Nuclear Instruments and Methods in Physics Research A 531 (2004) 416–427

Stopping energetic heavy-ions in one-bar helium: broadincident momentum distributions

L. Weissman*, D.A. Davies, P.A. Lofy, D.J. Morrissey

National Superconducting Cyclotron Laboratory and Department of Chemistry, Michigan State University, 164, South Shaw Lane,

East Lansing, MI-48824, USA

Received 1 March 2004; received in revised form 3 May 2004; accepted 10 May 2004

Available online 17 June 2004

Abstract

Various tests for stopping energetic 32P fragments in a 50 cm gas cell filled with helium were performed. The fraction

of ions stopped in the gas was measured as a function of the width of the incident beam momentum distribution. The

use of a shaped degrader placed in a dispersive plane before the gas cell significantly improves the stopping efficiency in

gas. A stopping efficiency of 35% was obtained for fragments with the broadest momentum distribution, which was an

improvement of approximately 80%. Qualitative agreement between the experimental results and stopping power

calculations was obtained.

r 2004 Elsevier B.V. All rights reserved.

PACS: 24.10.Lx; 34.50.Bw

Keywords: Stopping ions; Gas-cell; Stopping range; Wedge degrader; Range bunching

1. Introduction

The collection of fast secondary beams afterthermalization in a buffer gas will allow a newrange of experiments to be performed with themost exotic beams. Therefore, the developmentand implementation of a so-called gas stopper isan important element of existing and plannedfragmentation facilities. The stopping and collec-tion of fast ions ðE=AX100 MeV=uÞ availablefrom projectile fragmentation reactions has the

additional difficulty that the range stragglingincreases with increasing incident energy and thebroad momentum distribution of the fragments[1,2].

In a previous publication [3], the results ofnumerous tests for stopping various nearly mono-energetic (100–150 MeV=u) ions in helium werereported. The fraction of ions stopped in a 50 cmlong gas cell was measured as a function ofthickness of energy degrader, gas pressure andpath length in helium. To obtain good agreementwith the stopping power calculations, the smalladjustment of only one parameter, the magneticrigidity of the beam, was required. All other

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*Corresponding author. Tel.: +517-324-8123.

E-mail address: weissman@nscl.msu.edu (L. Weissman).

0168-9002/$ - see front matter r 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.nima.2004.05.093

parameters in the calculations were fixed at thebest known values. The tests demonstrated that atypical stopping efficiency higher than 50% canbe achieved at a gas pressure of 1 bar: Thesetests were performed either with primary beams,that have a narrow beam momentum spreadDP=P ¼ 0:07%, or with secondary beams wherethe momentum distribution ð0:2%oDP=Po0:5%Þwas cut by narrow momentum slits placed in thedispersive plane of the A1900 separator [4]. Thetotal momentum spread of typical projectilefragment beams is determined by differentialenergy loss and energy straggling in the productiontarget, the achromatic wedge used for beampurification, and by the reaction mechanism itself.A larger momentum acceptance of a fragmentseparator (5.5% in the case of the A1900) allowsefficient collection of the momentum spread offragmentation beams and, hence, maximizes theyields of exotic fragments. On the other hand, thelarge momentum spread of the beam beforethe slowing down process would result in a largerange distribution and, consequently, a drasticreduction of the stopping efficiency in a gas cellwith a realistic areal density. The gas has verysmall effective thickness, less than 10 mg=cm2 inthe case of the NSCL gas cell at 1 bar pressure.The problem can be overcome in part if thelast stage of the slowing down process includesan ion-optical dispersive plane where the geome-trical position of an ion depends on its energyas described by Weick et al. [1]. A speciallyshaped, monoenergetic degrader can be placedin the dispersive plane just before the gas cellin order to compensate for the energy spreadof a geometrically dispersed beam by larger(smaller) energy losses. This range compen-sation technique has been tested recently at theFRS separator [5] using standard ionizationchambers.

We report on measurements made with adedicated system under development that willprovide a broad range of thermalized ions fromthe A1900 projectile fragment separator. Theresults include the first tests of stopping energeticsecondary beams with broad momentum distribu-tions and demonstrate the proposed energybunching method.

2. Experiment

Fully-stripped primary beams of 36Ar ions at150 MeV=u beam energy were delivered from thecoupled K500 and K1200 cyclotrons to the targetposition of the A1900 separator where a berylliumproduction target with 487 mg=cm2 nominalthickness was placed. A 450 mg=cm2 thick alumi-num achromatic degrader was placed in thedispersive central plane (Image 2) of the separator.The curvature of the degrader corresponded to theeffective wedge angle of �0:88 mrad: The shape ofthe degrader resulted in achromatic trajectories ofthe fragments in the remaining part of theseparator and allowed purification of the frag-ments of interest by using narrow slits placed inthe A1900 focal plane. A thin ðE30 mg=cm2Þplastic scintillator was placed in the center of thedevice (Image 2) for monitoring the beam inten-sity. Slits placed in the next dispersive plane of theA1900 after the achromatic wedge (Image 3)allowed variation of the final incident momentumdistribution of the beam. The dispersion at Image3 is 30 mm per percent in momentum, e.g. a30 mm gap between the momentum slits allows1% momentum spread of the beam at the exit ofthe A1900 separator.

The separator was tuned for transport andpurification of 32P fragmentation products. Thechoice of 32P was primarily dictated by its high-production yield. The magnetic rigidity, Br; of thebeam after passing the achromatic wedge and thethin scintillator was 3:359 Tm: The beam consistsmostly of 32P and some 33S fragments with analmost negligible admixture of 31Si (Table 1).

The beam of the fragments was delivered to thegas stopping station described in detail in aprevious publication [3]. A schematic diagram ofthe experimental setup is shown in Fig. 1. Theoptics of the beam line was tuned to produce adispersive image in the horizontal plane at positionA and an approximately parallel beam into the gascell. The dispersion value at position A wasmeasured and found to be 9:5 mm per percent ofbeam momentum spread.

The energy of 32P fragments was degraded by aset of borosilicate glass (BSL7) plates that couldbe tilted in the horizontal plane. A computer

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L. Weissman et al. / Nuclear Instruments and Methods in Physics Research A 531 (2004) 416–427 417

controlled drive held a pair of 1:488 mm thickoptically polished plates (90 mm horizontal�30 mm vertical). The plates were rotated inopposite directions by a mechanical drive provid-ing a smooth increase in thickness of the absorbingmaterial that cancels, to first order, the effect ofthe small angular divergence of the beam. Theconservative uncertainty in the degrader angle wasestimated to be 0:25�; which should be combinedwith the uncertainty in the thickness of the platesðp2:5 mmÞ: A ladder, placed at the point A, in Fig.1, contained three positions with a phosphorscreen, used for observation of the beam spot, amonochromatic wedge degrader (M-wedge) and ahomogeneous degrader (H-wedge). The monoe-nergetic and homogeneous wedges were manufac-

tured from 2024 alloy of aluminum using precisionelectric discharge machining. The area of thedegraders was 60� 38 mm2; and the wedge anglewas along the longer side. The thicknesses of thewedges were measured with a digital micrometer.The typical local imperfection of the wedgesurfaces was found to be less than 5 mm: The H-wedge was found to be 2:281ð3Þ mm thick withglobal wedging angle less than 0:25 mrad: Thick-ness in the middle of the M-wedge was2:241ð6Þ mm and the wedge’s angle was10:8ð2Þ mrad: The value of the wedge angleprovides energy loss compensation as determinedby the value of the horizontal dispersion at thepoint A, and the beam energy and energy loss ofthe 32P ions in aluminum [5]. The density of the

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glass quadrupole doublet gas cell

Si pindetector

Bewindow detectors

dispersivefocus

10 cm 166 cm 86 cm 50 cm

A

45 cm

vacuum He 0-1 bar

beam

thin plasticdetector

degrader

wedgeladder

phosphorscreen

B

Fig. 1. General schematic view of the experimental setup.

Table 1

Counting rate of 32P; 33S and 31Si fragments as a function of the momentum slit gap

Slits(mm) Nominal DP=Pð%Þ Effective DP=Pð%Þ Effective BrðTmÞ Counting rate

32P(pps) 33S(pps) 31Si(pps)

10 0.3 0.1 3.358 65 1.5 0.2

30 1 0.4 3.355 170 6 0.8

60 2 0.85 3.352 270 13 2

The obtained effective beam momentum spreads and rigidities (see text) are also shown.

L. Weissman et al. / Nuclear Instruments and Methods in Physics Research A 531 (2004) 416–427418

wedge material was measured and found to be2:759ð1Þ g=cm3 and its chemical composition wastaken from the literature. The Br for the two lastquadrupole elements (see Fig. 1) was set to2:030 T m to account for the average energy lossin the degraders. A large Si PIN-detectorð50 mm� 50 mm� 0:5 mmÞ can be introduced inthe beam at position B in Fig. 1 upstream from thegas cell during beam transport. The beam passedthrough a beryllium window into the gas cell filledwith helium. The thickness of the window anddiameter were 1:50 mm and 5:32 cm; respectively.The thickness and diameter of the berylliumwindow were chosen so that deflection under theload from the helium gas would not cause asignificant change in effective thickness across itsdiameter.

A telescope consisting of two surface barrierdetectors of 300 mm2 active area and 0:1; 1:5 mmthick, respectively, was mounted on a central postinside the gas cell and was used for detection andidentification of particles. The telescope wasplaced at the distance of 45ð0:2Þ cm from theberyllium window. The relatively small area of thedetectors used was dictated by the geometry of theelectrodes placed inside the gas cell for extractionof the stopped fragments [6]. The Si telescopeallowed identification of the 32P fragments andcontaminants that have a similar magnetic rigidityand cannot be completely separated by the A1900,as well as, from the lighter reaction productsproduced by interaction of the fragments in thedegraders and the window. The time differencemeasured between a reference signal from thecyclotron and the fragment detection (time-of-flight) allowed for additional particle identifica-tion. Typical particle identification plots are shownin Fig. 2. As it can be seen from Fig. 2, the 32Pfragments were well separated from the maincontaminants in the DE-TOF diagram down to thedetector threshold. The signals were recorded onan event-by-event basis and energy histogramswere obtained in off-line analysis.

Energy spectra observed in the detectors with-out the degrader or with thin degraders and withan evacuated gas cell consisted of sharp DE peaks.Comparison of positions of the DE peaks with thepredictions of the stopping power calculations

yielded the energy calibration. As the energycalibration relies on the stopping power calcula-tions, its typical uncertainty is about 5% [7].

The low-energy threshold of the first detectorwas approximately 3 MeV: Thus, transmittedions with lower energies were not registered.The under-threshold fraction can be calculatedand corrected to first order by using spectraobtained from stopping power calculations [3].This correction is significant (up to 10%) onlyfor the largest glass degrader thickness and sincethe transmission fraction for these degraderangles is small, the applied correction does notsignificantly change the shape of transmissionprofiles.

The data were taken for various sets ofparameters such as the type of wedge, the tiltingangle of the glass degraders, gas pressure and valueof the momentum acceptance. The momentumslits were set to 10, 30 and 60 mm; whichcorresponded to the 0.3%, 1% and 2% incidentmomentum spread at the exit of the A1900. Theoptical setting of the beam line used to transportthe secondary ions to the gas cell and produce adispersion on the wedges introduced a correlationbetween angle and dispersion that limited therange of momenta that reached the detector in thegas. The reduced effective momentum acceptanceis discussed below.

Numerous short, 1–2 min; measurements wereperformed. For example, after setting the gap ofthe momentum slits and gas pressure in the cell,the counting rate in the telescope was measuredseparately for the M- and H-wedges as a functionof the tilting angle of the glass degraders. Thus, thetransmission (number-distance) curves were ob-tained for the two wedges. The whole sequence ofthe measurements was then repeated for differentvalues of the gap of the momentum slits. Then theentire series of measurements was repeated with anevacuated gas cell. For each measurement, thenumber of detected 32P fragments was integratedusing the identification plots (Fig. 2). All of theexperimental results presented below have beencorrected for fluctuations of the beam intensity asmonitored by the plastic scintillator at Image 2,and for the small fraction of events below thethreshold.

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L. Weissman et al. / Nuclear Instruments and Methods in Physics Research A 531 (2004) 416–427 419

3. Results

A summary of the measurements is presented inFig. 3 where the normalized transmission profiles,e.g. the dependence of the counting rate as afunction of the glass degrader effective thicknessfor three values of the incident momentum

distribution are represented by squares (M-wedge)and triangles (H-wedge). Open symbols corre-spond to the data for the evacuated chamber andfilled symbols for the measurements taken at ahelium pressure of 825 Torr: The vertical errorbars are the combined statistical errors formeasurements in the upstream plastic detector

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Fig. 2. Typical identification plots : DE � E (a) and DE � TOF (b). The spectra were taken for the nominal momentum distribution of

2%, without gas and the degraders.

L. Weissman et al. / Nuclear Instruments and Methods in Physics Research A 531 (2004) 416–427420

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Fig. 3. The summary of measurements for the 0.3%, 1% and 2% nominal incident momentum distributions (0.1%, 0.4% and 0.85%

effective distributions). For each case, empty symbols correspond to the normalized data for the evacuated chamber and filled ones for

the corresponding measurements taken at a gas pressure of P ¼ 825 Torr: To obtain the absolute rates, the normalized data has to be

multiplied by the counting rates from Table 1. The solid lines correspond to the fits of the transmission profiles and the dotted lines

represent the obtained stopping profiles

L. Weissman et al. / Nuclear Instruments and Methods in Physics Research A 531 (2004) 416–427 421

and the first detector of the telescope plus the erroron the low-threshold correction (taken conserva-tively as 50% of the added value for the narrowmomentum distribution). As the stopping powercalculations were found to be less reliable for thecases of broad momentum distributions (seebelow), the corresponding error on the low-threshold correction was taken as 100%. Thehorizontal error bars are due to uncertainties inthe determination of the degrader angle plusabsolute thickness uncertainty. The drop in thecounting rate with increasing degrader thicknessfor the case of the evacuated chamber is due to theincreasing fraction of ions stopped in the berylliumwindow. As expected, when helium is present,additional stopping of ions in helium results in anearlier drop in the counting rate with increasingdegrader thickness. The transmission profiles werefitted with a simple function:

y ¼a

1þ expð�ðx� bÞ=kÞ:

The results of a least-square fitting procedure areshown in Fig. 3 as solid curves and the numericalresults are contained in Table 2. The table showsthat the mid-point of the falling curve (b para-meter) for the M-wedge is systematically largerthan the corresponding value for the H-wedge.This difference, bM � bH; ranges from 74 mm fornarrow momentum distribution, to 104 mm for the

largest momentum distribution. Part of thisdifference ðE40 mmÞ is due to a slightly thinnerM-wedge compared to the H-wedge. The thicknessof the M-wedge varies in the horizontal direction,therefore, the optimum thickness of the glassdegrader depends on the relative positioning ofthe beam on the M-wedge. The larger bM can beexplained by a few mm shift of the beam spot withrespect to the middle of the M-wedge.

The difference between transmission profileswith and without helium corresponds to thefraction of ions stopped in gas as a function ofthe degrader angle (stopping profile). The stoppingprofiles obtained by subtracting the fitted trans-mission functions are shown in Fig. 3 by dottedlines. The stopping profiles in turn were fitted bystandard Gaussian functions in order to obtain thestopping efficiencies:

y ¼ yc exp�ðx� xcÞ

2

2w2

where xc is the thickness of the degrader thatcorresponds to the maximum stopped fraction, ycis the value of the maximum stopped fraction(maximum stopping efficiency) and w is thestandard deviation of the stopping profiles. Foreach stopping profile, the conservative errors onthe xc; yc and w parameters were obtained bytaking limiting values of the b and k parametersfrom the fitting of the corresponding transmission

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Table 2

Fitting results for the obtained transmission profiles

Fit parameter Nominal DP=P ¼ 0:3% Nominal DP=P ¼ 1% Nominal DP=P ¼ 2%

H H H

0 Torr 825 Torr 0 Torr 825 Torr 0 Torr 825 Torr

a 1.02(1) 1.025(10) 1.04(2) 1.04(2) 1.05(2) 1.04(5)

b 3.149(1) 3.111(1) 3.125(2) 3.076(1) 3.081(2) 3.035(6)

k 0.0179(8) 0.0159(7) 0.0366(14) 0.0400(13) 0.0515(12) 0.0494(21)

Fit parameter M M M

0 Torr 825 Torr 0 Torr 825 Torr 0 Torr 825 Torr

a 1.00(1) 0.99(1) 1.015(10) 1.01(1) 1.01(1) 1.02(1)

b 3.223(1) 3.185(2) 3.212(1) 3.170(1) 3.185(8) 3.145 (6)

k 0.0149(9) 0.0142(6) 0.0221(9) 0.0221(9) 0.0319(8) 0.0283(8)

bM � bH 0.075(2) 0.074(2) 0.087(2) 0.094(1) 0.104(8) 0.101(8)

L. Weissman et al. / Nuclear Instruments and Methods in Physics Research A 531 (2004) 416–427422

profiles. The results of the fittings procedure arepresented in Table 3.

As seen in Fig. 3 and Table 3, the stoppingprofiles for the M-wedge are considerably differentfrom the corresponding profiles for the H-wedge.The former profiles are narrower and have highermaximum stopping efficiencies, yc; than the latterones. In the case of the broadest momentumspread, the optimum stopping efficiency, yc;obtained for the M-wedge is almost 80% higherand the corresponding width of the profile, w; ismore than 60% smaller, indicating that the use ofthe monoenergetic degrader resulted in consider-able energy compression. The effects of the smallereffective thickness of the M-wedge is also seen inthe xMc � xHc values (Table 3). It is also worthnoting that the areas under the normalizedstopping profiles, S; are the same for the twowedges (Table 3) within the experimental error.

Although the Si detectors register ions after theBe-window and gas, e.g. after large energystraggling, rather than directly after the wedges,the energy bunching effect can also be seen in theresidual energy spectra (the energy registered inthe DE- and E- detectors were summed with thecorresponding calibration coefficients). The resi-dual energy spectra taken on an event-by-eventbasis for the H- and M-wedges, collected fordifferent values of the momentum spread, arecompared in Fig. 4a,b. The spectra were gated bythe 32P group using DE-TOF plots. The spectrapresented in Fig. 4 were taken for zero angle of the

glass degrader and the evacuated gas cell. Exam-ining the residual spectra, one can observe thestrong bunching effect for the case of the M-wedge. One also can observe that for both wedges,the behavior of the energy distribution is notconsistent with the symmetric setting of themomentum slits, as low-energy counts are addedto the spectra as the momentum slits gap iswidened. This effect indicates that ions from thehigh-energy part of the momentum distributionwere not detected in the telescope. When the PINdetector (2500 mm2 active area) is introduced inthe beam, the ratio of counting rates in the PINand in the telescope (300 mm2 active area) isconstant as a function of the momentum slits gapsin both Image 2 and 3 dispersive images, indicatinggood centering of the beam. However, retractionof both glass and wedge degraders resulted in anincreased counting rate in the telescope withrespect to the PIN detector and the Image 2plastic detector by a factor ofE2: The beam opticsthat produces the dispersion at the wedge positionis more sensitive to angle than to momentum.Small misalignment of the beam in the transportsystem can introduce an angle-momentum correla-tion that would easily deflect part of the secondarybeam, resulting in a cut of the measured effectivemomentum spread. The beam spot is larger thanthe size of the telescope in the gas cell, andunfortunately, the present geometry of the gas celldoes not allow the introduction of larger areadetectors in the cell that might avoid such

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Table 3

Fitting results for the stopping profiles. The areas under the stopping profiles, S; are also shown

Fit parameter Nominal DP=P ¼ 0:3% Nominal DP=P ¼ 1% Nominal DP=P ¼ 2%

H M H M H M

xc 3.132(2) 3.206(2) 3.095(5) 3.191(2) 3.069(10) 3.172(3)

yc 0.51(2) 0.58(2) 0.31(3) 0.44(2) 0.20(4) 0.355(40)

w 0.029(1) 0.027(1) 0.061(2) 0.038(1) 0.078(3) 0.049(2)

S 0.037(1) 0.038(1) 0.047(4) 0.042(2) 0.039(7) 0.043(5)

wðmg=cm2Þ 7.3(1) 6.6(1) 15.2(3) 9.3(2) 19.5(4) 12.3(3)

wðcm of HeÞ 41 37 85 55 110 69

xMc � xHc 0.074(3) 0.096(6) 0.093(4)

All values are given in millimeters, except the two rows where the width of the stopping profile is given in mg=cm2 and the equivalent

length of He at 825 Torr pressure.

L. Weissman et al. / Nuclear Instruments and Methods in Physics Research A 531 (2004) 416–427 423

ambiguities. The energy spectra can be qualita-tively reproduced by calculations (see below) ifeffective momentum distributions and magneticrigidities are introduced.

4. Stopping power calculations

The experimental results for primary beamswith narrow incident momentum distribution werereproduced well by stopping power calculations byslightly adjusting just one parameter, the beammagnetic rigidity [3]. However, the case ofsecondary beam is more complicated due toadditional uncertainties associated with the wedgeand beam transport. For example, a shift of beamposition with respect to a center of a wedgedegrader results in a shift in transmission andstopping profiles. Similarly, angle and momentum

correlations generated in the beam line used tocreate the dispersion at the wedge may introducean effective cut and shift in the momentumdistributions measured in a small area detector.The measured residual energy and stopping powerprofiles were used to determine the effective beammomentum distribution and magnetic rigidities.The effective thickness of the M-wedge wasslightly adjusted due to uncertainty in the positionof the beam on the wedge surface.

The stopping power calculations were per-formed with the LISE code [8] that simulates allmagneto-optical elements used for beam transportfrom the cyclotron to the gas cell and includes allslits and materials used for beam degradation.Many parameters in the calculations, such asthicknesses of all degraders (except the M-wedge),their physical, chemical and geometrical propertiesand their geometrical position along the beam line,

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0

20

40

60

80

Cou

nts

Cou

nts

0

20

40

60

80

0 100 200 300 400 500 600 700 800 900 1000

Energy (MeV)

0

20

40

60

80

Inte

nsit

y (a

rb. u

n.)

Inte

nsit

y (a

rb. u

n.)

0

20

40

60

80

(a)

H-wedge

∆ P/Peff 0.85 %

∆ P/Peff 0.4 %

∆ P/Peff 0.1 %

(b)

M-wedge ∆ P/Peff 0.85 %

∆ P/Peff 0.4 %

∆ P/Peff 0.1 %

M-wedge

∆ P/Peff 0.1 %

∆ P/Peff 0.4 %

∆ P/Peff 0.85 %

∆ P/Peff 0.85 %

∆ P/Peff 0.4 %∆ P/Peff 0.1 %

H-wedge

(c)

(d)

0 100 200 300 400 500 600 700 800 900 1000

Energy (MeV)

0 100 200 300 400 500 600 700 800 900 1000

Energy (MeV)

0 100 200 300 400 500 600 700 800 900 1000

Energy (MeV)

Fig. 4. (a–b) The residual energy spectra taken for the M- and H-wedges and 0.3%, 1% and 2% nominal incident momentum

distributions (0.1%, 0.4% and 0.85% effective distributions). (c–d) The corresponding energy spectra calculated with the LISE

program [8] for the effective momentum distributions and beam rigidities.

L. Weissman et al. / Nuclear Instruments and Methods in Physics Research A 531 (2004) 416–427424

and the value of dispersion at the point A; werefixed to the best known values. Some of the beamoptics parameters like the magnification andangular divergence of the beam were not knownexperimentally, and only the values calculatedfrom a beam optic transport code were used. Tosimulate the effective cut in the measured beammomentum distribution, the gap of the Image 3momentum slits and the beam rigidity wereadjusted in calculations for each value of thenominal beam momentum spread. Both the ob-tained experimental stopping profiles and theresidual energy spectra were used to adjustthe latter parameters. The experimental stoppingprofiles are more suitable for adjusting the

effective beam rigidity, as the calibration of theenergy spectra has significant uncertainty. Thecomparison with experimental residual energyspectra was useful for obtaining the effectivemomentum distributions. The ATIMA model [9]integrated into the LISE code was used forstopping power calculations. The obtained effec-tive parameters for the H-wedge data are listed inTable 1.

As the next step, the thickness in the middle ofthe M-wedge was slightly adjusted to compensatethe small offset of the beam position with respectto the wedge center. Good agreement between thecalculations and the experiment corresponds to a2:210 mm thick M-wedge or E3 mm shift withrespect to the wedge center. The calculatedresidual energy spectra and stopping profiles arecompared with experimental data in Figs. 4 and 5,respectively. One can observe that the qualitativeagreement between the result of calculations andexperiment is achieved. The effect of energybunching for the M-wedge is clearly seen in thecalculations. Thus, the calculation can be used inthe future for design of shaped degraders.

5. Discussion and conclusion

Tests for stopping fragmentation beams withvariable incident momentum distributions wereperformed. The energy bunching method using ashaped degrader for a geometrically dispersedbeam was demonstrated. For the case ofDP=P ¼ 2% nominal momentum spread, thestopping efficiency of 35% in 45 cm of heliumgas was achieved. This value is larger by a factor80% than the corresponding efficiency obtainedwithout the energy compression. As the stoppingefficiencies were measured for the 45 cm length ofhelium and the total length of the gas cell is 50 cm;one can presume that the stopping efficiencies forthe cell in first order are 10% higher than the ycvalues in Table 3. The measured momentumspread is reduced by a factor of 1.6 for the caseof the broadest momentum distribution. The smallarea of the Si detectors makes the measurementsvery sensitive to the fine details of beam optics,and qualitative agreement between the calculations

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Fig. 5. The calculated stopping profiles (thin lines) are

compared to the experimental data (dotted lines) for the two

wedges and the three values of the beam momentum spread.

The calculations are done for the effective beam momentum

distributions and rigidities (see text).

L. Weissman et al. / Nuclear Instruments and Methods in Physics Research A 531 (2004) 416–427 425

and the experiment was achieved only afterintroduction of an assumption regarding the beamtransport.

It is interesting to compare the experimentalresults with the theoretical limit of the monoener-getic degrader performance. Following the discus-sion in Refs. [5,10], one can estimate the limit offragment velocity spread that can be obtained witha monoenergetic degrader used in an ion-opticsystem:

s2n ¼MWn

D

� �2

s2x þ s2dn:

The first term corresponds to the optical resolvingpower of the system, with M and D the dispersionand magnification at the wedge position corre-spondingly (M=DE10�2 m for our system), sx isthe beam size at the entrance of the ion-opticsystem and Wn is defined by the beam velocitiesand the stopping powers in front and behind of thewedge degrader:

Wn ¼b21g1ðdE=dxÞ2b22g2ðdE=dxÞ1

:

The second term, sdn; is the standard deviation ofthe velocity straggling due to the degrader. Thecontribution of the resolving power term for the32P fragments is 0.3% spread per mm of the beamspot at the entrance to the system. Both LISE andMocadi [11] calculations show that the velocityspread of a monoenergetic 32P beam due to energystraggling in the glass, wedge, and the Be windowis on the order of 3%. Thus, the limit of the finalmomentum distribution is determined mostly byenergy straggling rather than by the opticalresolution of the system. The smallest sn corre-sponds to a stopping profile with a standarddeviation, w; of approximately 0:019 mm glassdegrader equivalent. This approaches the valuesobtained for the narrowest momentum distribu-tion (see Table 3). In the case of an idealmonoenergetic degrader, the final momentumdistribution should not depend on the initialmomentum spread of the beam [5,10]. This is notthe case for the experimental results (Fig. 3 andTable 3). One of the possible reasons for the non-ideal behavior is the wedge geometry. The desir-able thickness tolerance for the degraders is on the

level of a few 10�4 [5]. In the present experiment, atmuch lower beam energy and, hence, much thinnerdegraders in comparison with Ref. [5], the thick-ness tolerance was at least an order of magnitudepoorer resulting in a reduction of the bunchingefficiency. The experiments with heavier ionsrequire thinner wedges and increased demandson the wedge accuracy. A larger value ofmomentum dispersion produced at the wedgeplane will relax significantly demands on wedgeaccuracy.

The angle-momentum correlations introducedin the dispersion plane by degraders combinedwith further energy straggling during passagethrough the Be window may also be responsiblefor non ideal bunching behavior.

The successful implementation of the energybunching method is important in the context of therecently proposed RIA facility [12] where a gasstopper will be used as a key element of thefragmentation based ISOL facility. The presentand previous [3] work demonstrate the feasibilityof efficient stopping of energetic fragmentationbeams in 1 bar helium. However, efficient extrac-tion of the stopped ions from the gas cell still hasto be demonstrated. The first results of ourextraction tests were briefly reported in Ref. [6].Continued work on the first tests for extraction ofstopped and thermalized radioactive ions will beaddressed in a future report.

Acknowledgements

We would like to thank Mr. J. Ottarson for hishelp with design and fabrication of the experi-mental setup and the staff the NSCL laboratoryfor their help during the experiments and Dr. O.Tarasov for his help in use of the LISE code. Thiswork is support by the National Science Founda-tion Grant PHY-01-10523 and by the US Depart-ment of Energy Grant 00ER41144.

References

[1] H. Weick, et al., Nucl. Instr. and Meth. B 164–165 (2000)

168.

[2] Y. Wada, et al., Nucl. Instr. and Meth. B 204 (2003) 570.

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L. Weissman et al. / Nuclear Instruments and Methods in Physics Research A 531 (2004) 416–427426

[3] L. Weissman, D. Davies, P.A. Lofy, D.J. Morrissey, Nucl.

Instr. and Meth. A 522 (2004) 212.

[4] D.J. Morrissey, B.M. Sherrill, M. Steiner, A. Stolz, I.

Wiedenhoever, Nucl. Instr. and Meth. B 204 (2003) 90.

[5] C. Scheidenberger, et al., Nucl. Instr. and Meth. B 204

(2003) 119.

[6] L. Weissman, P.A. Lofy, D.A. Davies, D.J. Morrissey, P.

Schury, S. Schwarz, T. Sun, G. Bollen, in: G. Savard (Ed.),

Proceedings of RNB6 ; Nucl. Phys. A, in press.

[7] J.F. Ziegler, computer code SRIM-2000, available from

http://www.srim.org/SRIM.

[8] D. Bazin, O. Tarasov, M. Lewitowicz, O. Sorlin, Nucl.

Instr. and Meth. A 482 (2002) 314 available from http://

groups.nscl.msu.edu/lise/lise.htm.

[9] C. Scheidenberger, H. Geissel, Nucl. Instr. and Meth. B

135 (1998) 25; http://www-aix.gsi.de/~scheid/ATIMA1.

html.

[10] H. Geissel, T. Schwab, P. Armbruster, J.P. Dufour, E.

Hanelt, K.H. Schmidt, B. Sherrill, G. Munzenberg, Nucl.

Instr. and Meth. A 282 (1989) 247.

[11] http://www-linux.gsi.de/~weick/mocadi/.

[12] http://www.phy.anl.gov/ria.

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