.

Detailed Theoretical Investigations on the L-Shell Absorption of Open-M-Shell Germanium Plasmas:Effect of Autoionization Resonance Broadening

Radiative opacity of open-M-shell germanium plasmas in the L-shell photon energy region were investigated in detail by using a fully relativistic detailed level accounting approach. Among other physical effects such as relativistic and the interaction between fine-structure levels belonging to the same non-relativistic configuration and different configurations, particular attention is paid on the effect of autoionization resonance broadening on the L-shell absorption. The results show that for plasmas at present and past typical experimental conditions, line width due to autoionization resonance broadening dominate among all the physical broadening mechanisms including electron impact and Doppler broadenings. Such an effect is most pronounced for ions with just a few 2p-nd transition lines such as Ge14+, while it is not so pronounced for complex ions such as Ge16+, where there are so many 2p-nd lines that line overlapping partly conceal the effect of autoionization resonance broadening. After taking the effect of autoionization resonance broadening into account, detailed comparisons are made with available experimental spectra at different physical conditions of different plasma temperatures and densities. The L-shell absorption is sensitive to the plasma temperature, especially in the 2p-3d excitation energy region. The potential of utlizing the relative shape and intensity of the 2p-3d spin-orbit splitting as temperature diagnostics is investigated.

SOLAR MIXTURE OPACITY CALCULATIONS USING DETAILED CONFIGURATION AND LEVEL ACCOUNTING TREATMENTS

An opacity model (OPAS) combining detailed configuration and level accounting treatments has been developed to calculate radiative opacity of plasmas in local thermodynamic equilibrium. The model is presented and used to compute spectral opacities of a solar mixture. Various density-temperature couples have been considered from the solar center up to the vicinity of the radiative/convective zone interface. For a given solar thermodynamic path, OPAS calculations are compared to Opacity Project (OP) and OPAL data. Rosseland mean opacity values are in very good agreement over all the considered solar thermodynamic path, while OPAS and OP spectral opacities of each element may vary considerably. Main sources of discrepancy are discussed.

Radiative opacity of low-Z plasma using screened hydrogenic model including l-splitting

Radiative opacities of low-Z plasma are computed using average atom model. Screened Hydrogenic Model including l-splitting (SHML) is used as the atomic model to obtain the internal structure of ions embedded in plasma. The phenomenon of pressure ionization of levels is described by a Gaussian density dependent degeneracy function. Use of the most recent compilation of the screening constants makes it possible to include l-splitting in a direct manner. The average ionization in the plasma is obtained by self-consistently solving the non-linear set of coupled SHML equations along with the charge neutrality condition of Wigner–Seitz cell. The frequency dependent opacity of Aluminum plasma is compared with the data obtained from Los Alamos (LANL) opacity library and a reasonable agreement is seen. The computed values of Rosseland and Planck opacity of C, Al and Fe plasma are also in good agreement with the LANL opacity database value for different plasma density and temperature.

The Pisa pre-main sequence tracks and isochrones

In recent years new observations of pre-main sequence stars (pre-MS) with Z <= Zsun have been made available. To take full advantage of the continuously growing amount of data of pre-MS stars in different environments, we need to develop updated pre-MS models for a wide range of metallicity to assign reliable ages and masses to the observed stars. We present updated evolutionary pre-MS models and isochrones for a fine grid of mass, age, metallicity, and helium values. We use a standard and well-tested stellar evolutionary code (i.e. FRANEC), that adopts outer boundary conditions from detailed and realistic atmosphere models. In this code, we incorporate additional improvements to the physical inputs related to the equation of state and the low temperature radiative opacities essential to computing low-mass stellar models. We make available via internet a large database of pre-MS tracks and isochrones for a wide range of chemical compositions (Z = 0.0002 - 0.03), masses (M = 0.2 - 7.0 Msun), and ages (1 - 100 Myr) for a solar-calibrated mixing length parameter \alpha (i.e. 1.68). For each chemical composition, additional models were computed with two different mixing length values, namely \alpha = 1.2 and 1.9. Moreover, for Z >= 0.008, we also provided models with two different initial deuterium abundances. The characteristics of the models have been discussed in detail and compared with other work in the literature. The main uncertainties affecting theoretical predictions have been critically discussed. Comparisons with selected data indicate that there is close agreement between theory and observation.

Radiative power losses and opacity calculations in fusion plasmas1This article is part of a Special Issue on the 10th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas.

We present recent results on radiative power losses of carbon and gold ions in fusion plasmas. Our approach is based on a detailed calculation, where the atomic database is provided by the MCDF code. A lineshape code, allowing for NLTE ionic populations, was adapted to the calculation of radiative power loss profiles. Because the calculation time is sometimes prohibitive, an alternative approach based on statistical distributions is proposed. This approach involves the first four moments of the radiative power losses. We have focused our attention on carbon and gold. The first element could be present in the ablator in some inertial confinement schemes. The second element is present in holraums and its X-ray emission contributes to the heating in inertial confinement fusion. Finally, opacity calculations are compared to measured transmission in aluminum ions.

One-dimensional space resolving flat-field holographic grating soft x-ray framing camera spectrograph for laser plasma diagnostics

A 1D space resolving x-ray spectrum diagnostic system has been developed to study the radiation opacity of hot plasma on SG-II laser facility. The diagnostic system consists of a 2400 lines/mm flat-field holographic grating and a gated microchannel plate coupled with an optical CCD and covers the wavelength range of 5-50 Å. The holographic grating was compared with a ruled one by measuring the emission spectra from a laser-produced molybdenum plasma. The results indicate that the holographic grating possesses better sensitivity than the ruled grating having nearly similar spectral resolution. The spectrograph has been used in radiative opacity measurement of Fe plasma. Simultaneous measurements of the backlight source and the transmission spectrum in appointed time range in one shot have been accomplished successfully with the holographic grating spectrometer. The 2p-3d transition absorption of Fe plasma near 15.5 Å in has been observed clearly.

Dynamical magnetic enhancement of light and heavy quark jet quenching at RHIC

A new Monte Carlo implementation of Djordjevicʼs dynamical scattering generalization of the DGLV radiative energy loss opacity series is used with a hybrid interpolation scheme to compute both light and heavy quark jet quenching up to third order in opacity. The enhancement of the ratio of bottom to charm quark energy loss due to perturbative long range color magnetic effects in nonuniform Bjorken expanding geometries is found to reduce the significance of the heavy quark jet puzzle posed by the observed near equality (within sizeable errors) of pion and nonphotonic electron nuclear modification at RHIC. Jet Flavor Spectroscopy discussed below will be a powerful tool to differentiate competing dynamical models of the QGP produced in ultra-relativistic nuclear collisions.

Plasma screening effects on the atomic structure and radiative opacity of dense carbon plasmas based on the DLA model

A study of plasma screening effects using a Debye-Hückel model is presented. The effects on the energy levels, oscillator strengths, ionization potential and photoionization cross sections of different ionization stages of carbon and on the radiative opacity of hot dense carbon plasmas are presented. The treatment of the atomic structure and radiative opacity is based on the detailed fine-structure level accounting formalism. For the basic atomic data, we compare our calculated energy levels and oscillator strengths with other theoretical results available in the literature and good agreement is found. The calculated ionization potential depressions of helium-like carbon, C V, are compared with the experimental and other theoretical results for a variety of plasma condition. Since the Saha–Boltzmann equation, which determines the ion stage populations, is dependent on the energy levels and ionization potentials of all ionization stages of carbon, the plasma screening effects on these quantities were included to obtain the population distribution. The screening effects play an important role on the spectrally resolved opacity by affecting the position and intensity of the absorption peaks and the K-shell ionization thresholds. With the decrease of Debye screening length, the number and intensity of the absorption peaks are reduced. In particular, the continuum opacity near the K-edge will be so sufficiently affected by the screening effects as to be experimentally observed. Finally, the plasma screening effects on the Rosseland and Planck mean opacities are investigated.

CONSTRAINTS ON THE OPACITY PROFILE OF THE SUN FROM HELIOSEISMIC OBSERVABLES AND SOLAR NEUTRINO FLUX MEASUREMENTS

Motivated by the solar composition problem and by using the recently developed Linear Solar Model approach, we analyze the role of opacity and metals in the sun. After a brief discussion of the relation between the effects produced by a variation of composition and those produced by a modification of the radiative opacity, we calculate numerically the opacity kernels that, in a linear approximation, relate an arbitrary opacity variation to the corresponding modification of the solar observable properties. We use these opacity kernels to discuss the present constraints on opacity (and composition) provided by helioseismic and solar neutrino data.

Detailed investigations on radiative opacity and emissivity of tin plasmas in the extreme-ultraviolet region

Radiative opacity and emissivity of tin plasmas at average ionization degree of about 10 was investigated in detail by using a fully relativistic detailed level accounting approach, in which main physical effects on the opacity were carefully taken into account. Among these physical effects, configuration interaction, in particular core-valence electron correlations, plays an important role on the determination of accurate atomic data required in the calculation of opacity. It results in a strong narrowing of lines from all transition arrays and strong absorption is located in a narrow wavelength region of 12.5-14 nm for Sn plasmas. Using a complete accurate atomic data, we investigated the opacity of Sn plasmas at a variety of physical condition. Among the respective ions of Xe6+-Xe15+ , Xe10+ has the largest absorption cross section at 13.5 nm, while the favorable physical condition for maximal absorption at 13.5 nm do not mean that Xe10+ has the largest fraction. Comparison with other theoretical results showed that a complete set of consistent accurate atomic data, which lacks very much, is essential to predict accurate opacity. Our atomic model is useful and can be applied to interpret opacity experiments. Further benchmark experiments are urgently needed to clarify the physical effects on the opacity of Sn plasmas.

Analytical expressions for radiative opacities of low Z plasmas

In this work we obtain analytical expressions for the radiative opacity of several low Z plasmas (He, Li, Be, and B) in a wide range of temperatures and densities. These formulas are obtained by fitting the proposed expression to mean opacities data calculated by using the code ABAKO/ RAPCAL. This code computes the radiative properties of plasmas, both in LTE and NLTE conditions, under the detailed-level-accounting approach. It has been successfully validated in the range of interest in previous works.

Radiative opacities of hot and solid-dense aluminium plasmas using a detailed level accounting model

An approach based on the self-consistent-field (SCF) multi-configuration Dirac–Fock (MCDF) model is developed to simulate radiative opacity of hot and solid-dense plasmas taking detailed levels into account. The correlation effects and the angular momentum coupling among the bound electrons are treated in the usual way employed in a normal MCDF method. Influences of plasma screening on transition energies, oscillator strengths and ionization potentials are included by introducing a correction to the one-electron potential to account for the screening of the ionized electrons. This correction depends on the detailed micro-space distribution of the ionized electrons in different ions. The total average number density of the ionized electrons in the plasma is obtained by solving the Saha equation with quantum degeneracy corrections. The ionized electron density distribution in each ion is described based on a Thomas–Fermi distribution in an atomic field. Since the electronic structure and the ionization balance depend on each other, the SCF procedure includes solving the MCDF and the Saha equations. As examples, calculations have been carried out to simulate the spectrally resolved radiative opacity and the Rosseland and Planck means of hot and solid-dense aluminium plasmas. Comparisons between the results of the present model, average atom model and experiments are made to show the significance of detailed line-by-line treatments on the calculated results.

New results on standard solar models

We describe the current status of solar modelling and focus on the problems originated with the introduction of solar abundance determinations with low CNO abundance values. We use models computed with solar abundance compilations obtained during the last decade, including the newest published abundances by Asplund and collaborators. Results presented here make focus both on helioseismic properties and the models as well as in the neutrino fluxes predictions. We also discuss changes in radiative opacities to restore agreement between helioseismology, solar models, and solar abundances and show the effect of such modifications on solar neutrino fluxes.

NEW SOLAR COMPOSITION: THE PROBLEM WITH SOLAR MODELS REVISITED

We construct updated solar models with different sets of solar abundances, including the most recent determinations by Asplund et al. (2009). The latter work predicts a larger ($\sim 10%$) solar metallicity compared to previous measurements by the same authors but significantly lower ($\sim 25%$) than the recommended value from a decade ago by Grevesse & Sauval (1998). We compare the results of our models with determinations of the solar structure inferred through helioseismology measurements. The model that uses the most recent solar abundance determinations predicts the base of the solar convective envelope to be located at $R_{\rm CZ}= 0.724{\rm R_\odot}$ and a surface helium mass fraction of $Y_{\rm surf}=0.231$. These results are in conflict with helioseismology data ($R_{\rm CZ}= 0.713\pm0.001{\rm R_\odot}$ and $Y_{\rm surf}=0.2485\pm0.0035$) at 5$-\sigma$ and 11$-\sigma$ levels respectively. Using the new solar abundances, we calculate the magnitude by which radiative opacities should be modified in order to restore agreement with helioseismology. We find that a maximum change of $\sim 15%$ at the base of the convective zone is required with a smooth decrease towards the core, where the change needed is $\sim 5%$. The required change at the base of the convective envelope is about half the value estimated previously. We also present the solar neutrino fluxes predicted by the new models. The most important changes brought about by the new solar abundances are the increase by $\sim 10%$ in the predicted $^{13}$N and $^{15}$O fluxes that arise mostly due to the increase in the C and N abundances in the newly determined solar composition.

Influence of the atomic description and configuration interaction effects on collisional-radiative calculations of low ionized carbon plasmas

An analysis of the influence of the atomic description and the configuration interaction effects in the calculation of plasma average ionization and relevant plasma radiative properties such as the spectrally resolved emissivities and opacities, radiative power losses and mean opacities, is performed. Since the larger effects of the configuration interaction are due to the lower ionization stages, i.e. CI and CII ions, the low temperature regime is analysed. However, a wide range of plasma densities is considered, covering this way different plasma thermodynamic regimes.

Spectrally resolved and Rosseland and Planck mean opacities of iron plasmas at temperatures above100eV: A systematic study

The radiative opacity of iron plasmas at high temperatures is very important in astrophysics. The spectrally resolved radiative opacity and Rosseland and Planck means were investigated by using the detailed-level-accounting (DLA) model for iron plasmas at high temperatures and a variety of density. The accuracy of atomic data such as energy levels and transition probabilities is checked by comparison with data from the National Institute of Standards and Technology. The transmission of iron plasma at a temperature of 156 eV and an electron density of 6.9 x 10(21) cm(-3) is studied in detail and compared with results of a recent experiment [Bailey et al., Phys. Rev. Lett. 99, 265002 (2007)] and other theoretical results. General good agreement is found between our DLA transmission and the experimental and other theoretical results. By using our developed DLA model, we can deduce valuable information on the physical condition of the plasma created in the experiment. The information includes the fractional distribution of different ion stages and whether the plasma is in local thermodynamic equilibrium or not. Illustrative results are given for three isothermal sequences of 100, 150, and 200 eV with different mass densities and for three isodensity sequences of 0.1, 0.05, and 0.01 g/cm3 with different temperatures. The Rosseland and Planck mean opacities are compared with other theoretical results obtained by the Los Alamos light element detailed configuration opacity code.