Atomic data on inelastic processes in lowenergy manganesehydrogen collisions ^{⋆}
^{1} MaxPlanck Institute for Astrophysics, Postfach 1371, 85741 Garching, Germany
email: andrey.k.belyaev@gmail.com
^{2} Department of Theoretical Physics and Astronomy, Herzen University, 191186 St. Petersburg, Russia
Received: 31 May 2017
Accepted: 3 July 2017
Aims. The aim of this paper is to calculate cross sections and rate coefficients for inelastic processes in lowenergy Mn + H and Mn^{+} + H^{−} collisions, especially, for processes with high and moderate rate coefficients. These processes are required for nonlocal thermodynamic equilibrium (nonLTE) modeling of manganese spectra in cool stellar atmospheres, and in particular, for metalpoor stars.
Methods. The calculations of the cross sections and the rate coefficients were performed by means of the quantum model approach within the framework of the BornOppenheimer formalism, that is, the asymptotic semiempirical method for the electronic MnH molecular structure calculation followed by the nonadiabatic nuclear dynamical calculation by means of the multichannel analytic formulas.
Results. The cross sections and the rate coefficients for lowenergy inelastic processes in manganesehydrogen collisions are calculated for all transitions between 21 lowlying covalent states and one ionic state. We show that the highest values of the cross sections and the rate coefficients correspond to the mutual neutralization processes into the final atomic states Mn(3d^{5}4s(^{7}S)5s e ^{6}S), Mn(3d^{5}4s(^{7}S)5p y ^{8}P°), Mn(3d^{5}4s(^{7}S)5s e ^{8}S), Mn(3d^{5}4s(^{7}S)4d e ^{8}D) [the first group], the processes with the rate coefficients (at temperature T = 6000 K) of the values 4.38 × 10^{8}, 2.72 × 10^{8}, 1.98 × 10^{8}, and 1.59 × 10^{8} cm^{3}/ s, respectively, that is, with the rate coefficients exceeding 10^{8} cm^{3}/ s. The processes with moderate rate coefficients, that is, with values between 10^{10} and 10^{8} cm^{3}/ s include many excitation, deexcitation, mutual neutralization and ionpair formation processes. In addition to other processes involving the atomic states from the first group, the processes from the second group include those involving the following atomic states: Mn(3d^{5}(^{6}S)4s4p (^{1}P°) y ^{6}P°), Mn(3d^{5}4s(^{7}S)4d e ^{6}D), Mn(3d^{5}4s(^{7}S)5p w ^{6}P°), Mn(3d^{5}(^{4}P)4s4p (^{3}P°) y ^{6}D°), Mn(3d^{5}(^{4}G)4s4p (^{3}P°) y ^{6}F°). The processes with the highest and moderate rate coefficients are expected to be important for nonLTE modeling of manganese spectra in stellar atmospheres.
Key words: atomic data / atomic processes / stars: abundances
Rate coefficients K_{if}(T) for the excitation, deexcitation, mutual neutralization, and ionpair formation processes in manganesehydrogen collisions are only available at the CDS via anonymous ftp to cdsarc.ustrasbg.fr (130.79.128.5) or via http://cdsarc.ustrasbg.fr/vizbin/qcat?J/A+A/606/A106
© ESO, 2017
1. Introduction
Nonlocal thermodynamic equilibrium (nonLTE) modelings of different astrophysical phenomena are important for many fundamental problems in modern astrophysics (see, e.g., reviews Asplund 2005; Mashonkina 2014; Barklem 2016a, and references therein). Suffices it to say that nonLTE modeling of stellar atmospheres are of importance, in particular, for determining absolute and relative abundances of different chemical elements, for the Galactic evolution, and so on. NonLTE modeling requires detailed and complete information about inelastic heavyparticle collision processes, most importantly ones in collisions with hydrogen atoms and negative ions. It has been emphasized several times (see, e.g., Asplund 2005; Barklem 2016a) that inelastic processes in collisions with hydrogen atoms and anions give the main uncertainty for nonLTE studies, especially in metalpoor stars.
The most accurate information about inelastic processes in lowenergy collisions with hydrogen is that obtained by full quantum calculations. Recently, the markable progress has been achieved in detailed quantum treatments of inelastic processes in collisions of different atoms and positive ions with hydrogen atoms and negative ions. The accurate quantum cross sections were calculated for transitions between many lowlying atomic and ionic states for Na, Li, Mg, He + H, as well as Na^{+}, Li^{+}, Mg^{+} + H^{−} collisions (Belyaev et al. 1999, 2010, 2012; Croft et al. 1999a,b; Belyaev & Barklem 2003; Guitou et al. 2015; Belyaev 2015) based on accurate ab initio (Belyaev et al. 1999; Guitou et al. 2010, 2015; Belyaev 2015) or pseudopotential (Croft et al. 1999a; Dickinson et al. 1999) quantumchemical data. The quantum cross sections were used for computing the inelastic rate coefficients (Barklem et al. 2003, 2010, 2012; Guitou et al. 2015) and finally for the nonLTE stellar atmosphere modeling (Barklem et al. 2003; Lind et al. 2009, 2011; Mashonkina 2013; Osorio et al. 2015; Osorio & Barklem 2016).
Nevertheless, full quantum calculations are still timeconsuming and, hence, rather seldom. For this reason, it was stated several times (see, e.g., Asplund 2005; Barklem et al. 2011) that there is a strong demand in more approximate, but reliable model approaches^{1}. Two quantum model approaches for nonadiabatic nuclear dynamics have been recently proposed and successfully applied: (i) the branching probability current method (Belyaev 2013a) and (ii) the multichannel model approach (Belyaev 1993; Belyaev et al. 2014b; Yakovleva et al. 2016). Both approaches are based on electronic structure calculations and the LandauZener model for nonadiabatic transitions. For electronic structure calculations, in addition to accurate ab initio methods, the following approximate methods have been used: the asymptotic method (Belyaev 2013a) and the Linear Combinations of Atomic Orbitals (LCAO) method (Grice & Herschbach 1974; Adelman & Herschbach 1977; Barklem 2016b). The quantum model approaches have been successfully applied to a number of lowenergy inelastic processes in collisions with hydrogen: Al (Belyaev 2013a), Li, Mg, Si (Belyaev et al. 2014b), Cs (Belyaev et al. 2014a), Be (Yakovleva et al. 2016), and Ca (Belyaev et al. 2016; Barklem 2016b; Mitrushchenkov et al. 2017). Comparison with the available results of quantum calculations has shown that both model approaches provide reliable collision data, especially for processes with high and moderate rate coefficients, the processes which are the most important for nonLTE modeling.
Manganese is an element of significant astrophysical importance (Asplund 2005; Bergemann & Gehren 2007, 2008; Bergemann et al. 2013; Scott et al. 2015, see also references therein). In particular, manganese is of interest because it belongs to the irongroup elements. As noted by Jofré et al. (2015): “measuring accurate abundances of Mn is also important for studying the structure of our Galaxy”, and further “it is important for discussions of the formation history of the Galactic halo”. In addition, Hawkins et al. (2015) recently showed Mn to be one of the best candidates to distinguish Galactic components.
The irongroup elements have complicated electronic structures and, hence, potentials for interactions between hydrogen and the highly excited Mnstates considered here are not accessible by rigorous ab initio calculations. For this reason, the model asymptotic potential approach (Belyaev 2013a) is applied in the present work for MnH electronic structure calculations. This quantum model approach has been already applied to interactions of hydrogen with atoms and ions of some chemical elements: Al (Belyaev 2013b), Si (Belyaev et al. 2014b), Ca (Belyaev et al. 2016), Be (Yakovleva et al. 2016). It has been shown that the approach provides reliable potentials needed for nonadiabatic nuclear dynamical treatments. For the nonadiabatic nuclear dynamics, the model multichannel approach (see Belyaev 1993; Yakovleva et al. 2016, for details and references) has been chosen.
In the present study of manganesehydrogen collisions, we take into account 21 lowlying covalent states and one (ground) ionic state. Transitions into other states in these collisions can be neglected^{2}. Cross sections and rate coefficients for partial inelastic processes (excitation, deexcitation, ionpair formation and mutual neutralization) are calculated for all transitions between the states treated.
2. Model approach
The present study of inelastic lowenergy manganesehydrogen collisions continues a series of systematic treatments of inelastic collisions of different atoms and positive ions with hydrogen atoms and its negative ions (Belyaev 2013b; Belyaev et al. 2014b, 2016; Yakovleva et al. 2016) by using the quantum model approaches within the framework of the BornOppenheimer formalism. Since these approaches have already been described in detail in previous papers, here we present only a brief description of the approach used.
The BornOppenheimer approach treats an inelastic collision process into two steps: (i) an electronic structure calculation of a considered (quasi)molecule and (ii) a nonadiabatic nuclear dynamical study. In the present paper, the electronic structure calculation of the MnH molecule was performed by the asymptotic method (Belyaev 2013a), while the nonadiabatic nuclear dynamics was studied by means of the multichannel formulas (Belyaev 1993; Yakovleva et al. 2016) based on the LandauZener model.
It has been shown by the full quantum studies of collisions with hydrogen (Belyaev et al. 2010, 2012) that inelastic rate coefficients with large and moderate values are determined by longrange ioniccovalent interactions within molecular symmetries of the ground ionic molecular states. For this reason, the first step, the electronic structure calculation, was performed by a construction of the electronic Hamiltonian matrix in a diabatic representation as a function of the internuclear distance R. Within the asymptotic method, the Hamiltonian matrix for each groundstate ionic molecular symmetry is constructed from diagonal matrix elements for ionic and corresponding covalent molecular states and the offdiagonal matrix elements for ioniccovalent interactions (see Belyaev 2013a, for details). The diagonal terms should have correct asymptotic behavior. For singleelectron transitions, the offdiagonal matrix elements, the exchange matrix elements, H_{jk} are obtained by means of the semiempirical OlsonSmithBauer formula (Olson et al. 1971) . However, some covalent molecular diabatic states are coupled with the ionic molecular diabatic states by twoelectron transitions. In this case, the semiempirical OlsonSmithBauer formula is not directly applicable, and Yakovleva et al. (2016) based on the results of (Belyaev 1993) have proposed estimating twoelectrontransition exchange matrix elements by the following expression: (1)The comparison with the accurate ab initio results for CaH (Mitrushchenkov et al. 2017) has shown that Eq. (1) provides reasonable estimates. Diagonalization of the electronic Hamiltonian matrix constructed by this way allows one to calculate the adiabatic potential energies for the MnH molecule, the data needed for the nuclear dynamics.
In the second step, the total inelastic transition probabilities for all transitions between considered states were calculated by means of the multichannel model. A nonadiabatic transition probability after a single traverse of a nonadiabatic region was calculated within the LandauZener model by the adiabaticpotentialbased formula (see Belyaev & Lebedev 2011). Since the longrange nonadiabatic regions created by the ioniccovalent interaction are located in a particular order^{3}, the analytic multichannel formulas (Belyaev & Tserkovnyi 1987; Belyaev 1993; Belyaev & Barklem 2003; Yakovleva et al. 2016) can be used for calculations of inelastic transition probabilities.
Two features that affect inelastic probabilities were taken into account in the present calculations. The first is a multiple passing of nonadiabatic regions for collision energies below the asymptote of the ionic channel, see (Devdariani & Zagrebin 1984; Belyaev 1985) for a threechannel case, as well as (Yakovleva et al. 2016) for a general case. This feature increases lowenergy inelastic cross sections and finally lowtemperature inelastic rate coefficients, which are the main interest for nonLTE modeling. The second feature is the tunneling effect, which takes place at large total angular momentum quantum numbers J. Taking this effect into account results in the additional factor for inelastic transition probabilities, see (Belyaev 1985), as well as (Yakovleva et al. 2016). Thus, the statetostate inelastic probability P_{if}(J,E) for a transition from an initial state i to a final state f for a given J and a given collision energy E can be calculated by using the multichannel formulas which are summarized by Yakovleva et al. (2016).
Cross sections and rate coefficients for exothermic (k → n, E_{k}>E_{n}) and endothermic (n → k) processes, σ_{kn}(E), K_{kn}(T) and σ_{nk}(E), K_{nk}(T), respectively, can be calculated by the following formulas:
where ΔE_{kn} = E_{k}−E_{n} is the energy defect between the asymptotic energies of the channels k and n, T the temperature, the statistical probability for population of the channel j, k_{B} the Boltzmann constant, and μ the reduced nuclear mass. The rate coefficients for exothermic processes are usually weakly dependent on the temperature T, so it is better to compute them first for exothermic processes by means of Eq. (4), and then for endothermic ones by means of the detailed balance Eq. (5).
3. Manganesehydrogen collisions
3.1. MnH electronic structure
MnH(j^{7}Σ^{+}) molecular states, the corresponding asymptotic atomic states (scattering channels), the manganese terms, the asymptotic energies (average experimental values taken from NIST; Kramida et al. 2012) with respect to the groundstate level, the electronic bound energies E_{j}, and the statistical probabilities for population of the molecular states.
The ground ionic Mn^{+}(3d^{5}4s ^{7}S) + H^{−}(1s^{2}^{1}S) molecular state has the only symmetry: , so inelastic transitions leading to high rate coefficients occur within this molecular symmetry. This restricts covalent molecular states effectively participating into the nonadiabatic nuclear dynamics, and finally this selects atomic states of Mn which should be taken into consideration. The 21 lowlying atomic states resulting in the MnH() covalent molecular states, as well as the ground ionic Mn^{+} + H^{−} molecular state are listed in Table 1. These are the states taken into account in the present study. Higherlying states are not efficiently coupled with these states and therefore not included into consideration.
We note that the considered covalent molecular states are mainly coupled with the ground ionic molecular state by singleelectron transition exchange matrix elements, but three of the considered states, Mn(3d^{6}(^{5}D)4p z ^{6}D^{o}), Mn(3d^{6}(^{5}D)4p z ^{6}F^{o}), Mn(3d^{6}(^{5}D)4p x ^{6}P^{o}) + H, are coupled by twoelectron transition ones. For this reason, as discussed above, the quantum model asymptotic approach was adjusted according to Eq. (1) (see also Yakovleva et al. 2016) for calculations of twoelectron transition matrix elements.
The electronic structure adiabatic potentials were obtained by the asymptotic method as described above and are presented in Fig. 1. To the best of our knowledge, these potentials are calculated for the first time, except for the ground molecular state Mn(3d^{5}4s^{2}^{6}S)+H(1s ^{2}S) (Blint et al. 1975), but a single potential does not allow one to consider a nonadiabatic nuclear dynamics.
The calculated adiabatic potentials depicted in Fig. 1 clearly show a series of the avoidedcrossing regions, where nonadiabatic transitions take place. The computed longrange adiabatic potentials allowed us to calculate inelastic transition probabilities, cross sections and rate coefficients, as discussed above.
Fig. 1 MnH(j^{7}Σ^{+}) adiabatic potential energies obtained by the asymptotic method. The key for the labels j is collected in Table 1. The state labeled by j = 22 corresponds to the ionic Mn^{+} + H^{−} one, while other states are covalent. 

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3.2. Cross sections and rate coefficients
Cross sections and rate coefficients were calculated by means of Eqs. (2)–(5) based on inelastic transition probabilities, which were in turn computed by the multichannel formulas. The partial inelastic cross sections of manganesehydrogen collisions for the energy range 10^{4}–10^{2} eV and the partial inelastic rate coefficients for the temperature range 1000–10 000 K were calculated for all transitions between the scattering states presented in Table 1.
It has been shown in our previous papers that the largest cross sections correspond to mutual neutralization processes and these processes play an important role in nonLTE modeling. It is also the case for manganesehydrogen collisions. For this reason, Fig. 2 presents the energy dependence of the cross sections for the mutual neutralization processes: Mn^{+}(3d^{5}4s ^{7}S) + H^{−}(1s^{2}^{1}S) → Mn^{∗} + H, that is, for the transitions j = 22 → k (the key for scattering channels is written in Table 1). It is seen that the scatter of the inelastic cross sections is up to several orders of magnitude. The largest cross sections correspond to the mutual neutralization processes into the final states Mn(3d^{5}4s(^{7}S)5s e ^{6}S), Mn(3d^{5}4s(^{7}S)5p y ^{8}P°), Mn(3d^{5}4s(^{7}S)5s e ^{8}S), Mn(3d^{5}4s(^{7}S)4d e ^{8}D) + H(1s ^{2}S), the states labeled by k = 7, 11, 6, 12, respectively. These cross sections, as well as those with the second largest values are depicted in Fig. 3. The states with the largest and the second largest cross sections are located in the optimal window for the final electronic bound energies in accordance with the general role, see (Belyaev & Yakovleva 2017) and discussion below.
It is interesting to notice that the cross sections for transitions j = 22 → k = 1−7 increase with collision energies above 1 eV while all the other neutralization cross sections decrease, see Figs. 2 and 3. This is connected with the shape of the relative potential energy curves, that is, the result of the fact that the potential energy splittings between lowlying states (k = 1−7) are rather large at the corresponding nonadiabatic regions (see Fig. 1), so the nonadiabatic transition probabilities and cross sections increase at relatively high collision energies, while for higherlying avoided crossings (k = 8−21) the splittings are small leading to decrease of the corresponding transition probabilities and cross sections.
Fig. 2 Manganesehydrogen mutual neutralization cross sections for all inelastic channels. See Table 1 for the key of the channel labels. 

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Fig. 3 Energy dependence of the cross sections for the mutual neutralization processes in Mn^{+} + H^{−} collisions with the largest values. For the label key see Table 1. 

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Fig. 4 Graphical representation of the rate coefficient matrix (in cm^{3}/s) for the partial processes of excitation, deexcitation, mutual neutralization and ionpair formation in Mn + H and Mn^{+} + H^{−} collisions at temperature T = 6000 K. The key is as for Fig. 1. 

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Rate coefficients K_{if}(T) for the excitation, deexcitation, mutual neutralization and ionpair formation processes in manganesehydrogen collisions were calculated in the present work and published at the CDS for the temperature range T = 1000−10 000 K. These rate coefficients for selected temperatures and for the processes from the optimal windows are presented in Table A.1. For the temperature T = 6000 K, the rate coefficients for the inelastic processes in manganesehydrogen collisions are also shown in Fig. 4 in the form of graphical representation. It is seen that the highest rate coefficients correspond to the mutual neutralization processes. The rate coefficients K_{if}(T = 6000 K) for these processes (i = 22 ≡ ionic) are depicted in Fig. 5 as a function of the electronic bound energy E_{f} for the final atomic state f (see Table 1 for the bound energies).
Fig. 5 Rate coefficients (at temperature T = 6000 K) for the mutual neutralization processes as a function of the electronic bound energy for the final atomic state. Filled circles represent the results for singleelectron transitions, stars for twoelectron transitions. 

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We can see that the highest rate coefficients correspond to the mutual neutralization processes with singleelectron transitions from the optimal windows in the vicinity of the electronic bound energy E_{f} = −2 eV in accordance with the general behavior (Belyaev & Yakovleva 2017). Outside of the optimal windows in both directions, increasing and decreasing the electronic bound energy, results in decreasing the rate coefficients, see Fig. 5. The processes characterized by twoelectron transitions (22 → 8,9,10 at present) have much lower rate coefficients, typically lower by a couple of orders of magnitude, even for the processes from the most optimal window, see Eq. (1). We note that presence of shortrange nonadiabatic regions can markedly increase rate coefficients for twoelectron transitions, but keeps the highest rates, as observed by Mitrushchenkov et al. (2017) for calciumhydrogen collisions; treating shortrange regions is outside of the scope of the present paper.
As mentioned in our previous papers, all partial processes can be divided into three groups according to the values of their rate coefficients: the groups with the higher (i), moderate (ii) and low (iii) rate coefficients. The first group with the largest values of rate coefficients, larger than 10^{8} cm^{3}/ s, consists of the mutual neutralization processes into the final states Mn(3d^{5}4s(^{7}S)5s e ^{6}S), Mn(3d^{5}4s(^{7}S)5p y ^{8}P°), Mn(3d^{5}4s(^{7}S)5s e ^{8}S), Mn(3d^{5}4s(^{7}S)4d e ^{8}D), the processes 22 → 7,11,6,12, respectively. For temperature T = 6000 K, the rate coefficients of these processes have the values 4.38 × 10^{8} cm^{3}/ s, 2.72 × 10^{8} cm^{3}/ s, 1.98 × 10^{8} cm^{3}/ s and 1.59 × 10^{8} cm^{3}/ s, respectively, see also Table A.1. These processes together with their inverse processes, the ionpair formation, are expected to be the most important in astrophysical applications. Temperature dependence of these processes, direct and inverse, are presented in Fig. 6. As we can see, the mutual neutralization rate coefficients demonstrate weak temperature dependence, while those for the ionpair formation processes depend rather strong on the temperature.
Fig. 6 Temperature dependence of the rate coefficients for the processes from the first group. 

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The second group consists of the processes with moderate rate coefficients, that is, with values in the range 10^{10}−10^{8} cm^{3}/ s. This group includes many excitation, deexcitation, mutual neutralization and ionpair formation processes. At temperature T = 6000 K, the rate coefficients with the largest values in this group correspond to the inelastic transitions 22 → 5 (K_{22 5} = 6.49 × 10^{9} cm^{3}/ s), 13 (9.38 × 10^{9} cm^{3}/ s), 14 (5.92 × 10^{9} cm^{3}/ s), 15 (4.57 × 10^{9} cm^{3}/ s), 16 (2.25 × 10^{9} cm^{3}/ s); 6 → 5 (1.99 × 10^{9} cm^{3}/ s), 6 → 7 (2.23 × 10^{9} cm^{3}/ s); 7 → 6 (4.78 × 10^{9} cm^{3}/ s), as well as their inverse processes and some other processes, see, for example, Table A.1. Temperature dependence of rate coefficients for these processes are presented in Fig. 7.
Fig. 7 Temperature dependence of the rate coefficients for the processes from the second group. 

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Finally, the third group consists of inelastic processes with low rate coefficients, typically lower than 10^{10} cm^{3}/ s. This group includes excitation and deexcitation processes involving the ground state (j = 1), the four lowlying excited states (j = 2−5), the three states which correspond to twoelectron transitions (j = 8−10), and the six highlying states (j = 16−21) but the ionic one.
The processes from the first and the second groups are expected to be important in astrophysical nonLTE applications, while the processes with low rate coefficients, the processes from the third group, are likely to be unimportant. Moreover, the rate coefficients of the processes from the first two groups are expected to have higher accuracy than those from the third group.
4. Conclusion
The present study of lowenergy inelastic manganesehydrogen collisions was performed by means of the model approach derived earlier. The approach is based on the electronic structure calculation by means of the asymptotic method followed by the nonadiabatic nuclear dynamical treatment by means of the multichannel model approach. The cross sections for the energy range 10^{4}–10^{2} eV and the rate coefficients for the temperature range 1000–10 000 K for all transitions between 21 covalent and one ionic states are calculated. We show that the largest values of the cross sections and the rate coefficients correspond to the mutual neutralization processes into the final states Mn(3d^{5}4s(^{7}S)5s e ^{6}S), Mn(3d^{5}4s(^{7}S)5p y ^{8}P°), Mn(3d^{5}4s(^{7}S)5s e ^{8}S), Mn(3d^{5}4s(^{7}S)4d e ^{8}D), the processes with the rate coefficients of the values 4.38 × 10^{8} cm^{3}/ s, 2.72 × 10^{8} cm^{3}/ s, 1.98 × 10^{8} cm^{3}/ s and 1.59 × 10^{8} cm^{3}/ s, respectively, at temperature T = 6000 K. There are also many other processes with the rate coefficient values between 10^{10} and 10^{8} cm^{3}/ s, the processes forming the second group of the processes with the moderate rate coefficients. These inelasticprocesses from these two groups are likely to be important in nonLTE astrophysical applications. Other processes, including those with twoelectron transitions, have low rate coefficients and are expected to be less important in astrophysical modeling. Nevertheless, the rate coefficients for these processes are also estimated though with lower accuracy, while the accuracy of the rate coefficients with large and moderate values is quite high.
Here we do not discuss the socalled Drawin formula, which is known to be unreliable, see (Barklem et al. 2011) for the critical analysis.
Other states are higherlying, create avoided crossings at large internuclear distances, larger than 100 atomic units, and, hence, have very small adiabatic splittings, which finally results in negligibly small inelastic transition probabilities, cross sections and rate coefficients, see, for example, (Belyaev et al. 2012).
This particular order means that the higher nonadiabatic region the larger internuclear distance of the region. This order is natural for avoided crossings created by the ioniccovalent interaction, see Fig. 1 below.
Acknowledgments
The work was supported by the Ministry for Education and Science (Russian Federation), projects # 3.1738.2017/4.6, 3.5042.2017/6.7.
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Appendix A: Additional table
Rate coefficients K_{if}(T) (in units of cm^{3}/s) at temperatures T = 1000, 4000, 6000, and 10 000 K for the processes from the optimal windows.
All Tables
MnH(j^{7}Σ^{+}) molecular states, the corresponding asymptotic atomic states (scattering channels), the manganese terms, the asymptotic energies (average experimental values taken from NIST; Kramida et al. 2012) with respect to the groundstate level, the electronic bound energies E_{j}, and the statistical probabilities for population of the molecular states.
Rate coefficients K_{if}(T) (in units of cm^{3}/s) at temperatures T = 1000, 4000, 6000, and 10 000 K for the processes from the optimal windows.
All Figures
Fig. 1 MnH(j^{7}Σ^{+}) adiabatic potential energies obtained by the asymptotic method. The key for the labels j is collected in Table 1. The state labeled by j = 22 corresponds to the ionic Mn^{+} + H^{−} one, while other states are covalent. 

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In the text 
Fig. 2 Manganesehydrogen mutual neutralization cross sections for all inelastic channels. See Table 1 for the key of the channel labels. 

Open with DEXTER  
In the text 
Fig. 3 Energy dependence of the cross sections for the mutual neutralization processes in Mn^{+} + H^{−} collisions with the largest values. For the label key see Table 1. 

Open with DEXTER  
In the text 
Fig. 4 Graphical representation of the rate coefficient matrix (in cm^{3}/s) for the partial processes of excitation, deexcitation, mutual neutralization and ionpair formation in Mn + H and Mn^{+} + H^{−} collisions at temperature T = 6000 K. The key is as for Fig. 1. 

Open with DEXTER  
In the text 
Fig. 5 Rate coefficients (at temperature T = 6000 K) for the mutual neutralization processes as a function of the electronic bound energy for the final atomic state. Filled circles represent the results for singleelectron transitions, stars for twoelectron transitions. 

Open with DEXTER  
In the text 
Fig. 6 Temperature dependence of the rate coefficients for the processes from the first group. 

Open with DEXTER  
In the text 
Fig. 7 Temperature dependence of the rate coefficients for the processes from the second group. 

Open with DEXTER  
In the text 