Electron spectroscopy study of single and double multiphoton ionization of strontium by visible picosecond laser light

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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�

Electron spectroscopy study ^of single and double multiphoton ^ionization

of strontium by ^visible picosecond ^laser light

G. Petite and P. Agostini

C.E.N. Saclay, Service de Physique, ^{Atomes et} Surfaces, ^{91191 Gif sur Yvette} Cedex, ^France

(Reçu le 31 octobre 1985, accepti ^sous forme définitive ^{le 24} janvier 1986)

Résumé.

Les techniques ^de spectroscopie d’électrons ont été appliquées ^à l’étude de l’ionisation multiphotonique simple ^{et double du} strontium par des 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.

Abstract.

Multiphoton single and double ionization of strontium was studied using ^electron spectroscopy techniques. ^{Both a} picosecond, frequency ^{doubled Nd :} Yag ^{Laser and a} picosecond ^{rhodamine 6G} Dye ^Laser

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} impor-

tant 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.

Classification

Physics ^Abstracts

32.80D - 32.80F - 32.80K

1. Introduction.

Multiphoton Ionization (MPI-[1] and references

therein) ^{has long been studied,} because it is the process which dominates the laser-atom interaction 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.

It was shown [2] that under such intensities an atom can absorb more than the number 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.}

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

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 multi-

photon excitation of either the atom or the ion

yields ^an excitation _energy close to an ionization threshold. Last, ^we present ^new observations ^con-

cerning 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) ^{ATI and} double ionization : what are the

relationships between these two ^« high ^{order »} pro- cesses ?

(iii) ^{What are the most} probable ^mechanisms leading ^to double ionization.

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 correspond- ing ^{to the results} presented ^later

^{those are still}

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} predictions concerning ^some aspects ^{of our} experi-

ment which have not been so far considered in the literature.

(ii) clarify ^the terminology concerning the diffe- rent ionization processes involved in ^our experiment.

(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.

Multipho-

ton 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 state I g) ^of energy E8, ^two continual I c1 ) and I c2 > (energies E1 ^and E2) ^{and one} auto-ionizing state I a > ^of energy E. lying between the ionization limits corresponding ^to continua I c, > and c2 >. ^We

use the dressed atom model and these states will be dressed respectively by n photons of the laser field

for I g), ^{n - 3} photons for a ) and I c1), ^and

n - 4 photons for c2 ^{), etc.}

Note that continual I cl > and I C2 > correspond ^to

different states of the core. For instance, ⁱⁿ strontium,

Fig. ^1. - Schematic representation ^{of the} couplings

involved in 3 and 4 photon ionization with a three photon

resonance on an auto-ionizing ^state.

I ci ) ^{is the} continuum Ss, E1 ) and I C2 > ^{could be}

the continuum 4d, 82 > -

Energies of the dressed states thus are :

If Ha ^is the atomic Hamiltonian and Hf ^{the field}

Hamiltonian, ^{these states are} eigenstates ^{of :}

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 :

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 even-} tually ^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.

through the inversion integral

with

Couplings between I g) and I a >, I cl > or I c2 >

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 Hamilto- nian such as :

so that our interaction Hamiltonian writes :

Note that DC2g represents ^the coupling ^between I g ) and c2 ) through ^{a set of non} resonant auto-

ionizing ^{states such} as I a ), ^{but does not} include the

I c1 ) continuum. The coupling between the continua

I c1 > and c2 ) ^{will be} neglected ^{as it was done in} [24].

With the above definitions, ^the equations ^deter- mining the resolvent operator ^{matrix elements are :}

At time t

0, ^{all the atoms are in the} ground state I g >, ^{so that the} ionization rates in continual I cl >

and I c2 ) ^{will be} determined by I Ug,,(t) 12 aid I Ug-2(t) 12.

We are thus interested in GClg ^and G129’ ^{which can be} expressed, ^from equations (9. c) ^and (9. d) by :

Using ^these expressions ⁱⁿ equations (9. a) ^and (9. b) ^{we get :}

we then define :

which represent the shifts of statues I g > and I a > ^{due to} their interaction with the continua :

which are the widths of states I g > and [ a ) ^{due to the same} interactions, ^{and :}

which is a modified effective interaction between states I g > and I a >, ^as defined in [24] ^{but with an additional}

term due to continuum I c2 > which should be small compared ^to the others because of its higher order in the laser intensity.

System (II) then writes :

which yields :

Expressions ^{which are} strikingly ^{similar to those} obtained in the case of resonant multiphoton ^ionization

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

continuum I c, > is made of two terms. The first one

describes direct ionization of I g > in I cl >, ^{when the}

second one describes the excitation of I a) ^followed by auto-ionization of I a) in I 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

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

of a > ^{is due to a} dipole interaction instead of a

Coulomb interaction. The same result was obtained

in the case of resonant multiphoton ^ionization

with a formalism sometimes referred to as « pseudo

auto-ionization » : : ionization in continuum I C2 > ^is

the result of interference between a resonant amplitude (Dc2a Dag) ^{and a non resonant one} (DC2g) ^{in the same}

way ^as ionization in I cl > ^{results of an} interference between ^a direct channel and the auto-ionizing ^one.

Considering expressions (17. a) ^and (17 . b) ^{a few}

remarks can 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 of c2 ),

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 continuum I 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 possibly I 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 mono-} electronic, only resonances on states with the same core can appear in excited ion states production.

This is true of course only ^when configuration ^inter-

actions are neglected. ^{In the} opposite ^case, interesting

indications can be obtained in this _way, ^on the impor-

tance 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 produc-

tion. 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 simulta-

neously 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 state g) ^of energy Eg ^{can be doubly ionized by} absorption ^{of two} photons ^of energy Ep, ^{giving a} doubly charged ion in its ground state 192 > ^{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 _opera- tor, ^can only couple g2, E1, G2 ) ^{to states} pertaining

to the continuum of simple ionization, that is of the

type I el, G1 >, our Ie1, G2 ) where I 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 ^inter-

action 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

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 ^diffe-

rent : 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

Fig. ^2.

Difl’erent double ionization processes : (A) ^lowest order ^{non 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 ground ^state.

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 experi-

ments 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 reso-}

nant, 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 negli- gible ^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 possi- ble, ^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.

3. Experimental ^set up.

Our experimental ^{set up 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.

3.1 LASER SYSTEM.

Two different lasers have been used in this experiment. ^{The first one is a commercial}

Fig. ^3.

Schematic of ^the experimental set-up.

Nd : Yag ^laser system (Quantel) delivering ²⁰ ps Fou- rier 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 pulse- to-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 compen-}

sated 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} electrosta- tic 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 micro- computer 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 varia- tion of the peak amplitude ^{shown in} figure ^{4. This}

variation has two different origins :

(i) variations of the collection angle ^{due to the}

acceleration of the electrons between the interaction 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 elec- trodes grounded but this does not allow detection of low energy electrons both because of _space charge,

contact potentials ^{and losses in the} flight tube. There- fore, 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

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.

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} experi-

ment is necessary, particulary ^to precise ^{a few ioniza-}

tion channels which play ^an important role in this

experiment, ^{and which are outlined on} figure ^5.

Fig. ^5.

Different ionization paths involved in Sr simple

and double ionization.

The 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 as a first step ^{can also occur :}

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. Varia- tions of the ion signal with the laser intensity ^are

shown in figure ⁶ using ^{the usual} log-log representa- tion. 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

ionization process. Slopes measured in the linear

region ^are respectively ^{3.3 for} single ionization and 5.4 for double ionization, ⁱⁿ agreement ^{with the} number of photons necessary ^to ionize the neutral atom (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

Fig. ^6.

^Variation of the number of singly (o---o) ^and doubly (.-.) charged ^{Sr ions} with the laser energy.

state of Sr II (# 7) ^which yield ^an electron of 1.23

or 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}

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 inten-

sity. ^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-}

respond ^{to 0.6 eV} electrons. This peak ^is clearly

visible in figure ^{7c, taken at an} intensity ^{of 1.2 x} 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 _pro-

cess # 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. ^7. - Different electron energy spectra ^{taken at} A

532 nm and for different experimental ^conditions (see text).

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 multi-

photon 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 collec- tion 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

Fig. ^8.

Variations of selected peaks amplitude (from Fig. 7) with the laser energy. Labels correspond ^{to different}

processes of figure ^5.

between figures ^{7 and 9 are due to the} change ^{in the}

laser wavelength ^{and are} all consistent with the inter-

pretations given here for each peak.

The peak ^{labelled 5 in} figure ^9a corresponds ^to

six photon ionization of the ground ^{state ion.} Depend- ing 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 superim- posed ^{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 wave-}

length dependence. ^The slight energy mismatch visible

in figure ^{9b is} probably ^{due to the use of a} separation

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 configura- tion, ^{our electron} spectrometer ^{works as a «} threshold spectrometer ^» because the weak accelerating ^{field is}

too low to collect electrons with energies ^above

0.1 eV - typically

^when they ^{are emitted} preferen- tially 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}

two thresholds are still clearly visible, ^{the ionization} probability presenting ^{in both cases a} maximum about 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 wave-} length dependences of different peaks. Figures ^{11 and}

12 correspond respectively ^{to a laser} linearly polarized along the direction of detection and circularly pola-

rized. 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].

Figure ^10.

Wavelength dependence ^of peak ^{4, of} figure ^9b (Sr (5s2) ^{+ 4 hv}

^Sr+ (5p) ⁺ e-) ^{in the} 5P 1/2,3/2 ^ionization

threshold region. Vertical bars indicate the position ^{of the} thresholds.

Fig. ^11. - Wavelength dependence of selected peaks ^of figure ^{9 in} the 558-nm-564 nm region, ^{for a linear} polariza-

tion of the laser, along ^the detection direction.

Changing the laser polarization ^{from linear to}

circular lead to a decrease of the ionization probabi- lity 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,

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. 12. - Same ^as figure ^{11, with a} circularly polarized

laser.