Non-sequential and sequential double ionization of NO in an intense femtosecond Ti:sapphire laser pulse

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1 J. Phys. B: At. Mol. Opt. Phys. 30 (1997) L245 L250. Printed in the UK PII: S (97) LETTER TO THE EDITOR Non-sequential and sequential double ionization of NO in an intense femtosecond Ti:sapphire laser pulse A Talebpour, S Larochelle and S L Chin Centre d Optique, Photonique, et Laser (COPL) and Dept de Physique, Universite Laval, Quebec, QC, Canada, G1K 7P4 Received 3 December 1996, in final form 12 February 1997 Abstract. Multiphoton, sequential and non-sequential double ionization of NO has been studied. It is found that the probability of non-sequential double ionization is proportional to the tunnelling probability to the first charge state. Also, the alignment of the singly charged molecular ion in the laser field enhances the probability of sequential double ionization. Sequential and non-sequential (NS) double ionization of diatomic molecules in strong laser fields have not yet been studied in detail. Such a study might be of interest in two respects. Firstly, it is not yet understood whether or not the dynamics of molecular ions between two stages of ionization (e.g. alignment of the molecular ion) does affect the sequential ionization. Secondly, extending the studies of NS double ionization to diatomic molecules might reveal some facts about the process behind the NS ionization. For example, recently Geltman (1995, 1996) has proposed that the data on double ionization of He (Walker et al 1994) and double and triple ionization of Ar (Augst et al 1995) can be explained based on the fact that the two ionizing electrons are equivalent (belong to the same shell). While to test this idea, rare-gas atoms are useful from the point of view of having equivalent electrons initially, a diatomic molecule such as NO with a single electron in its outer shell is an excellent complement. In this letter, we study sequential and NS double ionization of the NO molecule. To the best of our knowledge, this is the first report on the observation of NS ionization in diatomic molecules. Also, we will show that the process of sequential double ionization of the molecule is affected and significantly enhanced by the alignment of the NO + ion in the laser field. As a result, the ionization probability is determined not by the field-free ionization potential of NO +, but by an effective ionization potential which is determined by the alignment of the molecular ion. We studied the multiphoton ionization of NO using a stable, fs Ti:sapphire laser operating at 800 nm, with a transform-limited pulse length of 200 fs. The laser was focused using f/100 optics into an ultra-high vacuum chamber having a background pressure of Torr. Ion species were separated with a time-of-flight mass spectrometer having a 60 cm long drift chamber. Ion curves were produced by combining a series of intensity scans each having a different fill pressure in the interaction chamber. The gas pressure ranged from 10 8 to 10 4 Torr. The resulting ion yield curves, which span over eight address: talebpou@phy.ulaval.ca /97/ $19.50 c 1997 IOP Publishing Ltd L245

2 L246 Letter to the Editor Figure 1. Multiphoton, double ionization of NO using linearly polarized laser pulses from a Ti:sapphire laser (800 nm). Each datum corresponds to a three-point average. The theoretical curves are discussed in the text. I p refers to effective ionization potential. Due to the fragmentation channel (not shown in the figure, but discussed in a separate paper (Talebpour et al 1997b)), the level of NO 2+ at its saturation is five times lower than the corresponding level of NO + ion at its own saturation. orders of magnitude, are presented in figure 1. Also presented in the figure is the ion versus intensity curve predicted by the ADK theory (Ammosov et al 1986) for NO +.Asis observed, the ionization of NO occurs mainly via multiphoton ionization (for a discussion of the structures on the NO + ion curve see Talebpour et al (1996a, b)). This is expected, since below the saturation intensity ( Wcm 2 ), the Keldysh parameter is higher than unity. However, the ionization is not pure multiphoton in the sense that tunnelling has a contribution, though very small, to the total ionization rate. Before proceeding further, we should briefly recall the main features of double ionization in atoms. As an example, we have chosen Ar, and obtained the ion versus intensity curves under the same conditions as NO. The result is presented in figure 2. The lower part of the Ar 2+ ion curve is nicely fitted by vertically downshifting the theoretical curve for Ar + using the ADK formula and the upper part by the sequential ionization using the same formula. Mathematically, the Ar 2+ signal (S(Ar 2+ )) is given by the following relation: S(Ar 2+ ) = αs ADK (Ar + ) + S ADK (Ar 2+ ) (1) where α(= 1 20 ) is the downshifting factor and S ADK(Ar + ) and S ADK (Ar 2+ ) are, respectively, the ion signals predicted by the ADK formula for Ar + and Ar 2+. Previous experiments on

3 Letter to the Editor L247 He (Walker et al 1994) and Kr and Xe (Talebpour et al 1997a) have shown that relation (1) is generally true for any atom A, and the signal of doubly charged ion A 2+ may be written as S(A 2+ ) = α A S ADK (A + ) + S ADK (A 2+ ). (2) In this relation the first term on the right-hand side (α A S ADK (A + )) is considered to be the contribution of NS double ionization. The second term is just the contribution from sequential double ionization. Relation (2) is the major experimental finding of the studies on NS double ionization with the consequence that most probably the shake-off process (Fittinghoff et al 1992) is responsible for NS ionization (Walker et al 1994). The shakeoff model describes the NS process as a mechanism where one electron is ionized by the laser field and the departure of this electron is so rapid that the remaining electrons do not have enough time to adjust themselves to the new energy states and therefore there is a certain probability that, after the ionization of the first electron, a second electron is excited to states with higher energy (shake-up) or even ionized (shake-off). We should mention that, up until now, there has been no quantitative calculation based on the shake-off model and the model is still qualitative. Going back to figure 1, a similar situation is again observed; i.e. at lower intensities S(NO 2+ ) is proportional to the tunnelling curve of NO +. The total signal is given by S(NO 2+ ) = α NO S ADK (NO + ) + S seq (NO 2+ ) (3) where α NO = 1. This relation readily indicates that the process of double ionization in 1500 Figure 2. Multiphoton, double ionization of Ar using linearly polarized laser pulses from a Ti:sapphire laser (800 nm). Each datum corresponds to a three-point average.

4 L248 Letter to the Editor diatomic molecules is very similar to that of atoms. In comparison with the atomic result, α NO S ADK (NO 2+ ) represents that part of the NO 2+ signal which results from NS double ionization of neutral NO molecules (note that the NO 2+ signal resulting from NS ionization is not affected by the fragmentation of the NO + ion). S seq (NO 2+ ) is the contribution of sequential double ionization. However, there are two subtle differences: firstly, α NO α Ar and secondly, in calculating S seq (NO 2+ ) instead of using the ionization potential of NO + (29.22 ev (Dawber et al 1994)) in the ADK formula, we have to use a lower value of 22 ev. In what follows we discuss these two observations. The Hartree equation for an electron occupying the one-electron level ϕ i (r) of an N- electron atom in atomic units is (Ashcroft and Mermin 1976, p 330) H 0 i ϕ i(r) { U ion (r) + [ j dr ϕ j (r ) 2 r r ]} ϕ i (r) = E i ϕ i (r) (4) where U ion (r) is the potential of the nucleus, and dr ϕ j (r ) 2 / r r is the potential energy due to the Coulomb interaction with the jth electron (occupying level ϕ j (r)) at point r. If one of the electrons, say k, is abruptly ionized through tunnelling, the Coulomb potential on the electron i due to the kth electron will suddenly disappear, resulting in a change of the Hamiltonian from H 0 i H i = H 0 i to H i where dr ϕ k(r) 2 r r H 0 i + H i (5) and ϕ i (r) is no longer an eigenfunction of the new Hamiltonian; therefore the electron already occupying ϕ i (r) will make a transition to one of the eigenstates of the new Hamiltonian (including the ionization continuum). Without performing a detailed calculation, we note that the probability of excitation of electron i to the excited states of the new Hamiltonian is proportional to H i (r) 2 = dr ϕ k (r ) 2 / r r 2 (Landau and Lifshitz 1977, p 148). However, H i (r) 2 is appreciable only when ϕ k (r) 2 (the probability of electron k at the position of electron i) is appreciable. In other words, the probability of transition to higher states of the new Hamiltonian is determined by the overlap of the wavefunction of the two electrons k and i. In Ar the first and the next ionizing electrons belong to the same shell, so their overlap is high. However, in the NO molecule with the lowest electron configuration of KK(σ g 2s) 2 (σ u 2s) 2 (σ g 2p) 2 (π u 2p) 4 π g 2p, the first ionizing electron will be from the antibonding level π g 2p and the next electron (which is supposed to be ionized through shake-off) will be from the bonding orbital (π u 2p) 4. Since the bonding electrons stay between the two nuclei and the antibonding electron resides outside, their overlap is very small. This explains why the probability of NS double ionization in NO is so small compared to that in Ar (and similarly in Kr and Xe). Now we discuss the sequential part of double ionization, i.e. S seq (NO 2+ ) in equation (3). As was already discussed, in the case of Ar, the sequential signal fits very well with the theoretical tunnelling signal, S ADK (Ar 2+ ), calculated using the ADK formula and the ionization potential of Ar +. In comparison, it is expected that if an extra process is not involved, the NO + ion will behave in the same manner as Ar +, i.e. the observed S seq (NO 2+ ) will be identical to the theoretical S ADK (NO 2+ ). However, in figure 1, S ADK (NO 2+ ) S seq (NO 2+ ) by many orders of magnitude. A good fit to the experimental S seq (NO 2+ ) is obtained using the ADK formula provided that the ionization potential of NO + is replaced by a smaller value of 22 ev. The explanation for this observation is as follows.

5 Letter to the Editor L249 Figure 3. (a) Electron potential energy in the molecular ion aligned in the direction of the laser field. (b) Electron potential energy in an atom which has the same ionization potential as the molecular ion of (a). Normand et al (1992), using two successive pulses with orthogonal polarizations, have found that after ionization of the molecule to a singly charged ion, the ion is aligned in the direction of the polarization of the laser. This result implies that NO + ions produced in the first stage of ionization will be aligned in the laser field. The tunnelling ionization of an aligned ion is substantially more probable than non-aligned ions. This fact can be understood from figure 3. Figure 3(a) shows the potential energy of the electron in the molecular ion (NO + )in the ground state and at the equilibrium internuclear distance, being aligned parallel to the direction of the laser field. Figure 3(b) shows the potential energy of an atom which has the same ionization potential as the molecular ion. The barrier which the electron encounters is not the same. The barrier width in (a) is smaller than that in (b). In other words, the barrier that the electron in figure 3(a) encounters is equivalent to the barrier of equal width that an electron in a virtual level of figure 3(b) (such a level does not exist) encounters. This is because the molecular size is larger along the internuclear axis which helps lower the potential. The tunnelling ionization of the aligned molecule is thus equivalent to the tunnelling ionization of an atom with the ionization potential reduced by a factor E i (see figure 3(b)). At an intensity of Wcm 2 (the onset of the dominance of sequential ionization in figure 1), E i is estimated from figure 3 to be 0.28 au = 7.6 ev; therefore in this intensity range the tunnelling ionization probability of NO + is expected to be similar to that of an atom with an ionization potential around ev (= ) which agrees very well with our observation. In conclusion the first observation of NS double ionization in a diatomic molecule was reported. The apparent small probability of NS double ionization in NO was attributed to the small screening effect of the outermost antibonding electron to the next low-lying bonding electrons. Finally, it was shown that, due to the alignment of the NO + molecular

6 L250 Letter to the Editor ion in the laser field, the sequential double ionization is greatly enhanced compared to the atomic case. It is our pleasure to acknowledge the technical assistance of S Lagace and J-P Giasson. This work was supported in part by NSERC, le Fonds FCAR and NATO. References Ammosov M V, Delone N B and Krainov V P 1986 Sov. Phys. JETP (Corrections to some of the equations can be found in Ilkov F A, Decker J E and Chin S L 1992 J. Phys. B: At. Mol. Opt. Phys ) Augst S, Talebpour A, Chin S L, Beaudoin Y and Chaker M 1995 Phys. Rev. A 52 R917 Ashcroft N W and Mermin N D 1976 Solid State Physics (Saunders College/HRW) Dawber G, McConkey A G, Avaldi L, MacDonald M A, King G C and Hall R I 1994 J. Phys. B: At. Mol. Opt. Phys Fittinghoff D N, Bolton P R, Chang B and Kulander K C 1992 Phys. Rev. Lett Geltman S 1995 Phys. Rev. A Phys. Rev. A Landau L D and Lifshitz E M 1977 Quantum Mechanics 3rd edn (Oxford: Pergamon) Normand D, Lompre L A and Cornaggia C 1992 J. Phys. B: At. Mol. Opt. Phys. 20 L497 Talebpour A, Chien C Y and Chin S L 1996a J. Phys. B: At. Mol. Opt. Phys Talebpour A, Chien C Y, Liang Y, Larochelle S and Chin S L 1997a J. Phys. B: At. Mol. Opt. Phys Talebpour A, Larochelle S and Chin S L 1997b J. Phys. B: At. Mol. Opt. Phys Talebpour A, Liang Y and Chin S L 1996b J. Phys. B: At. Mol. Opt. Phys Walker B, Sheehy B, Dimauro L F, Agostini P, Schafer K J and Kulander K C 1994 Phys. Rev. Lett