A number of unexpected features of small molecules subjected to intense laser fields, with wavelengths ranging from infrared to ultraviolet, have been observed or predicted in the past few years: above-threshold dissociation, molecular bond softening, vibrational population trapping. We review these processes for the case of the molecular ion H2+ and discuss the experimental and theoretical tools that are used to study this system. Both electron and proton energy distributions are used to interpret the experimental results. Theoretically, the fragmentation dynamics can be described equivalently as a laser-assisted half-collision process, using solutions of the time-independent Floquet theory, or as the evolution of a wavepacket subjected to a classical radiation held with a given pulse shape, using solutions of the time-dependent Schrodinger equation. A broad range of laser intensity and pulsewidth has been explored, with the short-pulse results (analysed in terms of 'dressed' potential curves) offering the best interface between theory and experiment. We finally report on a promising new avenue for coherent control of fragmentation dynamics, through the use of two-colour phase-locked radiation.

We present nonperturbative, time-ind tense las aser fields. The energ distrib ime-Independent calculations o s of the photodissociation rate of H + ' y is rl ution of the protons consists of a se u p yg g' mu tip oton absorpth d' t ib t'o of}li hk op " p g vector o a linear polarized laser is n utlon of the PAC CS numbers: 33.80.Gj, 33,80.%'z, 34 50 RkĨ t is well d demonstrated that multi hot intense laser fields u ip oton transitions in aser e s may radically change the d namics o isions (photoionizan particular, the process of abovization (ATI), in w ' s o above-threshold ionin which free-free hoton takes place once th 1 p on absorption ce e e ectron is alread in t as een actively studied both experimentalmolecular systems. The ex a oms ut also in a few this s. e experimental signature of is process is the appearance of successiv separated b one e o successive peaks, evenly kinetic-energy distribution f energy, in the i u ion o ejected photoelectrons. -co ision process of e address the analogous half-11' ' e-threshold dissociation (ATD) durin dissociation of d uring the photoa iatomic molecule. In this ca ditional quanta of h n is case the ada o p oton energy would a ea spaced peaks th k appear as evenly h f in e inetic-ener s p o o ra ments. revious wave-acket 7 o on issociation by infrared lasers has oug various experiments involvin str field photoionization of H ' isuggest to us that multp o on free-free absorptions mi h b o -' ns mig t be occurrin in the issociation continuum of the roduct is y no means unequivocal at this o our aim in thi L a is point, and it is is etter to encoura e mo ination f th' s o is possibility. g more careful examSpecifically, we present non ert onperturbative calculations E /eV l2-Vg IO I-DISSOC lATiON 8 energy e(n . H / 2 gy th . However, even in mod t fi ld epending on the photon ener hv state, we find th b energy v and initial n at absor tion of easi y ea to pathways to dissociation n & nth that are e re er to such processes as above-threshold d' p asize the similarity with the ATI process. Our time-independent cl pe close-coupled scattering formuation is based on defining a finite set ' g i rent photon-number t t e s ates involvin diffe N+ 1), iN~2), . . . . e ex a sacs q esignate the total a molecule. At each tal angular momentum of the fi lde e -free eac interatomic distance R 1 on y H2+~ls( o sJ, gM, v)+nhv H++H(l )+ s( e. n 1 H+H As indicated in Fig. 1 we onl co th 1 e repulsive H2 (2 tr we on y consider dissociation via ptr") electronic state which is asymptotically degenerate th H + ( e wtt H2 iso ). ensi ies, photodissociation will norma y proceed via the first energeticall e ica y accessible conber of photons n s a e w ic requires absor ti p ion of the least numr o p otons n&h and yields the lowest 1 t k re ative kinetic R/0 o FIG. 1. Po otentlal-energy curves for the r cited states of H2 wi es or t e ground and first exs o 2, with schematic continuum wave functions ft b s a er a sorption of 1, 2 or uum vibrational length 329.7 n , 2, or 3 photons of wavenm from the v...

We calculate the dissociation of H2 + in intense short pulsed laser fields for a variety of wavelengths and a wide range of initial vibrational states (v=0-\4). While the low-u levels achieve 100% dissociation in the leading edge of the pulse, for high v there is an onset of stabilization, and significant [(5-50)%l population remains in bound vibrational states throughout the entire pulse. The dissociation is incomplete, and a coherent distribution of excited vibrational states is formed. This survival effect can be attributed to the trapping of portions of the initial vibrational wave packet in transient laser-induced potential wells.PACS numbers: 33.80.Gj, 33.80.Wz, 34.50.Rk Starting from some initial stable state of a diatomic molecule, and given an intense pulsed laser with peak intensity I p , we might expect that the intensity in the rising edge of the pulse could be sufficient to completely dissociate the molecule well before I p is reached. Hence no bound-state population will ever experience the peak intensity much less survive to the end of the pulse. Comparable leading-edge saturation effects have been postulated for photoionization [l] and have obfuscated the observation of the strong-field effects associated with the peak intensity. Obviously, for a given / p , the onset of this saturation effect depends on the photon frequency co and the duration T p of the pulse. One might also expect that increasing the initial vibrational level of the molecule v would enhance the early depletion of bound-state population by making the dissociative "bond-softening" effect [2] accessible at lower intensities. Indeed for lower-u states this supposition is nicely confirmed by our calculations for the following process [3]: W 2 + (\so gy J,v) + nh

The multichannel quantum defect theory (MQDT) method and large scale wave functions are applied to the calculation of the cross sections and rates for dissociative recombination of O 2 + along the I~u+ dissociative potential. Indirect dissociative recombination is accounted for by simultaneously including both the vibronic and electronic coupling to the intermediate Rydberg resonances. An enhanced MQDT approach involving a second order K matrix is described. Cross sections and rates for the lowest three vibrational levels of the ion are reported. The shapes of the cross sections are discussed in terms of Fano's profile index. We find that for each of the three ion vibrational levels, the intermediate Rydberg resonances reduce the dissociative recombination rate below the direct recombination rate. Just above threshold, resonances with centers below threshold play an important role.