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SH$^+$ is a surprisingly widespread molecular ion in diffuse interstellar clouds. There, it plays an important role triggering the sulfur chemistry. In addition, SH$^+$ emission lines have been detected at the UV-illuminated edges of dense molecular clouds, mbox{so-called} photo-dissociation regions (PDRs), and toward high-mass protostars. An accurate determination of the SH$^+$ abundance and of the physical conditions prevailing in these energetic environments relies on knowing the rate coefficients of inelastic collisions between SH$^+$ molecules and hydrogen atoms, hydrogen molecules, and electrons. In this paper, we derive SH$^+$--H fine and hyperfine-resolved rate coefficients from the recent quantum calculations for the SH$^+$--H collisions, including inelastic, exchange and reactive processes. The method used is based on the infinite order sudden approach. State-to-state rate coefficients between the first 31 fine levels and 61 hyperfine levels of SH$^+$ were obtained for temperatures ranging from 10 to 1000 K. Fine structure-resolved rate coefficients present a strong propensity rule in favour of $Delta j = Delta N$ transitions. The $Delta j = Delta F$ propensity rule is observed for the hyperfine transitions. {The new rate coefficients will help significantly in the interpretation of SH$^+$ spectra from PDRs and UV-irradiated shocks where the abundance of hydrogen atoms with respect to hydrogen molecules can be significant.
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The modelling of emission spectra of molecules seen in interstellar clouds requires the knowledge of collisional rate coefficients. Among the commonly observed species, N$_2$H$^+$ is of particular interest since it was shown to be a good probe of the physical conditions of cold molecular clouds. Thus, we have calculated hyperfine-structure resolved excitation rate coefficients of N$_2$H$^+$(X$^1Sigma^+$) by H$_2(j=0)$, the most abundant collisional partner in the cold interstellar medium. The calculations are based on a new potential energy surface, obtained from highly correlated {it ab initio} calculations. State-to-state rate coefficients between the first hyperfine levels were calculated, for temperatures ranging from 5 K to 70 K. By comparison with previously published N$_2$H$^+$-He rate coefficients, we found significant differences which cannot be reproduced by a simple scaling relationship. As a first application, we also performed radiative transfer calculations, for physical conditions typical of cold molecular clouds. We found that the simulated line intensities significantly increase when using the new H$_2$ rate coefficients, by comparison with the predictions based on the He rate coefficients. In particular, we revisited the modelling of the N$_2$H$^+$ emission in the LDN 183 core, using the new collisional data, and found that all three of the density, gas kinetic temperature and N$_2$H$^+$ abundance had to be revised.
Advances in merged-beams instruments have allowed experimental studies of the mutual neutralisation (MN) processes in collisions of both Li$^+$ and Na$^+$ ions with D$^-$ at energies below 1 eV. These experimental results place constraints on theoretical predictions of MN processes of Li$^+$ and Na$^+$ with H$^-$, important for non-LTE modelling of Li and Na spectra in late-type stars. We compare experimental results with calculations for methods typically used to calculate MN processes, namely the full quantum (FQ) approach, and asymptotic model approaches based on the linear combination of atomic orbitals (LCAO) and semi-empirical (SE) methods for deriving couplings. It is found that FQ calculations compare best overall with the experiments, followed by the LCAO, and the SE approaches. The experimental results together with the theoretical calculations, allow us to investigate the effects on modelled spectra and derived abundances and their uncertainties arising from uncertainties in the MN rates. Numerical experiments in a large grid of 1D model atmospheres, and a smaller set of 3D models, indicate that neglect of MN can lead to abundance errors of up to 0.1 dex (26%) for Li at low metallicity, and 0.2 dex (58%) for Na at high metallicity, while the uncertainties in the relevant MN rates as constrained by experiments correspond to uncertainties in abundances of much less than 0.01~dex (2%). This agreement for simple atoms gives confidence in the FQ, LCAO and SE model approaches to be able to predict MN with the accuracy required for non-LTE modelling in stellar atmospheres.
The rate constants for the formation, destruction, and collisional excitation of SH$^+$ are calculated from quantum mechanical approaches using two new SH$_2^+$ potential energy surfaces (PESs) of $^4A$ and $^2A$ electronic symmetry. The PESs were developed to describe all adiabatic states correlating to the SH$^+$ ($^3Sigma^-$) + H($^2S$) channel. The formation of SH$^+$ through the S$^+$ + H$_2$ reaction is endothermic by $approx$ 9860 K, and requires at least two vibrational quanta on the H$_2$ molecule to yield significant reactivity. Quasi-classical calculations of the total formation rate constant for H$_2$($v=2$) are in very good agreement with the quantum results above 100K. Further quasi-classical calculations are then performed for $v=3$, 4, and 5 to cover all vibrationally excited H$_2$ levels significantly populated in dense photodissociation regions (PDR). The new calculated formation and destruction rate constants are two to six times larger than the previous ones and have been introduced in the Meudon PDR code to simulate the physical and illuminating conditions in the Orion bar prototypical PDR. New astrochemical models based on the new molecular data produce four times larger SH$^+$ column densities, in agreement with those inferred from recent ALMA observations of the Orion bar.
Using our deep optical and near-infrared photometry along with multiwavelength archival data, we here present a detailed study of the Galactic H II region Sh 2-305, to understand the star/star-cluster formation. On the basis of excess infra-red emission, we have identified 116 young stellar objects (YSOs) within a field of view of ~ 18.5 arcminute x 18.5 arcminute, around Sh 2-305. The average age, mass and extinction (A_V) for this sample of YSOs are 1.8 Myr, 2.9 solar mass and 7.1 mag, respectively. The density distribution of stellar sources along with minimal spanning tree calculations on the location of YSOs reveals at least three stellar sub-clusterings in Sh 2-305. One cluster is seen toward the center (i.e., Mayer 3), while the other two are distributed toward the north and south directions. Two massive O-type stars (VM2 and VM4; ages ~ 5 Myr) are located at the center of the Sh 2-305 H II region. The analysis of the infrared and radio maps traces the photon dominant regions (PDRs) in the Sh 2-305. Association of younger generation of stars with the PDRs is also investigated in the Sh 2-305. This result suggests that these two massive stars might have influenced the star formation history in the Sh 2-305. This argument is also supported with the calculation of various pressures driven by massive stars, slope of mass function/K-band luminosity function, star formation efficiency, fraction of Class I sources, and mass of the dense gas toward the sub-clusterings in the Sh 2-305.
The generator-coordinate method is a flexible and powerful reformulation of the variational principle. Here we show that by introducing a generator coordinate in the Kohn-Sham equation of density-functional theory, excitation energies can be obtained from ground-state density functionals. As a viability test, the method is applied to ground-state energies and various types of excited-state energies of atoms and ions from the He and the Li isoelectronic series. Results are compared to a variety of alternative DFT-based approaches to excited states, in particular time-dependent density-functional theory with exact and approximate potentials.
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