- Email: [email protected]
Transport efficiency of the Argonne fragment mass analyzer
Nuclear Instruments and Methods in Physics Research A 379 (1996) 206-211
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH
Section A
EISE&lER
Transport efficiency of the Argonne fragment mass analyzer B.B. Back*, D.J. Blumenthal,
C.N. Davids, D.J. Henderson, H.T. PenttiEi2, A.H. Wuosmaa
Physics Division,
Argonne National Laboratory,
Argonne,
R.H. Hermann’,
C.L. Jiang,
IL 60439, USA
Received 28 December 1995 Abstract Absolute transmission efficiencies for the Argonne fragment mass analyzer (FMA) have been measured for ions of ls4W, *“Pb, and Z3*Th with energies in the range E = 20-45 MeV. These were obtained by Rutherford scattering of ?S beams of 50, 80 and 110 MeV into backward angles, Measurements were performed for a range of settings for the FMA in order to determine the acceptance of the instrument as a function of energy and angle of the incident ion. The transport efficiency across the focal plane was also measured. The results are compared with predictions of the transport code GIOS [H. Wollnik et al., Nucl. Instr. and Meth. A 258 (1987) 4081, which agree well with the data. With these data we conclude that the transport efficiency of the FMA is sufficiently well known to support measurements of absolute cross sections with an accuracy of 210%.
1. Introdtiction
2. Method
In this paper we describe a simple and efficient method for measuring the transport efficiency of low energy recoil mass spectrometers of the type that have found widespread use in recent years [2-81. Such measurements are crucial for determining accurate cross sections using such devices. The present method is applicable for determining the transport efficiency of fusion products formed in normal kinematic reactions, i.e. with light projectiles onto a heavier target for beam energies up to several times the Coulomb barrier. We also present measurements of the absolute transport efficiency of the Argonne fragment mass analyzer (FMA) obtained by elastic backscattering of ?S by targets of is4W, “‘Pb, and ?‘h at three beam energies, 50, 80, and 110 MeV, all of which are well below the Coulomb barrier of the targets used. The method of using elastic recoils for efficiency measurements is discussed in Section 2, followed by a presentation of the experimental procedure in Section 3. The resulting transport efficiencies are discussed and compared with theoretical calculations in Section 4, followed by a summary in Section 5.
* Corresponding author. Tel. + 1 630 2523618, e-mail: [email protected]. ’ Now at Technische Universitit Miinchen, * Now at University of Jyvlskyll, Finland.
fax + 1 630
2526210,
0168-9002/96/$15.00 Copyright PZZ SO168-9002(96)00650-X
Munich,
0 1996 Published
Germany.
The method relies on the fact that target recoils from elastic heavy-ion scattering can be produced abundantly with well-known rates and energies into forward angles (where most spectrometers are located). Thus, if an evaporation residue of mass, M, is formed by fusion of a projectile with mass m, and energy E, and a target nucleus of mass M,, then its mean energy (E,,) is
Depending on the availability of targets with the same (or similar) mass it is possible to lower the beam energy to a value
(2) such that elastic recoils will emerge with the same energy as the evaporation residues under study. For normal kinematics (i.e. m, CM,), E, is substantially lower than the beam energy used to study the fusion process. Depending on the ease of changing (lowering) the beam energy of the accelerator in question, it becomes rather straightforward to measure the transport efficiency of the mass spectrometer in a very short time. In addition, by choosing a target of the same Z as the fusion products under study, one can use elastic backscattering to quickly measure the
by Elsevier Science B.V. All rights reserved
207
B.B. Back et al. I Nucl. Instr. and Meth. in Phys. Res. A 379 (1996) 206-211
charge state distribution, a feature that is important when the cross sections for evaporation residue production is low. As demonstrated below, it is, however, sufficient to map out the transport efficiency of the spectrometer only once because of the scaling properties of ion trajectories in electrostatic and magnetic fields. Thus, ion trajectories depend only on the ratios Elq and m/q, where E, m, and CJ are the energy, mass and charge of the ion respectively. The radii of curvature of the ion trajectory in the electric, %, and magnetic, B, field regions are given by
R,=E
and
R,,,=%,
q8’ respectively. In order to transport ions with parameters E,lq, and m,lq, entering the spectrometer on a central trajectory, the electric, 8 and magnetic B fields must be set such that the radii of curvature of the ion-trajectories match the ion-optical design parameters i.e.
(4) Using these field settings we therefore o E/q
R,=R,~o/4o,
and
R,=Ri
I. 0.6
find
mlq -d mJq,
I.
8.
I.
I.
I
0.8
1.0
1.2
1.4
1.6
VW&%,)
Elq Eo/qo
I
’
(5)
Furthermore, since Rz and Ri are fixed we can conclude that the trajectories through the spectrometer for ions which are initially injected on axis depend on the ion parameters only through these ratios. Similar arguments apply for off-axis trajectories, and consequently, the transmission probability E depends only on the ratios (EIq)I(E,,/q,), (mlq)l(m,lq,) and the entrance angles 0, 4, relative to the spectrometer axis (not the beam axis) i.e.
In the measurements described in the following sections, we have determined the dependencies of the transport efficiency s.MA for the ATLAS fragment mass analyzer as a function of all four parameters, albeit in only very coarse steps for the angular dependencies. Since it is much less time-consuming to change the settings of the FMA, the dependence on the ion energy and mass was mapped out by varying the parameters E,, and qO. The transport efficiency of the FMA as a function of angle and energy of the incident ions has been calculated using the computer code GIOS [I] as shown in Fig. 1. We note that the transport efficiency has a strong dependence on the angle 0 in the horizontal plane relative to the axis of the spectrometer. In order to map out the dependence over the angular acceptance we used five different entrance apertures, which are listed in Table 1, and illustrated in Fig. 1.
Fig. 1. Contour plots of the transmission efficiencies for the FMA calculated with the GIOS code. Panel (a) shows the dependence on the horizontal entrance angle 8 and the ion energy-to-charge ratio E/q, whereas the dependence on m/q and E/q are displayed in panel (b).
3. Experiment The measurements were carried out using a 45 cm diameter sliding-seal target-chamber coupled to the FMA (see Fig. 2). The FMA was placed at an angle of 5” relative to the beam axis in order to avoid the backgrounds from beam scattered off the first anode. Five square apertures, one subtending opening angles of 4.5” X 4.5” labelled “full”, and four subtending 1.5” X 1.5” labelled “left”, “center”, “right”, and “top” according to their placement were used to map out the entrance angle dependence
Table 1 Angular coverage
Aperture Full Left Center Right TOP
of entrance
aperhxes
c
4mai
a
[deal
[degl
[de@
[de,@
[msrl
-2: -2; -+
2$ -f I 24 :4
-2; -$
2$ z4 1 f 2;
6.25 0.694 0.694 0.694 0.694
@,,,
14 43
max
mln
43 --9 :4
B.B. Back et al. I Nucl. Instr. and Meth. in Phys. Res. A 379 (1996) 206-211
208
FMA
Entrance apertures
Fig. 2. Schematic of the Argonne fragment mass analyzer emphasizing the details of the target and focal plane detector regions.
of the transmission efficiency (see Fig. 1 and Table 1). The absolute transport efficiency was obtained by normalizing to elastic scattering in a monitor (Si) detector subtending a solid angle of L&_,” = 0.245 msr placed at 30”. Although it was not required for these measurements, a 40 yg/cm’ carbon foil was placed between the target and the entrance aperture in order to be compatible with an earlier measurement of the evaporation residue cross section for ?S + ‘*“W, where this foil was used to reset the charge state distribution before entering the FMA. Elastically scattered target recoils were registered in a position-sensitive parallel grid avalanche counter (PGAC) placed in the focal plane of the FMA followed, after a 40 cm flight path, by a 5 X 5 cm2 double-sided Si strip detector (DSSD) with sixteen strips in orthogonal directions on the front and back side of the detector. This detector was used to measure the efficiency, epGAc, of the PGAC detector, which has been slightly damaged in previous experiments. This was done by determining the probability for obtaining a signal in the PGAC for events detected in the DSSD.
4. Results The measurements were carried out at ?S beam energies of 50, 80, and 110 MeV on targets of ls4W, “‘Pb, and 232Th. A total 456 measurements were performed over a period of four days. The absolute transport efficiencies were calculated as follows: N PGAC
qFM.4=
Lnmonaklas 4 MA~~ec0ilEPGAC N mon ’
(7)
where NpGAC and N,,, are the counts in the PGAC and monitor detectors, respectively, and crecoi, and ueelasare the corresponding differential elastic scattering cross sections. Rutherford scattering cross sections were used since the beam energies were in all cases substantially lower than the interaction barrier. 4.1. Charge state distributions For each target/beam-energy case the FMA was set up for the nominal recoil energy and the charge distribution
was measured using the “full” aperture. The results are displayed in Fig. 3 as solid points. The charge states selected for the subsequent measurements of energy and m/q acceptance are indicated by arrows. Optimal Gaussian fits to the measured charge state distributions are shown as solid curves, whereas the dashed curves represent theoretical predictions using the formula proposed by Shima et al. [9]. We observe some deviations from these predictions, but find that the overall agreement is quite good. The fraction associated with the charge state setting chosen for subsequent measurements was obtained by normalizing to the integral of the fitted Gaussian. 4.2. Energy acceptance The energy dependence of the transport efficiency was obtained by performing measurements for different energy settings, E,,, of the FMA after selecting a charge state at or near the maximum of the distribution in each case (arrows in Fig. 3). The results for elastic ls4W recoils from backscattering of 3’s at energies of 50, 80, and 110 MeV are shown in Fig. 4 as a function of the parameter E/E,,, where E is the calculated recoil energy including energy losses in the target and reset foils. aperture we see that the transport For the “center” efficiency reaches nearly 100% over an energy region from approximately 80 to 120% of the energy set for the FMA. Beyond this region the acceptance falls off relatively sharply. As expected, we observe that the relative energy acceptance, e(EIE,J, is essentially independent of the beam (recoil) energy and for all the different entrance aperatures, thus demonstrating the scaling properties discussed in Section 2. By comparison of the data obtained with the “left”, “center”, and “right” apertures, we observe that the energy acceptance depends rather strongly on the horizontal entrance angle 0 into the spectrometer. The energy acceptance for the “left” aperture is thus shifted to lower energies than those for the “right” aperture. One may exploit this feature to extend the bending power of the FMA to higher energies than otherwise feasible by using an entrance aperture covering only a fraction of the total angular acceptance in the positive f3 region. We also observe that the energy acceptance does not depend on the
B.B. Back et al. I Nucl. Ins@. and Meth. in Phys. Res. A 379 (1996) 206-211
209
“S+?h
---Theory
10
15
20
25
10
15
20
25
IO
15
20
25
Charge slate q
Fig. 3. Measured (solid points) and Gaussian fits (solid curves) of charge-state distributions for elastic recoils are shown. Dashed curves represent theoretical predictions [9].
out-of-plane angle 4 as seen from the similarity of the spectra for the “center” and “top” apertures. The transport efficiency for the “full” aperture is seen to reach only about 85% and displays a smoother fall-off to both lower and higher energies. This is, in fact, exactly what is expected by combining the measurements for the apertures. The data are “center”, and “right” “left”, compared to the calculated efficiencies (solid curves) obtained from the code GIOS for the beam energy of 110 MeV. It is evident that the calculations generally predict a slightly more constant transport efficiency over the acceptance region followed by a sharper fall-off at the limits. Although the exact reason for this discrepancy is
not well understood, we suspect that it is associated with inadequacies in the description of the magnetic and electrostatic fringe fields used in the calculations. Fig. 5 shows the transport efficiency for a combination of all seven data sets obtained in the present study for both the “full” (upper panel) and “center” (lower panel) apertures. Again, we observe good agreement between the different data sets, which are combined to derive universal transport efficiency curves (solid curves), which can be used in a folding procedure to obtain absolute detection efficiencies for recoil products with specific energy distributions. It is emphasized, however, that these energy acceptance curves apply only to the specific apertures used
32S+‘84W elastic recoils
Fig. 4. Measured absolute transport efficiencies for different entrance apertures and energy settings of the J?MA (solid symbols). Solid curves represent GIOS predictions.
210
B.B. Back et al. I Nucl. Instr. and Meth. in Phys. Res. A 379 (1996) 206-211
FMA transport efficiency ----
r
z
Full aperture
Linearfii Cubic fit
300 -
f : s - 250 s E H x 200 -
t
150
:::::::::::I:::::::::::. Full aperture
@)
Center aperture l ilOMeVS+Pb
.?,+W
;:J_‘,,,,., +g?jyq,l
11OMeV
. S+Pb 110 MeV a
0.94
l S+Th SO MeV
I
--
0.8
Theoly Exp. average
0.9
1.0
1.1
0.98
1 .oo
1.02
1.04
1.06
WsYWqd
i. 0.7
0.96
1.2
1.3
1.4
1.5
1.6
.I
Fig. 6. The scaling of the position along the focal plane (X position) with the m/q ratio relative to the FMA setting mo/qo is demonstrated for three systems (panel a). The measured transport efficiency (symbols) is compared to theoretical predictions using the GIOS code (dashed curve) in panel b.
WW(E&,)
Fig. 5. Measured absolute transport efficiencies (symbols) are compared with GIOS calculations for both the “full” (panel a) and the “center” (panel b) apertures. The solid curves are three point averages of the experimental data. in this work. The use of other apertures with different sizes and/or shapes will result in different energy acceptance curves.
calculation which is seen to predict a slightly more constant efficiency function. The discrepancy is again thought to arise mainly from inadequacies in the description of fringe fields in the GIOS calculations. The position, X, along the focal plane is plotted in Fig. 6a as a function of the ratio (m/q)l(m,lq,). We observe that the relation is almost linear (dashed line) with a small cubic component (solid curve), which presumably is caused by higher order aberrations in the spectrometer.
4.3. mlq acceptance The transport efficiency of the FMA was also measured as a function of the mass-to-charge ratio, m/q, of the incident ion relative to the setting of the FMA, i.e. (m/q)/ (m,/qo). This was done by varying the charge state setting, qo, in steps of l/l0 units for the FMA while the energy setting was kept at the correct energy of the recoils i.e. E. = E. The transport efficiency also depends on the ratio (Elq)l(E,lq,) as shown in Fig. 5, and, therefore, it includes also this dependence. The data shown in Fig. 6b have, however, been corrected for this dependence such that they represent the dependence on the ratio (mlq)l(m,l q,,) for a fixed value of E/q = E,,lq,. We observe that the FMA has an essentially constant acceptance over the range (m/q)l(m,lq,) = 0.965-1.035 or t3+% around the central &due, outside of which it falls off quite rapidly. The dashed curve in Fig. 6b represents the result of a GIOS
5. Summary A rather general method for measuring the transport efficiency for recoil mass spectrometers used in lowenergy heavy-ion fusion experiments has been described. This method has been used to map the acceptance of the Argonne fragment mass analyzer as a function of entrance angle, mass-to-charge, and energy-to-charge ratios of the incident ion relative to the setting of the instrument. The measurements show that the scaling properties in terms of the ratios E/q and m/q are valid (as expected), and that the transport efficiency as a function of Elq and mlq closely follows the theoretical predictions using the GIOS code, but they reach only about ~85% at the maximum for the “full’ ’ aperture. The measurements have been combined to generate universal acceptance curves as a function Elq and
B.B. Back et al. I Nucl.
Instr. and Meth. in Phys. Res. A 379 (1996) 206-211
mlq of the incoming ions, which may be used for absolute cross section measurements using the fragment mass analyzer at Argonne.
Acknowledgements
This work was carried out under the auspecies of the US Department of Energy under Contract No. W-31-109-Eng3%.
References [l] H. Wollnik, J. Brezina and M. Berz, Nucl. Instr. and Meth. A ‘258 (1987) 408. [2] G. Miinzenberg, W. Faust, S. Hofmann, P. Armbruster, K.
Giittner and H. Ewald, Nucl. Instr. and Meth. 161 (1979) 65.
211
[31 A.N. James, T.P. Morrison, K.L. Ying, K.A. Connell, H.G.
Price and J. Simpson, Nucl. Ins& and Meth. A 267 (1988) 144. [41 P. Spolaore, J.D. Larson, C. Signorini, S. Beghini, X.K. Zhu and H.Z. Si, Nucl. Instr. and Meth. A 238 (1985) 381. PI C.N. Davids and J.D. Larson, Nucl. Instr. and Meth. B 40/41 (1989) 1224. C.N. Davids, B.B. Back, K. Bindra, D.J. Henderson, W. [61 Kutschera, T. Lauritsen, Y. Nagame, P. Sugathan, A.V. Rammaya and W.B. Walters, Nucl. In&. and Meth. B 70 (1992) 358. [71 A.K. Sinha, N. Madhavan, J.J. Das, P Sugathan, D.O. Kataxia, A.P. Patro and G.K. Mehta, Nucl. Instr. and Meth. A 339 (1994) 543. PI A.V.Yeremin, A.N. Andreyev, D.D. Bogdanov, V.I. Chepigin, VA. Gorshkov, A.I. Ivanenko, A.P. Kabachenko, L.A. Rubinskaya, E.M. Smimova, S.V. Stepantsov, E.N. Voronkov and G.M. Ter-Akopian, Nucl. Instr. and Meth. A 274 (1989) 528. [91 K. Shima et al., Nucl. Instr. and Meth. A 200 (1982) 277.
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH
Section A
EISE&lER
Transport efficiency of the Argonne fragment mass analyzer B.B. Back*, D.J. Blumenthal,
C.N. Davids, D.J. Henderson, H.T. PenttiEi2, A.H. Wuosmaa
Physics Division,
Argonne National Laboratory,
Argonne,
R.H. Hermann’,
C.L. Jiang,
IL 60439, USA
Received 28 December 1995 Abstract Absolute transmission efficiencies for the Argonne fragment mass analyzer (FMA) have been measured for ions of ls4W, *“Pb, and Z3*Th with energies in the range E = 20-45 MeV. These were obtained by Rutherford scattering of ?S beams of 50, 80 and 110 MeV into backward angles, Measurements were performed for a range of settings for the FMA in order to determine the acceptance of the instrument as a function of energy and angle of the incident ion. The transport efficiency across the focal plane was also measured. The results are compared with predictions of the transport code GIOS [H. Wollnik et al., Nucl. Instr. and Meth. A 258 (1987) 4081, which agree well with the data. With these data we conclude that the transport efficiency of the FMA is sufficiently well known to support measurements of absolute cross sections with an accuracy of 210%.
1. Introdtiction
2. Method
In this paper we describe a simple and efficient method for measuring the transport efficiency of low energy recoil mass spectrometers of the type that have found widespread use in recent years [2-81. Such measurements are crucial for determining accurate cross sections using such devices. The present method is applicable for determining the transport efficiency of fusion products formed in normal kinematic reactions, i.e. with light projectiles onto a heavier target for beam energies up to several times the Coulomb barrier. We also present measurements of the absolute transport efficiency of the Argonne fragment mass analyzer (FMA) obtained by elastic backscattering of ?S by targets of is4W, “‘Pb, and ?‘h at three beam energies, 50, 80, and 110 MeV, all of which are well below the Coulomb barrier of the targets used. The method of using elastic recoils for efficiency measurements is discussed in Section 2, followed by a presentation of the experimental procedure in Section 3. The resulting transport efficiencies are discussed and compared with theoretical calculations in Section 4, followed by a summary in Section 5.
* Corresponding author. Tel. + 1 630 2523618, e-mail: [email protected]. ’ Now at Technische Universitit Miinchen, * Now at University of Jyvlskyll, Finland.
fax + 1 630
2526210,
0168-9002/96/$15.00 Copyright PZZ SO168-9002(96)00650-X
Munich,
0 1996 Published
Germany.
The method relies on the fact that target recoils from elastic heavy-ion scattering can be produced abundantly with well-known rates and energies into forward angles (where most spectrometers are located). Thus, if an evaporation residue of mass, M, is formed by fusion of a projectile with mass m, and energy E, and a target nucleus of mass M,, then its mean energy (E,,) is
Depending on the availability of targets with the same (or similar) mass it is possible to lower the beam energy to a value
(2) such that elastic recoils will emerge with the same energy as the evaporation residues under study. For normal kinematics (i.e. m, CM,), E, is substantially lower than the beam energy used to study the fusion process. Depending on the ease of changing (lowering) the beam energy of the accelerator in question, it becomes rather straightforward to measure the transport efficiency of the mass spectrometer in a very short time. In addition, by choosing a target of the same Z as the fusion products under study, one can use elastic backscattering to quickly measure the
by Elsevier Science B.V. All rights reserved
207
B.B. Back et al. I Nucl. Instr. and Meth. in Phys. Res. A 379 (1996) 206-211
charge state distribution, a feature that is important when the cross sections for evaporation residue production is low. As demonstrated below, it is, however, sufficient to map out the transport efficiency of the spectrometer only once because of the scaling properties of ion trajectories in electrostatic and magnetic fields. Thus, ion trajectories depend only on the ratios Elq and m/q, where E, m, and CJ are the energy, mass and charge of the ion respectively. The radii of curvature of the ion trajectory in the electric, %, and magnetic, B, field regions are given by
R,=E
and
R,,,=%,
q8’ respectively. In order to transport ions with parameters E,lq, and m,lq, entering the spectrometer on a central trajectory, the electric, 8 and magnetic B fields must be set such that the radii of curvature of the ion-trajectories match the ion-optical design parameters i.e.
(4) Using these field settings we therefore o E/q
R,=R,~o/4o,
and
R,=Ri
I. 0.6
find
mlq -d mJq,
I.
8.
I.
I.
I
0.8
1.0
1.2
1.4
1.6
VW&%,)
Elq Eo/qo
I
’
(5)
Furthermore, since Rz and Ri are fixed we can conclude that the trajectories through the spectrometer for ions which are initially injected on axis depend on the ion parameters only through these ratios. Similar arguments apply for off-axis trajectories, and consequently, the transmission probability E depends only on the ratios (EIq)I(E,,/q,), (mlq)l(m,lq,) and the entrance angles 0, 4, relative to the spectrometer axis (not the beam axis) i.e.
In the measurements described in the following sections, we have determined the dependencies of the transport efficiency s.MA for the ATLAS fragment mass analyzer as a function of all four parameters, albeit in only very coarse steps for the angular dependencies. Since it is much less time-consuming to change the settings of the FMA, the dependence on the ion energy and mass was mapped out by varying the parameters E,, and qO. The transport efficiency of the FMA as a function of angle and energy of the incident ions has been calculated using the computer code GIOS [I] as shown in Fig. 1. We note that the transport efficiency has a strong dependence on the angle 0 in the horizontal plane relative to the axis of the spectrometer. In order to map out the dependence over the angular acceptance we used five different entrance apertures, which are listed in Table 1, and illustrated in Fig. 1.
Fig. 1. Contour plots of the transmission efficiencies for the FMA calculated with the GIOS code. Panel (a) shows the dependence on the horizontal entrance angle 8 and the ion energy-to-charge ratio E/q, whereas the dependence on m/q and E/q are displayed in panel (b).
3. Experiment The measurements were carried out using a 45 cm diameter sliding-seal target-chamber coupled to the FMA (see Fig. 2). The FMA was placed at an angle of 5” relative to the beam axis in order to avoid the backgrounds from beam scattered off the first anode. Five square apertures, one subtending opening angles of 4.5” X 4.5” labelled “full”, and four subtending 1.5” X 1.5” labelled “left”, “center”, “right”, and “top” according to their placement were used to map out the entrance angle dependence
Table 1 Angular coverage
Aperture Full Left Center Right TOP
of entrance
aperhxes
c
4mai
a
[deal
[degl
[de@
[de,@
[msrl
-2: -2; -+
2$ -f I 24 :4
-2; -$
2$ z4 1 f 2;
6.25 0.694 0.694 0.694 0.694
@,,,
14 43
max
mln
43 --9 :4
B.B. Back et al. I Nucl. Instr. and Meth. in Phys. Res. A 379 (1996) 206-211
208
FMA
Entrance apertures
Fig. 2. Schematic of the Argonne fragment mass analyzer emphasizing the details of the target and focal plane detector regions.
of the transmission efficiency (see Fig. 1 and Table 1). The absolute transport efficiency was obtained by normalizing to elastic scattering in a monitor (Si) detector subtending a solid angle of L&_,” = 0.245 msr placed at 30”. Although it was not required for these measurements, a 40 yg/cm’ carbon foil was placed between the target and the entrance aperture in order to be compatible with an earlier measurement of the evaporation residue cross section for ?S + ‘*“W, where this foil was used to reset the charge state distribution before entering the FMA. Elastically scattered target recoils were registered in a position-sensitive parallel grid avalanche counter (PGAC) placed in the focal plane of the FMA followed, after a 40 cm flight path, by a 5 X 5 cm2 double-sided Si strip detector (DSSD) with sixteen strips in orthogonal directions on the front and back side of the detector. This detector was used to measure the efficiency, epGAc, of the PGAC detector, which has been slightly damaged in previous experiments. This was done by determining the probability for obtaining a signal in the PGAC for events detected in the DSSD.
4. Results The measurements were carried out at ?S beam energies of 50, 80, and 110 MeV on targets of ls4W, “‘Pb, and 232Th. A total 456 measurements were performed over a period of four days. The absolute transport efficiencies were calculated as follows: N PGAC
qFM.4=
Lnmonaklas 4 MA~~ec0ilEPGAC N mon ’
(7)
where NpGAC and N,,, are the counts in the PGAC and monitor detectors, respectively, and crecoi, and ueelasare the corresponding differential elastic scattering cross sections. Rutherford scattering cross sections were used since the beam energies were in all cases substantially lower than the interaction barrier. 4.1. Charge state distributions For each target/beam-energy case the FMA was set up for the nominal recoil energy and the charge distribution
was measured using the “full” aperture. The results are displayed in Fig. 3 as solid points. The charge states selected for the subsequent measurements of energy and m/q acceptance are indicated by arrows. Optimal Gaussian fits to the measured charge state distributions are shown as solid curves, whereas the dashed curves represent theoretical predictions using the formula proposed by Shima et al. [9]. We observe some deviations from these predictions, but find that the overall agreement is quite good. The fraction associated with the charge state setting chosen for subsequent measurements was obtained by normalizing to the integral of the fitted Gaussian. 4.2. Energy acceptance The energy dependence of the transport efficiency was obtained by performing measurements for different energy settings, E,,, of the FMA after selecting a charge state at or near the maximum of the distribution in each case (arrows in Fig. 3). The results for elastic ls4W recoils from backscattering of 3’s at energies of 50, 80, and 110 MeV are shown in Fig. 4 as a function of the parameter E/E,,, where E is the calculated recoil energy including energy losses in the target and reset foils. aperture we see that the transport For the “center” efficiency reaches nearly 100% over an energy region from approximately 80 to 120% of the energy set for the FMA. Beyond this region the acceptance falls off relatively sharply. As expected, we observe that the relative energy acceptance, e(EIE,J, is essentially independent of the beam (recoil) energy and for all the different entrance aperatures, thus demonstrating the scaling properties discussed in Section 2. By comparison of the data obtained with the “left”, “center”, and “right” apertures, we observe that the energy acceptance depends rather strongly on the horizontal entrance angle 0 into the spectrometer. The energy acceptance for the “left” aperture is thus shifted to lower energies than those for the “right” aperture. One may exploit this feature to extend the bending power of the FMA to higher energies than otherwise feasible by using an entrance aperture covering only a fraction of the total angular acceptance in the positive f3 region. We also observe that the energy acceptance does not depend on the
B.B. Back et al. I Nucl. Ins@. and Meth. in Phys. Res. A 379 (1996) 206-211
209
“S+?h
---Theory
10
15
20
25
10
15
20
25
IO
15
20
25
Charge slate q
Fig. 3. Measured (solid points) and Gaussian fits (solid curves) of charge-state distributions for elastic recoils are shown. Dashed curves represent theoretical predictions [9].
out-of-plane angle 4 as seen from the similarity of the spectra for the “center” and “top” apertures. The transport efficiency for the “full” aperture is seen to reach only about 85% and displays a smoother fall-off to both lower and higher energies. This is, in fact, exactly what is expected by combining the measurements for the apertures. The data are “center”, and “right” “left”, compared to the calculated efficiencies (solid curves) obtained from the code GIOS for the beam energy of 110 MeV. It is evident that the calculations generally predict a slightly more constant transport efficiency over the acceptance region followed by a sharper fall-off at the limits. Although the exact reason for this discrepancy is
not well understood, we suspect that it is associated with inadequacies in the description of the magnetic and electrostatic fringe fields used in the calculations. Fig. 5 shows the transport efficiency for a combination of all seven data sets obtained in the present study for both the “full” (upper panel) and “center” (lower panel) apertures. Again, we observe good agreement between the different data sets, which are combined to derive universal transport efficiency curves (solid curves), which can be used in a folding procedure to obtain absolute detection efficiencies for recoil products with specific energy distributions. It is emphasized, however, that these energy acceptance curves apply only to the specific apertures used
32S+‘84W elastic recoils
Fig. 4. Measured absolute transport efficiencies for different entrance apertures and energy settings of the J?MA (solid symbols). Solid curves represent GIOS predictions.
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B.B. Back et al. I Nucl. Instr. and Meth. in Phys. Res. A 379 (1996) 206-211
FMA transport efficiency ----
r
z
Full aperture
Linearfii Cubic fit
300 -
f : s - 250 s E H x 200 -
t
150
:::::::::::I:::::::::::. Full aperture
@)
Center aperture l ilOMeVS+Pb
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. S+Pb 110 MeV a
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l S+Th SO MeV
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--
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Theoly Exp. average
0.9
1.0
1.1
0.98
1 .oo
1.02
1.04
1.06
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0.96
1.2
1.3
1.4
1.5
1.6
.I
Fig. 6. The scaling of the position along the focal plane (X position) with the m/q ratio relative to the FMA setting mo/qo is demonstrated for three systems (panel a). The measured transport efficiency (symbols) is compared to theoretical predictions using the GIOS code (dashed curve) in panel b.
WW(E&,)
Fig. 5. Measured absolute transport efficiencies (symbols) are compared with GIOS calculations for both the “full” (panel a) and the “center” (panel b) apertures. The solid curves are three point averages of the experimental data. in this work. The use of other apertures with different sizes and/or shapes will result in different energy acceptance curves.
calculation which is seen to predict a slightly more constant efficiency function. The discrepancy is again thought to arise mainly from inadequacies in the description of fringe fields in the GIOS calculations. The position, X, along the focal plane is plotted in Fig. 6a as a function of the ratio (m/q)l(m,lq,). We observe that the relation is almost linear (dashed line) with a small cubic component (solid curve), which presumably is caused by higher order aberrations in the spectrometer.
4.3. mlq acceptance The transport efficiency of the FMA was also measured as a function of the mass-to-charge ratio, m/q, of the incident ion relative to the setting of the FMA, i.e. (m/q)/ (m,/qo). This was done by varying the charge state setting, qo, in steps of l/l0 units for the FMA while the energy setting was kept at the correct energy of the recoils i.e. E. = E. The transport efficiency also depends on the ratio (Elq)l(E,lq,) as shown in Fig. 5, and, therefore, it includes also this dependence. The data shown in Fig. 6b have, however, been corrected for this dependence such that they represent the dependence on the ratio (mlq)l(m,l q,,) for a fixed value of E/q = E,,lq,. We observe that the FMA has an essentially constant acceptance over the range (m/q)l(m,lq,) = 0.965-1.035 or t3+% around the central &due, outside of which it falls off quite rapidly. The dashed curve in Fig. 6b represents the result of a GIOS
5. Summary A rather general method for measuring the transport efficiency for recoil mass spectrometers used in lowenergy heavy-ion fusion experiments has been described. This method has been used to map the acceptance of the Argonne fragment mass analyzer as a function of entrance angle, mass-to-charge, and energy-to-charge ratios of the incident ion relative to the setting of the instrument. The measurements show that the scaling properties in terms of the ratios E/q and m/q are valid (as expected), and that the transport efficiency as a function of Elq and mlq closely follows the theoretical predictions using the GIOS code, but they reach only about ~85% at the maximum for the “full’ ’ aperture. The measurements have been combined to generate universal acceptance curves as a function Elq and
B.B. Back et al. I Nucl.
Instr. and Meth. in Phys. Res. A 379 (1996) 206-211
mlq of the incoming ions, which may be used for absolute cross section measurements using the fragment mass analyzer at Argonne.
Acknowledgements
This work was carried out under the auspecies of the US Department of Energy under Contract No. W-31-109-Eng3%.
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