Collisional excitation of HC3N by para- and ortho-H2

New calculations for rotational excitation of cyanoacetylene by collisions with hydrogen molecules are performed to include the lowest 38 rotational levels of HC3N and kinetic temperatures to 300 K. Calculations are based on the interaction potential of Wernli et al. A&A, 464, 1147 (2007) whose accuracy is checked against spectroscopic measurements of the HC3N-H2 complex. The quantum coupled-channel approach is employed and complemented by quasi-classical trajectory calculations. Rate coefficients for ortho-H2 are provided for the first time. Hyperfine resolved rate coefficients are also deduced. Collisional propensity rules are discussed and comparisons between quantum and classical rate coefficients are presented. This collisional data should prove useful in interpreting HC3N observations in the cold and warm ISM, as well as in protoplanetary disks.Comment: 8 pages, 2 tables, 4 figures, accepted for publication in MNRA

Quasi-classical rate coefficient calculations for the rotational (de)excitation of H2O by H2

The interpretation of water line emission from existing observations and future HIFI/Herschel data requires a detailed knowledge of collisional rate coefficients. Among all relevant collisional mechanisms, the rotational (de)excitation of H2O by H2 molecules is the process of most interest in interstellar space. To determine rate coefficients for rotational de-excitation among the lowest 45 para and 45 ortho rotational levels of H2O colliding with both para and ortho-H2 in the temperature range 20-2000 K. Rate coefficients are calculated on a recent high-accuracy H2O-H2 potential energy surface using quasi-classical trajectory calculations. Trajectories are sampled by a canonical Monte-Carlo procedure. H2 molecules are assumed to be rotationally thermalized at the kinetic temperature. By comparison with quantum calculations available for low lying levels, classical rates are found to be accurate within a factor of 1-3 for the dominant transitions, that is those with rates larger than a few 10^{-12}cm^{3}s^{-1}. Large velocity gradient modelling shows that the new rates have a significant impact on emission line fluxes and that they should be adopted in any detailed population model of water in warm and hot environments.Comment: 8 pages, 2 figures, 1 table (the online material (4 tables) can be obtained upon request to [email protected]

Rotational Excitation of HC_3N by H_2 and He at low temperatures

Rates for rotational excitation of HC3N by collisions with He atoms and H2 molecules are computed for kinetic temperatures in the range 5-20K and 5-100K, respectively. These rates are obtained from extensive quantum and quasi-classical calculations using new accurate potential energy surfaces (PES)

Contracting for liability limitation

Today terrorism has become a world-wide phenomenon which does not stop at the European borders. Following the 9/11 attacks on the World Trade Centre and terrorist attacks in Paris, Madrid and London, concerns have arisen in Europe about potential liability exposure for terrorism-related damage. This book tackles the problem of civil liability for damage caused by terrorist acts from several angles. The authors expertly deliver a comprehensive analysis of terrorism-related risk under international and EU law and the national tort law systems of seven representative EU Member States. They also provide a comparison of the situation in Europe to the liability environment in the US. Risk mitigation strategies are considered and critically assessed, as are alternative systems for redressing terrorism-related risks. The book concludes with a reflection on the analysis and presents possible strategies for future regulation by the European lawmakers

Collisional excitation of singly deuterated ammonia NH2_2D by H2_2

The availability of collisional rate coefficients with H$_2$ is a pre-requisite for interpretation of observations of molecules whose energy levels are populated under non local thermodynamical equilibrium conditions. In the current study, we present collisional rate coefficients for the NH$_2$D / para--H$_2$($J_2 = 0,2$) collisional system, for energy levels up to $J_\tau = 7_7$ ($E_u$$\sim$735 K) and for gas temperatures in the range $T = 5-300$K. The cross sections are obtained using the essentially exact close--coupling (CC) formalism at low energy and at the highest energies, we used the coupled--states (CS) approximation. For the energy levels up to $J_\tau = 4_2$ ($E_u$$\sim$215 K), the cross sections obtained through the CS formalism are scaled according to a few CC reference points. These reference points are subsequently used to estimate the accuracy of the rate coefficients for higher levels, which is mainly limited by the use of the CS formalism. Considering the current potential energy surface, the rate coefficients are thus expected to be accurate to within 5\% for the levels below $J_\tau = 4_2$, while we estimate an accuracy of 30\% for higher levels

Collisional excitation of water by hydrogen atoms

We present quantum dynamical calculations that describe the rotational excitation of H$_2$O due to collisions with H atoms. We used a recent, high accuracy potential energy surface, and solved the collisional dynamics with the close-coupling formalism, for total energies up to 12 000 cm$^{-1}$. From these calculations, we obtained collisional rate coefficients for the first 45 energy levels of both ortho- and para-H$_2$O and for temperatures in the range T = 5-1500 K. These rate coefficients are subsequently compared to the values previously published for the H$_2$O / He and H$_2$O / H$_2$ collisional systems. It is shown that no simple relation exists between the three systems and that specific calculations are thus mandatory

Upper bound on the density of Ruelle resonances for Anosov flows

Using a semiclassical approach we show that the spectrum of a smooth Anosov vector field V on a compact manifold is discrete (in suitable anisotropic Sobolev spaces) and then we provide an upper bound for the density of eigenvalues of the operator (-i)V, called Ruelle resonances, close to the real axis and for large real parts.Comment: 57 page

On the influence of collisional rate coefficients on the water vapour excitation

Water is a key molecule in many astrophysical studies. Its high dipole moment makes this molecule to be subthermally populated under the typical conditions of most astrophysical objects. This motivated the calculation of various sets of collisional rate coefficients (CRC) for H$_2$O (with He or H$_2$) which are necessary to model its rotational excitation and line emission. We performed accurate non--local non--LTE radiative transfer calculations using different sets of CRC in order to predict the line intensities from transitions that involve the lowest energy levels of H$_2$O (E $<$ 900 K). The results obtained from the different CRC sets are then compared using line intensity ratio statistics. For the whole range of physical conditions considered in this work, we obtain that the intensities based on the quantum and QCT CRC are in good agreement. However, at relatively low H$_2$ volume density ($n$(H$_2$) $<$ 10$^7$ cm$^{-3}$) and low water abundance ($\chi$(H$_2$O) $<$ 10$^{-6}$), these physical conditions being relevant to describe most molecular clouds, we find differences in the predicted line intensities of up to a factor of $\sim$ 3 for the bulk of the lines. Most of the recent studies interpreting early Herschel Space Observatory spectra used the QCT CRC. Our results show that although the global conclusions from those studies will not be drastically changed, each case has to be considered individually, since depending on the physical conditions, the use of the QCT CRC may lead to a mis--estimate of the water vapour abundance of up to a factor of $\sim$ 3