Recombination cool and fast

Molecular physicists and astrophysicists alike would like to know how fast the H₃⁺ molecular ion recombines with electrons. Fast, seems to be the answer — with an awkward consequence for the astrophysicists.

Every schoolchild knows that, like opposing poles of a magnet, opposite charges attract. But what happens when charged bodies are small enough that the rules of quantum mechanics come to bear, for instance when an electron and a positively charged molecule attract? Here, the situation is more complicated: even the reaction between an electron and the simplest polyatomic molecule, H₃⁺ (which can be thought of as a hydrogen molecule, H₂, with an extra proton, H⁺) has puzzled both theorists and experimentalists for decades. In a contribution to Physical Review Letters, Kreckel et al.¹ describe an ingenious experiment that provides further elucidation of the speed of this fundamental reaction.

When an electron approaches a singly charged positive ion (call it X⁺), both bodies experience an attraction that accelerates them and causes them to collide. They can recombine to form neutral X, provided that the extra kinetic energy that they have gained by being accelerated can somehow be removed. For macroscopic objects, this is not generally a problem: friction dissipates the energy. At the quantum-mechanical level, however, this cannot happen. If X⁺ is the ion of a single atom, energy can be lost only by emitting a photon, a slow process that seldom happens during the short time a collision takes. In most such collisions, the ion and electron fly away from each other again. If X⁺ is a molecular ion, however, there is a much more efficient option: the molecule can break apart following recombination with the electron, and the resulting neutral fragments can carry away kinetic energy. This is the process known as dissociative recombination.

The H₃⁺ ion assumes an important role in astrophysics as the first link in a chain of chemical reactions in interstellar clouds through which most of the molecules found in interstellar space form (Fig. 1). Interstellar clouds were recently seen to contain much more H₃⁺ than expected², bringing the persistent enigma of its recombination rate back to the fore. Exactly how the dissociative recombination of H₃⁺ works was explained theoretically only recently^3,4, and, starting in 1973, many experimental measurements have yielded drastically differing values for the rate at which it occurs⁵.

Figure 1: Cosmic mystery.

When an electron and a positively charged H₃⁺ ion meet, three separate neutral hydrogen atoms are formed in a process known as dissociative recombination. The image is overlaid on a wide-field image of the Perseus region: the bright stars at bottom left are the Pleiades, or Seven Sisters, and the red region to the right is the California nebula. The bright star at the arrow's head is ζ Persei, where H₃⁺ has been observed in unexpectedly high abundance². The results of Kreckel et al.¹ imply this cannot be due to slow dissociative recombination. The most likely explanation is instead an enhanced rate of ionization by cosmic rays.

H₃⁺ is produced in ionized gases known as plasmas. Different plasma conditions will lead to different degrees of vibrational and rotational excitation of the H₃⁺ ions, perhaps accounting for some of the variation in the experimental recombination rates. If the rate of recombination were lower than assumed, especially at the lower temperatures of interstellar space, the overabundance of H₃⁺ in diffuse clouds could be easily explained. But without accurate values for the rate, further progress in understanding the mystery of H₃⁺ abundance is impossible.

Hence the efforts to understand dissociative recombination in terrestrial laboratories. In order to best simulate the conditions in interstellar space, the ions in the laboratory must be cooled to a state of minimum rotation and vibration. Vibrational cooling was first achieved using the CRYRING storage ring in Stockholm, Sweden, by injecting mass-selected ions into an accelerator, and allowing them to relax to their vibrational ground state⁶. Achieving a low rotational temperature is more difficult: H₃⁺ cannot cool rotationally by emitting radiation⁷, so the ions must be prepared in a rotationally cold state before they are injected into the storage ring. At CRYRING, this is done by sparking a discharge to ionize a jet of hydrogen gas as it expands through an opened valve into the vacuum of the storage ring and cools⁸. Once the H₃⁺ ions are in both their vibrational and rotational ground states, an electron beam travelling at a well-defined velocity is merged with the ion beam, and dissociative recombination occurs. The neutral fragments produced are counted as a function of the relative velocity of the two beams, yielding the ‘spectrum’ of the rate of recombination as a function of the collision energy.

Kreckel and colleagues' experiments¹, performed at the Test Storage Ring (TSR) in Heidelberg, Germany, follow a similar scheme, but make two improvements over the previous studies. First, they produced their electron beam with a newly developed cryogenic photocathode, allowing more precise control of the ion–electron collision energy and so higher resolution in the dissociative-recombination spectrum. Second, they used a new type of ion source, called a radiofrequency multipole ion trap. In such a trap, H₃⁺ ions are stored before injection into the ring at low temperature in the presence of helium gas. The large number of collisions of the ions with the helium means that the rotational energy of the ions can be transferred to the helium, thus ensuring that the ions are rotationally cold. (In contrast, with the expanding jet source used at CRYRING, a small fraction of ions may remain rotationally warm.)

The result of the TSR experiment is in excellent agreement with the CRYRING results, and, thanks to its higher resolution, reveals the fine detail of the spectrum more clearly. It confirms that the rate of dissociative recombination is fast under cool, interstellar conditions. Improved theoretical calculations^3,4 also yield a rate that agrees well with both experiments. Some minor discrepancies remain, but the general concord implies that the long-standing enigma of the rate of H₃⁺ recombination might finally be resolved. If so, the onus is back on the astrophysicists: how can the large observed abundance of H₃⁺ in diffuse clouds be explained if recombination is so fast? One likely solution would seem to be enhanced production of H₃⁺ through ionization by cosmic rays².

Kreckel and colleagues' results¹ do contain an intriguing twist. At the low temperatures of their measurements (and of the interstellar medium), H₃⁺ exists almost entirely in its two lowest rotational states, which have a total nuclear spin of 3/2 (ortho-H₃⁺) and 1/2 (para-H₃⁺). But by using para-H₂ in their ion source, and thus enhancing the ratio of para- to ortho-H₃⁺, the authors saw a marked difference in the rate of dissociative recombination at low energies. Unfortunately, they were not able to measure the degree of the para-H₃⁺ enhancement, and because of the nature of their ion source, it is probably not very large. Future experiments with pure para-H₃⁺ would be highly desirable to elucidate the difference in the rate of recombination between the two states. That would indeed represent the first dissociative recombination measurement of a single quantum state.