Angular distributions in multiphoton detachment of negative halogens

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Angular distributions in multiphoton detachment of negative halogens

C. Blondel, M. Crance, C. Delsart, A. Giraud

To cite this version:

C. Blondel, M. Crance, C. Delsart, A. Giraud. Angular distributions in multiphoton detach- ment of negative halogens. Journal de Physique II, EDP Sciences, 1992, 2 (4), pp.839-852.

�10.1051/jp2:1992170�. �jpa-00247676�

Classification Physics Abstracts

32.80F 32.80K

Angular distributions in multiphoton detachment of negative halogens

C. Blondel, M. Crance, C. Delsart and A. Giraud

Laboratoire Aimd-Cotton, C-N-R-S- II, b£timent 505, 91405 Orsay cedex~ France

(Received 30 October 1991, accepted 17 January 1992)

R4sum4. On utilise _un laser Nd:YAG _pour dtudier le d6tachement multiphotonique des ions F~, Cl~, Br~ et I~, £ la longueur d'onde de 1064 nm, au h la longueur d'onde de 532 _nm.

On s£lectionne angulairement et on compte ^{les 41ectrons} produits, de fagon h obtenir la distribu- tion angulaire de d4tachement. Neuf distributions angulaires sont pr6sent4es, et compardes _aux

calculs correspondants. Corriger l'approximation des ondes planes _par l'approximation de Born

au premier ordre rapproche elfectivement les distributions angulaires calculdes des distributions angulaires mesur4es. Les amplitudes relatives de transition _vers les difl4rentes voies du conti-

nuum montrent _une tendance g6n6rale de l'41ectron 4ject6 £ 6tre produit _{avec une} probabilitd

plus grande _que pr6vu dans des stats de moment cin6tique 61ev6.

Abstract. A Nd:YAG laser is used to study multiphoton detachment of the ions F~~ Cl~~

Br~ and I~, either at ₌ 1064 _{nm, or}

= 532 _nm. The electrons produced _are angularly selected and counted, in order to give _a measurement of the detachment angular distributions.

Nine different angular distributions _are presented and compared to corresponding calculations.

Correcting the plane-wave calculation by the first Born approximation actually brings the cal- culated angular distributions closer to the measured

ones. The relative transition amplitudes

to the different continuum channels show

a general tendency of the outgoing electron to be

produced with _a probability larger than predicted in high angular momentum states.

1 Introduction.

Analysing the angular distribution of the ejected electron has been well known _{as a very} precise probe of photoionisation _or photodetachment _processes [1, 2]. This method of investigation

appears even more useful in the _cases of multiphoton ionisation (MPI) [3, 4] ^and multipl~oton

detachment (MPD), for the final state of the electron is then _a linear combination of _a variety

of angular momentum states. Angular distribution measurements give _access to the amplitudes of these different channels, and to their relative phases.

E (eV) 4.66

~ ~ ~Pl/2

~ ~~ 3.82

3.61 = 3,49

-~

3.40 3.36

3.06 2p~j~

2.33

( 1.165

iira f

F Cl _{Br I} I

Fig. I. Energy scheme for multiphoton excitation in the four negative halogen ions.

MPI angular distributions have _now been investigated in many situations (see _[5] for _a

review). MPD angular distributions, _on the contrary, were first investigated only recently [5, 6].

MPD deserves _a special study however because near-threshold photodetachment obeys rel-

atively unusual laws. In neutral atoms, the centrifugal barrier

can be _overcome by the _outer

electron in the discrete spectrum. Every increase of the principal quantum ^number by _one unit

brings in _{one more} allowed £ angular momentum value. When ionisation _occurs, except for the selection rules, all angular momentum channels _{are open.}

This is not the _case with negative ions. Negative ions have _no Rydberg series. Every partial

detachment cross-section _at starts from _zero at threshold. Overcoming the centrifugal barrier in the continuum takes the form of the Wigner _{law [7]}

at c< ~+1'2

where _e is the _energy above threshold.

As _a consequence, any photodetachment angular distribution will be dominated by the lowest-allowed £ partial _{wave near} threshold. Other channels will become continuously _more important _as the energy increases. Even non-resonant MPD angular distributions will thus exhibit rapid variations _{as a} function off-

MPD must be non-resonant anyhow. Most negative ions have _no discrete excited _states.

Halogen negative ions _are chosen because of their electronic similarity to _rare gases, which

were widely studied in MPI experiments. Moreover, the electron affinities of halogens (from 3 to 3.6 eV) make possible 3- and 4-photon ^detachment experiments at the 1064 _nm wavelength

of the Nd:YAG laser, _or 2-photon detachment with the 532 _nm frequency-doubled radiation, with the instantaneous _power reached by _a ^standard lJ-per-pulse laser.

Figure I gives the _energy scheme of multiphoton excitation in the four negative halogen ions,

either by the fundamental 1064 _{nm, or} by the 532 _nm fight. The special situation of1064 _nm three-photon detachment of F~, which yields _very low kinetic energy electrons, _was exploited

in _a particular experiment, ^described in _a previous _{paper [8].}

2. Experilnental set-up.

2, I ION BEAM. Figure 2 gives _a scheme of the experimental set-up, ^which was described

already _[5, 6, 8]. ^The experiment is performed _{on a} beam of ions produced in _a hot cathode

discharge _source. The low-voltage (30 +10 V) discharge is _run in argon. It is fed with the halogen species ^under study by evaporation of the corresponding sodium _or potassium halide,

a small quantity of which has been deposited _near the hot filament. Only ^{for fluorine is another}

method employed, which consists in replacing the _{pure argon} injection by injection of

a mixture of _argon and carbon tetrafluoride.

E

T

s G

H ^w

L ~

o

F

Fig. 2. Scheme of the experimental set-up, with 5 the ion _source, W the Wien velocity filter, D _a

liquid-nitrogen cooled diaphragm, I the electrically and magnetically shielded interaction _zone, F

a

Faraday _cup, G _a Glan-prism polarizer, H the rotatable half-wave plate, L the focusing lens, T the time-of-flight tube and E the electron multiplier.

The whole _source is set at _a voltage of -1200 V with respect to the rest of the apparatus.

Negatively charged species _are extracted from the _source through _a 0.8 _mm hole bored in the anode. A small electrostatic lens (3 cm of overall diameter) is _{set a} few _mm in front of this aperture. It makes _a parallel beam out of the accelerated ions, which is then aligned and sent into _a Wien velocity filter. The electric to magnetic field ratio of this filter is adjusted _{so as}

to make the halogen ions under study only flight straightforward to the interaction chamber.

The ion _current which _crosses the interaction region is usually of the order of 50 nA.

2.2 INTERACTION _REGION. In the interaction region, the halogen ion beam is illuminated at right angles by the linearly polarized fight of _a Nd:YAG laser, either with the fundamental 1064 _{nm or} with the frequency-doubled 532 _nm radiation. Focusing is achieved by _an anti-

reflection coated plano-spherical lens of focal length 40 _or 30 _cm (respectively). In order _to

keep ^the background ^electrons produced by multiphoton ionisation of the residual _gas

as few

as possible, the interaction chamber is differentially pumped by _a turbomolecular _pump, while

JOURNAL DE PHYSIQUE ii T 2,N' 4, APKL 1932 31

most of the buffer gas and spurious molecules emitted by the _{source are} evacuated directly from the first chamber by _an oil-diffusion _pump. A liquid-nitrogen cooled diaphragm set _on the ion beam helps keeping the _pressure of the interaction chamber around 5x10~~ _Pa while the ion beam is running.

2.3 DETECTION. Electrons produced by multiphoton detachment _are detected orthogo-

natty to both beams, at the top ^of a magnetically shielded time-of-flight (TOF) tube. The field-free TOF volume _can be set at _a positive voltage, in order to increase the collection efficiency of the detector, at the _expense of _a reduction in the _energy and angular resolutions.

The detector is set at _a fixed position in _space. Recording the angular distribution of the detached electrons thus requires that

we can rotate the polarisation ^direction of the light, which is achieved by moving _a half-wave plate, set _on the laser beam before the focusing lens. Its rotation is made automatic, by _means of _a step-to-step ^rotatable mount, with _a precision of

1/100 _a degree. A complete revolution of the half-wave plate corresponds to two revolutions of the polarisation direction, I-e- four periods of the angular variations of the photodetachment

rate. Identity of the variations observed from _one period to another makes _sure that _none of these variations result from defects of the half-wave plate, or defects of its anti-reflection

coating.

The number of ions that _cross the laser focus during ^the laser pulse (12 _ns FWHM) is of the order of _one thousand. With the angular selection of _our electron detection system, we do not expect to have _more than _one electron detected _per laser shot. Electron counting methods

are well adapted to such _a situation

The electric pulses of the electron multiplier _are first amplified, then _{sent to a} discriminator.

The resulting calibrated pulses _go into the counting board of _a PC computer, ^{which records} the electron count _{as a} function of the polarisation direction, with _an angular resolution of 0.2 degree.

Several revolutions of the half-wave plate _are performed to eliminate the influence of _any low-frequency noise. The counts that result from _every revolution _are added _to the previous

ones. Finally the data stored in the computer after _a few hours' accumulation consist of four-

period (720 degrees) recordings of the ihotoelectron _angular distribution, with _a total number of counts of the order of _a few thousand electrons.

3. Data processing.

3.1 FORMATTII4G _THE DATA. Because of the angular acceptance ^of our electron detector~

(4 to 10 degrees of total aperture, depending _on the TOF voltage and _on the initial kinetic energy of the emitted electrons), keeping electron _counts in channels with _a 0.2 degree's interval appears superfluous. There is _no loss of actual resolution in making the data _more compact, by adding the contents of _{every n} (3 ^< n < 18) adjacent channels. This has the advantage

of dividing the time necessary for data processing by the _same factor. A factor of 4 _can still be gained by folding the records from their 720 degrees format into _one single 180 degrees period of the angular distribution. Both operations have the advantage of increasing the _mean

number of counts per channel, which automatically reduces the statistical dispersion of the counts around the expectation value, thus making the angular distribution _more readable by the naked _eye.

3.2 DEFINITION OF THE FITTING CURVE. Let be the angle between the electric field

of the linearly polarized light and the detection direction. The general theory for angular

distributions of electrons removed from unpolarised _targets shows that the differential _cross- section varies _{as a} linear combination of cos(2@), cos(4@), ^with as many ^terms as there

were photons absorbed in the _process [4]. ^{It is thus natural} to fit the data by such _a linear combination _or, equivalently, by _a linear combination of Legendre polynomials of _even order~

with the _same number of terms.

In addition to the coefficients of this linear combination, which contain all the atomic in- formation that _we look for, two _more parameters are needed, namely the actual position of the angle _zero in the recording (the angle at which _we detect electrons that have been emitted along the polarisation direction), and the angular acceptance ^{of the} detector.

3.3 DETERMINING THE ₌ 0 DIRECTION. Determining the _zero direction is _a priori

possible by measuring the polarisation direction of the laser light after it has crossed the half-

wave plate and taking into _account the transformation from the ions'moving frame to the laboratory frame _: electrons that _are detected perpendicularly to the ion beam must have been emitted backwards, in the ions'frame, to compensate for the velocity of the beam.

The corresponding shift of the angular distributions _ranges from only _a few degrees for fast electrons emitted from heavy (hence slow) ions to _more than 60 degrees in the very peculiar

case of 1064 _nm three-photon ^detachment of F~.

Trouble _comes from the fact that residual electric and magnetic fields still bend the elec- tron trajectories, between the interaction region and the detector. For this _reason, the best detection efficiency _may be obtained _{at a} few degrees'shift from the theoretical detection axis.

Despite the _a priori calculation, the real origin thus remains _an unknown. But fortunately, due to symmetry reasons, this angle origin _{appears as a} centre of symmetry of the angular distri- butions. It _can thus be precisely re-adjusted by the fitting _program. The standard deviation of this correction is lower than five degrees.

3.4 DETERMINING THE ANGULAR ACCEPTANCE. Taking ^the angular acceptance of the

detector into account _means fitting the data by _a convolution of _some shape function with the expected theoretical function. If _{we assume} the transfer through the detector to be for instance

square-shaped, we still have to choose its width. Can this width be let free~ _so as to be finer

adjusted by the fitting procedure ? The _answer here is _no.

This stems from the fact that whatever _a linear combination of _cos (2pf) is convoluted with,

it _can always be represented in the _same mathematical form. In other words, convoluting does neither add _any degree of freedom _to optimize the fitting, _nor put _any additional constraint

on the parameters. ^{This makes the} quality of the fit (but not the coefficients that _are read out as the result) completely unsensitive _to the shape function. We thus _{assume a square}

shape, and rely _on the _a priori calculation of the angular acceptance ^{of the detector} to obtain its width. Convolution of this _square shape function by the expected linear combination of

Legendre polynomials is then performed, and fitted to the angular counts by _a x~-minimizing

method [5].

4. Calculation of angular distributions.

4. I PLANE-WAVE APPROXIMATION, The plane-wave approximation provides _an efficient

and simple method _to investigate multiphoton absorption _processes in negative ions. For

halogens, comparison of theoretical predictions with experimental data has shown _an overall

qualitative _agreement for total multiphoton detachment cross-sections which becomes _quan- titative for light halogens _IQ]. The richer information provided by angular distributions gives

an additional _test for the plane-wave approximation, which _can be improved by introducing

different phases for the continuum wave-functions~ the latter being calculated via the first Born

approximation. We recall the principle of the calculation.

The initial state is the ion ground state )g), ^of _energy Eg ^with respect to the detachment threshold. Absorption of _n photons brings the ion into _a continuum state of _{energy e}

=

Eg + nhw. The ground state is described by the Hartree-Fock wavefunctions, _as calculated by Clementi [10].

The plane-wave approximation consists in keeping only the kinetic _energy of the outer elec- tron in the hamiltonian, which is then denoted Ho. Continuum states are taken _{as a} frozen

~2~2

core plus _a free-electron of _{energy e =} Such states, ^which are eigenstates of Hoi _may be 2m

defined by the quantum ^numbers SiLi (describing the coupling of the _core p~), £ the orbital momentum of the outer electron, SL the total spin and momentum and _e. Monoelectronic wavefunctions thus factor12e _as [SiLi£, S,L) (angular part) and R~t(r), ^whith is proportional

to _a regular Bessel function (radial part).

4.2 INTRODUCII4G THE FIRST BORN APPROXIMATION. The final state may be described

either in the plane-wave approximation, [ae), or in the first Born approximation [6i)~ a stands for the set of quantum ^numbers labelling the state. Intermediate _states involved in the calcu-

lation of transition amplitudes _are taken in the plane-wave approximation.

The basic assumption in the following treatment is that the first Born correction to the wavefunction is negligible inside the _core, but _must be kept asymptotically.

The hamiltonian in the Hartree-Fock fro2en _core approximation is H. The perturbing _po-

tential is defined implicitly _as

w= H-Ho

The modified wavefunctions in the first Born approximation _are obtained formally from

(1 + GOW) [ae) ₌ [SiLi£, S,L)R~t(r) + GOW)SILif, _S~L) R~t(r)

after normalisation.

Go is the Green function deduced from Ho- Let _us define S~t(r) _as the radial function _propor- tional to the spherical Bessel function of the second kind yt(kr), with the _same normalisation

conveition

as R~t(r). We _can write the Green function _as

Go _" £ _{)SiLif, S,L)(SiLi£,S,L[}R~t(r< )S~t(r>

Si~Lit,S~L

with the usual notation r< = inf(r, r') and _{r> =} sup(r, r'). The modified wavefunction is

lsi Li£, s, L)R<t(r) +

£ [S(L(t',S', L')(S(LIP,S',_L'[

/

The latter radial integral decomposes _as

Ret'(~)

f

r

r

+ S<t,(r) Ret,(r') (S[L[£',S', L' (W( SiLi£, S,L) Ret(r') ^r'2 dr'

Due to the finite _range of W, for large _r the first integral is _zero and, in the second _one, the upper limit _can be _set to infinity. The latter integral ^then _appears as the matrix element of W between two continuum states in the plane-wave approximation. We need _not thus define

explicitly W.

As )ae) stands for )SiLil~$_{L) R~t,}

we write [SiLi£,S, L)S~t _as [6i).

Aa,o ₌ (a'e)W(ae)

The modified wave-function is

(&i) =

Ni~ _)ae)

+ £ _{A«,« a'e}

«,

where NJ ^I is the normalisation factor. Asymptotically the [ae) and the [6i) _are orthogonal

to each other _so that

No = I + £ _(A«,«(~

~>

4.3 MULTIPHOTON DETACHMENT CROS~SECTIONS. The ion-light interaction is V, the

dipole interaction written in length form. In the plane-wave approximation~ the probability amplitude for the transition between [g) and )ae) due to the absorption of _n photons ^is

P(ae) ₌ (ae_[VGO(Eg + (n I)hw)V VGO(Eg + 2hw)VGO(Eg + hw)V[g)

After detachment the final state is described by [#) ₌ £~ P(ae) [ae). ^The angular distribution is obtained by integration of [(Si>Li> _r,@,~a[#)[~ over r.

When applying the first Born approximation, _{we assume} that the correction is negligible for small _r. In the calculation of probability amplitudes [ae) needs only be replaced by No_i~ [ae).

This _now yields _as the final state

)I) = L

~t~

[

Ill)

« «

Going &om the plane-wave to the first Born approximation finally _means replacing the

probabflity amplitude P(ae) by

ioo iii

lo 120

( _to

jj 8°

e 40

Q~ 40

20

30 to 30 20 50 lo 30 to 30 20 150 1lo

50 go

~

40

) ~~

# 30₂₀ ^~~

,

lo ^2fl

e

0 30 60 30 120 150 l10 30 to _{3fl 12fl} lsfl _18fl

lsfl

~~~

m loo ^12fl

cf

t lo ,

( _5fl ,

4fl ^'

c

30 to 30 120 150 l10 0 30 to 30 120 150 l10

angle ldegreesl angle ldegreesl

Fig, 3. Two-photon detachment angular distributions~ in the order of increasing values off (kinetic

energy of the ejected electron), a) _{e =} 0.66 eV (I~Pi j~),^b) e = 0.84 eV (Br~Pi_j~)~c)

e = 1.04 eV (Cl)~

d) _e

= 1.23 eV (F)~e) _e

= 1.29 eV (Br ~P~j~), f) e = 1.60 eV (I ~P~j~). ^{The continuous} line is the best fit of the experimental data to the expected form of _a linear combination of Legendre polynomials. The dot-dashed line is the result of the plane-wave approximation. The dashed line shows the first Born approximation. In _case d) (fluorine), the dotted line shows the result of _a calculation with correlations

[Ii].

5, ltesults.

5 I ANGULAR DISTRIBUTIONS. Results of multiphoton angular distribution measurements are presented in figures 3 and 4. Figures 3 _a to f show the angular distributions obtained by two-photon detachment _at the wavelength 532 _nm. For the _two heavier _atoms Br and _I~ the

fine-structure is large enough to make the selection of the final fine-structure state possible, by

electron TOF.

For the two lighter _{ones~ our} TO F apparatus cannot distinguish between the two thresholds.

However the fine structure is small enough to make the respective angular distributions _very similar. The experimental result, which mixes both channels~ will be compared to a weighted

average of the calculated angular distributions.