- Email: [email protected]
A setup for simultaneous many-angle measurements of elastic backscattering cross sections
a
Nuclear Instruments and Methods in Physics Research A 376 (1996) 185-191
NUCLEAR INSTRUMENTS & METHODS IN PHVSICS RESEARCH SectconA
. _-
33 fi!!!il EISEVIER
A setup for simultaneous many-angle measurements backscattering cross sections
of elastic
M. Chiari, L. Giuntini, l?A. Mand6*, N. Taccetti Dipartirnento
di Fisica
dell ‘Universit&
Firenze,
and Istifuto Nazionale
di Fisica Nucleare,
Sezione di Firenze.
Italy
Received 22 January 1996 Abstract A scattering chamber is described, which was constructed and installed at the KN3000 Van de Graaff accelerator in Florence, for a systematic study of proton and alpha elastic backscattering cross sections on light nuclei, as a function of both bombarding energy and scattering angle. Sixteen silicon detectors. which can be cooled down to LN, temperature, have been mounted at backward angles from 95” to 170”. Test measurements show that an overall accuracy of the order of l-2% is attainable for the cross section values. These measurements also point out that special care should be devoted to the determination of the effective target thickness under beam bombardment.
1. Introduction
2. Scattering
The knowledge of elastic backscattering cross sections of light bombarding particles on light nuclei -for which large deviations from the Coulomb interaction behaviour may occur - is a piece of experimental information of the utmost importance, both for the investigation of the nuclear structure, and for the quantitative use of backscattering spectrometry as an analytical tool in the continuously growing field of applied nuclear physics [l-3]. The available data on such elastic backscattering cross sections are mostly referred to limited bombarding energy ranges and often to a single scattering angle [4]. In view of this, we believed it worthwhile to undertake a systematic investigation, starting with proton scattering cross sections on nuclei from carbon to calcium, in the energy range 0%3.0MeV and with a high-granularity coverage of the backward angles. This work concerns the construction of a scattering chamber just devoted to this kind of measurements and its installation on a beam line of the KN3000 Van de Graaff accelerator in Florence. The chamber allocates 16 particle detectors covering the backward angular range from 9.5” to 170” in 5” steps. In the perspective of use for Rutherford backscattering measurements, LN2 cooling of the detectors has been provided, which makes it possible to achieve a good energy resolution.
Fig. 1 shows pictures of the upper lid and of the inside of the chamber, to which reference will be made in the following. The chamber is made of stainless steel and its inner diameter is 400 mm. All the elements defining the scattering geometry are connected to the upper chamber lid. namely: the input and exit beam collimators (1 mm diameter, 320 mm apart from each other), the target holder and rotator, and the detector collimators assembly. They are kept thermally isolated from the cryogenic structure supporting the detectors (mounted on the lower lid of the chamber) to ensure a scattering geometry independent of the temperature of the detectors. The target holder is equipped with a bellows-coupled linear slider, making the selection amongst five target positions possible without breaking the vacuum. One of the positions is usually left blank for beam alignment. The holder may rotate around a vertical axis passing - orthogonally - through the beam direction within 20.1 mm. The angular position of the rotator is measured to be better than 0.1” and is reproducible to the same accuracy. Detector collimators are placed at 138.0 mm from the beam spot on the target. The effective scattering angles. corresponding to the centers of the detector collimators (apertures of 1 mm diameter have been used at this stage) have been verified by means of a laser beam aligned through the input and exit collimators, and of a mirror mounted on the target holder, with the reflecting plane containing the rotation axis. We estimate an uncertainty of
* Corresponding author. Tel. f39 330. e-mail: [email protected]. 0168-9002/96/$1.5.00 Copyright PII SO168-9002(96)00176-3
55 2307 776, fax +39 55 229
0 1996 Elsevier Science B.V. All rights reserved
chamber and detector mount design
186
M. Chick
et cd. I Nucl. Irrm.
md Mrth.
in Phys. Rrs. A 376 (19961
185-191
Fig. 1. (a) View of the upper lid of the chamber: A) beam input collimator; B) detector collimators; C) cylindrical guide: D) target holder: E) beam exit collimator plus forward scattered beam trap. (b) Inside of the chamber, as seen from the same direction of part (a), showing the detector bank (with the PTIOO resistor next to the copper braiding), the cold finger connection and the electrical feedthroughs.
M. Chiari
et al.
I Nucl. Insir.
and Meth.
t-0.1” in the determination of the actual scattering angle 6. By the same procedure, the deviations from coplanarity for the centers of the collimators has been verified to be less than 20.2 mm. The 16 detectors (manufactured by Hamamatsu) are silicon PIN junction “bare chips” of 10 X 10 mm’ active area and 300 km thickness. A cryogenic mount has been provided, to make LNZ cooling possible, as shown in the lower part of Fig. I. The detectors are mounted on an aluminium support. connected to the lower chamber lid by means of a stainless steel tube (32 mm diameter, 70 mm height, 0.1 mm thickness) which acts as a thermal decoupier. The cold finger is connected through a large-section copper braiding to the support of the detectors. The temperature of the support is measured by a PTlOO resistor: temperature monitoring is useful in the warm-up phases to avoid moisture contamination of the detectors’ surfaces by an early ventilation of the chamber. The mechanical connection of the individual detectors to the support is crucial, since the back contact of each chip with the support should not get loose. even over a large number of temperature cycles, to ensure both electrical grounding and good thermal contact. However, in a very tight fitting, detectors may be damaged during the thermal cycles by the mechanical stress induced by the different thermal coefficients of the surrounding materials. For instance, serious problems have been experienced in early attempts to keep the detectors in place by a conductive glue. The adopted solution, shown in Fig. 2, proved to
in Phw.
Re.r. A 376 (1996)
185-191
safely withstand thermal cycles with no problem at all. while keeping a reliable contact. Provision is also made for an easy installation - on the upper lid - of four more detector-collimator systems, kept at room temperature and placed at the forward scattering angles of 20”, 40”, 60”, 80”. As will be discussed in Section 3.3. this makes it possible to measure the target thickness from the yield of pure Coulomb scattering, even in the case of the lighter target nuclei which are going to be investigated (C, N, etc.). Pumping is accomplished by means of oil-free systems, to avoid both contamination of the passivated surfaces of the cold detectors and carbon build-up on the target. High vacuum is reached by means of a Turbo-Spiro pumping system, working on ceramic ball bearings and backed by a three-stage rotary pump with self-lubricating graphite vans. Steady-state high vacuum is maintained by a cryogenic head, coupled to the chamber through bellows for mechanical damping. All the sealings are in metal: copper gaskets for the ConFlat@ flanges, tin wire for the upper and lower lids.
3. Implementations for absolute measurements elastic cross sections
contact
0 I
Aluminium Glass fiber n Silicon Oxide
Fig. 2. View of a detector mount. In the blow-up, showing how the detector is kept in place.
a side section
of
To obtain accurate absolute cross section data, the following requirements are to be met: - collection of sufficient statistics in the peak integral of the scattered particles; _ accurate knowledge of live charge, solid angle subtended by each detector, target thickness. The intrinsic full-energy peak efficiency of the silicon detectors for proton or alpha detection is assumed to be equal to I at the particle energies we are dealing with. 3.1. Beam alignment procedure and measurement charge
/
187
of live
The system of input and exit collimators, target holder and Faraday cup (FC), schematically shown in Fig. 3, is used both to align the beam through the chamber and to measure the beam current during the measurements. A stainless steel cylinder acts as a guide of the linear and rotary motions of the target holder, whose axis is thus constrained to the proper direction with great accuracy. The cylinder has a slot through which the beam impinges on the target and the backscattered particles reach the detectors: the slot is vertically centered around the beam spot on the target and horizontally spans an angle from 85” to 190” to the incoming beam direction. Downstream, on the backside of the cylindrical guide. a hole allows the beam transmission and four more holes of 1 mm diameter have been drilled in correspondence to the forward angles of the room temperature detectors. The cylindrical guide acts as a catcher both for sec-
+50
v
-1
-4
+50
+50
a)
v
lT
_I
23
+sov -1
-I
v
1
T
&
Faraday cup
exit
beamtrap
,
\,,,,
b) E
collimator
‘target
’
CylilldliCd
holder
guide
I I
I,?:
input
collimator
..>m -. ..- .-Y
I
I
-
Fig. 3. trodes: through through
Schematic diagram of the beam current collecting elec(a) vertical section passing through the beam axis and the axis of the target holder: (b) horizontal section passing the beam axis and orthogonal to the target holder axis.
ondary
electrons,
released
under
beam
bombardment.
and
for forward scattered beam particles. Cylinder and target holder are electrically connected together and isolated from the upper lid of the chamber by ceramic breaks. Input and exit beam collimators and FC are also isolated from the chamber by ceramic breaks. All these current-collecting electrodes are individually biased to a voltage of +50 V with respect to the chamber, strongly inhibiting the escape of secondary electrons. A very accurate beam alignment can be achieved: typically, with a 10 nA beam, residual currents on input and exit collimators are less than 0.1 nA. In the presence of a thick target. the beam current is read directly from the target holder plus cylindrical guide electrode. With thin targets, currents collected from the target holder plus cylindrical guide, exit collimator and FC are summed up. In order to collect all the forward scattered beam particles, a cylindrical beam trap has been added to the exit collimator, as shown in Figs. 1 and 3. The beam current from the charge-collection system feeds a Digital Current Integrator (DCI) characterized by a conversion rate of IO counts/nC. The accuracy of the conversion rate and its long term stability have been measured to be better than -CO.l% over a range I 1OOOnC. The DC1 digital output consists of positive TTL pulses which, when necessary, can be scaled down to I /256 in steps of 2. Direct or pre-scaled pulses are used to trigger sixteen tail pulse generators. The output signals of each of them are linearly mixed with the signals of a preamplifier. The decay time constant of the “charge signals” from each of the tail pulse generators is adjustable to strictly mimic the signals of the corresponding preamplifier. Their amplitude are also individually adjustable. In this way a “live-charge peak” is produced in each spectrum. The “charge-signal mixing” procedure, automatically taking into account dead-time and pile-up effects, makes accurate measurements of live charge possible. In fact, the charge signals undergo exactly the same processing as those following particle detection.
In order to get a rough count-rate equalization in different detectors, collimators having two different diameters have been mounted: namely, collimators with a diameter of 2000 pm for detectors from 95” to 130” and of 3000 pm for detectors from 135” to 170”. The solid angle subtended by each detector was calculated from the aperture area and distance from the beam spot of the corresponding collimator. As to the latter. even in the largely unrealistic case of a kO.25 mm lateral displacement of the beam, the effect on solid angle remains within +0.35% (the mean spot to collimator distance being 138.0 mm). On the other hand. the collimators have been drilled by reamers of 4 km tolerance and an accuracy better than that has actually been found by measuring under optical microscope several diameters per collimator. From these measurements, we assume a conservative uncertainty of +0.5% in the determination of solid angles. 3.3. Measurement
of’ target thickntm
For differential measurements of cross sections as a function of energy, very thin targets (self-supporting or on a backing) must be used to avoid integration over energy. For instance, if energy loss-induced integration is chosen to be kept below 5 keV for I MeV protons, low-Z targets should not exceed a thickness of 20-30 kg/cm’. At these values, the target thickness is not directly measurable with the desired accuracy of the order of 1%; moreover, its evolution under beam bombardment is quite unpredictable. Nevertheless. the target thickness can be deduced with the intended accuracy whenever it is possible to collect a peak of protons scattered by purely Coulomb interaction: in that case, since the cross section is known, the target thickness (pt) can be inferred once the solid angle AR and live charge Q are independently measured. It should be emphasized that in this way. rather than the values of the individual terms, the overall value of the product Ati . pt . Q is determined. As discussed in the preceding sections, the uncertainties in A.0 and Q have been estimated to be i-OS% and 20.1% respectively; it follows that, in principle. Pt can be inferred with an accuracy of about 0.5%:. besides the contribution of the peak integral statistics. This technique makes it possible to measure the effective local target thickness just pertinent to each measurement, since it automatically takes into account the thickness variations either induced by beam bombardment or associated with possible inhomogeneities and beam displacements. To point out the conditions under which this procedure can be safely adopted Fig. 4 shows the maximum scattering angle (19,,,,~)for a purely Coulomb interaction, as a function of the proton bombarding energy (Ep) for some target nuclei. The displayed curves, limited to the forward half plane, are based on the usual assumption of a minimum distance of approach of 3 nuclear radii [5]; only
M. Chiari
et (11. I Mrcl.
Instr.
and Mrth.
in Phys. Res. A 376 (1996)
KM I:.,
90
T()JJ
185-191
189
C
AU
.“‘.,
600
80
ml
70 60 50 40 30
0
--_r--
20
1
--Lq
-----,
1700
175”
-A-
2250
Channel number
10
oi 0.5
j
1
I
1
1.5
2
2.5
3
3.5
E, WV) E.g. 4.
-
,650
Maximum scattering angle
scattering in the forward half-plane. energy for different target nuclei.
G,,,, for a purely Coulomb versus proton bombarding
values of pairs (E,,. 8) falling below the curve labelled by the nucleus under consideration fulfill the required condition. This means, e.g.. that using a detector placed at 20”. the above procedure can be safely applied to the case of a thin C target up to a proton energy greater than 2 MeV.
4. Performance system
of the detectors and data acquisition
Signals from cooled silicon detectors are processed by home-made preamplifiers which consist of a charge integrating input loop which feeds, through a pole-zero network, a booster output stage. To minimize the input capacitance, each preamplifier. though mounted outside the chamber, is fitted in correspondence to the detector electrical feedthrough. Unipolar Gaussian shaping is performed by means of mod. 572 amplifiers (supplied by EG&G ORTEC): using a time constant of 2 p,s a noise FWHM of about 3.5 keV is found. Obviously, the contribution due to detection statistics should be summed up in quadrature: for instance. in the case of detection of 3 MeV protons. the statistics FWHM of 2.5 keV is to be added. thus producing a FWHM of 4.3 keV. Such energy resolution is partly masked in particlespectra collected under beam since the shape of a scattered particles peak actually depends also on target-induced effects (such as energy loss, straggling, surface roughness). kinematic spread and straggling in the entrance dead layer of the detectors (in our case, nominally 15OOi of SiO?). In practice, a very good FWHM has been still achieved even under actual measuring conditions. As an example, Fig. 5 shows the relevant portion of a spectrum obtained by bombardment with 3 MeV protons of a target of -50 pg/cm’ Au evaporated onto a thick polymeric sub-
Fig. 5. Spectrum of a 50 kg/cm’ Au layer on a thick polymeric substrate, detected at 170” scattering angle (3.0 MeV proton bombarding energy). The energy dispersion is -1.3 keVlch. The edges of carbon, nitrogen and oxygen of the polymeric substrate are also displayed.
strate (Upilex@). The overall FWHM of the Au peak comes out to be 7.8 keV, about 4 of which are accounted for by the target thickness itself. A value of about 4 keV for noise-plus-statistics FWHM is again obtained from the slope of the C edge after deconvoluting for the energy straggling in the overlying Au layer. Data acquisition is based on a system, manufactured by Silena, which provides I6 fully independent channels. Each of them consists of a 100 MHz ADC (mod. 741 I-S), followed by a Direct Memory Increment circuitry operating on one section (4096 addresses of 32 bit) of a four-section memory buffer card (MBC) which can be installed in any commercial tower PC. The home-made acquisition software was developed to drive up to six MBC, and can be easily upgraded to support more cards. An easy and fast on-line analysis of all spectra is possible.
5. Preliminary
tests under beam
Test measurements have been performed with a Au target - for which backscattering of 3 MeV protons is due to purely Coulomb interaction at all detection angles with the aim of establishing the accuracy to which absolute measurements of elastic backscattering cross sections can be obtained with the apparatus described in the preceding sections. Following a standard routine, the energy of the proton beam has been previously calibrated over the range 0.53.0MeV by means of some selected resonances in the (p. y) and (p, p’y) reactions on “Al. After the calibration, the bombarding energy is known to better than 2 keV A first measurement was made by bombarding a Au target of =I00 kg/cm’, evaporated on a Fotmvar@ foil of =I5 &cm’, with a proton beam of 3 MeV energy and IO nA current. After few minutes of bombardment, the Formvar foil is locally vaporized, so that the peak corresponding to scattering on Au is largely pre-eminent in the collected spectra. Measurements were performed with a set
190
M. Chinri rt ul. I NW/. Instr. and Meth. in Ptty.\. Rex. A 376 (1996) 185-191
Table I Normalized integrals (arbitrary units) of the Au peaks obtained at four different scattering angles by 3 MeV proton bombardment of a 100 pg/cm’ target. Only the statistical uncertainties on the peak integrals are given
95” 110” 135” 170”
I .000?0.006 0.993-c0.007 I .005 +0.006 1.002~0.007
of four detectors placed at the backscattering angles of 95”, 1lo”, 135”, 170”. During this run, the measured value of the beam current was unreliable because of a leaky electrical feedthrough; these data have been therefore used only for a check of the angular scaling of the Au peak integrals. Since the differences of the measured live time among the four acquisition channels came out to be less than 0. I ‘%, no live charge correction was in fact necessary. After normalization for the different solid angles, the Au peak integrals (I) directly display the Rutherford behaviour, (sin 6/2))J. as shown in Table 1. Once the beam current was correctly measured, further spectra were recorded in order to ascertain the accuracy attainable in absolute measurements of cross sections. As an example, we discuss the data collected with the detector placed at 170” and bombarding the 100 Kg/cm’ Au target with a beam of 10 nA. at proton energies of 2.4 and 3.0 MeV The relevant parts of the spectra are shown in Fig. 6; they include the live charge peaks which have been used for determining both the integrated live charge and the electrical noise FWHM. By a minimum of xZ procedure, the Au peaks have been compared with Rutherford simulations based on pure Coulomb interaction (simulation code DVBS [6]). each time forcing the target tilting angle, the scattering angle, the subtended solid angle, the noise-plus-statistics FWHM and the integrated live charge to the measured values.
100000
Before discussing the comparison of simulations and experimental data, it must be anticipated that the currently used simulation codes-such as DVBS and the largely diffused RUMP [7] - may be faulty in the treatment of the energy straggling. since the latter is always considered to be of the Bohr type (apart from the possibility of introducing a scaling factor to the FWHM,,,,). This means that asymmetrical, long-tailed line shapes, characteristic of the Vavilov energy straggling regime in thin targets, cannot be reproduced. Under these conditions. when noise and statistics contributions are small. the Bohr straggling hypothesis leads to outstanding differences between the simulated and experimental peaks. In analysing peaks of good statistics, this has the consequence that, in spite of scaling the straggling FWHM to larger values than the FWHM,<,,,. the reduced xf,,, still remains remarkably above unity. The minimum of xz was sought by leaving the target thickness and the enhancement factor of the FWHM,<,,, as free parameters in the simulation. In Fig. 6, the simulated Au peaks corresponding to xl,, are superimposed to the experimental data. Although the general agreement looks good, the bad reproduction of the peak tails causes the reduced xi,, values to be considerably larger than unity (see Table 2). In Fig. 7, the ,y’ trend around its minimum is reported, for the measurement at 2.4 MeV, as a function of both thickness and straggling FWHM,c,,r enhancement factor. From these curves, which look substantially symmetrical, an uncertainty of ?2% (at 68% confidence level) can be inferred both for thickness and enhancement factor. With reference to the last column of Table 2, it is to be noted that the simulated Au peak integrals corresponding to XL” equal the experimental ones within one standard deviation, and that the agreement with the expected purely Coulomb character of the Au test measurements is achieved within a statistical uncertainty of 1%. Concerning the target thickness, it can be observed that the values reported in Table 2 for the measurements at 2.4
100000
r
0% on
1000 % 3 u
2350
2400 Energy (keV) a)
100 10
.. 1 L 2950
Q .= .
Au
10000
O P
.
,t8 ..I.0
. *
0
I :.,
~~-----
3000 Energy (keV) b)
Fig. 6. Relevant parts of the spectra at 2.4 and 3.0 MeV proton bombarding energy (part (a) and (b). respectively) on a 100 I*.glcm’ Au target on Formvar”. Detection angle is 170”. The backscattering peaks of Au and the “live charge” peaks Q are displayed. Also shown in open diamonds are the simulated An peaks at the minimum of x2,
M. Chiari et al. I Nucl. [email protected] Meth. in Phys. Rex. A 376 (1996) IM-191 Table 2 Parameters
given by the simulations
E,, [MeVl
Reduced
2.4 3.0
1.8 3.4
“X 6.00
3.00 2.00
.
r.
.. .
at the minimum
xi,,,
“x 6.00
of the reduced xZ value (see text)
FWHM,<>,r enhancement factor
Au target thickness
1.18?0.015 1.15zo.02
107.6?2.6 99.1 -t2.0
0.992-tO.012 1.012~0.013
Acknowledgement
7 1.
. ....... .
target thickness (pg/cm’)
‘,,,/I,,,
(I*g/cm’)
.:. 68%4.
1.00 1 102.0 106.0 110.0 114.0
I91
1.10 FWHM,,
1.20
1.30
enhancement factor
Fig. 7. Trends of the reduced xz around its minimum. as a function of the parameters target thickness and enhancement factor of the FWHM,,,,,. The results refer to the measurement at 2.4 MeV proton energy.
This work has been funded by Istituto Nazionale di Fisica Nucleare, Committee 3. and by the Italian Ministry of University and Scientific Research (grants 40%. project Use of small accelerators). We are deeply indebted to G. Poggi, who wrote the acquisition software. The technical support of M. Montecchi and A. Pecchioli, and of the mechanical workshop of the Physics Department (M. Falorsi, M. Merciai, B. Sarti and, in particular. A. Catelani) was decisive. Warm thanks are also due to V. Rigato and G. Manente, of the Laboratori Nazionali di Legnaro, for target preparation.
References and 3.0 MeV compare well with those obtained from the peak integrals, following the more direct procedure mentioned in Section 3.3, which provides more accurate values [( 106.6+ 1.2) kg/cm’ and (100.4? 1.2) kg/cm’, respectively] and is independent of the straggling regime. In any procedure is adopted, the difference case, whichever between the two measured thickness values comes out to be statistically significant, and this points out the importance of a simultaneous detection, whenever possible. of a purely Coulomb scattering in order to achieve the measurement of the effective thickness during each run (Section 3.3). As a conclusion. it can be said that the preliminary results show that absolute measurements of cross sections are indeed possible at a l-2’% accuracy level with the apparatus presented in this work. At the same time, they point out that the main limiting factor to reaching such an accuracy is represented by the knowledge of the effective target thickness under beam bombardment.
[I] E. Rauhala, Nucl. Instr. and Meth. B 40/41 (1989) 790. [2] M. Bozoian, K.M. Hubbard and M. Nastasi, Nucl. Instr. and Meth. B 51 (1990) 311. [3] J.M. Knox, Nucl. Instr. and Meth. B 66 (1992) 31. [4] J.R. Tesmer and M. Nastasi, Handbook of Modern Ion Beam Materials Analysis (Material Research Society, Pittsburgh, 1995). [5] J.A. Davies, W.N. Lennard and 1.V. Mitchell, Pitfalls in Ion Beam Analysis. in: J.R. Tesmer and M. Nastasi, Handbook of Modem Ion Beam Materials Analysis (Material Research Society, Pittsburgh, 1995). [6] V. Bohric and D.M. Shirokov, Nucl. Instr. and Meth. B 84 ( 1994) 497. [7] L.R. Doolittle, Nucl. Instr. and Meth. B 9 (1985) 344.
Nuclear Instruments and Methods in Physics Research A 376 (1996) 185-191
NUCLEAR INSTRUMENTS & METHODS IN PHVSICS RESEARCH SectconA
. _-
33 fi!!!il EISEVIER
A setup for simultaneous many-angle measurements backscattering cross sections
of elastic
M. Chiari, L. Giuntini, l?A. Mand6*, N. Taccetti Dipartirnento
di Fisica
dell ‘Universit&
Firenze,
and Istifuto Nazionale
di Fisica Nucleare,
Sezione di Firenze.
Italy
Received 22 January 1996 Abstract A scattering chamber is described, which was constructed and installed at the KN3000 Van de Graaff accelerator in Florence, for a systematic study of proton and alpha elastic backscattering cross sections on light nuclei, as a function of both bombarding energy and scattering angle. Sixteen silicon detectors. which can be cooled down to LN, temperature, have been mounted at backward angles from 95” to 170”. Test measurements show that an overall accuracy of the order of l-2% is attainable for the cross section values. These measurements also point out that special care should be devoted to the determination of the effective target thickness under beam bombardment.
1. Introduction
2. Scattering
The knowledge of elastic backscattering cross sections of light bombarding particles on light nuclei -for which large deviations from the Coulomb interaction behaviour may occur - is a piece of experimental information of the utmost importance, both for the investigation of the nuclear structure, and for the quantitative use of backscattering spectrometry as an analytical tool in the continuously growing field of applied nuclear physics [l-3]. The available data on such elastic backscattering cross sections are mostly referred to limited bombarding energy ranges and often to a single scattering angle [4]. In view of this, we believed it worthwhile to undertake a systematic investigation, starting with proton scattering cross sections on nuclei from carbon to calcium, in the energy range 0%3.0MeV and with a high-granularity coverage of the backward angles. This work concerns the construction of a scattering chamber just devoted to this kind of measurements and its installation on a beam line of the KN3000 Van de Graaff accelerator in Florence. The chamber allocates 16 particle detectors covering the backward angular range from 9.5” to 170” in 5” steps. In the perspective of use for Rutherford backscattering measurements, LN2 cooling of the detectors has been provided, which makes it possible to achieve a good energy resolution.
Fig. 1 shows pictures of the upper lid and of the inside of the chamber, to which reference will be made in the following. The chamber is made of stainless steel and its inner diameter is 400 mm. All the elements defining the scattering geometry are connected to the upper chamber lid. namely: the input and exit beam collimators (1 mm diameter, 320 mm apart from each other), the target holder and rotator, and the detector collimators assembly. They are kept thermally isolated from the cryogenic structure supporting the detectors (mounted on the lower lid of the chamber) to ensure a scattering geometry independent of the temperature of the detectors. The target holder is equipped with a bellows-coupled linear slider, making the selection amongst five target positions possible without breaking the vacuum. One of the positions is usually left blank for beam alignment. The holder may rotate around a vertical axis passing - orthogonally - through the beam direction within 20.1 mm. The angular position of the rotator is measured to be better than 0.1” and is reproducible to the same accuracy. Detector collimators are placed at 138.0 mm from the beam spot on the target. The effective scattering angles. corresponding to the centers of the detector collimators (apertures of 1 mm diameter have been used at this stage) have been verified by means of a laser beam aligned through the input and exit collimators, and of a mirror mounted on the target holder, with the reflecting plane containing the rotation axis. We estimate an uncertainty of
* Corresponding author. Tel. f39 330. e-mail: [email protected]. 0168-9002/96/$1.5.00 Copyright PII SO168-9002(96)00176-3
55 2307 776, fax +39 55 229
0 1996 Elsevier Science B.V. All rights reserved
chamber and detector mount design
186
M. Chick
et cd. I Nucl. Irrm.
md Mrth.
in Phys. Rrs. A 376 (19961
185-191
Fig. 1. (a) View of the upper lid of the chamber: A) beam input collimator; B) detector collimators; C) cylindrical guide: D) target holder: E) beam exit collimator plus forward scattered beam trap. (b) Inside of the chamber, as seen from the same direction of part (a), showing the detector bank (with the PTIOO resistor next to the copper braiding), the cold finger connection and the electrical feedthroughs.
M. Chiari
et al.
I Nucl. Insir.
and Meth.
t-0.1” in the determination of the actual scattering angle 6. By the same procedure, the deviations from coplanarity for the centers of the collimators has been verified to be less than 20.2 mm. The 16 detectors (manufactured by Hamamatsu) are silicon PIN junction “bare chips” of 10 X 10 mm’ active area and 300 km thickness. A cryogenic mount has been provided, to make LNZ cooling possible, as shown in the lower part of Fig. I. The detectors are mounted on an aluminium support. connected to the lower chamber lid by means of a stainless steel tube (32 mm diameter, 70 mm height, 0.1 mm thickness) which acts as a thermal decoupier. The cold finger is connected through a large-section copper braiding to the support of the detectors. The temperature of the support is measured by a PTlOO resistor: temperature monitoring is useful in the warm-up phases to avoid moisture contamination of the detectors’ surfaces by an early ventilation of the chamber. The mechanical connection of the individual detectors to the support is crucial, since the back contact of each chip with the support should not get loose. even over a large number of temperature cycles, to ensure both electrical grounding and good thermal contact. However, in a very tight fitting, detectors may be damaged during the thermal cycles by the mechanical stress induced by the different thermal coefficients of the surrounding materials. For instance, serious problems have been experienced in early attempts to keep the detectors in place by a conductive glue. The adopted solution, shown in Fig. 2, proved to
in Phw.
Re.r. A 376 (1996)
185-191
safely withstand thermal cycles with no problem at all. while keeping a reliable contact. Provision is also made for an easy installation - on the upper lid - of four more detector-collimator systems, kept at room temperature and placed at the forward scattering angles of 20”, 40”, 60”, 80”. As will be discussed in Section 3.3. this makes it possible to measure the target thickness from the yield of pure Coulomb scattering, even in the case of the lighter target nuclei which are going to be investigated (C, N, etc.). Pumping is accomplished by means of oil-free systems, to avoid both contamination of the passivated surfaces of the cold detectors and carbon build-up on the target. High vacuum is reached by means of a Turbo-Spiro pumping system, working on ceramic ball bearings and backed by a three-stage rotary pump with self-lubricating graphite vans. Steady-state high vacuum is maintained by a cryogenic head, coupled to the chamber through bellows for mechanical damping. All the sealings are in metal: copper gaskets for the ConFlat@ flanges, tin wire for the upper and lower lids.
3. Implementations for absolute measurements elastic cross sections
contact
0 I
Aluminium Glass fiber n Silicon Oxide
Fig. 2. View of a detector mount. In the blow-up, showing how the detector is kept in place.
a side section
of
To obtain accurate absolute cross section data, the following requirements are to be met: - collection of sufficient statistics in the peak integral of the scattered particles; _ accurate knowledge of live charge, solid angle subtended by each detector, target thickness. The intrinsic full-energy peak efficiency of the silicon detectors for proton or alpha detection is assumed to be equal to I at the particle energies we are dealing with. 3.1. Beam alignment procedure and measurement charge
/
187
of live
The system of input and exit collimators, target holder and Faraday cup (FC), schematically shown in Fig. 3, is used both to align the beam through the chamber and to measure the beam current during the measurements. A stainless steel cylinder acts as a guide of the linear and rotary motions of the target holder, whose axis is thus constrained to the proper direction with great accuracy. The cylinder has a slot through which the beam impinges on the target and the backscattered particles reach the detectors: the slot is vertically centered around the beam spot on the target and horizontally spans an angle from 85” to 190” to the incoming beam direction. Downstream, on the backside of the cylindrical guide. a hole allows the beam transmission and four more holes of 1 mm diameter have been drilled in correspondence to the forward angles of the room temperature detectors. The cylindrical guide acts as a catcher both for sec-
+50
v
-1
-4
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a)
v
lT
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-I
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Faraday cup
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beamtrap
,
\,,,,
b) E
collimator
‘target
’
CylilldliCd
holder
guide
I I
I,?:
input
collimator
..>m -. ..- .-Y
I
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-
Fig. 3. trodes: through through
Schematic diagram of the beam current collecting elec(a) vertical section passing through the beam axis and the axis of the target holder: (b) horizontal section passing the beam axis and orthogonal to the target holder axis.
ondary
electrons,
released
under
beam
bombardment.
and
for forward scattered beam particles. Cylinder and target holder are electrically connected together and isolated from the upper lid of the chamber by ceramic breaks. Input and exit beam collimators and FC are also isolated from the chamber by ceramic breaks. All these current-collecting electrodes are individually biased to a voltage of +50 V with respect to the chamber, strongly inhibiting the escape of secondary electrons. A very accurate beam alignment can be achieved: typically, with a 10 nA beam, residual currents on input and exit collimators are less than 0.1 nA. In the presence of a thick target. the beam current is read directly from the target holder plus cylindrical guide electrode. With thin targets, currents collected from the target holder plus cylindrical guide, exit collimator and FC are summed up. In order to collect all the forward scattered beam particles, a cylindrical beam trap has been added to the exit collimator, as shown in Figs. 1 and 3. The beam current from the charge-collection system feeds a Digital Current Integrator (DCI) characterized by a conversion rate of IO counts/nC. The accuracy of the conversion rate and its long term stability have been measured to be better than -CO.l% over a range I 1OOOnC. The DC1 digital output consists of positive TTL pulses which, when necessary, can be scaled down to I /256 in steps of 2. Direct or pre-scaled pulses are used to trigger sixteen tail pulse generators. The output signals of each of them are linearly mixed with the signals of a preamplifier. The decay time constant of the “charge signals” from each of the tail pulse generators is adjustable to strictly mimic the signals of the corresponding preamplifier. Their amplitude are also individually adjustable. In this way a “live-charge peak” is produced in each spectrum. The “charge-signal mixing” procedure, automatically taking into account dead-time and pile-up effects, makes accurate measurements of live charge possible. In fact, the charge signals undergo exactly the same processing as those following particle detection.
In order to get a rough count-rate equalization in different detectors, collimators having two different diameters have been mounted: namely, collimators with a diameter of 2000 pm for detectors from 95” to 130” and of 3000 pm for detectors from 135” to 170”. The solid angle subtended by each detector was calculated from the aperture area and distance from the beam spot of the corresponding collimator. As to the latter. even in the largely unrealistic case of a kO.25 mm lateral displacement of the beam, the effect on solid angle remains within +0.35% (the mean spot to collimator distance being 138.0 mm). On the other hand. the collimators have been drilled by reamers of 4 km tolerance and an accuracy better than that has actually been found by measuring under optical microscope several diameters per collimator. From these measurements, we assume a conservative uncertainty of +0.5% in the determination of solid angles. 3.3. Measurement
of’ target thickntm
For differential measurements of cross sections as a function of energy, very thin targets (self-supporting or on a backing) must be used to avoid integration over energy. For instance, if energy loss-induced integration is chosen to be kept below 5 keV for I MeV protons, low-Z targets should not exceed a thickness of 20-30 kg/cm’. At these values, the target thickness is not directly measurable with the desired accuracy of the order of 1%; moreover, its evolution under beam bombardment is quite unpredictable. Nevertheless. the target thickness can be deduced with the intended accuracy whenever it is possible to collect a peak of protons scattered by purely Coulomb interaction: in that case, since the cross section is known, the target thickness (pt) can be inferred once the solid angle AR and live charge Q are independently measured. It should be emphasized that in this way. rather than the values of the individual terms, the overall value of the product Ati . pt . Q is determined. As discussed in the preceding sections, the uncertainties in A.0 and Q have been estimated to be i-OS% and 20.1% respectively; it follows that, in principle. Pt can be inferred with an accuracy of about 0.5%:. besides the contribution of the peak integral statistics. This technique makes it possible to measure the effective local target thickness just pertinent to each measurement, since it automatically takes into account the thickness variations either induced by beam bombardment or associated with possible inhomogeneities and beam displacements. To point out the conditions under which this procedure can be safely adopted Fig. 4 shows the maximum scattering angle (19,,,,~)for a purely Coulomb interaction, as a function of the proton bombarding energy (Ep) for some target nuclei. The displayed curves, limited to the forward half plane, are based on the usual assumption of a minimum distance of approach of 3 nuclear radii [5]; only
M. Chiari
et (11. I Mrcl.
Instr.
and Mrth.
in Phys. Res. A 376 (1996)
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185-191
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scattering in the forward half-plane. energy for different target nuclei.
G,,,, for a purely Coulomb versus proton bombarding
values of pairs (E,,. 8) falling below the curve labelled by the nucleus under consideration fulfill the required condition. This means, e.g.. that using a detector placed at 20”. the above procedure can be safely applied to the case of a thin C target up to a proton energy greater than 2 MeV.
4. Performance system
of the detectors and data acquisition
Signals from cooled silicon detectors are processed by home-made preamplifiers which consist of a charge integrating input loop which feeds, through a pole-zero network, a booster output stage. To minimize the input capacitance, each preamplifier. though mounted outside the chamber, is fitted in correspondence to the detector electrical feedthrough. Unipolar Gaussian shaping is performed by means of mod. 572 amplifiers (supplied by EG&G ORTEC): using a time constant of 2 p,s a noise FWHM of about 3.5 keV is found. Obviously, the contribution due to detection statistics should be summed up in quadrature: for instance. in the case of detection of 3 MeV protons. the statistics FWHM of 2.5 keV is to be added. thus producing a FWHM of 4.3 keV. Such energy resolution is partly masked in particlespectra collected under beam since the shape of a scattered particles peak actually depends also on target-induced effects (such as energy loss, straggling, surface roughness). kinematic spread and straggling in the entrance dead layer of the detectors (in our case, nominally 15OOi of SiO?). In practice, a very good FWHM has been still achieved even under actual measuring conditions. As an example, Fig. 5 shows the relevant portion of a spectrum obtained by bombardment with 3 MeV protons of a target of -50 pg/cm’ Au evaporated onto a thick polymeric sub-
Fig. 5. Spectrum of a 50 kg/cm’ Au layer on a thick polymeric substrate, detected at 170” scattering angle (3.0 MeV proton bombarding energy). The energy dispersion is -1.3 keVlch. The edges of carbon, nitrogen and oxygen of the polymeric substrate are also displayed.
strate (Upilex@). The overall FWHM of the Au peak comes out to be 7.8 keV, about 4 of which are accounted for by the target thickness itself. A value of about 4 keV for noise-plus-statistics FWHM is again obtained from the slope of the C edge after deconvoluting for the energy straggling in the overlying Au layer. Data acquisition is based on a system, manufactured by Silena, which provides I6 fully independent channels. Each of them consists of a 100 MHz ADC (mod. 741 I-S), followed by a Direct Memory Increment circuitry operating on one section (4096 addresses of 32 bit) of a four-section memory buffer card (MBC) which can be installed in any commercial tower PC. The home-made acquisition software was developed to drive up to six MBC, and can be easily upgraded to support more cards. An easy and fast on-line analysis of all spectra is possible.
5. Preliminary
tests under beam
Test measurements have been performed with a Au target - for which backscattering of 3 MeV protons is due to purely Coulomb interaction at all detection angles with the aim of establishing the accuracy to which absolute measurements of elastic backscattering cross sections can be obtained with the apparatus described in the preceding sections. Following a standard routine, the energy of the proton beam has been previously calibrated over the range 0.53.0MeV by means of some selected resonances in the (p. y) and (p, p’y) reactions on “Al. After the calibration, the bombarding energy is known to better than 2 keV A first measurement was made by bombarding a Au target of =I00 kg/cm’, evaporated on a Fotmvar@ foil of =I5 &cm’, with a proton beam of 3 MeV energy and IO nA current. After few minutes of bombardment, the Formvar foil is locally vaporized, so that the peak corresponding to scattering on Au is largely pre-eminent in the collected spectra. Measurements were performed with a set
190
M. Chinri rt ul. I NW/. Instr. and Meth. in Ptty.\. Rex. A 376 (1996) 185-191
Table I Normalized integrals (arbitrary units) of the Au peaks obtained at four different scattering angles by 3 MeV proton bombardment of a 100 pg/cm’ target. Only the statistical uncertainties on the peak integrals are given
95” 110” 135” 170”
I .000?0.006 0.993-c0.007 I .005 +0.006 1.002~0.007
of four detectors placed at the backscattering angles of 95”, 1lo”, 135”, 170”. During this run, the measured value of the beam current was unreliable because of a leaky electrical feedthrough; these data have been therefore used only for a check of the angular scaling of the Au peak integrals. Since the differences of the measured live time among the four acquisition channels came out to be less than 0. I ‘%, no live charge correction was in fact necessary. After normalization for the different solid angles, the Au peak integrals (I) directly display the Rutherford behaviour, (sin 6/2))J. as shown in Table 1. Once the beam current was correctly measured, further spectra were recorded in order to ascertain the accuracy attainable in absolute measurements of cross sections. As an example, we discuss the data collected with the detector placed at 170” and bombarding the 100 Kg/cm’ Au target with a beam of 10 nA. at proton energies of 2.4 and 3.0 MeV The relevant parts of the spectra are shown in Fig. 6; they include the live charge peaks which have been used for determining both the integrated live charge and the electrical noise FWHM. By a minimum of xZ procedure, the Au peaks have been compared with Rutherford simulations based on pure Coulomb interaction (simulation code DVBS [6]). each time forcing the target tilting angle, the scattering angle, the subtended solid angle, the noise-plus-statistics FWHM and the integrated live charge to the measured values.
100000
Before discussing the comparison of simulations and experimental data, it must be anticipated that the currently used simulation codes-such as DVBS and the largely diffused RUMP [7] - may be faulty in the treatment of the energy straggling. since the latter is always considered to be of the Bohr type (apart from the possibility of introducing a scaling factor to the FWHM,,,,). This means that asymmetrical, long-tailed line shapes, characteristic of the Vavilov energy straggling regime in thin targets, cannot be reproduced. Under these conditions. when noise and statistics contributions are small. the Bohr straggling hypothesis leads to outstanding differences between the simulated and experimental peaks. In analysing peaks of good statistics, this has the consequence that, in spite of scaling the straggling FWHM to larger values than the FWHM,<,,,. the reduced xf,,, still remains remarkably above unity. The minimum of xz was sought by leaving the target thickness and the enhancement factor of the FWHM,<,,, as free parameters in the simulation. In Fig. 6, the simulated Au peaks corresponding to xl,, are superimposed to the experimental data. Although the general agreement looks good, the bad reproduction of the peak tails causes the reduced xi,, values to be considerably larger than unity (see Table 2). In Fig. 7, the ,y’ trend around its minimum is reported, for the measurement at 2.4 MeV, as a function of both thickness and straggling FWHM,c,,r enhancement factor. From these curves, which look substantially symmetrical, an uncertainty of ?2% (at 68% confidence level) can be inferred both for thickness and enhancement factor. With reference to the last column of Table 2, it is to be noted that the simulated Au peak integrals corresponding to XL” equal the experimental ones within one standard deviation, and that the agreement with the expected purely Coulomb character of the Au test measurements is achieved within a statistical uncertainty of 1%. Concerning the target thickness, it can be observed that the values reported in Table 2 for the measurements at 2.4
100000
r
0% on
1000 % 3 u
2350
2400 Energy (keV) a)
100 10
.. 1 L 2950
Q .= .
Au
10000
O P
.
,t8 ..I.0
. *
0
I :.,
~~-----
3000 Energy (keV) b)
Fig. 6. Relevant parts of the spectra at 2.4 and 3.0 MeV proton bombarding energy (part (a) and (b). respectively) on a 100 I*.glcm’ Au target on Formvar”. Detection angle is 170”. The backscattering peaks of Au and the “live charge” peaks Q are displayed. Also shown in open diamonds are the simulated An peaks at the minimum of x2,
M. Chiari et al. I Nucl. [email protected] Meth. in Phys. Rex. A 376 (1996) IM-191 Table 2 Parameters
given by the simulations
E,, [MeVl
Reduced
2.4 3.0
1.8 3.4
“X 6.00
3.00 2.00
.
r.
.. .
at the minimum
xi,,,
“x 6.00
of the reduced xZ value (see text)
FWHM,<>,r enhancement factor
Au target thickness
1.18?0.015 1.15zo.02
107.6?2.6 99.1 -t2.0
0.992-tO.012 1.012~0.013
Acknowledgement
7 1.
. ....... .
target thickness (pg/cm’)
‘,,,/I,,,
(I*g/cm’)
.:. 68%4.
1.00 1 102.0 106.0 110.0 114.0
I91
1.10 FWHM,,
1.20
1.30
enhancement factor
Fig. 7. Trends of the reduced xz around its minimum. as a function of the parameters target thickness and enhancement factor of the FWHM,,,,,. The results refer to the measurement at 2.4 MeV proton energy.
This work has been funded by Istituto Nazionale di Fisica Nucleare, Committee 3. and by the Italian Ministry of University and Scientific Research (grants 40%. project Use of small accelerators). We are deeply indebted to G. Poggi, who wrote the acquisition software. The technical support of M. Montecchi and A. Pecchioli, and of the mechanical workshop of the Physics Department (M. Falorsi, M. Merciai, B. Sarti and, in particular. A. Catelani) was decisive. Warm thanks are also due to V. Rigato and G. Manente, of the Laboratori Nazionali di Legnaro, for target preparation.
References and 3.0 MeV compare well with those obtained from the peak integrals, following the more direct procedure mentioned in Section 3.3, which provides more accurate values [( 106.6+ 1.2) kg/cm’ and (100.4? 1.2) kg/cm’, respectively] and is independent of the straggling regime. In any procedure is adopted, the difference case, whichever between the two measured thickness values comes out to be statistically significant, and this points out the importance of a simultaneous detection, whenever possible. of a purely Coulomb scattering in order to achieve the measurement of the effective thickness during each run (Section 3.3). As a conclusion. it can be said that the preliminary results show that absolute measurements of cross sections are indeed possible at a l-2’% accuracy level with the apparatus presented in this work. At the same time, they point out that the main limiting factor to reaching such an accuracy is represented by the knowledge of the effective target thickness under beam bombardment.
[I] E. Rauhala, Nucl. Instr. and Meth. B 40/41 (1989) 790. [2] M. Bozoian, K.M. Hubbard and M. Nastasi, Nucl. Instr. and Meth. B 51 (1990) 311. [3] J.M. Knox, Nucl. Instr. and Meth. B 66 (1992) 31. [4] J.R. Tesmer and M. Nastasi, Handbook of Modern Ion Beam Materials Analysis (Material Research Society, Pittsburgh, 1995). [5] J.A. Davies, W.N. Lennard and 1.V. Mitchell, Pitfalls in Ion Beam Analysis. in: J.R. Tesmer and M. Nastasi, Handbook of Modem Ion Beam Materials Analysis (Material Research Society, Pittsburgh, 1995). [6] V. Bohric and D.M. Shirokov, Nucl. Instr. and Meth. B 84 ( 1994) 497. [7] L.R. Doolittle, Nucl. Instr. and Meth. B 9 (1985) 344.