Isomerization of a highly excited vibrational state of acetylene was studied using the Coulomb explosion imaging technique. A vinylidene isomer was prepared by electron photodetachment of the negative molecular ion and the corresponding distribution function of the nuclear configurations of the molecule was sampled after a time period of 3.5 ms. The population of the vinylidene isomer was found to be significantly high (ϳ50%), in contrast to the commonly accepted notion of vinylidene as a short-lived isomer. [S0031-9007(98)07417-1]

The relative dissociative recombination rate coefficients for specific vibrational states of HD ϩ have been measured. The method is based on using merged electron and molecular ion beams in a heavy-ion storage ring together with molecular fragment imaging techniques which allow us to probe the vibrational-state population of the stored beam as a function of time as well as the final state of the dissociation. The initial vibrational distribution of the stored ion beam ͑from a Penning ion source͒ is found to be in good agreement with a Franck-Condon model of electron impact ionization, apart from slightly larger experimental populations found for low vibrational states; its time evolution in the storage ring reflects the predicted vibrational level lifetimes. Dissociative recombination measurements were performed with the electron and ion beams at matched velocities ͑corresponding to average collision energies of about 10 meV͒, and at several well-defined collision energies in the range of 3-11 eV. The obtained vibrational-state specific recombination rate coefficients are compared with theoretical calculations and show that, although an overall agreement exists between experiment and theory, large discrepancies occur for certain vibrational states at low electron energy.

In §2 an explicit formula, (2.2), for the solution of (1.1) in terms of its initial matrix and a fundamental matrix for an associated linear system of differential equations, (2.1), is given. Several theorems relating (1.1) and (2.1) are given in this section. For ni = n2=l (2.2) is a well-known result for the scalar Riccati equation. For ni = n2 Theorem 1 is equivalent to Theorem 3.1 of [9]. In §3 a theorem (Theorem 5) is obtained for the case ni = n2 = n which reduces when n = 1 to the classical cross-ratio property for solutions of the scalar Riccati equation. It is different from a theorem due to Reid [9], which also reduces to the classical cross-ratio property in the scalar case, in that it involves only four solutions of the matrix Riccati equation whereas Reid's theorem involves w2 + 3 solutions. The proof is, however, similar to Reid's as they both follow the classical proof, see Ince [3], and rely heavily on a theorem for linear systems due to Reid [8].

The vibrational relaxation of H 3 ϩ molecules from a conventional plasma ion source is studied performing Coulomb explosion imaging on the ions extracted from a storage ring after variable times of storage. Storage for 2 s is found sufficient for radiative relaxation of the breathing excitation and the fragment velocity distribution in the breathing coordinate then agrees well with simulations based on the calculated ground-state wave function. The radiative decay of the two lowest pure breathing levels (1,0 0 ) and (2,0 0 ) is seen to be considerably faster than expected from rotationless calculations. Assuming a high rotational excitation of the H 3 ϩ ions, as suggested already in earlier experiments, the theoretical transition probabilities of the University College London line list for H 3 ϩ ͓L. Neale, S. Miller, and J. Tennyson, Astrophys. J. 464, 516 ͑1996͔͒ can explain the increase of the vibrational cooling rates and reproduce the observed decay curve for the lowest breathing-excited level, confirming the absolute transition probabilities of these line tables. The observations give evidence for a quasistable population of high-lying rotational levels in the stored ion beam, relevant for the interpretation of storage ring measurements on the rate coefficients for dissociative recombination of H 3 ϩ ions with low-energy electrons.

Fragmentation patterns for dissociative recombination of the triatomic hydrogen molecular ion H(3)(+) in the vibrational ground state have been measured using the storage ring technique and molecular fragment imaging. A broad distribution of vibrational states in the H(2) fragment after two-body dissociation and a large predominance of nearly linear momentum geometries after three-body dissociation are found. The fragmentation results are directly contrasted with Coulomb explosion imaging data on the initial H(3)(+) geometry, compared to existing wave-packet calculations, and considered in the light of a simple physical picture.