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Astron. Astrophys. 358, 276-286 (2000)

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2. Background

2.1. Rydberg states

Rydberg Matter is a condensed phase of rather weakly interacting long-lived circular Rydberg atoms or molecules. The radiative lifetime of single Rydberg atoms with electrons in circular orbits is large. It increases rapidly with increasing excitation energy and principal quantum number n as [FORMULA], and at n = 100, it reaches 100 ms. The long lifetimes are due to the extremely low overlap between the circular states and the lower states. The radiative lifetime for a circular Rydberg atom averaged over the angular momentum quantum numbers is 0.18 s at n = 40 and 17 s for n = 100 (Beigman & Lebedev 1995). The diameter of Rydberg atoms varies as [FORMULA], being 170 nm at n = 40 and 1.06 µm at n = 100 (see Stebbings & Dunning 1983; Gallagher 1994 for general information on Rydberg states).

2.2. Formation of RM

In space, energetic particles and quanta ionize atoms and molecules, and the consecutive recombination processes with free electrons will initially form very highly excited Rydberg, thus very long-lived circular states. The long radiative lifetimes means that such states are dark, almost not interacting with radiation in the visible or IR ranges. It is well known that Rydberg states with n of the order of 100 exist in space. At a typical density in diffuse ISM of 5x107 m-3, a free high Rydberg state with n = 500 will make several collisions during the radiative lifetime of 5x104 s, calculated with a rather small cross section of 104 nm2 for Rydberg-Rydberg collisions (Fabrikant 1993). Such Rydberg - Rydberg collisions may be one starting point for condensation. The number of collisions with ground state atoms or molecules will be smaller, due to the much smaller cross sections for such interactions. However, the likely outcome of such collisions which are nearly resonant is excitation energy transfer, and not simply deexcitation. One type of such energy transfer is to ground state clusters, which will then be excited to a Rydberg state. For small clusters, the excitation energy may be large enough to form an RM cluster directly. Otherwise, collisions with further Rydberg states may provide enough energy to transfer the Rydberg cluster to an RM cluster, which will have a much larger radiative lifetime. This is the second possible route to form RM in space.

The third major route to RM formation, which is the one observed to be most rapid in the laboratory, is the desorption of Rydberg states from surfaces by high enough temperature, by visible or more energetic radiation, and possibly energetic particles. Atoms adsorbed on surfaces of carbon or metal oxides, e.g. alkali metal atoms, desorb often thermally directly into Rydberg states (Wang & Holmlid 1998; Holmlid 1998a; Engvall et al. 1999) since the ground state is not stable on the surface (Holmlid 1998c). Circular Rydberg states are formed directly, often in large densities close to the surfaces, and facile condensation to RM clusters with long radiative lifetimes is observed (Wang & Holmlid 2000a). Rydberg atoms at surfaces also directly form Rydberg clusters in the surface sheath bound to the surface (Wang et al. 1999). In subsequent collisions between the desorbing Rydberg atoms (or clusters) and gas atoms and molecules outside the surface, transfer of excitation energy is possible, as observed in the formation of RM clusters of H2 and N2 at metal oxide surfaces in ultrahigh vacuum (Wang & Holmlid 2000b). In such cases the initially desorbed Rydberg atom or cluster, in space maybe mainly alkali or hydrogen Rydberg atoms, will act as a kind of catalyst for the formation of Rydberg states also of small molecules. The mechanisms involving surfaces of interstellar particles of carbon or other nonmetal surfaces are the most likely ones to form Rydberg Matter in the ISM. This means that there is no limit in the gas phase density, below which the RM forming processes can not operate. On the contrary, the lower the temperature and the gas density is, the slower are competing processes, which will tend to increase the formation of RM.

One further possibility to desorb Rydberg states is by photons absorbed by particle surfaces. Photons with rather low energy may desorb alkali metal atoms into Rydberg states from carbon and metal oxide surfaces (Wang & Holmlid 1998, 2000a,b). The same process should also be possible to form Rydberg atoms of H. Wavelengths of 560-570 nm (2.2 eV energy) were used to cause Rydberg state desorption from surfaces at room temperature by stray laser light, but no studies were made of the wavelength dependence over a larger range. It is also likely that carbonaceous and similar small particles will absorb radiation in the visible and NIR quite efficiently. In general, the simplest process to form Rydberg states rapidly in the laboratory is to heat a carbon or metal oxide surface with some alkali metal impurities to T [FORMULA] 1200 K (Holmlid 1998a). Thus, a mild heating even by NIR and visible photons in space with a typical radiation temperature of [FORMULA] 1200 K should give desorption of Rydberg states and RM formation. Otherwise, a more energetic radiation may give direct desorption of Rydberg states to form RM at lower temperatures. The limiting requirement here may be that the temperature of the carbon or metal oxide particles is high enough to allow diffusion of hydrogen or alkali atoms in the bulk.

Thus in the laboratory, it is sufficient to heat a graphite or other surface with a graphite layer, or a metal oxide surface, to rapidly form Rydberg states of alkali metal impurities, which then condense to form Rydberg clusters and RM clusters. A rather low intensity visible light is also shown to desorb Rydberg states and to form RM. These states also have catalytic effects and transfer their energy to gas molecules to form Rydberg states and RM. It is likely that the same processes take place in the ISM at particle surfaces at much lower temperatures, since the quenching rate of the Rydberg species is lower due to the much lower density.

2.3. Electronic structure in RM

RM is a condensed matter with good electronic conductivity. Thus, it is similar to a metal in its properties. The conduction band contains the excited electrons and is half-filled as for ordinary metals. Within the phase of RM, the bare ions M+ are surrounded by the electron cloud which forms cavities in which the ions reside. The work function of RM is very low, of the order of 0.1 eV at large excitation levels (Holmlid 1998b), while the bottom of the conduction band is at approximately twice this value below the ionization limit. This means that RM at not too low temperatures is a very good electron emitter, which may give charging of adjacent atoms and molecules, even of Rydberg states to form excited negative ions of e.g. hydrogen (Pinnaduwage et al. 1999).

It is necessary to determine the excitation state, and thus the width of the conduction band to know the electronic state of RM in space. For high density RM, electron emission experiments give work functions down to 0.4 eV (Holmlid & Manykin 1997), but similar measurements for low density RM are not possible. Laser Raman experiments give higher excitation levels for dense RM, corresponding to n [FORMULA] 55 (Svensson & Holmlid 1999). Recent interpretation studies of DIB lines in the ISM give an average value under such conditions of n = 80-90 (Holmlid 2000). In cold regions of the ISM, even higher values of n are likely.

It is predicted from theory that a stable phase of RM will not absorb or emit in the visible, and that there will exist an absorption edge in the IR. At the likely excitation level of n [FORMULA] 50 in space, this absorption edge will be moved very far away, probably into the cm wavelength range. In the laboratory, RM does not absorb or radiate in the visible range even in macroscopic quantities at high temperatures. Thus, stable RM will transmit almost all quanta in the visible and IR without interacting with them.

2.4. Clusters of RM

Laser induced fragmentation of RM clusters (Wang & Holmlid 1998) gives a clear microscopic proof of the shape of such clusters. Depletion experiments show that the clusters contain 7, 14, 19, 37, and 61 atoms. These numbers are called the magic numbers for the most stable cluster forms, and they do not agree with the magic numbers for spherical clusters. Instead, they are characteristic for planar closepacked (hexagonal) monolayer clusters. The cluster form with 14 atoms is interpreted as a dimer of the basic cluster with 7 atoms. Since the electron in a circular Rydberg state moves quite accurately in a planar circular orbit, a picture with all the electrons in an RM cluster moving in one plane emerges. Classical calculations including correlation effects show that this is indeed the case (Holmlid 1998b). Work functions and binding energies were calculated in reasonable agreement with the previous QM calculations due to Manykin et al. (1992a). The very high quantum numbers involved means that a classical description of the electron motion should be possible, which is found to be correct for many processes involving Rydberg states (Wang & Olson 1994). A classical electron in RM moves in a circular orbit around its core ion, which means that it has both a large principal quantum number n and a large angular momentum quantum number l. The electron motion takes place in a plane, and if bonding shall exist, all the highly excited electrons have to move in one plane (Holmlid 1998b). Thus, RM has the form of planar monolayer of atoms. A view of a 19-atom or 19-molecule cluster of RM is shown in Fig. 1. There exist some effects which will prevent the formation of stable RM sheaths with hundreds of atoms or more, namely the retardation effects due to the finite propagation speed of light. This means that the electron motion will not be synchronous for very large clusters, and that the binding forces in the RM sheaths will be weakened (Holmlid 1998b).

[FIGURE] Fig. 1. A perspective view of a cluster of Rydberg Matter with 19 atoms or molecules. The core ions in interstellar space will in general be H+ and [FORMULA], with one electron per atom or molecule excited to the RM region. The core ions giving the two-electron UIR bands must however contain at least one excitable electron.

2.5. Chemical composition of RM

It is important to realize that the RM structure will be the same independent of which atom or molecule it is built up from, as long as the internal degrees of freedom in the molecules do not couple directly to the excited electrons in the RM, or the molecule is too large to be accommodated into the RM structure. This means, that even if most experiments to date have been made with alkali metals due to the simplicity of forming such RM, any atom (especially hydrogen) can replace the alkali atoms in RM. In some experiments referenced here, the special features of the various atoms and molecules in RM are used to extract information about RM: this would certainly be much harder to do if the RM in the laboratory was built up only from H atoms. Thus, the information on the RM structure and properties is believed to be very general, even if each system studied experimentally has its own special features. Studies similar to the ones on alkali RM clusters have also been done with RM clusters formed by small gas molecules, like N2 and H2 (Wang & Holmlid 2000a,b). The formation of H2 (RM) is of course of great interest in relation to RM formation in space.

2.6. Bond distances in RM

Both the classical and QM calculations on RM gives a simple relation between the excitation level of RM and the bond distances between the core ions in the RM. At the excitation level of n = 80 likely to be approximately valid for most of the ISM due to the interpretation of the so called DIB lines as caused by RM (Holmlid 2000), the interionic bonding distance is 1 µm. At n = 55, the distance is slightly smaller, namely 500 nm. These quite large distances have not yet been measured in the laboratory, probably due to too rapid quenching by molecules incorporated into the RM and to residual gases in the vacuum chambers used. Further, the energy spread due to thermal initial energy is too large to make it possible to observe the expected small kinetic energy releases in laser fragmentation experiments. So far, laser induced Coulomb explosions in RM clusters indicate a bonding distance of 4-6 nm giving an energy release of 0.2-1.0 eV.

2.7. Lifetime of RM

Manykin et al. also calculated the lifetime of RM in different excitation levels, and found it to be long, of the order of 100 years at an excitation level of n = 16. The main deexcitation processes for RM were found to be Auger processes (Manykin et al. 1992b), involving two electrons which simultaneously change their energy and orbital angular momentum. At n = 80 which may be correct for the ISM, the lifetimes from a simple extrapolation would be extremely large according to this calculation, longer than the lifetime of the universe. Of course, the background radiation of a few K temperature will interact with RM and possibly shorten the lifetime, an effect which is well documented for isolated Rydberg atoms (Gallagher 1994). Other external interactions like energetic particles and quanta will disturb the RM even stronger, and internal interactions like coupling to molecular rotation in RM will shorten the lifetime drastically.

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© European Southern Observatory (ESO) 2000

Online publication: June 26, 2000