For the sake of clarity and for congruity with the actual chemistry taking place, it is suggested that the term ionization and ionization constant be used exclusively in those contexts in which ions are formed from nonionic species. At B= 1014 G, He2 is not present because even the ground state becomes auto-ionized to He+2 ion due to the finite nuclear mass effect although He2 remains bound with respect to two helium atoms. We expect that a realistic ionic and molecular fraction will be somewhere between the two cases. Since the motional Stark field breaks the cylindrical symmetry preserved in magnetic field, it is non-trivial to evaluate motional Stark field effects. The calculated binding energy values are not smooth near the energy minimum (Fig. In order to illustrate different physical effects, we show the fraction of helium atoms and He2 molecules as a function of temperature in Fig. Therefore, following LS95, we considered two limiting cases: (i) and (ii) and determined general formula which can be applied to a wide range of B and K⊥. These acids are termed as strong acids. Haberl F. Hence, the degree of ionization of acids and bases depends on the degree of dissociation of compounds into their constituent ions. This reaction implies that acid dissociation equilibrium is dynamic in nature where the transfer of proton can take place in both forward and backward direction. Is diffuse intracluster light a good tracer of the galaxy cluster matter distribution? Words to Know Crystal: A solid composed of positively and negatively charged ions. Note that the density function calculation overestimates binding energies by ∼10 per cent compared with more accurate Hartree–Fock calculation (ML06). Accurate atomic and molecular data are available mostly for the He+ ion (Pavlov & Bezchastnov 2005), the helium atom (Neuhauser, Koonin & Langanke 1987; Demeur, Heenen & Godefroid 1994), He3+2 (Turbiner & López Vieyra 2004) and He2+2 (Turbiner & Guevara 2006). (2004) and Chang & Bildsten (2004) have shown that diffusive nuclear burning may quickly deplete the hydrogen by so the NS surface may be composed of helium or heavier elements. Chang P. Kaplan D. L. The authors were visitors at the Pacific Institute of Theoretical Physics during the nascent stages of this research. 3). 10 shows contours of the He3 molecule fraction with respect to He2 molecule at B= 1013 G. In the dotted area, the fraction of diatomic helium molecular ions is larger than 10 per cent. . Herold H. In this paper, we extend our Hartree–Fock-type calculation (Mori & Hailey 2002) to helium molecules in the Born–Oppenheimer approximation. This is because of the high degree of ionization of strong acids and bases. Number of rotovibrational states in helium molecular ions. At first we adopt the Born–Oppenheimer approximation and neglected any effects associated with motion of atoms and molecules in a magnetic field. We would like to thank the anonymous referee for comments that helped to improve the paper. Notice, Smithsonian Terms of For molecular ions that exist in strong magnetic fields (B= 1012–1014 G), we achieved ≲1 and ≲10 per cent agreement in binding energies and vibrational energies in comparison with other more accurate studies mainly on hydrogen molecules. Therefore, the molecular fraction will be underestimated in this case (the top panel in Fig. (or is it just me...), Smithsonian Privacy Fig. Burwitz V. Born–Oppenheimer approximation) as ε(0)κ (<0) for an electronic state κ. Heenen P. For full access to this pdf, sign in to an existing account, or purchase an annual subscription. Godefroid M. He+2 and He2), we expect the accuracy of aligned vibrational energy is ≲10 per cent. Van Kerkwijk M. H. 2004). One trend observed is that longer wavelengths provide small amounts of higher mass peaks (the CH 3 CCl 2 + peaks), in contrast to the 266 nm case in which case these peaks are not present. López Vieyra J. C. As the observational data on INSs have improved over the past decade (Hailey & Mori 2002; Sanwal et al. The study of ML06 and Lai (2001) also suggests the critical temperature below which helium molecule chains form is ∼2 × 106 K at B= 2 × 1014 G. This is close to the blackbody temperature of 1E1207. Hence, the degree of ionization of acids and bases depends on the degree of dissociation of compounds into their constituent ions. sκ= 4 for He2 molecule in the ground state). The separation of the centre-of-mass motion is non-trivial when a magnetic field is present (Herold, Ruder & Wunner 1981). Van Kerkwijk M. H. A more rigorous calculation was performed for He+ ion by Bezchastnov, Pavlov & Ventura (1998) and Pavlov & Bezchastnov (2005). The transition from molecules to helium atoms and ions takes place rapidly at T∼ 3 × 105 and ∼6 × 105 K for B= 1012 and 1013 G. Ionization and dissociation balance of helium at T= 105.5 K (top panel) and 106 K (bottom panel) at B= 1012 G. Ionization and dissociation balance of helium at T= 105.5 K (top panel) and T= 106 K (bottom panel) at B= 1013 G. Ionization and dissociation balance of helium at T= 105.5 K (top panel) and T= 106 K (bottom panel) at B= 1014 G. Temperature dependence of helium atomic and molecular fraction at B= 1012 G (ρ= 10 g cm−3), B= 1013 G (ρ= 102 g cm−3) and B= 1014 G (ρ= 103 g cm−3). We determined Em from the fitting procedure using the function given by equation (3) since we found that it provides more accurate results than the minimum energies from our grid calculation. If \(HA\) has a higher tendency to donate proton in comparison to \(H_3O^+\), \(HA\) acts as a strong acid in comparison to \(H_3O^+\). The numbers in the brackets are (eV). Also, a strong acid implies good proton donor whereas strong base implies good proton acceptor. The dotted line corresponds to the summed energy of one helium atom in (0, 3) state and the other in (1, 2) state . Ionization, dissociation and electric excitation energies of helium molecules are larger than 100 eV at B≳ 1013 G. On the other hand, rotovibrational excitation energies are in the range of 10–100 eV at B= 1012–1014 G. If helium molecules are abundant, their spectroscopic signatures may be detected in the optical, ultraviolet and X-ray band. 1). There are two effects both of which reduce the accuracy of our results particularly for highly ionized molecules at low magnetic fields. Electronic excited states with ν > 0 have small binding energies, therefore their population in the atmosphere is tiny due to small Boltzmann factors and pressure ionization. Wunner G. Kaplan D. L. This function is similar to the relationship of reactivity with electron configuration and ionization reported by Hartung & Adkins (1927). In the black region singly ionized atomic helium dominates, and the white region demarcates fully ionized helium. Accordingly, there are three types of molecular motion: vibration along and transverse to the magnetic field and rotation around the magnetic field. It is therefore straightforward to calculate aligned vibrational energy quanta using the results from Section 2. Hailey C. J. Qualitatively it is clear that the dissociation and ionization processes are very similar in these experiments, with a few minor exceptions. . 2002; van Kerkwijk & Kaplan 2006), both hydrogen and iron atmospheres have lost favour, and atmospheres composed of other elements have been invoked to interpret both the continuum and spectral properties of neutron stars. Your email address will not be published. Some acids such as perchloric acid (\(HClO_4\)), hydrochloric acid (\(HCl\)) dissociate completely into their constituent ions in aqueous medium. Secondly, highly ionized molecular ions are either unbound or weakly bound at low magnetic fields, therefore the numerical errors in binding energies significantly affect determination of ζ since the binding energy curve is shallow. 12). This work was supported in part by a Discovery Grant from NSERC (JSH). Including these excitations increases the expected abundance of molecules by up to two orders of magnitude relative to calculations that ignore the internal states of the molecule.
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