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Electron spectroscopy study of single and double multiphoton ionization of strontium by visible picosecond laser light G. Petite, P. Agostini To cite this version: G. Petite, P. Agostini. Electron spectroscopy study of single and double multiphoton ionization of strontium by visible picosecond laser light. Journal de Physique, 1986, 47 (5), pp.795-808. <10.1051/jphys:01986004705079500>. <jpa-00210263> HAL Id: jpa-00210263 https://hal.archives-ouvertes.fr/jpa-00210263 Submitted on 1 Jan 1986 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. J. Physique 47 (1986) 795-808’ m 1986, 795 Classification Physics Abstracts 32.80D - 32.80F - 32.80K Electron spectroscopy study of single and double multiphoton ionization of strontium by visible picosecond laser light G. Petite and P. C.E.N. Agostini Saclay, Service de Physique, Atomes et Surfaces, 91191 Gif (Reçu le 31 octobre 1985, sur Yvette Cedex, France accepti sous forme définitive le 24 janvier 1986) Les techniques de spectroscopie d’électrons ont été appliquées à l’étude de l’ionisation multiphotonique impulsions picosecondes de 1011 à quelque 1012 W cm-2, foumies soit par un laser Nd : Yag doublé en fréquence, soit par un laser accordable (à rhodamine 6G). Les spectres d’énergie d’électrons montrent que l’ionisation multiphotonique simple laisse l’ion soit dans son état fondamental, par un processus à trois photons, soit après absorption d’un quatrième photon, dans un des premiers états excités. Des résonances à deux et trois photons sur des états à un ou deux électrons excités peuvent intervenir dans ces processus et créer une excitation importante du coeur. L’ionisation double apparaît essentiellement comme un processus en deux étapes, dont la seconde peut avoir pour état initial un état excité de l’ion. Résumé. simple 2014 et double du strontium par des Multiphoton single and double ionization of strontium was studied using electron spectroscopy a picosecond, frequency doubled Nd : Yag Laser and a picosecond rhodamine 6G Dye Laser Both techniques. were used, with intensities ranging from 1011 W . cm- 2 to a few 1012 W . cm-2. Single MPI was shown to produce ions in both the ground state (3 photon) and several low lying excited states, through a four photon process. Two and three photon resonances were observed, on singly and doubly excited states of the atom, resulting in an important degree of core excitation. Double ionization was shown to be essentially a « stepwise » process which can involve excited states of the ion as the initial state of the second part of the process. Abstract. 2014 1. Introduction. Multiphoton Ionization (MPI-[1] and therein) has long been studied, because references it is the laser-atom interaction dominates the which process when high laser intensities are used. Most of the emphasis has been put, in the past few years on the study of MPI under very high laser intensities (1011 W.cm-2 and above) for which new processes can occur. under such intensities an of photon necessary for ionization, in a process known as «Above Threshold Ionization » (ATI) leading to the production of hot electrons. ATI was studied in the case of rare gases [2, 6] and caesium [7]. Both perturbative [8, 9] and non perturbative [10, 11] approaches were considered in theoretical work. In [7] a good agreement between experimental results and a perturbative calculation was obtained. In the case of rare gases, which deals with both higher intensities and more complex atoms, such comparisons are still out of hand. It was shown [2] that atom can absorb more than the number The study of MPI processes under very high laser intensities also led to the observation of multiple ionization of atoms. It was observed in the case of rare gases [12-15], alkaline earths [16-20] alkalis [21] and rare earths [13, 22]. In several cases, double ionization was observed at the same intensity where simple ionization occurs though being of a much higher order. Here again different situations are encountered depending on the type of atom considered. Rare gases, with a complete outer shell require very high laser intensities. They were at the origin of the most impressive results concerning both the number of electrons ejected (up to the complete outer shell), and the number of photon absorptions involved (a hundred and more). Clearly, for such high order processes, the perturbative approach is not adequate and new types of formalisms have to be developed. A statistical approach of this problem [23] has been recently proposed and is one of the possible paths towards a better understanding of these processes. Alkaline earths on the other hand present a quite different picture. They are easily ionized, involving Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01986004705079500 796 processes of a lower order. Though the calculation of ionization probabilities is not easy, one can still consider the perturbative approach as reasonably fit to this problem. Moreover, in the case of strontium, some specific ionization paths leading to double ionization have been proposed [17, 20] and some observations seem to indicate that ATI can play an important role in double ionization. Resonances in the double ionization signal were observed which were assigned to transitions in the ion spectrum whose initial state is an excited ion state which can only be reached by absorption of extra photons. However the electron spectra presented in proof did not show the components implied by this inter- pretation. In this paper, we present electron energy spectra, and their variations with the laser wavelength, intensity and in some cases, polarization for single and double ionization of strontium atoms by a rhodamine 6G picosecond dye laser and a frequency doubled Nd : Yag Laser. In addition we present new observations of MPI in situations were multiphoton excitation of either the atom or the ion yields an excitation energy close to an ionization threshold. Last, we present new observations concerning electrons which can be unambiguously assigned to a double ionization process. Besides providing a decisive proof of the interpretations given in references [17, 20], we discuss the following issues. (i) ATI in a complex atom : how does it differ from ATI in a single electron atom; are the definitions and concepts used in a single electron atom still valid in the case of alkaline earths ? Can ATI lead to the production of excited ion states ? (ii) clarify the terminology concerning the diffeour experiment. rent ionization processes involved in (iii) briefly discuss the issue of double ionization of strontium (direct or stepwise process). The first two points of this discussion strictly deal with single ionization of strontium. 2.1 SINGLE IONIZATION OF STRONTIUM. Multiphoton ionization of alkaline earth has been the subject of several theoretical publications these last years, the emphasis being put on the central question of autoionization under strong laser field [24-26]. These models all predict strong modifications of the Fano auto-ionization profile under high laser intensity. Both single photon ionization [24] and MPI [25, 26] were considered and a quite complete calculation in the case of strontium can be found in [26] in an attempt to analyse experimental results reported in [27, 28]. However some of the features of our experiment are not considered in these papers, and will be the subject of this theoretical part. We use the resolvent operator formalism, as presented in [24], and later developed in [25, 26]. The different couplings relevant to our experiment are shown on figure 1. States of interest are : the ground stateI g) of energy E8, two continual I c1 ) andI c2 > (energies E1 and E2) and one auto-ionizing stateI a > of energy E. lying between the ionization limits corresponding to continuaI c, > andc2 >. We use the dressed atom model and these states will be dressed respectively by n photons of the laser field forI g), n - 3 photons fora ) andI c1), and n - 4 photons forc2 ), etc. Note that continualI cl > andI C2 > correspond to different states of the core. For instance, in strontium, - (ii) ATI and double ionization : what are the relationships between these two « high order » processes ? (iii) What are the most probable leading to double ionization. mechanisms Section 2 is devoted to a theoretical discussion of the points mentioned above. Our aim is to give clear definitions of the concepts to be used in this paper rather than to present calculations correspondthose are still ing to the results presented later out of reach for the moment. Section 3 will describe our experimental set up. Our experimental results will be presented and discussed in section 4 : electron energy spectra, and their variations with the laser wavelength, intensity and in some cases, polarization. - 2. Theory. In this part, our goals are the following : (i) using the simplest possible model, we obtain of our predictions concerning aspects experiment which have not been so far considered in the literature. some Fig. 1. - Schematic representation of the couplings involved in 3 and 4 photon ionization with a three photon resonance on an auto-ionizing state. 797 I ci ) is the continuumSs, E1 ) andI C2 > could be the continuum4d, 82 > Energies of the dressed states thus are : through the inversion integral with Couplings betweenI g) andI a >,I cl > orI c2 > Ha is the atomic Hamiltonian and Hf the field Hamiltonian, these states are eigenstates of : If If we use the dipole approximation for the atom field interaction, the total Hamiltonian of our system will be : Where D is the dipole operator : involve several photons so that it would be necessary to complete the atomic spectrum of figure 1 with a set of non resonant intermediate states, as it was made in references [25, 26]. Instead we choose to represent the coupling between the different states by effective interaction Hamiltonian such as : that so in which 8 is the electric field amplitude and E the polarization vector. V is the Coulomb interaction responsible for the auto-ionization of)[ a ) and eventually for configuration mixing of other states too. We can then proceed as in references [24, 26] and compute the evolution operator U(t) of our system from the resolvent operator. our interaction Hamiltonian writes : Note that DC2g represents the coupling between I g ) andc2 ) through a set of non resonant autoionizing states such asI a ), but does not include the I c1 ) continuum. The coupling between the continua I c1 > andc2 ) will be neglected as it was done in [24]. With the above definitions, the equations determining the resolvent operator matrix elements are : At time t 0, all the atoms are in the ground stateI g >, so that the ionization rates in continualI cl > andI c2 ) will be determined byI Ug,,(t) aidI Ug-2(t) We are thus interested in GClg and G129’ which can be expressed, from equations (9. c) and (9. d) by : = 12 Using these expressions in equations (9. a) and (9. b) 12. we get : 798 we then define : which represent the shifts of which are which is a the widths of statuesI g > andI a > due statesI g > and[ a ) due to their interaction with the continua : to the same interactions, and : modified effective interaction between statesI g > andI a >, as defined in [24] but with an additional continuumI c2 > which should be small compared to the others because of its higher order in the term due to laser intensity. System (II) which then writes : yields : Expressions which are strikingly similar to those obtained in the of hydrogenic atoms. We then obtain for GCIS and G,,,,, : From this point on, the calculations have to be carried out numerically, but the physics of our system is already apparent in these expressions. Expression (17. a), which describes ionization in continuumI c, > is made of two terms. The first one describes direct ionization ofI g > inI cl >, when the second one describes the excitation ofI a) followed by auto-ionization ofI a) inI c, >. The interference between these two terms leads to the well known Fano profile. This result is identical to the one obtained in [24]. Because of the use of effective Hamiltonians it differs from the results of references [25, 261 : Stark case of resonant multiphoton ionization shift of the ground and auto-ionizing states due to one photon coupling with intermediate bound states are not apparent, and also the modification brought to VaC1 by a two photon coupling via the bound states is missing. The latter could probably be taken into account by using a modified VaC1 instead of VaC1’ like it was done in reference [26]. If we now consider expression (17. b) it is strikingly identical to (17. a) apart from the fact that ionization ofa > is due to a dipole interaction instead of a Coulomb interaction. The same result was obtained in the case of resonant multiphoton ionization 799 with a formalism sometimes referred to as « pseudo auto-ionization » :: ionization in continuumI C2 > is the result of interference between a resonant amplitude (Dc2a Dag) and a non resonant one (DC2g) in the same way as ionization inI cl > results of an interference between a direct channel and the auto-ionizing one. Considering expressions (17. a) and (17 . b) remarks can a few be made. (i) Expression (17. a), describing ionization to the first continuum is identical to the one obtained in [24] when only one continuum is considered. The only differences are in the position of the poles which are slightly modified by the presence ofc2 ), and in one additional term in Dag which should be small if not negligible. (ii) Considering ionization in upper continua, as described by equation (17.b) it appears to be an usual MPI process, involving a number of bound transitions and one bound-free transition. Since no free-free transition is involved, and though absorption of one photon above the lowest ionization threshold is necessary to reach continuumI c2), ATI is not involved, as it has sometimes been stated before [ 17, 20]. In this respect the acronym ATI can be somewhat confusing in the case of two-electron atoms. It must be applied only to ionizing processes involving c - c transitions inside the same continuum (I c1) or possiblyI c2 >), that is without change of the excitation state of the « core » electron. As a conclusion to this paragraph, we note that, apart from the high intensity effects already predicted in auto-ionization, production of excited ion states can exhibit resonances on auto-ionizing states lying between the two ionization limits in a way analoguous to resonant multiphoton ionization. The same width should be measured on these resonances and in the usual auto-ionization in the lower continuum; because this width is determined by the poles imaginary parts, which are the same in (17. a) and (17. b) so that the intensity effects predicted in [25, 26] should be seen in the production of excited ion states. Note that because the dipole operator is monoelectronic, only resonances on states with the same core can appear in excited ion states production. This is true of course only when configuration interactions are neglected. In the opposite case, interesting indications can be obtained in this way, on the importance of these interactions. 2.2 DOUBLE IONIZATION. Multiple ionization has been repeatedly observed for about ten years now [12-22, 27-29] and not much is known about the mechanisms leading to multiply charged ion production. In the framework of perturbation theory, two apparently different mechanisms can lead to double ionization which will be discussed here : (i) direct ionization : two electrons are simultaneously excited and ejected yielding a doubly charged ion obtained directly from the neutral atom. (ii) stepwise ionization : a singly charged ion is obtained first, and a doubly charged ion results from multiphoton ionization of this ion. Thus far, the question of the competition between these two processes has been considered as a central one. It was recently considered in a paper [30] which thoroughly discusses this question in view of an application to two-photon ionization of helium. The following discussion directly stems from the conclusions of this paper, and only that part of the calculations which are necessary to the understanding of the discussion will be reproduced. We consider here, as in [30] and for the sake of simplicity of the expressions, a two-photon double ionization process, but the discussion can easily be generalized to a higher order process. We are thus interested in the case where an atom in its ground stateg) of energy Eg can be doubly ionized by absorption of two photons of energy Ep, giving a doubly charged ion in its ground state192 > and two electrons with energies 81’ and 82 such that : In the framework of lowest order perturbation theory, the probability of such a process can be expressed, by : where I is the laser intensity, d the atomic dipole operator and Ii) an intermediate state with energy E;. In doing this, we of course neglect correlation for the continuum states. We then note that d, being a monoelectronic operator, can only coupleg2, E1, G2 ) to states pertaining to the continuum of simple ionization, that is of the typeI el, G1 >, ourIe1, G2 ) whereI el > is one of the singly charged ion states (ground or excited), so that (19) yields. - This expression clearly describes the interferences between two series of time ordered two photon interaction diagrams representing the following process : absorption of one photon by the atom in its ground state yielding a singly charged ion and an electron of energy s, (or P2), followed by an absorption of a second photon resulting in ionization of the singly 800 charged ion, yielding another electron of energy 82 (resp. Ei). This shows that, in this framework, double ionization is a sequential process, even if there is no way to decide which electron has been emitted first. With this in mind, two different cases have to be considered. Equation (12) reflects the fact that a limited range of electron energies can be obtained in such processes, and different situations will occur depending whether in the intermediate state, real ionic states can be reached with emission of an electron in this energy range, as schematised on figure 2. If not (case A of Fig. 2), the intermediate states of expression (20) can only be virtual ionic state, and no particular problem arises in expression (20). But such states are very short lived (a few optical cycles) and double ionization can be considered as a direct process. If a real atomic state (ground or excited) can be reached (case B of Fig. 2), the situation is quite different : one of the denominators of equation (20) will vanish, in a way similar to what happens in resonant multiphoton ionization (while the first case considered above was typically a non resonant process). Also, real ionic states have much longer lifetimes than virtual states so that it is reasonable to think of double ionization as a two step process. We should however remember that this approach has failed giving a satisfying description of resonant multiphoton ionization. Therefore, though the terms of « direct » and « stepwise » will still be used throughout this paper it should be remembered that these two processes are not fundamentally different : stepwise double ionization is only a double ionization process presenting a resonance in electron energy which should however be distinguished from resonances in photon energy which may occur in higher order processes. The use of o stepwise » should not conceal the fact that the ionization process takes place in a time much shorter that the radiative lifetime of the real states involved in these resonances. Such resonances will of course produce peaks in the electron energy distribution but cannot be detected in experiments based on ion detection only. So far we have limited ourselves to the case of lowest order processes. Considering processes of higher order increases the energy range in which electrons can be ejected, and thus the number or resonances which can be reached, as shown on figure 2, case C. Though of a higher order, such processes, because they are resonant, may not be negligible if no resonance occurs in the lowest order process. This is thoroughly discussed in the case of helium in reference [30], and the conclusion in this case is that the non resonant process is negligible when compared to resonant processes of the same order, which was expected, and cannot be neglected when compared to resonant processes of a higher order. However generalization to high order multiphoton processes is not trivial and only a precise calculation in the experimental situation, when possible, will give an unambiguous answer to this question. Concerning now the question of ATI and double ionization, the same remarks can be made than for production of excited ion states : ATI does produce excited electrons whose energy would, in the case of two photon double ionization discussed above, lio above the second ionization limit, but it does not produce core excitation and thus cannot yield multiple ionization, and therefore states reached by ATI are not privileged intermediate states of the multiple ionization process. Experimental set up. Our experimental set up 3. is schematized in figure 3. Most of its elements have been described in previous publications so that we will limit ourselves to a brief description of its main characteristics. Two different lasers have been 3.1 LASER SYSTEM. used in this experiment. The first one is a commercial - Difl’erent double ionization processes : (A) lowest resonant (direct) process; (B) lowest order resonant (stepwise) process; (C) higher order resonant (stepwise) process.I g > : neutral atom ground state; I g1 > : singly charged ion ground state; !I e1 > : singly charged ion excited state ;g2 > : doubly charged ion Fig. 2. order - non ground state. Fig. 3. - Schematic of the experimental set-up. 801 Nd : Yag laser system (Quantel) delivering 20 ps Fourier limited pulses at a 10 Hertz repetition rate. After frequency doubling, this system can deliver at 0.53 gm up to 20 mJ per pulse. The Nd : Yag oscillator is both passively and actively mode locked, keeping the pulseto-pulse energy fluctuations at a low level (± 5 %). This system can be used directly in the experiment, or it can alternatively be used to synchronously pump a dye oscillator-amplifier system as described in [31]. This system can deliver up to 2 mJ in a single 20 ps Fourier limited pulse whose wavelength can be tuned throughout the rhodamine 6G emission band (557 to 575 nm). Because of the long duration of such a wavelength scan (up to 15 h when one electron spectrum is taken every angstrom) it is necessary to lock the energy per pulse mean value. This is achieved through a servo controlled Fresnel rhomb-Glan prism attenuator placed in front of the experiment chamber with this system, the long term intensity drifts can be compensated for, and the mean laser intensity kept stable within ± 5 % throughout one wavelength scan. Different focusing lenses have been used in this experiment. At low intensity a 140 mm focal length plano-convex lens is used. When high intensities are necessary, a 70 mm focal length sphero-parabolic lens can be used. It allows to reach intensities of a few Tw . cm - 2 in the interaction region without having to face overwhelming space charge problems. 3.2 ELECTRON SPECTROMETER. - The laser beam is focused in a vacuum chamber (residual pressure of 10- 8 torr), crossed at a right angle with an effusive Sr beam similar to the one used in [7], with Sr densities of a few 109 cm- 3. The electron spe’ctrometer is also identical to the one described in [7]. It is an electrostatic time of flight spectrometer with a 23 cm length. As shown in figure 3, a grid system allows to apply an acceleration field in the interaction region while keeping the analysis energy at any desired value. This system is very useful in the case of very low energy electrons which are very sensitive to both space charge and stray magnetic fields. At the exit of the flight tube, the electrons are detected by a separated dynodes electron multiplier and fed into a multichannel analyser : counts are temporarily stored into shifts registers, before being accumulated into the analyser memory. Up to 1024 channels of 10 ns to 1 gs time width are available. After accumulation, the content of the analyser memory can be transferred to a LSI 11 microcomputer system which is in charge of data processing and storage. This computer is also used to tune the dye laser and if necessary control the laser intensity and the spectrometer settings. The spectrometer can also be used in ion detection. In this case, an analog signal is obtained which is processed by a boxcar averager after being, if necessary, amplified. Because throughout this paper, peaks of different electron energy will be compared, the question of the spectrometer transmission has to be considered. Figure 4 shows an experimental measurement of this transmission in the energy range of interest here, which was obtained as follows : a well known and well isolated peak of our electron spectrum (three photon ionization of Sr, leaving the ion in its ground state and an electron of energy 0.89 eV, obtained at low laser intensities) was shifted by scanning the flight tube voltage between - 0.2 and 2 eV, resulting in the variation of the peak amplitude shown in figure 4. This variation has two different origins : of the collection angle due to the the electrons between the interaction of acceleration volume and the flight tube; (ii) variations of the flight tube transmission due probably to stray magnetic fields whose action on low energy electrons is strong and energy dependent. The first of these two effects can easily be computed and subtracted from the measurement of figure 4, allowing a measurement of the second effect only (broken line in Fig. 4). It shows that for electron energies less than 1.5 eV, losses in the flight tube cannot be neglected. However, contrary to the variations of the collection angle due to acceleration, they do not depend on the electron initial energy but on the electron energy inside the flight tube only, and can be taken into account using the curve of figure 4. Two typical voltage settings have been used in this experiment. Some spectra were taken with all electrodes grounded but this does not allow detection of low energy electrons both because of space charge, contact potentials and losses in the flight tube. Therefore, when such electrons were studied, a small d.c. electric field (between 5 and 10 V/cm) was applied in the interaction volume to help charge separation (i) variations Fig. 4. Variations of the spectrometer transmission with the electron energy : 0-0 : variations of the electron peak amplitude with the accelerating voltage; . :: variation of the t.o.f. tube transmission with the analysis energy. - 802 and the flight tube potential was set to a positive value (1 V generally), to prevent important losses in the flight tube. 4. Experimental results. Multiphoton ionization of Sr was studied at 532 nm (Nd : Yag second harmonic) and between 558 nm and 575 nm (tuning range of our rhodamine 6G dye laser). Both the ions and the electrons were studied, but the results on ions obtained with the dye laser have already been published [20] and will not be discussed here. Some preliminary results on the electrons have also been reported in [32] and will be presented in more details here. Before presenting the experimental results, a brief summary of the Sr spectroscopy relevant to our experiment is necessary, particulary to precise a few ionization channels which play an important role in this experiment, and which are outlined on figure 5. The Fig. 5. Different ionization and double ionization. - paths involved in Sr simple simplest ionization process for Sr is the three photon ionization of the ground state neutral Absorption of a fourth photon can leave the Sr II ion in either the ground state, or two excited states : « Stepwise » (resonant) double ionization using the above transitions Note that the non resonant ionization process (# 8) is of order 8. Resonant processes can be of order 8 or 9 depending on the laser wavelength. The electron energies also depend on the laser wavelength. Within the tuning range of the dye laser two thresholds are crossed in channels # 4 and # 5. Channel # 6 is of order 4 with the frequency doubled Nd : Yag laser and of order 5 with the dye laser. 4 .1 IONIZATION oF Sr AT 532 nm. Single ionization of Sr was detected for intensities of the order of 1012 W . cm- 2 and above, using a 75 mm focal length lens. Double ionization was detected for intensities of the order of 5 x 1012 W.cm-2 and above. Variations of the ion signal with the laser intensity are shown in figure 6 using the usual log-log representation. They show that doubly ionized Sr is detected for intensities just above the onset of saturation for single ionization. This behaviour has usually been considered as the signature of a stepwise double - as a first step can also occur : Slopes measured in the linear respectively 3.3 for single ionization and ionization process. region are 5.4 for double ionization, in agreement with the number of photons necessary to ionize the neutral (3 photons) or the ground state singly charged ion (5 photons). In many respects these results are analogous to those obtained in Ca [19] at the same wavelength, except that the intensity gap between single and second ionization is larger in the case of Ca. Figure 7 shows different electron spectra obtained at this wavelength in different conditions. The spectrum of figure 7a was obtained for a laser intensity of 2.8 x 1012 W . cm- 2 and without electron acceleration. The energies of the three peaks displayed on this spectrum are found to be 1.2, 1.8 and 3.1 eV. Two processes can be responsible for the peak at 1.2 eV, which are the three photon ionization of neutral Sr (# 1 or Fig. 5) which yield an electron of 1.29 eV, and four photon ionization of the 5p atom 803 to 0.6 eV electrons. This peak is clearly in figure 7c, taken at an intensity of 1.2 x respond visible 1012 W.CM-2 . Electrons with such an energy can be created in both processes # 4 ( four photon ionization in the 5p ion state) and # 5 (five photon ionization of the ground state ion). A third peak is clearly visible on figure 7c, corresponding to electrons with an energy of 0.1 eV, such as the ones created in process # 6 (four photon ionization of the 4d ions). The electrons created in process # 7 would appear at the same energy as those of process # 1 (1.3 eV). The intensity behaviour of these different peaks, shown in figure 8 indicates that the electrons of the 0.6 eV peak are mostly created in the double ionization process, as those of the 0.1 eV peak, since they do not saturate as the 1.3 eV peak does. Even the 1.3 eV peak does not saturate as strongly as the singly charged ion signal does (Fig. 6), Fig. 6. Variation of the number of singly (o---o) doubly (.-.) charged Sr ions with the laser energy. - and (# 7) which yield an electron of 1.23 1.32 eV (depending of the J value of the 5p state). These energies are too close to be separated in our spectrometer, but comparing the ion signals at this intensity shows that this peak is certainly mainly due to single ionization of channel # 1. The peak at 1.8 eV can unambiguously be assigned to the process of channel # 3 (single ionization leaving the ion in one of the 4d states). The last peak at 3.1 eV is certainly due to ATI, but here the resolution of our spectrometer is too low to ascertain whether it is due to ATI following single ionization of channel # 2 (yielding 3.5 eV electrons) or ATI following double ionization of channel # 5 (yielding 2.9 eV electrons) which, as we will see, is already important at such state of Sr II or an intensity. The two following spectra (Figs. 7b and c) have been obtained using a 6.7 V/cm separation field and a 1 V acceleration voltage on the flight tube. The increase of the collection efficiency allows to work at both a lower neutral density and laser intensity. The spectrum of figure 7b is taken at an intensity of 0.3 x 1012 W. Crn - 2. It shows only one peak at 2.2 eV, which is the remnant of the 1.2 eV peak of figure 7a. The 1.8 eV peak either has disappeared or is not separated from the main peak. On the trailing edge of the main peak, there is a weak feature whose position would cor- 804 Fig. A = 7. - Different electron energy spectra taken at 532 nm and for different experimental conditions (see text). Fig. 8. Variations of selected peaks amplitude (from Fig. 7) with the laser energy. Labels correspond to different processes of figure 5. - and this may be due to the contribution of electrons of channel # 7, which may not be negligible at high intensities. The main conclusion arising from these data is that double ionization of Sr at 530 nm is essentially a « stepwise » (resonant) process involving principally the ground state and the first two excited states of the Sr ion. It can also be deduced from the comparison of the two higher energy peaks of figure 7a that excited ion state production is more probable than ATI of the same order. This suggests than multiphoton ionization of alkaline earths goes along with a noticeable degree of core excitation. 4.2 IONIZATION OF Sr FROM 558 nm TO 574 nm. This experiment was repeated using our dye laser, in the wavelength range between 558 and 574 nm. Spectra corresponding to those of figure 7 were obtained and are presented in figure 9. The spectrum of figure 9a was taken without collection field and at an intensity of 3 x 1012 W.em-2. The spectrum of figure 9b was obtained with a few V. cm-1 collection field and a 1 V net acceleration between the focal volume and the flight tube. The intensity in this case was about 1011 W . cm - 2. On these spectra, peaks corresponding to all the processes discussed in the previous chapter can be observed. Processes # 2, 5 and 6 do not appear on the spectrum of figure 9b because it is taken at a much lower intensity, and they disappear of the spectrum of figure 9a when the intensity is decreased. Some aspects of these results have already been presented in [32] and will be further discussed here. We first note that the differences in the peak positions - between figures 7 and 9 are due to the change in the laser wavelength and are all consistent with the interpretations given here for each peak. The peak labelled 5 in figure 9a corresponds to six photon ionization of the ground state ion. Depending whether the wavelength is shorter or longer than 520 nm (five photon ionization threshold for the ground state ion) this is either a normal MPI peak or a first order ATI peak. As reported in [32], no rapid variation of this peak amplitude is observed when the laser wavelength is scanned through the threshold wavelength. This was interpreted on the ground of the continuity between the wavefunctions of the discrete spectrum when n - oo and of the continuum when E - 0. However it is impossible to identify a five photon ionization peak which should appear at short wavelength, because it is superimposed to the peak # 4, and the dye laser intensity is too small to allow an identification through the intensity dependence. As shown in the previous paragraph, this is possible at 532 nm and gives us full confidence in the above interpretation. The peak labelled 4 (in Fig. 9b) is essentially due (totally at low intensities) to 4 photon ionization of Sr, leaving the ion in the 5p excited states. The one labelled (1) + (3) by following peaks (1) and (3) of figure 9 a when increasing the accellerating field. Peak (4) is identified, as discussed below, by its wavelength dependence. The slight energy mismatch visible in figure 9b is probably due to the use of a separation 805 0.1 eV - typically when they are emitted preferentially along the laser polarization direction). This detection scheme was usefull in identifying peak # 4 but causes strong variations of the collection efficiency with the energy. Figure 10 represents the variations of the peak # 4 amplitude, for a laser intensity of 1011 W.cm-’, and for laser wavelengths between 565 nm and 574 nm. The laser polarization is along the detection direction so that this peak amplitude is a good representation of the excitation probability for the 5p ion states. The - are still clearly visible, the ionization probability presenting in both cases a maximum about two thresholds Fig. 9. - Two different electron energy spectra taken with the Dye laser for different conditions (see text). Labels on the peaks correspond to different ionization processes of figure 5. field which makes the electron energies (inside the flight tube) critically dependent on the position of the laser focus. Here again, the two thresholds corresponding to excitations of the 5P3/2 and 5P 1/2 states of Sr+ are crossed within the dye laser wavelength range, for 567,8 nm and 574,4 nm respectively. In [32], in order to emphasize the threshold effect, the variations of the peak # 4 with the laser wavelength in the threshold region were recorded with the laser polarization at a right angle from the collection axis. (In this configuration, our electron spectrometer works as a « threshold spectrometer » because the weak accelerating field is too low to collect electrons with energies above 45 cm-1 above the ionization threshold. In addition, for wavelengths between 590 nm and 572 nm, a broad maximum can be seen, which was completely cut-off by the transmission drop in [32]. It corresponds to two photon intermediate resonances on the 5p2 3p 0 and 5s 5d 3Di states of Sr which were observed on the ion signal in [20, 28]. As will be shown in a forthcoming paper at the intensity used in this experiment, these resonances are strongly shifted and broadened and thus are not clearly resolved on the spectrum of figure 10. We finally note that in this wavelength range, the peak labelled 3 on figure 8a, corresponding to four photon ionization in the 4d states is negligible. Many two and three photon resonances in the ion signal were also observed in the wavelength range between 558 nm and 564 nm [20, 28]. These resonances can also be seen on the electron signals, as shown in figures 11 and 12. These two figures show the wavelength dependences of different peaks. Figures 11 and 12 correspond respectively to a laser linearly polarized along the direction of detection and circularly polarized. Figures 11 (12) a, b and c correspond respectively to three photon ionization into the Sr+ ground state (channel # 1), four photon ionization into the 4d (channel # 3) and 5p (channel # 4) states. Figure 11c, was taken at a laser intensity of 1011 W . cm- 2, figures 11a and b at an intensity of 1.6 x 1011 W .cm-2, and figures 12a, b, c at 2 x 1011 W .em-2. As usual with tightly focused picosecond pulses, absolute intensities are not determined to a better precision than a factor 2. However comparison between the different figures quoted above is exact within 20 %. Intensity changes between the different spectra of figures 11 and 12 were made necessary by experimental constraints owing to the limited range of satisfying operating conditions for the spectrometer and of course to the accumulation time. The wavelengths plotted in abscissa are in the vacuum and are taken directly from the computer scanning program, so that the small differences between the positions of the peaks in different spectra only reflect the limited precision of our wavelength scanning/measurement system, which is about 1 angstrom. Some general remarks can be made concerning these spectra. All the resonances of figures 11 and 12 have already been seen with ion detection [20, 28]. 806 Figure 10. Wavelength dependence of peak 4, of figure 9b (Sr (5s2) + 4 hv threshold region. Vertical bars indicate the position of the thresholds. - -+ Sr+ (5p) + e-) in the 5P 1/2,3/2 ionization labelled (I) to (V) in figure l la which can be seen, to a different degree, on all the spectra of figures 11 and 12. Resonance (I) at 559.4 nm, with a small satellite at 559.6 nm (which in some cases appears merely as a shoulder) appears, as in [20, 28] at the wavelength corresponding to a three photon resonance on the 5p 6s 1P’ state as deduced from the results of reference [33]. The fact that this resonance is clearly seen with a circularly polarized laser is a first indication that Fig. 11. - Wavelength dependence of selected peaks of figure 9 in the 558-nm-564 nm region, for a linear polarization of the laser, along the detection direction. Changing the laser polarization from linear to circular lead to a decrease of the ionization probability which made necessary and increase of the laser intensity by a factor of 1.5 to 2 to restore the signal level. It also results in a sharpening of the resonances, Fig. laser. 12. - Same as figure 11, with a circularly polarized 807 configuration mixing has to be considered to interpret data. Resonance our (II) is at 560.6 nm where two different explanations can be considered : a two photon resonance on the state or/and a three photon resonance on the 4d state of [33]. 4f(3/2 5p2 3P2 (2D5/2) 1)01 Both are allowed with circular polarization. Note that for linear polarization, this resonance appears only as a broad weak feature in process # 3, while for circular polarization it is, on the contrary, the tallest and thinest resonance on spectrum b. On the two other spectra, though keeping the same shape, its importance decreases for circular polarization, compared to linear. No known state can be found in the literature to explain resonance (III) at 561.6 nm. It can only be said that it should correspond to a state with J 3 because it is certainly a three photon resonance and it is maintained in circular polarization. In [28], resonance (IV), at 563 nm was tentatively assigned to a three photon resonance on the 4f(3/2)’ state [33]. In [20], it was noted that a better wavelength fit was obtained for this state with resonance (V) at 563.5 nm. The new results do not support this hypothesis for two reasons : first resonance (V) is suppressed in circular polarization, which should not be the case for such a state; secondly because on the different spectra of figure 10, it appears to be much stronger in ionization towards the 5p state (c) than towards the 4d (b) or 5s (a) state. It follows from the analysis of 2 .1 that, if a definite core can be assigned to the state responsible for resonance (V), it should be a 5p core rather than a 4d despite the wavelength difference our results tend to confirm the interpretation given in [28] for resonance (IV), which leaves (V) unidentified. = 4d(2D3!2) Figures 11 and 12 bring up an other problem : the analysis of 2.1 led to the hope that strong differences between the different resonance spectra would help assigning a core to the different states responsible for the observed resonances. This is obviously not the case, except may be for resonance (V). Two explanations be considered for this behaviour. It could first be argued that the ionization mechanism involved in the production of ion excited states is not the one considered in section 2. The fourth photon could hit the wing of a broad (because relatively low lying) 6s nl autoionizing resonance, which then ionizes into all the available channels. In this case, the spectra of figures 11,12b and c would only differ by a branching ratio which would not be wavelength dependent, and the spectra should be strictly identical, which is not observed. It seems more reasonable to think that a strong configuration mixing has to be considered for the states involved in these resonances. Note that this configuration mixing must be also invoked to explain the three photon excitation of 4d nf states from a 5S2 ground state. One might also ask which are the possible candidates for the unidentified resonances. Two remarks can be can made : in [33] three 4d 4f states identified : both 4f(3/2)0, states, but are 4d(2DsI2)’ 4f(3/2)0 an&4d(2 D 3/ ) only the 4d(2DS/4) 4f(1/2)1, state. Simply using the energy of this state and the 4d(2DsI2,3/2) fine structure a splitting deduced from the other pair of states gives wavelength of 560.9 nm, close to resonance (II) which already has two candidates. However, this calculation is probably a little crude in such a complicated situation. Another possible candidate is a 5p 5d state. This state does not appear in [33]. It has been searched for unsuccessfully by absorption techniques using U.V. light [34] where it is concluded that, in Sr, transition from 5s2 to 5p 5d is anomalously weak. A possible explanation for this is that such a one photon transition can only originate from an admixture of 5p2 in the 5s2 ground state. This is not true anymore when three photon transitions are considered. It should also be said that some results on the a.c. stark shift of the 5p2 and 5d 5s states seems to point at the presence of such a state in this energy region. Note that a 5p 5d 1P01 state would be a reasonable candidate for resonance (V), but our data are too limited to consistently back up such an assignment. Last, one should consider the question of the branching ratios. Data of figures 10 and 11 are raw electron counts per laser shot. Corrections from the transmission effects have not been introduced. Spectra a and b are taken together without acceleration field so that the only correction to be made is that of the flight tube transmission between 0.9 eV and 1.3 eV. From the results of figure 4 it can be deduced that compared to a, spectrum b is overestimated by a factor 1.5, as noted in the top left comer. In the case of spectra c, a 1 V acceleration is used which is rather efficient on 0.1 eV electrons so that spectra c are overestimated by a factor of about 11. If, in figure 11, we take 0.04 as an average value of the signal for spectrum a, 0.015 for spectrum b and 0.5 for spectrum c, it can be concluded that on the average, at intensities of the order of 1011 W . cm2 and in this wavelength range, about 10 % of the ionization occurs in state 4d and almost 50 % in state 5p which is certainly an important effect. Of course this ratio is wavelength dependent : almost no 4d state is reached for wavelengths above 564 nm, and close to the 5P3/2 ionization threshold, this channel is the dominant one. 5. Conclusion. Single and double multiphoton ionization of Sr has been studied using electron spectroscopy techniques. Single ionization has been shown to occur for a significant part in excited states of the ion even though these processes require the absorption of one more photon than ionization in the ground state. A multiphoton process of the same order, that is first order ATI leaving the ion in the ground state, is shown in this case, to be less probable. This leads to the conclusion that the question of multiphoton ionization of alkaline 808 earth cannot be tackled without considering that of core excitation (or equivalently the question of two electron excited states). It is also clear that configuration mixing plays a major role in the problem of resonant multiphoton ionization of Sr, be the resonance on an intermediate state or on an auto-ionizing final state. All this makes the problem of MPI of alkaline earths considerably more complicated than that of one electron atoms. Concerning double ionization, it has been shown to be essentially a stepwise (or resonant) process. Low lying two-electron excited states or ion excited states play a major role in these resonant transitions but it merely results in the excitation of a few low lying ion states. Of course this may be a particular property of alkaline earths because they have low lying ion states, and the situation may be different for rare gases whose first excited ion state is lying at about one half of the ion ionization threshold. Although the assignement of resonances was sometimes uncertain, no clear evidence of resonances on two electron states could be found. No evidence was found either of non resonant double ionization. We conclude that these processes have a low probability at the wavelengths investigated here. Given the reasonable number of photons involved and the fact that one can even point at some specific MPI channels, the perturbative approach, even if it does not lead to easy calculations, still seems reasonably qualified to treat the problem of double multiphoton ionization of alkaline earths. high lying 6. Acknowledgments. The authors would like to thank A. L’Huillier, Pr W. Cooke and P. Lambropoulos for many interesting discussions, and Dr Manus for his critical reading of the manuscript. They also would like to acknowledge the help of C. Boudigues and M. Bougeard in building up the equipment and that of A. Sanchez in designing and maintaining the intricated electronical equipment which was used in this experiment. References [1] MORELLEC, J., NORMAND, D. and PETITE, G., in Adv. At. Mol. Phys. 18 (1982) 97. 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