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In-beam conversion electron spectrometer
N U C L E A R I N S T R U M E N T S AND METHODS 151 (1978)
135-141 ; ©
N O R T H - H O L L A N D PUBLISHING CO.
IN-BEAM CONVERSION ELECTRON SPECTROMETER JAMES E. DRAPER, RICHARD J. McDONALD and WALTER G. WYCKOFF
Crocker Nuclear Laboratory* and Physics Department, University of Cali.lbrnia, Davis, Cal(lbrnia 95616, U.S.A. Received 27 September 1977 An in-beam electron spectrometer, in use in this laboratory since 1970, is described with respect to its design, construction and performance. Its salient features are 4 ns time resolution, 2.5 keV energy resolution, unswept overall efficiency of 0.9x 10 -2 approximating a Gaussian of width dp/p=O.18 (fwhm), rejection of positrons (or electrons, by choice) by a factor > 850, rejection of all heavy charged particles, rejection of X-rays and shielding against y-rays, small volume for easily measuring angular distributions in vacuo, simple and smooth dependence of efficiency on energy, fast enough sweeping to average over accelerator fluctuations, low input power ~ 2 kW for an energy range of 40-2000 keV, - 1.(2 resistance to match solid state power supplies and extreme simplicity of construction at minimal cost. These constitute a versatile and powerful combination of qualifications for in-beam spectroscopy. 1. I n t r o d u c t i o n
In-beam experiments on conversion electrons following nuclear reactions produced by a particle accelerator usually require a spectrometer with good energy resolution ( ~ 3 keV), large efficiency, good time resolution and greatly reduced sensitivity to unwanted radiations such as gamma rays, scattered beam particles, X-rays, positrons and other reaction products. Such a system has been in use at this laboratory since 1970 and will be described here. More recently, other systems have been described1), and the earliest such experiment was reported 2) in 1963. However, we believe that the present system has a highly satisfactory combination of performance parameters of the type required for in-beam experiments, e.g., with 20-80 MeV alpha particle beams in (o~,xn) reactions, and that this combination is particularly suitable for this and other in-beam experiments. To anticipate subsequent topics, these characteristics include 2.5 keV energy resolution, 4 ns time resolution, unswept overall efficiency of 0.9× 10 -2 , rejection of positrons in favor of electrons (or vice versa) by at least a factor of 850 (a necessary feature when many neutron deficient nuclei are produced in the reactions), complete rejection of protons and more massive particles, rejection of X-rays, minimal sensitivity to gamma rays and no interfering peaks from them, light weight ( ~ 3 kg) and small volume for measuring angular distributions in vacuo, simple and smooth curve of unswept transmission vs. energy with no sudden changes of slope and a single-function dependence on the ratio of momentum to solenoid * Partially supported by National Science Foundation.
current, a swept transmission efficiency which is simply proportional to momentum, fast enough sweeping that fluctuations of accelerator current are unimportant, low power input of ~ 2 kW for an energy range of 40-2000 keV, convenient resistance (1-2 f2) for commercial power supplies and extreme simplicity of construction at minimal cost. The efficiency is large enough that at Vpj Point ector o
e
b
f
B=O
B=O
-
L
q
Fig. 1 (a). Electron trajectory from a point source to a point detector for the model in which B is parallel to-the axis af inside the cylinder of length L and B = 0 elsewhere.
C
a,f
/
/
d
Fig. 1 (b). Projection, onto a plane perpendicular to axis af, of three electron trajectories with various O and the same ~.
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DRAPER et al.
100 keV the cyclotron beam must be kept below 15 nA to control dead time in the data acquisition system. The system consists of a solenoidal magnet, a set of helical Pb vanes and a cooled Si(Li) detector of 110 m m 2 x 3 mm.
2. Principle of operation Much of the performance of the system can be understood with a simple model for the spatial distribution of the solenoidal magnetic field B. This is illustrated in fig. la where a uniform axial B exists inside the cylinder of length L, and B = 0 outside. Consider first a point source at a and a point detector at b. A trajectory from source to detector must look like one of the curves in fig. lb, and must return through the axis af. Since the speed of the electron is unchanged, then
TABLE 1 Angle ~ of fig. lb and eq. (4). L/ab
¢ (degrees)
6 5 4 3 2 1
281 273 262 248 233 211
turn are counted at a particular value of B. Furthermore, p cos 0,, B. Electrons may also reach the detector by havin~ the ¢ of eq. (4) increased by any integer multiple of 2zL For a given L, this would require a substantially smaller axial component of velocity, oh than that of eq. (5). In our instrument vanes arc used to reduce background, and these vanes alsc ab = e f (1) eliminate such lower energy electrons with multi. pie revolutions. is required for this return through the axis. Since p cos 0 is fixed by eq. (5), then for a give~ In fig. lb all angles ¢ must be the same, as will B a band of electron momenta reaches the detecnow be shown. First, relativistically, tor. From fig. la the largest ratio p / B (largest 0~ = ( . o e L / v h -~ vpL/ppt)h, (2) is dictated by the radius of the cylinder in which where coc is the cyclotron angular frequency, Op B ~ 0 , i.e., the bore of the solenoid. Conversely~ and Oh are shown in fig. la, and the electron mo- assuming that there is some shield of smaller ramentum is p = eBp. Also, geometrically, dius along the line af to reduce straight-through tk = r~+2 tan- a ( p p / b c ) . (3) background, the radius of the shield determines the lower limit on 0 which determines the smalCombining eqs. (2) and (3) gives lest p / B in the band. All of the trajectories in fig. ~b = rr+2 tan-1 (L/(oab). (4) lb are drawn with the same ~, as required. This suggests the use of helical vanes in order to reject Thus, ¢ is fixed, depending only on L / a b , a particles in the undesired range of charge-to-mass geometric factor, and not on the emission angle 0 ratio. Thus, for in-beam use with an accelerator o! nor the momentum p. Values of O are given in particles the scattered beam, emitted protons~ table 1. electrons of the undesired sign of charge (i.e., posNote that for a given 0, or bc, we could draw itrons if electrons are desired, or vice versa), and a circle with a different pp than that in fig. lb. lower energy photons could be prevented from However, for that trajectory to return to the axis, reaching the detector. the value of O would be different from that reIn particular, the trajectories of particles with quired by eq. (4), so eqs. (2) and (3) would not be the same relativistic mass and charge (same cysatisfied together. Thus, for a given 0 there is clotron frequency), leaving the target with velocities uniquely associated a particular pp and conse- in the plane abc, will at any given axial position quently a particular p. intersect a line (same for all such particles) passing Eq. (2) may be rewritten as through the axis af but perpendicular to af. The ~p = eBL/p cos 0. (5) angle from that line to the plane abc will increase somewhat uniformly as the intersection of that Since ~ is fixed for a given L / a b then p cos 0 is line with af moves from b to e. The spiral locus fixed by eq. (5). So for this idealized geometry, all of intersections of these lines with the bore of the electrons with a fixed axial component of momen- magnet is approximately a helix.
137
CONVERSION ELECTRON S P E C T R O M E T E R
If one wants to accept electrons and reject all positrons, or vice versa, then the vanes should be no farther apart than 2(~-zc). To appreciate this, consider an electron in fig. lb going clockwise on a trajectory and a positron going counterclockwise on the same curve. In this model of fig. 1, the timing resolution for electrons will be excellent. For a given B, eq. (5) requires a fixed value of p cos 0. For nonrelativistic electrons, for which the time-of-flight is appreciable, a fixed value of p cos 0 implies a fixed time-of-flight from source to detector. For 300 keV electrons this exact result is smeared. Nevertheless, with the spiral vanes the spread in time-of-flight is small. If the model of fig. 1 is made more realistic by considering a point source and small circular detector, then a small range of ~ is accepted. From eq. (5) this gives a small range of p cos 0, thus broadening the band of detected p/B approximately symmetrically. If also the source is changed from a point to a small circle of the same size as the detector then the momentum band is widened farther. Note, however, that this last effect is not large since in fig. la B is uniform so the line af may be displaced parallel to itself with no effect on eqs. (1)-(5). The final step to reality is a realistic spatial distribution of B. It is unnecessary to analyze this since experimental tests of the actual system with radioactive sources and with a current-carrying wire show that the analysis above is sufficient. 3. Construction In order to collect ~ 2 MeV electrons, considerable power is required in the solenoid to generate the B. It was determined that the most effective construction for cooling, efficiency and impedancematching to the power supply is to use a continuous copper ribbon for the conductor and a continuous mylar ribbon for insulation. The cooling is primarily by axial heat flow out the two end faces of the cylinder. Fig. 2 shows the construction, to scale. The coil contains about 450 ft of copper ribbon 0.002"× 1.5" next to approximately the same length of 0.0005"× 15" mylar ribbon, the pair being wound on a brass spool of 1.50" i.d. and 3/32" wall thickness. The final coil was 4.25"o.d., so it was as compactly wound as is possible. After winding, a thin layer of epoxy was poured, under vacuum, over each end. After hardening, the epoxy and
mylar were ground away to within 0.020" of the average edges of the copper foil. A few edges of copper were thus exposed and shorting, but the electrical resistance of the coil was restored by etching that surface briefly in dilute nitric acid. The epoxy, selected for its low viscosity and reasonable thermal conductivity (0.0026cal/cm.s. °C), was EPO-TEK 920 FL 3). After grinding, a very thin layer of epoxy was used to cement the cooling plate onto each end. Wire tests were conducted to determine the angle ( ¢ - r 0 , fig. lb, for the actual spatial distribution of B for fig. 2. A thin (#40) wire conducting 1 A was supported at two points corresponding to the center of the target and the center of the Si(Li) detector in fig. 2. The separation was 7.25", af in fig. la. The wire is constrained by the magnetic forces to follow a trajectory of an electron. For the idealization of fig. 1 the angle ( S - n ) should be independent of the solenoid current, the length of the wire, the tension in the wire and the current in the wire. Experimentally, this was the case, within ___3°, for all combinations of 5 to 20 A ~" ~ BEAM *'%. TARGET
IRON
~G
33 in
i i i i i
Si(Li)
Fig 2. Scale drawing of actual system. The helical vanes, 2.75" in length along the target-Si(Li) axis, are not shown, but they fill the bore of the solenoidal magnet.
138
J.E.
D R A P E R et al.
in the solenoid, 0.5 to 1.5 A in the thin wire and 1" variation in the wire length. The experimental result was e - n = 85° for the 7.25" symmetrical separation between centers of source and detector. Eel. (4) gives ¢,--n=85 ° for L = 5 . 0 0 " and L + 2 a b = 7.25". This effective L = 5.00" is to be compared with 4.88" for the sum of the outer edge-to-edge length of the iron casing and the inner diameter of the iron casing. Off-axis source and detector were tested by changing, from 0°, the angle between the axis of the solenoid and a line joining the ends of the thin wire. There was no measurable change (E 3°) in ( ~ - n ) for any possible combination of starting point in the source and landing point in the detector of fig. 2. In some experiments it is useful to measure the angular distribution of electrons with respect to the accelerator beam direction, or to use a different fixed angle for a particular run. For this reason, the entire system of fig. 2 is located inside the evacuated scattering chamber on a movable arm pivoted on an axis through the target. The Si(Li) detector assembly is cooled by using flexible, multistrand, woven copper wire strap 1" wide and ~ 10" long to connect the movable Si(Li) head assembly to a fixed liquid-nitrogen trap. During cyclotron runs, the total energy resolution at 1 MeV is 2.5 keV fwhm, uncorrected for the effect of the 1/4 mil. Mylar window, in front of the detector in fig. 2, which minimizes condensation of pump oil, etc., on the Si(Li) surface. It is noteworthy that the Kevex Si(Li) head assembly4), including the input FET, has survived ~ 50 cyclings between room temperature and liquid-nitrogen temperature. Such thermal cycling has apparently not caused any problem. 4, Helical vanes From these investigations it was decided to use a four-vane system, the vanes b e i n g made of 1/16" lead sheet. Adjacent vanes start 90° apart and each vane twists through 90° . Thus, the vane system is just optically opaque (straight through). One edge (straight) of each of the four sheets was on axis, joined to the other three by solder, and the sheets were curved so the outer edge of each sheet traced a helix. The helix was 2.75" long with a pitch of 4×2.75" corresponding to the 90° twist of each vane from beginning to end. The outer edges of the helical vanes fitted snugly into the bore of the solenoid. A plug ~0.3" thick, and
with the diameter of the detector, was built up ¢ solder at the center of the vanes. This afforded ad ditional X-ray and gamma-ray shielding. An interesting geometrical problem is the shap of the sheet before it is twisted to form a vane Consider that the axial length of the helix is L and the azimuthal angular difference from on end of a helical vane to the other end is a~, 90° iJ the present case. The proper shape of the shee before twisting can be shown to be a segment a circular annulus of inner radius r, outer radiu ( r + R ) and of angle fl subtended by the segmen of sheet. Then r = D R ] [ ( D 2 --I-R 2 ~2)~ _ D ' l ,
((
and = D/r.
('7
When the inner arc of radius r is pulled straigh to form a line, the outer arc is forced to a helix The projected thickness of lead contributed, a radius x, to the 7-ray shielding by any one vane is the smaller of D or t[1 +(D/x~)2] ½. Here t is th thickness of the lead sheet, 1/16" in the presen case. The value of this square root, for the geome try of fig. 3, is 8.9 at the detector radius o x = 5 mm, and it is 2.5 at the maximum radius o the vanes.
5. Transmission efficiency Any single trajectory of an electron of given B~ i.e., momentum, is composed of a series of infin itesimal segments each with a particular center o curvature and radius of curvature dictated by th~ magnitude and direction of B at that location Consider increasing the magnitude B by a con hO3 z
_o -~ IOz
'k
/ I' ./ /
\* \ \° \ \ .
/ I /
101
•/
t-
,~
\ * •
o
I
IO
/
/ I It2
I
14
ll6
18
210
CURRENT (A)
Fig. 3. Experimental curve of counting rate of 624 keV 13rc K-conversion electrons vs solenoid current L The dash~ curve is a Gaussian fitting the central region of data, drawJ for comparison.
CONVERSION
ELECTRON
stant factor everywhere without changing the direction of 11 anywhere. Then an electron with the same starting position and direction will follow exactly the same trajectory if its Bp, or momentum, is increased by the same factor. That is, it will then have, everywhere, exactly the same radius of curvature and center of curvature as before. Consequently, the transmission efficiency for the real solenoid will be a single function of I/p, if the iron does not saturate magnetically. This was corroborated experimentally. A plot of the experimental /max, the solenoid current giving maximum counting rate, vs p for the system of fig. 2 had the expected linearity for the range tested, 5-20 A. The empirical curve, for the first solenoid constructed, is Im~ = 14.8 (E2+2mc2E) ½,
(8)
where E is the electron kinetic energy in MeV and mc 2 is the rest energy of an electron. The transmission efficiency X(I,p) is here defined as the ratio of the counting rate of electrons of momentum p, with the solenoid current I, divided by the counting rate at p with I = 0 and the vanes removed, i.e., bare detector. Experimentally at I =/max, we have X = 80 without the vanes and 2 as much with the vanes. The rejection of positrons by the vanes was tested by optimizing I for 624 keV electrons from 137Cs and then reversing the direction of I. No line could be seen in the reversed case, so the rejection factor is ~ 850. Fig. 3 shows the relative transmission. This is simply the counting rate in the 624 keV K-conversion line of ~37Cs vs the current I in the solenoid. The ordinate is proportional to transmission efficiency, which is a single function of I/p, as discussed above. Consequently, the curve would have the same shape if we could fix I and vary the momentum p of monoergic electrons and plot the counting rate vs p-~. The full width at half maximum (fwhm) is 19% in momentum for any I, as deduced from fig. 3. The overall experimental efficiency at 624 keV is 0.9× 10 -2 for an isotropic source. This is with the vanes in place.
6. Efficiency when swept Sometimes the electron energies of interest in an experiment are within ~ 20% of each other, in which case a fixed I might be used. In other experiments, a wider range of energies is needed, so
SPECTROMETER
139
we sweep the current I linearly up and down (sawtooth waveform) at 12.8 s/cycle. This period could be decreased substantially before the inductance of the solenoid would cause problems, as discussed below. In this swept mode, it is important to know the relative efficiency vs E. Fortunately, this is simply proportional to momentum p, which can be seen as follows. Assume that the current is swept repeatedly between limits 11 and I2 for an integer number of cycles. Then the swept relative efficiency Sx is
Sx(p, 11, I2)oc
X(I/p) IdI/dt1-1 dI,
(9)
,111
where dI/dt is the slope of current vs time. Since X is a universal function of I/p=y, and Id//dtl = constant,
Sx(p, 11, I2) oc P fl2/p X(y) dy.
(10)
d ltlp
The curve X(y) is fig. 3 with ordinate o, X and abscissa = y. If I~ and 12 are sufficiently far on either side of the/max of eq. (8), so that X is negligible at those limits, then S~(p, 11, I2) oCp. (11) This efficiency increases with momentum simply because the fwhm of fig. 3 increases with p, X(I/p) being a universal curve. This is somewhat compensated by the decrease in conversion coefficients with increasing energy. Approximately, /2 must be about 25% larger than the/max of the largest energy of interest, and 11 must be 25 % smaller than the I,~ x of the smallest energy of interest in order for eq. (11) to apply adequately. This is determined from fig. 3. 7. Swept SCA The background from gamma rays and from electrons scattered inside the solenoid is further reduced by using a swept single-channel analyzer (SCA) to reject events in which the pulse height from the Si(Li) detector does not fall within the proper range of X(I/p) for the ! at the time of the event. To accomplish this, an on-line computer calculates from the instantaneous current I~ the energies Eu and EL satisfying eq. (8) for
imax/l i = lfv> 1,
[fL
(12)
140
J.E.
DRAPER
and delivers voltages corresponding to Eu and E L as the upper and lower bounds of a SCA. We usually use f u = 1.14 and fL=0.86. Again, the universality of X(I/p) is useful here. Considerable care is required in the setup to obtain the correct relation between the solenoid.current programming voltage from the computer and the pulse heights from the detector. With such care, eq. (l l) remains valid with the swept SCA. One point of concern is that for a voltage-controlling power supply the programming voltage may be linear with time, but the inductance of the solenoid causes a phase shift and rounding of the sharp peak and valley of the sawtooth waveform of current L To check this and other problems, a "blink" program was developed for setup in which the swept SCA is only opened for a narrow range of current I on the rise of the sawtooth, or on the fall of the sawtooth, and the spectra are compared. It was found that the phase shift and rounding were not significant at 12.8 s/cycle. This " b l i n k " program further avoids the problem that the solenoid comes to a different thermal equilibrium during sweeping than with fixed current, thus changing its impedance. With the "blink" program all tests and adjustments are made while sweeping, and this alleviates several problems and uncertainties. The upper limit on solenoid power (electron energy) was determined by putting the solenoid in an oven and measuring the coil resistance vs temperature. It was decided, somewhat arbitrarily, that it can withstand a maximum of 250 °C ( - × 2 in resistance). Our highest-energy run, swept to afford increased maximum energy, has been 0-33.5 A for which eq. (8) gives 0-1800 keV. Probably a sweep to 2500 keV would have been possible, if necessary. The average power in sweeping linearly between 11 and l 2 is proportional to the solenoid resistance, which increases with average power but may be determined from the voltage and current meters on the power supply. The average power is also proportional to the average square of the current which is, for the linear sweep, = :}(12+12 + 1112).
et al.
pressure of cooling water, temperature overrange or long ( > 1 s) interruption of the sweeping. 8. Performance Fig. 4 shows the conversion electron spectrum from a - 0 . 3 m g / c m 2 s o u r c e of 133Ba. This commercially prepared source is marginally uniform in thickness, so the 4 5 k e V peak is somewhat broadened. The run was for 4 rain, and the source strength was N 60/~Ci. The K peak of the 356 keV 81.0 356.0
383.9 --'--I1
160.6
O CHANNEL
500 NUMBER
lit
IO()O
Fig. 4. Spectrum of 133Baconversion electrons. The transition energies (keV) are indicated, and the flags show K, L, M energies. This commercial radioactive source is thick enough to broaden the 45 keV (lowest) peak, but the 356 keV K peak is 2.5 keV fwhm. The solenoid current is swept. 50
u3 CO:E 7
• =52E U
uJ j.J tJJ rr
(13)
For example, a linear sweep with I1 = 0 is equivalent in power to a constant current of 0.577/2. Operator failure or computer malfunction could overheat the solenoid. Consequently, protective circuits were installed to set I = 0 in case of low
z6o
460
660
sbo
adoo ~z'oo ~4bo
ELECTRON ENERGY
(keV)
Fig. 5. Counting rate of various electron peaks from =33Baand 152Eu sources. This is the relative efficiency of the full system in the swept mode. The curve is proportional to electron momentum as in e,q. (11).
CONVERSION ELECTRON S P E C T R O M E T E R 1 0 S ~
,
,
,
,
,
,
,
,
,
,
141
The performance at energies ~ 150 keV is considerably enhanced by the fast timing capabilities L of this system since prompt recoil electrons (6rays) may be distinguished from more delayed low-energy conversion electrons. This is especially evident in ref. 8 in which a 55 keV electron line from a 12+ state in 2°6pb was investigated. Since the time of flight of ~ 50 keV electrons through the system is ~1.5 ns, the timing resolution is limited only by the collection time in the Si(Li) detector and the timing spread due to electronic noise. For electrons ~ 300 keV our in-beam timing iOI curve is ~ 4 n s fwhm. At 50keV it is ~ 1 5 n s fwhm due to electronic noise. To utilize this fast time resolution, the data ac2oo 400 600 BOO tOOO quisition program, using CAMAC, sorts the CHANNEL NUMBER events into eight time bands of adjustable widths. Fig. 6. In-beam spectra from 30 MeV 2°4Hg(a(, 2n)2°6pb. The These are timed with respect to the ~ 2 ns beam cutoff near channel 1000 is at - 1670 keV. The upper curve is without the swept SCA, and the lower curve is with the swept bursts. The early bands are often ~ 4 ns wide, inSCA, showing an improvement in signal/noise ratio by a faccreasing to - 4 0 ns for the last band. tor of 4 at 1281 keV. The vertical scale is arbitrary for both Data are also taken in a repeating beam-on, curves, but the largest number of counts in any channel is beam-off mode, with 12.8 s and eight time bands 12 300 in the upper curve and 1800 in the lower curve. for beam-on and with 12.8 s and 1 band for beamoff. Alternatively, more bands may be used for transition is 2.5 keV wide (fwhm). The sweep was beam-off. The purpose is to distinguish longer1.0-13.5 A for I. The helical vanes were in place, lived ( ~ 1 0 s ) decays from the shorter (0.2/zs to but the swept SCA was not used. 10 s) with only a x 2 loss in counting rate. This Fig. 5 shows the curve of swept, relative effi- supplements the direct measurement, above, of ciency over 45-1361 keV, using tuba and 152Eu half lives of 5-200 ns. By pulsing the dee-voltage sources. Relative conversion coefficients for tuBa amplifier, the cyclotron beam can be switched on are from Nuclear Data5); those from m E u are or off in - 5 ms, so this 12.8 s sequence could be from Malmsten et al.6), modified by SpennyT). speeded substantially, if desired. The improvement from the swept SCA is shown in fig. 6. This was taken in-beam 8) with 3 0 M e V 2°4Hg(a~,2n)2°6pb and powder targets, References covering the range to 1670 keV electron energy. 1) Recent references are T. Lindblad and C. G. Lind6n, Nuci. The improvement in the signal-to-noise ratio from I~str. and Meth. 126 (1975) 397, and Y. Gono, R. L. Watthe swept SCA is x3.3 at 250 keV and ×4.0 at son, T. T. Sugihara and R. A. Kuebbing, Nucl. Instr. and Meth. 127 (1975) 391. See also references contained therein. 1281 keV. 2) G. B. Hansen, B. Elbek, K. A. Hagemann and W. F. HorThe bottom curve in fig. 6 was run for 2.5 h at nyak, Nucl. Phys. 47 (1963) 529. 20 nA beam current with ~ 0.6 m g / c m 2 target; the 3) Epoxy Technology, Inc. Watertown, Massachusetts, U.S.A. electronic threshold was raised to reduce the 4) Kevex Corporation, Burlingame, California, U.S.A. 5) E. A. Henry, Nucl. Data Sheets 11 (1974) 497. counting rate from spillover of &rays from the 6) G. Malmsten, O. Nilsson and I. Andersson, Ark. Fysik 33 target. The time band is 20-70 ns. The/2 for the (1966) 361. bottom curve is the solution of eq. (8) for 7) D. L. Spenny, (University of Colorado, Boulder, Colorado, 1560keV and that for the upper curve is for 1970) (unpublished), University Microfilm Order No. 711700 keV. The performance in-beam is considera5933. 8) j. E. Draper and R. J. McDonald, Phys. Rev. (October, bly enhanced by the rejection of positrons from 1977). the neutron-deficient nuclei formed by (a~,xn) 9) W. G. Wyckoff and J. E. Draper, Phys. Rev. C8 (1973) 796; reactions. Other in-beam experiments with this J. E. Draper, N. S. P. King and W. G. Wyckoff, Phys. Rev. system have been reportedg), and the manuscripts C9 (1974) 948. 10) j. E. Draper, Nucl. Instr. and Meth. 136 (1976) 151. for others are being written.
135-141 ; ©
N O R T H - H O L L A N D PUBLISHING CO.
IN-BEAM CONVERSION ELECTRON SPECTROMETER JAMES E. DRAPER, RICHARD J. McDONALD and WALTER G. WYCKOFF
Crocker Nuclear Laboratory* and Physics Department, University of Cali.lbrnia, Davis, Cal(lbrnia 95616, U.S.A. Received 27 September 1977 An in-beam electron spectrometer, in use in this laboratory since 1970, is described with respect to its design, construction and performance. Its salient features are 4 ns time resolution, 2.5 keV energy resolution, unswept overall efficiency of 0.9x 10 -2 approximating a Gaussian of width dp/p=O.18 (fwhm), rejection of positrons (or electrons, by choice) by a factor > 850, rejection of all heavy charged particles, rejection of X-rays and shielding against y-rays, small volume for easily measuring angular distributions in vacuo, simple and smooth dependence of efficiency on energy, fast enough sweeping to average over accelerator fluctuations, low input power ~ 2 kW for an energy range of 40-2000 keV, - 1.(2 resistance to match solid state power supplies and extreme simplicity of construction at minimal cost. These constitute a versatile and powerful combination of qualifications for in-beam spectroscopy. 1. I n t r o d u c t i o n
In-beam experiments on conversion electrons following nuclear reactions produced by a particle accelerator usually require a spectrometer with good energy resolution ( ~ 3 keV), large efficiency, good time resolution and greatly reduced sensitivity to unwanted radiations such as gamma rays, scattered beam particles, X-rays, positrons and other reaction products. Such a system has been in use at this laboratory since 1970 and will be described here. More recently, other systems have been described1), and the earliest such experiment was reported 2) in 1963. However, we believe that the present system has a highly satisfactory combination of performance parameters of the type required for in-beam experiments, e.g., with 20-80 MeV alpha particle beams in (o~,xn) reactions, and that this combination is particularly suitable for this and other in-beam experiments. To anticipate subsequent topics, these characteristics include 2.5 keV energy resolution, 4 ns time resolution, unswept overall efficiency of 0.9× 10 -2 , rejection of positrons in favor of electrons (or vice versa) by at least a factor of 850 (a necessary feature when many neutron deficient nuclei are produced in the reactions), complete rejection of protons and more massive particles, rejection of X-rays, minimal sensitivity to gamma rays and no interfering peaks from them, light weight ( ~ 3 kg) and small volume for measuring angular distributions in vacuo, simple and smooth curve of unswept transmission vs. energy with no sudden changes of slope and a single-function dependence on the ratio of momentum to solenoid * Partially supported by National Science Foundation.
current, a swept transmission efficiency which is simply proportional to momentum, fast enough sweeping that fluctuations of accelerator current are unimportant, low power input of ~ 2 kW for an energy range of 40-2000 keV, convenient resistance (1-2 f2) for commercial power supplies and extreme simplicity of construction at minimal cost. The efficiency is large enough that at Vpj Point ector o
e
b
f
B=O
B=O
-
L
q
Fig. 1 (a). Electron trajectory from a point source to a point detector for the model in which B is parallel to-the axis af inside the cylinder of length L and B = 0 elsewhere.
C
a,f
/
/
d
Fig. 1 (b). Projection, onto a plane perpendicular to axis af, of three electron trajectories with various O and the same ~.
136
J.E.
DRAPER et al.
100 keV the cyclotron beam must be kept below 15 nA to control dead time in the data acquisition system. The system consists of a solenoidal magnet, a set of helical Pb vanes and a cooled Si(Li) detector of 110 m m 2 x 3 mm.
2. Principle of operation Much of the performance of the system can be understood with a simple model for the spatial distribution of the solenoidal magnetic field B. This is illustrated in fig. la where a uniform axial B exists inside the cylinder of length L, and B = 0 outside. Consider first a point source at a and a point detector at b. A trajectory from source to detector must look like one of the curves in fig. lb, and must return through the axis af. Since the speed of the electron is unchanged, then
TABLE 1 Angle ~ of fig. lb and eq. (4). L/ab
¢ (degrees)
6 5 4 3 2 1
281 273 262 248 233 211
turn are counted at a particular value of B. Furthermore, p cos 0,, B. Electrons may also reach the detector by havin~ the ¢ of eq. (4) increased by any integer multiple of 2zL For a given L, this would require a substantially smaller axial component of velocity, oh than that of eq. (5). In our instrument vanes arc used to reduce background, and these vanes alsc ab = e f (1) eliminate such lower energy electrons with multi. pie revolutions. is required for this return through the axis. Since p cos 0 is fixed by eq. (5), then for a give~ In fig. lb all angles ¢ must be the same, as will B a band of electron momenta reaches the detecnow be shown. First, relativistically, tor. From fig. la the largest ratio p / B (largest 0~ = ( . o e L / v h -~ vpL/ppt)h, (2) is dictated by the radius of the cylinder in which where coc is the cyclotron angular frequency, Op B ~ 0 , i.e., the bore of the solenoid. Conversely~ and Oh are shown in fig. la, and the electron mo- assuming that there is some shield of smaller ramentum is p = eBp. Also, geometrically, dius along the line af to reduce straight-through tk = r~+2 tan- a ( p p / b c ) . (3) background, the radius of the shield determines the lower limit on 0 which determines the smalCombining eqs. (2) and (3) gives lest p / B in the band. All of the trajectories in fig. ~b = rr+2 tan-1 (L/(oab). (4) lb are drawn with the same ~, as required. This suggests the use of helical vanes in order to reject Thus, ¢ is fixed, depending only on L / a b , a particles in the undesired range of charge-to-mass geometric factor, and not on the emission angle 0 ratio. Thus, for in-beam use with an accelerator o! nor the momentum p. Values of O are given in particles the scattered beam, emitted protons~ table 1. electrons of the undesired sign of charge (i.e., posNote that for a given 0, or bc, we could draw itrons if electrons are desired, or vice versa), and a circle with a different pp than that in fig. lb. lower energy photons could be prevented from However, for that trajectory to return to the axis, reaching the detector. the value of O would be different from that reIn particular, the trajectories of particles with quired by eq. (4), so eqs. (2) and (3) would not be the same relativistic mass and charge (same cysatisfied together. Thus, for a given 0 there is clotron frequency), leaving the target with velocities uniquely associated a particular pp and conse- in the plane abc, will at any given axial position quently a particular p. intersect a line (same for all such particles) passing Eq. (2) may be rewritten as through the axis af but perpendicular to af. The ~p = eBL/p cos 0. (5) angle from that line to the plane abc will increase somewhat uniformly as the intersection of that Since ~ is fixed for a given L / a b then p cos 0 is line with af moves from b to e. The spiral locus fixed by eq. (5). So for this idealized geometry, all of intersections of these lines with the bore of the electrons with a fixed axial component of momen- magnet is approximately a helix.
137
CONVERSION ELECTRON S P E C T R O M E T E R
If one wants to accept electrons and reject all positrons, or vice versa, then the vanes should be no farther apart than 2(~-zc). To appreciate this, consider an electron in fig. lb going clockwise on a trajectory and a positron going counterclockwise on the same curve. In this model of fig. 1, the timing resolution for electrons will be excellent. For a given B, eq. (5) requires a fixed value of p cos 0. For nonrelativistic electrons, for which the time-of-flight is appreciable, a fixed value of p cos 0 implies a fixed time-of-flight from source to detector. For 300 keV electrons this exact result is smeared. Nevertheless, with the spiral vanes the spread in time-of-flight is small. If the model of fig. 1 is made more realistic by considering a point source and small circular detector, then a small range of ~ is accepted. From eq. (5) this gives a small range of p cos 0, thus broadening the band of detected p/B approximately symmetrically. If also the source is changed from a point to a small circle of the same size as the detector then the momentum band is widened farther. Note, however, that this last effect is not large since in fig. la B is uniform so the line af may be displaced parallel to itself with no effect on eqs. (1)-(5). The final step to reality is a realistic spatial distribution of B. It is unnecessary to analyze this since experimental tests of the actual system with radioactive sources and with a current-carrying wire show that the analysis above is sufficient. 3. Construction In order to collect ~ 2 MeV electrons, considerable power is required in the solenoid to generate the B. It was determined that the most effective construction for cooling, efficiency and impedancematching to the power supply is to use a continuous copper ribbon for the conductor and a continuous mylar ribbon for insulation. The cooling is primarily by axial heat flow out the two end faces of the cylinder. Fig. 2 shows the construction, to scale. The coil contains about 450 ft of copper ribbon 0.002"× 1.5" next to approximately the same length of 0.0005"× 15" mylar ribbon, the pair being wound on a brass spool of 1.50" i.d. and 3/32" wall thickness. The final coil was 4.25"o.d., so it was as compactly wound as is possible. After winding, a thin layer of epoxy was poured, under vacuum, over each end. After hardening, the epoxy and
mylar were ground away to within 0.020" of the average edges of the copper foil. A few edges of copper were thus exposed and shorting, but the electrical resistance of the coil was restored by etching that surface briefly in dilute nitric acid. The epoxy, selected for its low viscosity and reasonable thermal conductivity (0.0026cal/cm.s. °C), was EPO-TEK 920 FL 3). After grinding, a very thin layer of epoxy was used to cement the cooling plate onto each end. Wire tests were conducted to determine the angle ( ¢ - r 0 , fig. lb, for the actual spatial distribution of B for fig. 2. A thin (#40) wire conducting 1 A was supported at two points corresponding to the center of the target and the center of the Si(Li) detector in fig. 2. The separation was 7.25", af in fig. la. The wire is constrained by the magnetic forces to follow a trajectory of an electron. For the idealization of fig. 1 the angle ( S - n ) should be independent of the solenoid current, the length of the wire, the tension in the wire and the current in the wire. Experimentally, this was the case, within ___3°, for all combinations of 5 to 20 A ~" ~ BEAM *'%. TARGET
IRON
~G
33 in
i i i i i
Si(Li)
Fig 2. Scale drawing of actual system. The helical vanes, 2.75" in length along the target-Si(Li) axis, are not shown, but they fill the bore of the solenoidal magnet.
138
J.E.
D R A P E R et al.
in the solenoid, 0.5 to 1.5 A in the thin wire and 1" variation in the wire length. The experimental result was e - n = 85° for the 7.25" symmetrical separation between centers of source and detector. Eel. (4) gives ¢,--n=85 ° for L = 5 . 0 0 " and L + 2 a b = 7.25". This effective L = 5.00" is to be compared with 4.88" for the sum of the outer edge-to-edge length of the iron casing and the inner diameter of the iron casing. Off-axis source and detector were tested by changing, from 0°, the angle between the axis of the solenoid and a line joining the ends of the thin wire. There was no measurable change (E 3°) in ( ~ - n ) for any possible combination of starting point in the source and landing point in the detector of fig. 2. In some experiments it is useful to measure the angular distribution of electrons with respect to the accelerator beam direction, or to use a different fixed angle for a particular run. For this reason, the entire system of fig. 2 is located inside the evacuated scattering chamber on a movable arm pivoted on an axis through the target. The Si(Li) detector assembly is cooled by using flexible, multistrand, woven copper wire strap 1" wide and ~ 10" long to connect the movable Si(Li) head assembly to a fixed liquid-nitrogen trap. During cyclotron runs, the total energy resolution at 1 MeV is 2.5 keV fwhm, uncorrected for the effect of the 1/4 mil. Mylar window, in front of the detector in fig. 2, which minimizes condensation of pump oil, etc., on the Si(Li) surface. It is noteworthy that the Kevex Si(Li) head assembly4), including the input FET, has survived ~ 50 cyclings between room temperature and liquid-nitrogen temperature. Such thermal cycling has apparently not caused any problem. 4, Helical vanes From these investigations it was decided to use a four-vane system, the vanes b e i n g made of 1/16" lead sheet. Adjacent vanes start 90° apart and each vane twists through 90° . Thus, the vane system is just optically opaque (straight through). One edge (straight) of each of the four sheets was on axis, joined to the other three by solder, and the sheets were curved so the outer edge of each sheet traced a helix. The helix was 2.75" long with a pitch of 4×2.75" corresponding to the 90° twist of each vane from beginning to end. The outer edges of the helical vanes fitted snugly into the bore of the solenoid. A plug ~0.3" thick, and
with the diameter of the detector, was built up ¢ solder at the center of the vanes. This afforded ad ditional X-ray and gamma-ray shielding. An interesting geometrical problem is the shap of the sheet before it is twisted to form a vane Consider that the axial length of the helix is L and the azimuthal angular difference from on end of a helical vane to the other end is a~, 90° iJ the present case. The proper shape of the shee before twisting can be shown to be a segment a circular annulus of inner radius r, outer radiu ( r + R ) and of angle fl subtended by the segmen of sheet. Then r = D R ] [ ( D 2 --I-R 2 ~2)~ _ D ' l ,
((
and = D/r.
('7
When the inner arc of radius r is pulled straigh to form a line, the outer arc is forced to a helix The projected thickness of lead contributed, a radius x, to the 7-ray shielding by any one vane is the smaller of D or t[1 +(D/x~)2] ½. Here t is th thickness of the lead sheet, 1/16" in the presen case. The value of this square root, for the geome try of fig. 3, is 8.9 at the detector radius o x = 5 mm, and it is 2.5 at the maximum radius o the vanes.
5. Transmission efficiency Any single trajectory of an electron of given B~ i.e., momentum, is composed of a series of infin itesimal segments each with a particular center o curvature and radius of curvature dictated by th~ magnitude and direction of B at that location Consider increasing the magnitude B by a con hO3 z
_o -~ IOz
'k
/ I' ./ /
\* \ \° \ \ .
/ I /
101
•/
t-
,~
\ * •
o
I
IO
/
/ I It2
I
14
ll6
18
210
CURRENT (A)
Fig. 3. Experimental curve of counting rate of 624 keV 13rc K-conversion electrons vs solenoid current L The dash~ curve is a Gaussian fitting the central region of data, drawJ for comparison.
CONVERSION
ELECTRON
stant factor everywhere without changing the direction of 11 anywhere. Then an electron with the same starting position and direction will follow exactly the same trajectory if its Bp, or momentum, is increased by the same factor. That is, it will then have, everywhere, exactly the same radius of curvature and center of curvature as before. Consequently, the transmission efficiency for the real solenoid will be a single function of I/p, if the iron does not saturate magnetically. This was corroborated experimentally. A plot of the experimental /max, the solenoid current giving maximum counting rate, vs p for the system of fig. 2 had the expected linearity for the range tested, 5-20 A. The empirical curve, for the first solenoid constructed, is Im~ = 14.8 (E2+2mc2E) ½,
(8)
where E is the electron kinetic energy in MeV and mc 2 is the rest energy of an electron. The transmission efficiency X(I,p) is here defined as the ratio of the counting rate of electrons of momentum p, with the solenoid current I, divided by the counting rate at p with I = 0 and the vanes removed, i.e., bare detector. Experimentally at I =/max, we have X = 80 without the vanes and 2 as much with the vanes. The rejection of positrons by the vanes was tested by optimizing I for 624 keV electrons from 137Cs and then reversing the direction of I. No line could be seen in the reversed case, so the rejection factor is ~ 850. Fig. 3 shows the relative transmission. This is simply the counting rate in the 624 keV K-conversion line of ~37Cs vs the current I in the solenoid. The ordinate is proportional to transmission efficiency, which is a single function of I/p, as discussed above. Consequently, the curve would have the same shape if we could fix I and vary the momentum p of monoergic electrons and plot the counting rate vs p-~. The full width at half maximum (fwhm) is 19% in momentum for any I, as deduced from fig. 3. The overall experimental efficiency at 624 keV is 0.9× 10 -2 for an isotropic source. This is with the vanes in place.
6. Efficiency when swept Sometimes the electron energies of interest in an experiment are within ~ 20% of each other, in which case a fixed I might be used. In other experiments, a wider range of energies is needed, so
SPECTROMETER
139
we sweep the current I linearly up and down (sawtooth waveform) at 12.8 s/cycle. This period could be decreased substantially before the inductance of the solenoid would cause problems, as discussed below. In this swept mode, it is important to know the relative efficiency vs E. Fortunately, this is simply proportional to momentum p, which can be seen as follows. Assume that the current is swept repeatedly between limits 11 and I2 for an integer number of cycles. Then the swept relative efficiency Sx is
Sx(p, 11, I2)oc
X(I/p) IdI/dt1-1 dI,
(9)
,111
where dI/dt is the slope of current vs time. Since X is a universal function of I/p=y, and Id//dtl = constant,
Sx(p, 11, I2) oc P fl2/p X(y) dy.
(10)
d ltlp
The curve X(y) is fig. 3 with ordinate o, X and abscissa = y. If I~ and 12 are sufficiently far on either side of the/max of eq. (8), so that X is negligible at those limits, then S~(p, 11, I2) oCp. (11) This efficiency increases with momentum simply because the fwhm of fig. 3 increases with p, X(I/p) being a universal curve. This is somewhat compensated by the decrease in conversion coefficients with increasing energy. Approximately, /2 must be about 25% larger than the/max of the largest energy of interest, and 11 must be 25 % smaller than the I,~ x of the smallest energy of interest in order for eq. (11) to apply adequately. This is determined from fig. 3. 7. Swept SCA The background from gamma rays and from electrons scattered inside the solenoid is further reduced by using a swept single-channel analyzer (SCA) to reject events in which the pulse height from the Si(Li) detector does not fall within the proper range of X(I/p) for the ! at the time of the event. To accomplish this, an on-line computer calculates from the instantaneous current I~ the energies Eu and EL satisfying eq. (8) for
imax/l i = lfv> 1,
[fL
(12)
140
J.E.
DRAPER
and delivers voltages corresponding to Eu and E L as the upper and lower bounds of a SCA. We usually use f u = 1.14 and fL=0.86. Again, the universality of X(I/p) is useful here. Considerable care is required in the setup to obtain the correct relation between the solenoid.current programming voltage from the computer and the pulse heights from the detector. With such care, eq. (l l) remains valid with the swept SCA. One point of concern is that for a voltage-controlling power supply the programming voltage may be linear with time, but the inductance of the solenoid causes a phase shift and rounding of the sharp peak and valley of the sawtooth waveform of current L To check this and other problems, a "blink" program was developed for setup in which the swept SCA is only opened for a narrow range of current I on the rise of the sawtooth, or on the fall of the sawtooth, and the spectra are compared. It was found that the phase shift and rounding were not significant at 12.8 s/cycle. This " b l i n k " program further avoids the problem that the solenoid comes to a different thermal equilibrium during sweeping than with fixed current, thus changing its impedance. With the "blink" program all tests and adjustments are made while sweeping, and this alleviates several problems and uncertainties. The upper limit on solenoid power (electron energy) was determined by putting the solenoid in an oven and measuring the coil resistance vs temperature. It was decided, somewhat arbitrarily, that it can withstand a maximum of 250 °C ( - × 2 in resistance). Our highest-energy run, swept to afford increased maximum energy, has been 0-33.5 A for which eq. (8) gives 0-1800 keV. Probably a sweep to 2500 keV would have been possible, if necessary. The average power in sweeping linearly between 11 and l 2 is proportional to the solenoid resistance, which increases with average power but may be determined from the voltage and current meters on the power supply. The average power is also proportional to the average square of the current which is, for the linear sweep, = :}(12+12 + 1112).
et al.
pressure of cooling water, temperature overrange or long ( > 1 s) interruption of the sweeping. 8. Performance Fig. 4 shows the conversion electron spectrum from a - 0 . 3 m g / c m 2 s o u r c e of 133Ba. This commercially prepared source is marginally uniform in thickness, so the 4 5 k e V peak is somewhat broadened. The run was for 4 rain, and the source strength was N 60/~Ci. The K peak of the 356 keV 81.0 356.0
383.9 --'--I1
160.6
O CHANNEL
500 NUMBER
lit
IO()O
Fig. 4. Spectrum of 133Baconversion electrons. The transition energies (keV) are indicated, and the flags show K, L, M energies. This commercial radioactive source is thick enough to broaden the 45 keV (lowest) peak, but the 356 keV K peak is 2.5 keV fwhm. The solenoid current is swept. 50
u3 CO:E 7
• =52E U
uJ j.J tJJ rr
(13)
For example, a linear sweep with I1 = 0 is equivalent in power to a constant current of 0.577/2. Operator failure or computer malfunction could overheat the solenoid. Consequently, protective circuits were installed to set I = 0 in case of low
z6o
460
660
sbo
adoo ~z'oo ~4bo
ELECTRON ENERGY
(keV)
Fig. 5. Counting rate of various electron peaks from =33Baand 152Eu sources. This is the relative efficiency of the full system in the swept mode. The curve is proportional to electron momentum as in e,q. (11).
CONVERSION ELECTRON S P E C T R O M E T E R 1 0 S ~
,
,
,
,
,
,
,
,
,
,
141
The performance at energies ~ 150 keV is considerably enhanced by the fast timing capabilities L of this system since prompt recoil electrons (6rays) may be distinguished from more delayed low-energy conversion electrons. This is especially evident in ref. 8 in which a 55 keV electron line from a 12+ state in 2°6pb was investigated. Since the time of flight of ~ 50 keV electrons through the system is ~1.5 ns, the timing resolution is limited only by the collection time in the Si(Li) detector and the timing spread due to electronic noise. For electrons ~ 300 keV our in-beam timing iOI curve is ~ 4 n s fwhm. At 50keV it is ~ 1 5 n s fwhm due to electronic noise. To utilize this fast time resolution, the data ac2oo 400 600 BOO tOOO quisition program, using CAMAC, sorts the CHANNEL NUMBER events into eight time bands of adjustable widths. Fig. 6. In-beam spectra from 30 MeV 2°4Hg(a(, 2n)2°6pb. The These are timed with respect to the ~ 2 ns beam cutoff near channel 1000 is at - 1670 keV. The upper curve is without the swept SCA, and the lower curve is with the swept bursts. The early bands are often ~ 4 ns wide, inSCA, showing an improvement in signal/noise ratio by a faccreasing to - 4 0 ns for the last band. tor of 4 at 1281 keV. The vertical scale is arbitrary for both Data are also taken in a repeating beam-on, curves, but the largest number of counts in any channel is beam-off mode, with 12.8 s and eight time bands 12 300 in the upper curve and 1800 in the lower curve. for beam-on and with 12.8 s and 1 band for beamoff. Alternatively, more bands may be used for transition is 2.5 keV wide (fwhm). The sweep was beam-off. The purpose is to distinguish longer1.0-13.5 A for I. The helical vanes were in place, lived ( ~ 1 0 s ) decays from the shorter (0.2/zs to but the swept SCA was not used. 10 s) with only a x 2 loss in counting rate. This Fig. 5 shows the curve of swept, relative effi- supplements the direct measurement, above, of ciency over 45-1361 keV, using tuba and 152Eu half lives of 5-200 ns. By pulsing the dee-voltage sources. Relative conversion coefficients for tuBa amplifier, the cyclotron beam can be switched on are from Nuclear Data5); those from m E u are or off in - 5 ms, so this 12.8 s sequence could be from Malmsten et al.6), modified by SpennyT). speeded substantially, if desired. The improvement from the swept SCA is shown in fig. 6. This was taken in-beam 8) with 3 0 M e V 2°4Hg(a~,2n)2°6pb and powder targets, References covering the range to 1670 keV electron energy. 1) Recent references are T. Lindblad and C. G. Lind6n, Nuci. The improvement in the signal-to-noise ratio from I~str. and Meth. 126 (1975) 397, and Y. Gono, R. L. Watthe swept SCA is x3.3 at 250 keV and ×4.0 at son, T. T. Sugihara and R. A. Kuebbing, Nucl. Instr. and Meth. 127 (1975) 391. See also references contained therein. 1281 keV. 2) G. B. Hansen, B. Elbek, K. A. Hagemann and W. F. HorThe bottom curve in fig. 6 was run for 2.5 h at nyak, Nucl. Phys. 47 (1963) 529. 20 nA beam current with ~ 0.6 m g / c m 2 target; the 3) Epoxy Technology, Inc. Watertown, Massachusetts, U.S.A. electronic threshold was raised to reduce the 4) Kevex Corporation, Burlingame, California, U.S.A. 5) E. A. Henry, Nucl. Data Sheets 11 (1974) 497. counting rate from spillover of &rays from the 6) G. Malmsten, O. Nilsson and I. Andersson, Ark. Fysik 33 target. The time band is 20-70 ns. The/2 for the (1966) 361. bottom curve is the solution of eq. (8) for 7) D. L. Spenny, (University of Colorado, Boulder, Colorado, 1560keV and that for the upper curve is for 1970) (unpublished), University Microfilm Order No. 711700 keV. The performance in-beam is considera5933. 8) j. E. Draper and R. J. McDonald, Phys. Rev. (October, bly enhanced by the rejection of positrons from 1977). the neutron-deficient nuclei formed by (a~,xn) 9) W. G. Wyckoff and J. E. Draper, Phys. Rev. C8 (1973) 796; reactions. Other in-beam experiments with this J. E. Draper, N. S. P. King and W. G. Wyckoff, Phys. Rev. system have been reportedg), and the manuscripts C9 (1974) 948. 10) j. E. Draper, Nucl. Instr. and Meth. 136 (1976) 151. for others are being written.