A very narrow resonance in 18O(p, α)15N near 150 keV: Application to isotopic tracing

Nuclear I~st~ments

and Methods in Physics Research B61(1Q91)369-376

369

Nort~~~olland

Received 29 April 19%

The as~ow resonance in the *sOfp, o)t”N nuetear reaction reported by the Monster group at 152 keV tooks very promising for high r~sol~tion depth profiiing of ‘s0, being isolated and corresponding to farge dE/dx values. Its width was investigated using the 2.5 MV Van de Graaff accelerator of UPS that has a proton beam energy spread of = 80 eV OHM at this energy, The u ~~nt~~~ rate from this rather weak resonance was enhanced by operating an annular surface barrier detector subtendjn8 a large solid angle. The measurements were carried out on Ta,O, targets prepared by anodizing polished high purity tantalum foils in 2% KCN aqueous solutions enriched to 98% ts0, using a vacuum line dedicated to the handling of H,‘“O chemically purifiad with proper distillation techniques. The thicknesses of the various targets were controlled by the voltage applied to the special anodizing tel. Assuming a Breit-Wigner shape for this resonance, its width was deduced from a careful measurement of the practically ba~k~~und free low energy taiis of thick target excitation curves. The use of the stochastic theory of energy toss for interpreting the resufts and the fit of the very short low ener8y tail found suggests that the most probable value of the width is r = SOeV, This u~~~~e~te~~y narrow resonance appears to br: an exceotionatb efficient tool for very high depth resohrtion isotopic tracing of %, as lvill be shown in the second part of this paper,

Isotopic tracing with “0 is a major tool for studying the microscopic mechanisms of chemical reactions or transport processes involving oxygen, With a natural abuadmxe of 0.204%, this stable isotope may label various compounds fike O,, H@, GO, or salts, etc., with enrichments approaching 100%: the ratio of j80 to the b~~k~onnd level may then be favorable, nearly 500. In the fieIds of solid state physics, materials sciences, solid state electrochemistry, etc., the off resonanix ““Q(p, a)r’N reac tion is part~~u~~rly weli suited for d~te~ining total amounts of IsO in thin films, as its ~r~ss~section around 700 keV is large and as the

r On leave from: Central Research Institute for Physics, H-1525 Budapest, Hungary, with a fellawship from the Ministere de ia Recherche et de la Technologie, France. * Work supported by the Centre National de la Reeherche Scieatifique QGDR 861, Prance and DSXR,New ZeaBnd. ~¶~-~8~~/9~/$~~.5~

negative Q value for the r60(p, CX)N*~reaction eliminates the ~s~ib~~i~ of inFerferen~ from the u~tural~y abundant isotope. On the other hand nuclear resonance depth profiling of ‘a0 has long been a standard technique for the fundamental study of transport processes in thm films growing under anodic, thermal or plasma oxidation of substrates fike Al, Ta, Nb, Zr, Ti, Si, etc. Oxygen exchange processes with the ~~d~~~~~ medium may be probed in the same way. More recently similar techniques were applied to studies of high fiuence oxygen implantation in sihcon or faser annealing of various substrates in oxygen, and high Tc supercondu~tars have been investigated for their oxygen uptake and release mechanisms under a large variety of tr~~~rn~nts. The two main %Xp, aI’% resonances that have been used for depth profiling are at 1165 keV [‘,,Z] of estimated width r= 50 eV 1341 and at 629 keV [.?I],of width f = 2.1 keV [4,6,7]. The 1145 keV resonance was the first ever used for depth profiling: the microscopic transport rnec~~~~srns of oxygen during the aflodic

0 1991 - Etsevier Scien~cePublishers B.V. All rights reserved

370

G. Battistig et al. / Width of the 180(p, CI)‘-~Nresonance

oxidation of aluminium were studied with this new technique [B]. It was also used, via its decay through the (p, y) channel [9] for depth profiling [7], and in a detailed study of the Lewis effect [4,7]. However this resonance is not very strong and occurs on a large continuum in the cross-section. In addition the cx channel is difficult to use at these energies, since the backscattered protons cannot be separated with an absorber foil from the (Y particles. Even though it gives relatively poor depth resolution due to its large natural width, and that it too lies on a cross-section continuum, the high intensity of the 629 keV resonance has meant that it is by far the most widely used of the two. A considerable number of publications devoted to various microscopic oxidation mechanisms has been published, in particular by the Paris group, based on the use of this resonance. Let us quote among them some studies: ion transport in anodic aluminium oxides [lo]; growth mechanisms of anodic zirconium oxides [ll]; anodization studies of superimposed niobium and tantalum layers [12]; oxygen transport during plasma oxidation [13,14]; oxygen incorporation under laser irradiation of silicon in various atmospheres [15]; oxygen mobility in YBaCuO thin films [16]; ionic transport in tantalum oxides with phosphorous incorporation [17]; growth mechanisms and oxygen transport during thermal oxidation of silicon [18-201. It is in this context that we read with great interest of the discovery by Lorenz-Wirzba et al. [21] of a narrow resonance in “O(p, o)“N at 152 5 1 keV, with isotropic angular distribution. In spite of its relatively low cross section this resonance is most promising for depth profiling as: it is the first with a sizable intensity and may hence be used without background at lower energies for near surface profiling even for thick 180 containing targets; it is well isolated, the next resonance being at 216 keV so that rather deepOconcentration curves may be measured, up to 6000 A along the beam in SiO, for example; it is practically continuum, and hence background free; the corresponding depth resolution must be high since at these low energies the dE/dx values are large. We therefore decided to investigate this resonance and its potential uses thoroughly. We have begun by measuring its width reported in ref. [21] to be r = 0.5 keV. We hoped to find a narrower width since in ref. [21] a rather thick target was used, and the excitation curve was measured over a very wide range but with relatively large energy steps. In the first of these two papers we present our measurement techniques and the estimated width of this resonance, which turned out to be very narrow, potentially giving unprecedented near surface resolution for “0 profiling. In a second paper we present the applications of this resonance to high depth resolution isotopic tracing of oxygen.

2. Experimental

2.1. Target preparation “0 enriched Ta,O, films on Ta backing were obtained by anodic oxidation of 99.95% pure, 0.2 mm thick tantalum foils in 2% by weight KCN aqueous solutions. The 98% “0 enriched water in the solutions was produced by the IsO separation plant of the Weizmann Institute of Science, Rehovot, Israel. This water was normalized to nearly natural hydrogen isotopic concentration and contained 0.3% “0. The enriched solutions were prepared and the anodizations carried out according to the standard procedures developed by the Paris group, in cooperation with the Isotope Department of the Weizmann Institute, for the study of anodic oxidation processes and for the production of absolute “0 standards [22,23]. The enriched water, as delivered, contains many impurities and for well controlled anodization must be chemically purified by distillation, using a glass vacuum line dedicated to the handling of H,‘sO. The gases dissolved in the water are first removed by freezing to liquid nitrogen temperature followed by pumping and melting, this cycle being repeated three times. The water is then transferred by distillation onto a small piece of sodium that fixes the volatile impurities like FH or CIH. After removal in the same way of the H, produced and a further transfer into a storage vessel by distillation, the water is ready for safe use. The precise and detailed description of this purification procedure will be described in ref. [24]. An additional advantage of using such distillation techniques for handling H21X0 is that a practically unlimited number of oxidations may be carried out without appreciable loss of the expensive solution or any degradation of its enrichment by contact with the atmosphere. This was particularly important because numerous “0 labelled Ta,O, film samples were used not only for the resonance width determination but also for studying the depth profiling capabilities of this resonance, as will be described in part II of this paper. The anodizations were carried out under vacuum in a special glass cell containing 7 cm3 of solution. The correct amount of KCN is put in the cell once and for all as, when the water is distilled out, the salt remains on the wall of the cell. Tantalum wires of 0.5 mm diameter were electrically welded to the 10 by 20 mm tantalum samples both for easy handling and for good electrical contact during anodization. These samples were degreased, then chemically polished for 15 seconds in a mixture of 5 volumes of 95% H2S0,, 2 volumes of 53% HNO, and 2 volumes of 45% HF [22]. Once transferred into the cell, the water completely covered the tantalum sample, only the thin wire emerging from the solution. In this way the overall oxidized

G. Battbtig et al. / Width of the ‘80(p, (Y)‘~Nresonance

area was well defined. The cathode was made of platinum. The anodizations were carried out at a constant current density of 0.5 mA/cm’, using a Harrison 6209B constant current power supply, until a predefined voltage V, was reached. This voltage was then kept constant until the current density decreased to 0.1 mA/cm’. Once the oxidation was finished the Hz produced was removed by freezing and the water transferred back into its storage vessel. In these conditions, according to ref. [22], the oxide films grow at a rate of 9.4 X 10”/cm2 oxygen atom per volt. Assuming a density of 8 g/cm3 for Ta,O, [22] we get the equivalence 1 A = 0.545 10’s atom/cm’. In what follows we shall express film thicknesses in terms of Angstrom units for convenience. The thicknesses calculated in this way must be corrected for the contact potential and for the native unlabeled oxide film present on the sample surface before anodization; the latter was measured classically using the “O(d, pli70* reaction at?75 keV and 150” and found to be equivalent to 35 A. It has been shown [22], that this native oxide undergoes no isotopic exchange during the growth of the ‘a0 labelled layer. Moreover it was demonstrated in ref [25] that the order in which the oxygen atoms are fixed by anodic oxidation of tantalum is conserved, that is to say that the native unlabeled oxide remains at the metaloxide interface, while all the oxide grown in the solution is uniformly labeled, an essential condition for our resonance measurements. We took the precaution to measure both the I60 and the “0 contents of our films with NRA, with the ‘“O(d, p)170* and 180(p, a)15N reactions at 97.5 keV and 725 keV, respectively. In this way we could check the calculated film thicknesses as well as the “0 labeling of the oxides. 2.2. Excitcltion curue recording The proton beam, with an energy spread of = 80 eV at low energies, was delivered by the 2.5 MV Van de Graaff accelerator of GPS. The corresponding IBA facility is described in ref. [26]. The operation of the accelerator is far from ideal around 1.50 kV, as ion optics problems show up below = 10% of the maximum potential. In these conditions proton beam currents of around 200 nA could be obtained with an on target beam diameter = 2 mm, at an analysing magnet deflection angle of 45 ‘. The excitation curves were recorded with the hysteresis-free energy scanning system based on an electrostatic deflection technique presented in refs. [26,27]. In this way reproducible energy steps of any required magnitude could be chosen with precision, with a scanning span, at these low energies, of +6 keV. For larger energy ranges, as required for depth profiling in thick targets, the field in

371

the magnet had to be changed manually, as will be seen in part II of this paper. All the techniques required to record high resolution resonance excitation curves, as developed in particular for studying the Lewis effect [28] were applied. Special care was taken to minimize beam induced carbon contamination during the experiments, a crucial requirement in the present work as will be seen. The residual vacuum of our chamber was = IO-’ mbar. An internal liquid nitrogen cold trap was used during the measurements to improve the quality of the vacuum: this leads to a drastic reduction of the carbon deposition rate [28]. The unavoidable hydrocarbon contamination from atmosphere and possible further beam induced carbon deposition present at the sample surface were estimated by NRA, using the 12C(d, p)13C reaction in the same conditions as for the “Q measurements mentioned above. Absolute “C coverages may be determined with an oxygen standard using the data of Davies and Norton [29]. In our preliminary experiments it was soon apparent that carbon deposition during the measurements had a far from negligible effect, in spite of the precautions taken, which were sufficient in our previous resonance studies at higher energies. This may be due to two causes: the large charge required to record each point, 20 kc, because of the low cross section involved, and the large value of dE/dx around 150 keV that entails a much stronger sensitivity to contamination than at higher energies and which might also enhance carbon deposition. A fresh target point was therefore used after each energy step in the critical regions of the excitation curves, where the yield varies rapidly with energy. The cy particles were detected with an annular detector to maximize the solid angle to compensate, as far as possible, for the low intensity of this resonance. The layout of the detector setup is shown schematically in fig. 1. The 3 cm2 detector, with a 4 mm diameter hole, is placed at 15 mm from the sample resulting in a detection cone with a half vertex angle of 350; increasing this angle, i.e., decreasing the distance would result in a degradation of the fy particle peak shape. The effective solid angle was 0.93 sr. A copper cover facing the beam, which protects the detector from being hit by incoming protons, supports a 3 mm inside diameter metallic tube itself protected by a tantalum diaphragm of slightly smaller diameter. This tube is surrounded by a thin Mylar foil to exclude any electrical contact with the detector. The protons backscattered by the target were stopped by a 3 km thick Mylar foil stretched in front of the detector. The Mylar foil was actually glued with cyanoacrylate onto a nylon cap so as to remain electrically floating, its self-charging by the secondary electrons from the target acting as an efficient electron suppressor. A small, thin stainless steel ring was glued in the center of the Mylar, facing the detector. After

312

G. Battistig et al. / Width of the “O(p, a)15N resonance Annular detector

1200

I

-5

,

,

I

I ,

0

,

10

5 E-E,/,

Nylon cap Fig. 1. Schematic plan of the annular detector setup; drawing not to scale.

,

,

,

15

[keVI

Fig. 2. Excitation curves for two uniform Ta,O, targets labelled to 98% I80 . Solid angle 0.93 sr; 20 p,C per point. Origin at the mid point E,,, of the rise.

3. Results and interpretation

the cyanoacrylate had set, the Mylar was pierced. The tension of the Mylar foil was sufficient to press firmly the thin ring against the short nylon ring shown in fig. 1, to prevent any backscattered proton from reaching the sensitive area of the detector, while the stainless steel ring remains isolated from the detector housing. This delicate assembling was the only critical part of an otherwise classical experimental setup: the smallest gap is enough to induce a huge proton counting rate producing unwanted background counts or, if large enough, blocking completely the electronics. In this geometry, protons up to an energy of 300 keV were safely stopped by the Mylar foil. The detector assembly could be moved in both the X and Y directions to allow for a precise centering of the hole around the 2 mm diameter beam to ensure correct current integration. This centering was checked by monitoring the current possibly induced by any beam portion grazing the copper tube. A classical electronic setup was adequate for the small count rates involved. The spectrum of the 3.1 MeV a particles on the average was rather broad due to the bad geometry of detection. Nevertheless a welldefined peak was observed with a small low energy tail that reached zero well above the noise induced tail: we had no problem integrating the peak area within a well chosen window and counting the a particles safely and reproducibly. In the crucial experiments with very low numbers of counts, we recorded spectra for each energy step to be sure of ruling out the possibility of any spurious counts.

An overall view of two thick target excitation curves is shown in fig. 2. One is well saturated with a long plateau and a width at half maximum of 10.5 keV, while the thickness of the target for the second was chosen in such a way that saturation is just reached. The details of the low energy tail of these curves are not shown in this figure; they play a central role in the

resonance width determination as shown below. From the widths and the shapes of the high energy tails of these curves we could extract the experimental d E/dx value and the straggling parameter for protons near resonance energy in Ta,O,. These two parameters are used in the theoretical calculation of excitation curves for interpreting the data both for the width determination and for depth profile extraction. Let us emphasize that, as the isotope effect on the slowing down process is negligible, the ‘a0 concentrations have no influence on these constants provided that the thicknesses are expressed in units other than mass/area. The 12% to 88% rise of these curves is 520 eV wide. The beam energy spread measured experimentally by sampling the signals from the capacitive pick-off plate [28] was = 80 eV FWHM, with a nearly Gaussian distribution. The Doppler broadening due to the thermal agitation of the “0 atoms, calculated at room temperature with the classical formula from kinetic theory [4,28] is = 50 eV FWHM. We have taken the total energy spread, as seen by the reacting 180 nuclei, as Gaussian with width r= 100 eV. Fig. 3 shows a first approach towards extracting the resonance width r from the data. In this “naive” interpretationowe try to fit the leading edge of the curve for the 170 A thick target by the convolution of a step function with a Gaussian and with Breit-Wigner line shapes of in-

G. Battistiget al. / Widthof the “O(p, n) 15Nresanance

o.020 2

1QOO

f fp.2

373

152 kev protons

in CN,

”

P-63

800

+j

600

ii 0

400

- 0.005

200

0

-2.0 -1.5

-1.0

-0.5

E-h/a

1.0

0.0

1.5

[kevl

Fig. 3. “Naive” i~te~retat~o~ of the rise of the excitation curve for the 170 A thick target: the sofid lines correspond to Breit-Wigner resonance shapes with increasing f values as indicated.

creasing I”“. It is clear from the outset that r cannot exceed 200 eV. However fig. 4 shows that at low energies the experimental points lie even below the curve corresponding to r = 100 eV. On the other hand the rise towards the saturation value in fig. 3 is slower than the curve labeled 200 eV. Clearly a more sophisticated attempt is necessav to explain the resdts. In a more elaborate approach we took into consideration the ever present hydrocarbon contamination on the surface of the targets. This was a standard practice in our preceding studies of the Lewis effect [4,7,28] or of narrow resonance widths, such as that occurring in “N(p, oy)“C at 429 keV with r= 120 eV [30]. The energy straggling distributions for 352 keV protons

40 3 30 S s 20

10

0

-6

-4

-2

0

Fig. 4. Detail of the low energy tails of the curves in fig. 3, Faint clusters correspond to several measurements at the same energy.

n nnn

1.0

0.5

Energy

Loss [keV]

Fig. 5. Energy staggling distributions catculated with the stochastic theary of energy toss for 152 keV protons having crossed hydrocarbon contamination layers of increasing thicknesses, assumed to have the average chemical composition CH,. Note the strong asymmetry showing up for the thinnest layers. The curves are normed to the same area.

crossing hydrocarbon layers of increasing thicknesses were therefore calculated using the stochastic theory of energy loss presented in [4,7] and which was more recently further developed 1311 and implemented with the PC program SPACES [32]. The contamination layers were assumed to have the average chemical composition CII, , the corresponding dEJdr vaiue being taken from the compilation [33] and Bohr straggling being considered for this low Z medium. Fig. 5 shows a set of such curves. Two points should be emphasized: the curves for the smaller thicknesses are most asymmetrical; they are very broad, illustrating the exceptional polendial depth sensitivity of this resonance, as anticipated. Next the ideal infinite target yield curve, 1_(u) (u being the energy loss 1, i.e., the Lewis effect, was calculated for Ta,Q, at 152 keV using the same theory and program, with the parameters extracted from fig 2, as mentioned above. Let us recall that I,(u) is the sum of the autoconvo~ut~ons of the normalized collision spectrum f(u) of the protons with the eiectrons of the medium: Yu> = Xf(u)*“. A set of excitation curves was then computed by folding into ZJu> the Gaussian defined above, a Breit-Wigner line shape of width r and an energy straggling distribution of the type in fig. 5 corresponding to a thickness T. The best combination of r and T fitting the experimental results was then sought. Due to the very different shapes of the pairs of curves considered, the coupling between the two is not too strong. In fact the number of the possible ~mbinat~ons narrows down when the fit of the 5% to 95% portion of the rise is attempted. A 0.4 ng thick contamination fayer turned

374

G. But&& et al. / Width of the “O(p, (r)tsN resonance

out to be optimal, especially to fit the rise towards the saturation value, while some liberty still remained for r. It is important to underline that the choice of the contamination layer is not critical with respect to the determination of r. The best fits are shown in fig. 6, which also contains the calculated Lewis effect for r= T = 0,i.e. for a contamination free sample as it would be observed in ultrahigh vacuum and for an infinitesimally narrow resonance. The shift induced by the contamination layer should be noted. The thickness of this layer was measured using the ‘*C(d, p)13C reaction, as described above. A thickness of the order of = 0.3 kg was found, in reasonable agreement with our assumptions, considering the possibility of other contaminations not containing carbon. From fig. 6 it would appear that the best fit is obtained for r= 100 eV. However the details of the low energy tails shown in fig. 7 seem to contradict this conclusion: more than 1 keV below E, the experimental points lie systematically under the P = 100 eV curve. An attempt to solve the conflict by considering a possible thickness nonuniformity of the contamination film failed to solve the problem. A quite different philosophy of interpretation of the data was therefore applied here. Instead of trying to fit the bulk of the rise, we may concentrate our attention on the low energy tail, ensufficiently far from E,, that the contamination, ergy spread, etc., have practically no influence on the excitation curve, now entirely dominated by the BreitWigner shape of the tail of the resonance yield. Such a technique has been applied by Damjantschitsch et al. f341 to determine the width of the ‘H(‘5N, ay)“C

1400

I,,/,,,,,,1,,/

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,

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1200 -

-

1000 3

800 -

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l

170 f TazlsO, Gaussian: G=lOO eV

:

Contamination

T=0.4 /.Jg CH,

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I I,, -2.0

-1.5

-1.0

-0.5

0.0

E-E,

[keV]

0.5

I,

1.0

I,,

1.5

Fig. 6. Best theoretical fits for the experimental curve in fig. 3 for two possible resonance widths.The origin is at the resonance energy E, = 152 keV. The sharply peaked curve corresponds to the Lewis effect calculated without hydrocarbon contami~tion and for f = 0. Note the shift of the excitation curve due to the hydrocarbon ~ntamination.

Gaussian: G=lOO eV s

30

2

Contamination T=0.4 pg CH,

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u” 20

100 eVu/

-6 Fig. 7. Detail of the low 0, 1,2, . . . counts may be corresponding

4

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-2 -4 0 energy tails in fig. 6. Note that read off from the point clusters to the same energy.

resonance at 6.35 MeV, obtaining identical results to those from the inverse reaction studied in [30], as mentioned above, where the bulk of the thick target yield curve was fitted. This principle is particularly well adapted to the present work since there is no 01 particle background in our experiments, in contrast to the case when y-rays are detected: in fact even for large beam charges no (Y counts were observed when bombarding natural tantalum oxide films below the resonance. The Iow energy tail of the excitation curve was therefore investigated with special care, at least three measurements being made at the same energy in each run, as represented by the point clusters in fig. 7. In a first experiment we tried to estimate far from the resonance, below 146 keV, the counts due to the continuum in the cross-section curve reported in ref. [21]. Let us note that since the yield varies very slowly in this region, large energy steps may be chosen; morcover carbon build up has here a negligible detrimental effect. Let us also observe that the excitation curve step height across the resonance is independent of thickness, provided that saturation is reached, while the yield from the continuum is proportional to thickness. It is for this reason that we used the thinnest possible target, still giving rise to saturation, for investigating tee resonance yield curve, a rather thicker target of 595 A being used to estimate the continuum. Between 140 keV and 146 keV (- 12 keV to - 6 keV on the scale of fig. 7) this target produced on the average = 1.5 coynts per 20 PC, equivalent to = 0.5 counts for the 170 A target for which we analyse the data, and in agreement with the cross-section determined in 1211.It appears clearly in fig. 7 that the experimental points below - 1 keV are scattered around the curve calcu-

lated four T = 50 eV. Hence using the ~r~~t-Wj~n~r shape criterion, the best vafue of the resonance width seems to he = 50 eV. A closer look at the points and the fact that we did not subfraet the slight ~o~fribntjon from the co~f~n~um, suggests Chat r might even be somewhat smafler, around 30 eV. The concfusions from the fits of the bulk of the ~~jfat~o~ curve and of ifs taiI are ~v~d~nt~y in conflict, ~ow~v~r~ white a slight negative: shift in energy of the cizfculated curves in fig. 7 may produce a better fit with the curve labeled 50 eV in the region around -0.5 keV, no reasonable shift can improve the fit of the tail with the curve labeled 100 eV. ~an~i~~~~~~the various errors that may affect otl~ aS@%iS we may conclude by stating that the pnost ~~o~~~fe vaitle of i‘ is 50 eV, while neither = 30 eV nor = 100 ev may be unequivocally excluded.

Since this narrow resonaffce is ~n~~r~~pns~~ on B small continuum, it may be argued that there could be a destructive interference effect that would lower the curve labeled 100 eV in fig. 7. We believe that this can he ruled out. First our measurements were averaged over Iaboratory detection angles be~~~~ = 145 D and = 170” (fig. 11, which should smear CM such effects. Second any interference seems u~~~k~l~ at distances exceeding 20 r, especially since the continuum is extremely smalf, with the ratio af the counts on the pbteau to those ~o~espa~din~ to the ~o~f~nuum being = BOO, Ey suggesting the poss~bi~~~ of a narrower resonance we imply an even smafter ~r~hah~~~~ of alf i~~~~f~r~~c~extending so far from E,, Does our interpretation of the tail region in fig, 7 based on very small numbers of counts make sense? Our argument was actually to say that the excitation curve dies out so fast below E, that its width must be smak Qur problem arises from the faef that the crosssectians observed being low and our beam currenf being limited, we recorded very small numbers in the region of interest. For such small numbers n the usual estimation of the error as i JZ has no meaning, in ~art~~n~ar for p1= 0. The question may he phrased in fact as: what is the ~robabi~~~ that the ~~k~ow~ mead vaIue p~1of a Poisson counting process exceeds a number m, knowing that a number of counts n was recorded? Let us call g(n: ml the F&son pr~babi~j~ of observing a number n in an Ex~~~~~~nt, the mean ~nrnb~~ being known to be m, We have g(n; ml = exp(--nr) m”,k!; the function g(n; rn) is normalized to 1 for both the discrete variable n and the continuous variable m. We may therefore consider g(n; ml as a ~robabi~i~ density in the variable ~?a. According to

general pri~~~~~~s expounded for example in /X$1, we may look at g(pl; m) as the probability density of the unknown mean value M, knowing the outcome rt uf the rne~~~rn~nt~ It should be underlined that the most probable value of m is then it. The ~r~~ab~li~ of m exceeding m. is then the integral of gfn; ml over nz from m0 to m. For exampfe if ff =O this ~r~ba~~~~f~is expC--m& for this value to be I/3, corr~spo~djr~~ to the usual &tr criterion, mg = 1.1. Thus an ind~v~du~~ Count. R = 0 might weif correspond actually to a value m exceeding I., We may carry out such c~~culat~~~s fo:or the large n~rn~~r af points in fig 7 Iying below the curve Iabeled IO0 eV. However, as these paints arise from ind~~~~d~~t measurements, the overall ~r~~~h~~” ity that the actual values corresponding to them are all shifted upwards is the product of the ~rohabi~ifi~s calculated in this way: this probab~~~~ is therefore: very small and our i~t~rpr~tat~on seems reasonable.

Whatever the precise value of f is, the above results illustrate the exceptional surface s~ns~t~v~t~and depth resolution that may be associated with this resonance. Its fuXl potential cannot be taken adventure of using a Van, de Graaff acceferafor or an ~r~~na~ vacuum chamber+ A high stabifity, high pro&m eurrebt ian ~~~~~~~~~~~~type machine would be ideat ta carry out both a totally conctusive resonance width measurement and the depth propping experiments that will be described in part II. af this paper, especially if it was caupfed to an ulfrahi~h vacuum chamber. In fact much larger beam currenfs than availabfe to us may be used for bornb~rd~~~ targets not too sensitive to ~~~i~tio~ damage 8s the heating capabili~ of such low energy beams is small. This may compensate for the only shortcoming of this resonance: its tow intensity. After we realized how narrow this ~~ona~~~ is a& fhat our ~~~~rim~nta~ setup is ill adapted to get the best out nf such experiments, contact was ~~tabiished with the lcsliinsccr group who discavered &is resonance tweive years ago [211, This group has recently built exactly the kind of low energy accelerator based facility that we d~s~rib~d above as idea& presented in r&Z>f%f, which also reports on very high resolution Lewis effect rneasur~m~~ts in UHV on (p, y) resonances. Cooperation in the field of high r~salutio~ I80 depth ~r~fil~~~, in particular with C. Ralfs and W.H. Schuhe, is ctsnsidered to be promoted, while the UHV facility wcmld be equipped with large solid angie OLparticle d~f~ct~~n ~apab~~~fy.In the meantime an aftempf to measure the width of this resonance through the gp, r> channel using both a thin gas target and our IgQ sabered Ta2U5 targets is planned.

G. Buttistig et al. / Width of the “O(p, (r)‘,‘N remnance

316

Acknowledgements The authors wish to thank J. Moulin for his invaluable help in designing and building the special annular detector holder used in this work, as well as for technical assistance during the measurements. They are grateful to A. Laurent who contributed with ah his knowledge and experience to the ‘“0 enriched water purification and transfer operations as weti as, with C. Ortega, ta the anodic oxidation experiments. E. Girard was always helpful when electronic problems showed up. Enlightening discussions with J.-P, Dedonder and I,. Valentin on nuclear physics related aspects of this work are gratefully acknowledged. We also thank W.H. Schulte for discussions and for favouring the cooperation between our groups.

References RI 6. Amsel and G. Bishop, Phys. Rev. 116 (1961) 957.

PI G. Amsel, Thesis, Universite d’Orsay, France (1963) and Annales de Physique 9 (19641 297.

RI K.L. Dunning, Ph.D Thesis, Washingtan

DC, USA, (1968). [41 B. Maurel, Thesis, Universite de Paris, France (19801. [Sl G. Amsel and D. Samuel, Anal. Cbem. 39 (1967) 1689. w Ion Beam Handbook for Material Analysis, eds. J.W. Mayer and E. Rimini {Academic Press, New York, 1977) p. 163. 01 3. Maurel, G. Amsel and J.P. Nadai, Nucl. fnstr. and Meth, 197 (19821 I. I81 G. Amsel and D. Samuel, J. Phys, Chem. Solids 23 f1962) 1707. ml J.W, Butler and H.D. Hofmgren, Phys. Rev. 116 (19.59) 14859. [IO1 R.S. Alwitt, C. Ortega, N. Thorne and J. Siejka, J. Electrochem. Sot. 135 (19881 2695. [I11 C. Ortega, and J. Siejka, J. Electrochem. Sot. 129 (19821 190s. [I21 J. Perriere and J. Siejka, J. Electrochem. Sot. 130 (1983) 1260. 1131 J. Perriirre, J. Siejka and R.P.H. Chang, J. Appl. Phys. 56 (198412716. [I41 B. Pelloie, Thesis, Universitb Paris VII, France (1987). fl51 M. Berti, L.F. Dona delie Rose, A.V. Drigo, 6. Cohen, J.

Siejka, G.G. Bentini and E. Jannitti, Phys. Rev. B34 (1986) 2346. 1161 C. Ortega, A. Sacuto, J. Siejka, I. Trimaille and G. Vizkelethy, KBA-10 Meeting (July 1991). 1171 1. Montero, B. Pelloie, J. Perrigre, J.C. Pivin and J.M. Albelta, J. Electrochem. Sec. 136 (198% 1869. 1181 E. Rosencher, A. Straboni, S. Rigo and G. Amsel, Appl. Phys. Lett. 34 (19791254. fl91 S. Rigo, Silica films on silicon, in: Instabilities in silicon devices, eds. G. Barbottin and A. Vapaille (Elsevier (North-Holland), 19861 pp. 5-100. [20] M.P. Murrel, C.J. Sofield and S. Sugden, submitted for publication in Philos. Mag. [21] H. Lorenz-Wirzba, P. Schmalbrock, H.P, Trautwetter, M. Wiescher, C. Rolfs and W.S. Rodney, Nucl. Phys. A313 (19791346. [22] J. Siejka, J.P. Nadai and G. Amsel, J. Electrochem. Sot. 118 (19711727. 1231 G. Amsel, J.P. Nadai, C. Ortega and J. Siejka, Nucl. Instr. and Meth. 149 09783 313. 1241 6. Amsel, C. Battistig and A. Laurent, to be published. t2Sl J.P.S. Pringle, J. Etectrochem. Sot. 120 (1973) 1391. [26f G. Amsei, J.P. Nadai, E. d’Artemare, D. David, E. Girard and J. Moutin, Nucl. Instr. and Meth. 92 (1971) 481. (271 G. Amsel, E. d’Artemare, and E. Girard, Nucl. Instr. and Meth. 205 0983) 5. [28] G. Amsel and B. Maurel, Nucl. Instr, and Meth. 218 (19831 183. [291 J. Davies and P.R. Norton, Nucl. Instr. and Meth. 168 (19801611. 1301 B. Maurel and G. Amsel, Nucl. Instr. and Meth. 218 (1983) 159. f31] G. Amsel and 1. Vickridge, Nucl. Ins&. and Meth B45 (19901 12. [321 1. Vickridge and G. Amset, Nuct. fnstr. and Meth, B45 f 1990) 6. 1331 CF. Williamson, J.-P. Boujot and J. Picard, Rapport CEA-R 3042 (1966). [34] H. Damjantschitsch, M. Weiser, G. Heusser, S. Kalbitzer and H. Mannsperger, Nucl. Instr. and Meth. 218 (1983) 129. [351 D. Taupin, Probabilities, Data Reduction and Error Analysis in the Physical Sciences (Les Editions de Physique, Les Ulis, France, 19881 pp. 47-51. 1361 S. Wiistenbecker, H. Ebbing, W.H. Schulte, H. Baumeister, H.W. Becker, B. Cleff, C. Rolfs, H.P. Trautvetter, G.E. Mitchell, J.S. Schweitzer and CA. Peterson, Nucl. fnstr. and Meth. $4279 fl989f 448.