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Excitation functions for the 24Mg(d,α)22Na, 26Mg(d,α)24Na and 27Al(d,αp)24Na reactions
J. inorg,nucl.Chem., 1969,Vol. 31, pp. 3345to 3356. PergamonPress. Printedin Great Britain
EXCITATION FUNCTIONS FOR THE 2aMg(d,a)Z2Na, Z6Mg(d,a)2aNa AND
2rAl(d,ap)24Na REACTIONS H. F. ROHM*, C. J. V E R W E Y t , J. STEYN and W. L. R A U T E N B A C H National Physical Research Laboratory and National Chemical Research Laboratory, P.O. Box 395, Pretoria, South Africa
(Received 13 March 1969) A l n t r a e t - E x c i t a t i o n functions were determined by the "stacked-foil" technique at the Pretoria 110-cm cyclotron for the ~4Mg(d,a)22Na and ~Mg(d,a)24Na reactions from 0 to 10 MeV, and the 2~AI(d,ap)24Na reaction from 0 to 16 MeV. The maximum measured cross-sections for the production of 22Na and ~4Na from magnesium were 185 mbarn (8-6 MeV) and 118 mbam (8.6 MeV) respectively. At 16.0 MeV the absolute cross-section for the production of 24Na from aluminium was 24.0 mbarn. Thick-target yields were calculated as a function of energy (0-16 MeV) for the production of 22Na and ~ N a from natural magnesium, and 24Na from aluminium. The calculated production rates of n N a and 24Na, by 16 MeV deuterons on natural magnesium, are 2.93/~Ci//zA-hr and 578-34 ~Ci//~A-hr respectively, while for production of 24Na from aluminium a value of 170.562/~Ci//~A-hr was obtained. INTRODUCTION
A c c u ~ x E excitation functions for the production of 22Na and 24Na by deuteron bombardment of magnesium and aluminium are needed: (a) to calculate the thick-target yields as functions of the incident deuteron energy, in order to optimize the commercial production of high specific activity 2ZNa and 24Na, (b) to determine the feasibility of charged-particle activation analysis of aluminium and magnesium [ 1], and (c) to use the induced 22Na and 24Na in magnesium and aluminium foils as monitors for deuteron beam intensity and energy, for instance in "stackedfoil" measurements, where aluminium catcher foils are often employed [2]. Published excitation curves for the production of ZZNa from magnesium differ by upwards of 30 per cent at the peak of the curve[3-5], while the thick-target yield for 14 MeV deuterons varies from 1-8 # Ci/mA-hr to 3.1 tzCi//~A-hr according to Irvine and Clarke [3] and to Vlasov e t al.[5], respectively. Reported crosssections for the ZrAl(d,ap)24Na reaction at 14 MeV differ by more than 80 per cent *Present address: Institut f'dr Radiochemie, Kernforschungszentrum Karlsruhe mbH, 75 Karlsruhe, Postfach 947, W. Germany. tDeceased. 1. 2. 3. 4. 5.
Enzo Ricci and R. L. Hahn, Analyt. Chem. 40, 55 (1968). A. Demildt, J. inorg, nucl. Chem. 23, 167 (1961). J.W. Irvine, Jr. and E. T. Clarke, J. chem. Phys. 16, 686 (1948). F.O. Bartell and Sheldon Softky, Phys. Rev. 84, 463 (1951). N. A. Vlasov, S. P. Kalinin, A. A. Ogloblin, V. M. Pankramov, V. P. Rudakov, N. N. Serikov and V. A. Sidorov,Atomn. Energ. 2, 169 (1957). 3345
3346
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[6-9]. Furthermore, the excitation function for the production of ~4Na from deuterons on magnesium, reported by Irvine and Clarke [3], showed a maximum at about 9 MeV and decreased with increasing energy. However, preliminary measurements at our laboratory showed a steep rise in the production of ~4Na above 1 1 MeV when a stack of magnesium foils was irradiated with deuterons. During the last decade, considerable progress has been made in techniques for the counting and absolute standardization of radioactivity, as well as in the quality of charged particle beams and beam diagnostics. Therefore, excitation functions determined at present by use of the "stacked-foil" technique should result in more accurate and reproducible measurements. We therefore remeasured the excitation curves for the production of 22Na and 24Na by deuterons on magnesium and aluminium, using the 16 MeV external beam of the Pretoria cyclotron. Special precautions were taken to ensure effective recoil collection in the catcher foils. The 4,rr-/3y coincidence counting method was used for the absolute measurement of the induced radioactivity, Since the standardization was done directly on selected target and catcher foils, possible errors introduced by chemical treatment and special source preparation were avoided. EXPERIMENTAL
(a) Preparation of the foil stacks. The stacks consisted of target foils sandwiched between appropriately chosen catcher foils to collect the recoils escaping from the targets, and absorbers which degraded the energy of the bombarding particles. The choice of recoil catcher foils was such that the reaction product induced therein by the bombarding particle differed from the reaction product of interest in the target material. Because the degraders were always of the same material as the catcher foils, corrections could be made for any Z2Na or 24Na resulting from deuteron activation of possible contamination in the catcher foils. Furthermore, in order to estimate the contribution of ~2Na or 24Na induced by fast and slow neutrons on 2aNa, target and catcher foils were stacked well beyond the range of 16 MeV deuterons. Three stacks were irradiated for each excitation function. Overlapping of the experimental points was avoided by staggering the target foils with respect to one another in the different stacks. All the pertinent information on the foils is listed in Table 1. Table 1. Material used in stacks Foil element
Inventory form
Natural Mg
Rods, 6.35 mm diam × 10 cm long Foils, 0.0005" and 0.001" thick
Natural Al
Mylar Sheets, (C, H and O - 3.5 mg/cm -2 as Polymethylmethacrylate) 6. 7. 8. 9.
Purity Spectrographically pure 99-997%
Supplier Johnson Matthey, London, England Materials Research Corporation, N e w York, U.S.A. Imperial Chemical Industries, England
E.T. Clarke, Phys. Rev. 71,187 (1947). R. E. Batzel, W. W. T. Crane and G. D. O'Kelly, Phys. Rev. 91,939 (1953). P. A. Lenk and R. J. Slobodrian, Phys. Rev. 102, 1229 (1959). G. Christaller, European Colloquium on A.V.F. Cyclotrons, Eindhoven (1965).
Excitation functions
3347
The aluminium and mylar foils were of commercial origin, whereas magnesium rods were rolled to pinhole-free foils of thickness varying from 0"3 to 2-7 mg/cm2. Because magnesium tends to workharden during rolling, these foils were rolled and annealed alternately down to the final thickness. Annealing was carried out at 330°C for about 3 hr in a vacuum oven (0.2 x 10-Storr), and the foils were then allowed to cool under vacuum. After the final anneal some foils were tested by X-ray diffraction. No preferred crystal orientation was found, which ruled out the possibility of "channelling" affecting the yield. The foils were punched into discs of diameter 2.24 cm. They fitted in a stack holder, which had an opening of diameter 2.0 cm for the beam to pass through. The foils were weighed in a humidity- and temperature-controlled room before the stacks were assembled for irradiation. The stacks used to measure 22Na production from magnesium contained aluminium catcher foils. The only way in which deuterons can produce 2~Na activity from aluminium is by either the ~7Al(d, ap2n)22Na or 27Al(d,aaH)22Na reactions, and since the incident energy of the deuteron beam was about 16 MeV neither of these reactions was energetically possible (Table 2). Table 2. Calculated Q-values, thresholds and Coulomb barriers for deuteron reactions on magnesium and aluminium leading to the production of 22Na and 24Na
Reaction
Q-Value (MeV)*
Threshold plus Coulomb barrier (MeV)
5" 16 5" 16 5.16
5" 16 10"96 22.89
24Mg(d, a)22Na ZSMg(d, otn)Z2Na
-- 5'369
26Mg(d, t~2n)22Na
- 16.464
-5"789 17-730
~Mg(d, c024Na 25Mg(d, He3)24Na 24Mg(d, 2p)24Na 25Mg(d, 2pn)24Na
2.915 -- 6-568 -- 6.957 - 14.286
-7.093 7.537 15.429
5.06 5-23 5.81 5.81
5-06 12.32 13.35 21.24
27Al(d, c~p)~4Na
-- 5.356 - 13.585 - 16-253 -- 24.735
5-752 14-591 17-457 26.567
7.97 7-20 7.81 8.13
13-72 21.79 25.27 34.70
2¢Al(d, a3H)22Na 27Al(d, ap2n)22Na
1"960
Threshold (MeV)
Coulomb barrier (MeV)t
*Calculated from 1964 atomic mass tables [ 10]. tThese values were calculated by use of the classical formula. Aluminium catcher foils could not be used in the stacks for the measurement of Z4Na production from magnesium, since 24Na is also produced by deuteron reactions on aluminium. Consequently mylar catcher foils were used in this case. For the production of 24Na from aluminium, the expected low cross-section precluded the use of mylar catchers and degrader foils. (Mylar is rather susceptible to radiation damage.) Consequently, a stack of aluminium foils only was used, in which the target foils were 3-416 mg/cm 2 thick and the degraders 6.833 mg/cm z thick. The percentage recoils escaping from aluminium foils of both the above-mentioned thicknesses was subsequently determined as a function of deuteron energy with the aid of mylar catchers in a supplementary experiment at much lower beam intensity. (b) Beam energy measurements. The energy of the cyclotron's external deuteron beam was measured by scattering it from a thin gold foil on to a semiconductor detector. A suitable aluminium absorber in front of the detector degraded the incident beam to 7.5 MeV, enabling one to use the 6.051 MeV and 8-785 MeV[I 1] a-particles from Th(B + C + C") for energy calibration. The uncertainty of the 10. J. H. E. Mattauch, W. Thiele and A. H. Wapstra, Nucl. Phys. 67, 1 (1965). 11. C. M. Lederer, J. M. Hollander and I. Perlman, Tables of Isotopes, 6 th Edn. Wiley, New York (1967).
3348
ROHM et al.
H.F.
incident energy as determined above was ___0" 1 MeV, while fluctuations in the primary beam energy during bombardment were estimated to be less than 0.2 MeV. (Taken in conjunction with the straggling in energy loss in the foils, effective energy spreads of 0.3 MeV for 10 MeV deuterons and 0-5 MeV for 4 MeV deuterons were obtained for a stack of aluminium, as calculated from range-energy tables[12]). Williamson's tables were used to calculate the energy degradation in aluminium and magnesium, and Brandt's tables [ 13] were used for mylar. The contribution of H~+ ions to the deuteron beam was checked during a scattering experiment [14] and was found to be non-existent. (c) Measurement of the integrated beam flux. The stack foils were clamped in a holder, which was located at the end of a Faraday cup assembly (Fig. 1). The base-plate, to which the holder was secured, was air-cooled, and, this cooling was found adequate for the beam currents used in this experiment. Two collimators, each 6 mm in diameter, were used to ensure a centrally-fixed beam spot on the stacks. Quadrupole lenses enabled sharp beam-focusing, resulting in 76 per cent transmission of the beam through the last collimator as measured both on the collimator and the Faraday cup.
ZnS Screen ~-Perspex-1. Foil stacks ~-- - ~ - - ~ n s u l o i o r s _ ~ (Quartz Screen)
Be°!~
A
=
I
r
Collimotors Scale:--
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0 I0 20 CM ~
:
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Fig. 1. Schematic representation of the experimental set-up. Before irradiating, the beam centre was checked by the ZnS screen between the two collimators and by temporarily placing a quartz screen in the stack position.
The possible contribution by secondary electrons to the beam current in the Faraday cup was investigated by applying a transverse magnetic field over the entrance of the Faraday cup and also by applying potentials of - 300 V and + 300 V to it. No effect was observed on the beam intensity under these conditions and it was therefore concluded that the effect of secondary electrons was negligible. During the irradiations of the stacks a precision integrator, working on the principle of an operational amplifier, was connected to the Faraday cup. The calibration of the current integrator was checked before and after each irradiation by using a known current for a fixed time. (d) Irradiations. All irradiations were carded out in the 0° beam port. It was not necessary to take into account beam intensity variations during the irradiations, because for each bombardment the irradiation time was short compared to the half-life of the reaction products. Table 3 gives average beam currents and irradiation times for the different stacks. Beam focus was checked between irradiations. Preliminary experiments showed that the mylar foils in the magnesium stacks could withstand beam current up to 40 x 10 -9 amp for 40 min without "burn-through" taking place. 12. C. F. Williamson, J. P. Boujot and J. Picard, Tables of Range and Stopping Power of Chemical Elements for Charged Particles of Energy 0.5 to 500 MeV No. CEA-R 3402, Saclay (1966). 13. Werner Brandt, Energy Loss of Charged Particles in Compounds. Research Rep., E. I. du Pont de Nemours, Delaware (1960). 14. G. Heymann, Private communication.
3349
Excitation functions Table 3. Beam intensities and duration of irradiation
Stack no. 1 2 3 4 5 6
Target foils
Degrader and catcher foils
Reaction
Incident deuteron energy (MeV)
Mg
AI*
24Mg(d, c022Na
16.2 -----0-1
Mg
Mylar
2eMg(d, c024Na
16.2 +--0.1
28 25 26
AI*
All"
27Al(d, otp)24Na
16-4 __+0-1
24 27
AI* Alt
Mylar
2TAl(d,ap)24Na
16.4 - 0-1
Average beam intensity (/~A)
Duration of irradiation (hr)
0.807 0.904 0-932 40-4 x 10-3 22.2 x 10-3 18.2 × 10-3
6.067 5.423 5.256 0.501 0.603 0.734
0.976 0.923 1.086
0.250 0.250 0.250
21"6 x 10-3 22.8 × 10-3
0.583 0.450
*Aluminium of 3.416 mg/cm2 thickness. tAluminium of 6.833 mg/cm2 thickness.
(e) Measurements of the activities produced (i) ~Na from magnesium. After irradiation, short-lived activities were allowed to decay for one month before relative counting and standardization of the 2"62 yr 22Na[11] commenced.Before counting the foils in a Nal(TI) well-type crystal, T-ray spectra were taken of several foils of magnesium and aluminium to verify that the only activity present was that from 22Na. During the relative counting, the electronic drift in the counting system was monitored over a period of 14 days and it was found that the maximum variation in the gain was between - 1 and + 1 per cent of the mean value. No detectable activity, outside the 3~r limit of background, was found for any of the degrader foils and magnesium foils beyond the deuteron range, and it may be concluded that 2~Na activity originating from 2SNa contamination was negligible. The amount of 22Na was measured absolutely in 20 magnesium foils from the three stacks by use of the 4*r-fiT coincidence method. Each foil was mounted between the two halves of a 41r-B proportional counter while the coincident gamma radiation was detected in a NaI(Tl) crystal. The mean beta counting efficiency was - 88 per cent, discrimination against annihilation radiation in the gamma channel was complete, and the accuracy obtained was within 1 per cent [ 15]. (ii) 24Na from magnesium. The relative counting of both the mylar and magnesium foils was carded out in a similar manner as previously described for 22Na. The activities found in the foils were 1.8 hr ~SF[I 1], 15-0 hr ~4Na[11] and 2.62 yr 22Na. Throughout the counting, these activities were followed in at least one of the most active foils from each stack. A typical decay curve obtained from one such foil is shown in Fig. 2. From the figure it may be seen that the 22Na activity is small compared to that of the 24Na induced in the magnesium. The small correction for the 22Na contribution therefore did not adversely affect the accuracy of the ~4Na measurement. Again no detectable 24Na or 22Na was recorded in the degrader foils. After the activity from lSF had decayed, I 1 target foils from the three stacks were standardized by the same method as that used for the 2~Na. The average beta counting efficiency here was 98 per cent. The accuracy obtained was 0-5 per cent. (iii) 24Nafrom aluminium. Both the relative counting and the standardization of the target foils were performed in a similar manner to that outlined in the previous section. Gamma-ray spectra from 15. J. Steyn and A. S. M. de Jesus, Coincidence Measurements on Nuclides Decaying by Electron Capture FIS 15, CSIR Special Rep., Pretoria, South Africa (1966).
3350
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Fig. 2. Decay curve of one of the magnesium foils, showing the presence of 2.62 yr 22Na and 15-hr 24Na only. several foils in the stack showed that the only activity present was 24Na (Fig. 3). In addition, the decay of activity was followed in at least one target and degrader foil from each of the stacks for about 12 days. The slope of the decay curve showed the presence of one activity only, with a 15-0-hr halflife.
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Excitation functions
3 3 51
(f) Percentage recoils of total activity Throughout this work meticulous care was taken to prevent the loss of activity. Thus the collection of recoils, by the catcher foils, was determined carefully in order to obtain its contribution to the total activity. (i) 22Na recoils from magnesium. 22Na recoiling in the forward direction (i.e. 2ZNa nuclei escaping from the target foil in the direction of the beam and which are collected in the adjacent aluminium catcher foil) was found to be about 28 per cent of the total 22Na activity produced in the target foils. This percentage decreased near the threshold of the (d,a) reaction on 24Mg. The average percentage recoils in the backward direction was about 0.7. For magnesium targets thicker than 2 mg/cm 2, these percentages should stay more or less constant. On the other hand, for magnesium targets thinner than 1 mg/cm z, the percentage recoils escaping out of the target foil will become more significant ll6]. (ii) 24Na recoils from magnesium. 24Na recoils escaping from the magnesium target foils in the forward direction were about 18 per cent of the total 24Na induced in each of the target foils, which varied from l to 2 mg/cm2 in thickness. One mylar foil was sufficient to stop all recoils escaping from the target foils. (iii) 24Na recoils from aluminium. In a supplementary experiment two stacks of aluminium foils with mylar catchers and degraders were irradiated at low beam intensity. The thickness of the aluminium targets in one stack was 3-416 mg/cm 2, while in the other it was 6'833 mg/cm2. (Aluminium foils of these thicknesses were used as targets and degraders, respectively, in the stacks used for the actual measurement of the 27 Al(d, ap)24N a reaction cross-section). ~4Na recoiling in the forward direction was found to vary from I l per cent of total target activity at 16 MeV to 5.1 per cent at 10 MeV, for the stack with the 3.416 mg/cm ~ target foils. For the stack with the 6.833 mg/cm 2 target foils, these percentages were 4.6 and 3-1, respectively. Thus the error in the absolute values for our cross-sections obtained with aluminium foils only should not be greater than about 6 per cent at 16 MeV and about 2 per cent at l0 MeV. Hence, it is concluded that if the recoil range of the reaction product is less than the target thickness, degraders of dissimilar material could be dispensed with (if convenient) and no serious error would result in the determination of the absolute cross-section.
RESULTS
AND
DISCUSSION
All the experimental results for the measured excitation functions are collected in Table 4. The 24Mg(d, ct)22Na reaction Figure 4 (Curve II) shows the cross-section in mbarn as function of energy. The experimental points were calculated for the (d,a) reaction on 24Mg using a value of 78.70 per cent [17] for the isotopic abundance. Table 2 lists the possible reactions leading to the production of 22Na from deuteron bombardment of magnesium, as well as the Q-values, threshold energies and Coulomb barriers of the compound nucleus for alpha particles. Thus, up to about 10 MeV only the 24Mg(d,ot)22Na reaction will contribute to the production of 22Na. The cross-section therefore strictly applies only up to about 10 MeV. At higher energies both the 24Mg(d,a)22Na and the 25Mg(d,an)Z2Na reactions can contribute. (Due to the difference in isotopic abundance between the 24Mg (78.70 per cent) and the 25Mg (10.13 per cent) isotopes in natural magnesium, it is probable that the reaction on 24Mg remains dominant up to 16 MeV.) Our results are in good agreement with that of Vlasov et al. [5]. However, it is not clear whether these authors used isotopically-pure magnesium targets above 16. J. Csikai, (Mrs.) P. Bornemesza and I. Hunyadi, Nucl. lnstrum. Meth. 24, 227 (1963). 17. W. Seelmann-Eggebert and G. Pfennig, Chart of Nuclides, 2nd Edn. Gersbach and Sohn, Miinchen (1965).
Table 4. Experimentally determined cross-sections Or) in mbarn as a function of deuteron energy (Ea) in MeV ~4Mg(d, a)~2Na 22Na activity ~Mg(d, a)24Na 24Na ~Al(d, otp)24Na Ea er activity Ea o" E2 Gr (ttCi/mg/cm2//zA.h)t (Mev) (mbarn) x 10a (Mev) (mbarn) (/~Ci/mg/cm~//zA-h)t (MeV) mbarn 16-1 16.1 16-1 15-6 15.1 14-9 14-6 14.2 13.9 13.5 13.1 12-6 12-4 12.1 11.5 11-1 10-8 10-3 10-0 9.5 8.7 8.3 7'8 7"3 6"9 6"8 5"6 4"7 4"6 4.1 2-5 1"9 0.9
79 82 77 78 86 89 97 97 109 111 123 136 151 154 145 160 167 174 172 170 190 185 179 175 176 165 144 106 111 87 23 14 3
7.99 8.26 7.81 7.88 8.71 8.99 9.74 9.83 10.96 11"21 12.41 13.73 15.17 15.50 14.61 16.12 16.86 17.60 17.31 17.17 19.27 18-57 18-13 17-58 17"81 16"62 14"48 10"67 11"21 8"72 2"36 1"41 0"27
16.2 i6.2 16.1 15.7 15.4 15.3 15"3 15" 1 14.8 14.7 14.4 14.3 14.0 13.7 13.4 13.3 13.2 12.8 12.8 12.7 12-6 12-2 11-7 11"6 11"6 11" 1 10"7 10"5 10"5 10-0 9.7 9"5 9.5 8"9 8"6 8.5 8-2 7"4 6'9 6-6 6-1 5"7 5"3 4.6 4"3 4-2 3"2 2"8 2"2
290 272 284 257 252 250 240 235 216 215 191 187 178 157 146 137 140 118 129 130 108 114 98 93 90 94 93 94 95 100 107 110 I10 118 116 114 120 112 110 108 102 98 90 79 72 72 46 31 13
5.76 5-42 5-65 5.12 5.02 4-96 4.75 4.68 4.30 4.27 3.81 3.71 3.53 3.13 2-90 2-73 2-77 2-34 2-57 2-59 2-14 2.27 1.96 1.84 1.79 1.86 1"85 1.86 1.88 1.98 2-13 2.18 2.19 2.34 2-32 2"27 2"38 2"25 2.18 2" 14 2-03 1-93 1-79 1"57 1"43 1"43 0.91 0-62 0.26
16-1 16-1 15"8 15"4 15"3 15"1 14"6 14-6 14.3 13-9 13-8 13.6 13"1 13"1 12"8 12.3 12.2 11.9 11.4 11"3 11"0 10-5,
23-8 24-2 22"0 18"3 18"6 16"1 13"3 13"3 11-3 8.6 8.4 6-9 4.8 4.5 3.4 2.0 1.8 1.2 0.6 0.5 0-3 0-1
*Energy of deuterons at centre of target foil. t/~Ci/mg/cm2//~A-hr represents the total activity of 22Na(or 24Na) produced by deuteron reactions on natural magnesium. ~tBelow 10.5 MeV the cross-section for the 27Al(d, ap)24Na reaction decreased from 0-1 mbarn to zero at 9 MeV. 3352
Excitationfunctions
3353
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/
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15
Fig. 4. A b s o l u t e excitation function curves f o r the reactions
~Mg(d,a)=4Na (I), =4Mg(d,a)"Na (II) and =~Al(d,ap)=4Na(III).
10 MeV, or calculated an effective cross-section based on the isotopic abundance of 24Mg in natural magnesium. It is difficult to give reasons for the disagreement with the other reported values [3,4], except to attribute it to possible loss of activity during the chemical treatment of the target material, to uncertainties inherent in their counting techniques, or to the possible presence of H2+ ions in cyclotron deuteron beams. In our work on the other hand, all relative activity measurements and standardizations were done on stack foils themselves, so that no chemical yield figures were required, because no chemical separations were carried out.
The 26Mg(d,a)24Na reaction Figure 4 (curve I) gives the measured cross-section as a function of energy. Table 2 gives the possible reactions leading to 24Na production. At energies below about l0 MeV only the 2~dg(d,a)~4Na reaction can contribute, and the cross-section given in mbarn applies to this reaction only. At energies above 10 MeV the 25Mg(d,aHe)24Na and 24Mg(d,2p)24Na reactions can also contribute, and the rise in the excitation curve with increasing energy beyond 12 MeV can probably be attributed to an increase in the cross-sections of these reactions with increasing deuteron energy. Our cross-sections for the (d,a) reaction from 0 to 10 MeV differ from those reported by Irvine and Clarke [3] by about 18 per cent at 8.6 MeV. They found a similar increase in yield at higher energies, but they ascribed it to a contribution of 24Na from the aluminium foils (by the 27Al(d,ap)~4Na reaction), which sandwiched their evaporated magnesium targets. They corrected for this in such a manner that their resultant excitation function showed no rise above 10 MeV. It appears that this effect may have been over-corrected, especially since our cross-sections
3354
H.F.
R(}HM et al.
for the 27Al(d, ap)24Na reaction are considerably lower than theirs in the energy range above 10 MeV (see below). Considering the work of Hall and Meinke [18], the reasons for disagreement are not clear, even though they did not take the recoils in the backward direction into account; this reflects at most a 1 per cent error in the cross-section at 9 MeV for a target of 1 mg/cm z thick. The ZrAl(d, otp)24Na reaction The excitation function for this reaction obtained with stacks of aluminium foils only is shown in Fig. 4, Curve III. I n comparison with our results, the reported values of Clarke [6] are too high by - 53 per cent at 14 MeV and those of Batzel et a/.[7] and of Lenk et a/.[8] are too low by 57 per cent at 15 MeV. The agreement with Christaller [9] is good. Thick-target yields Table 5 gives the thick-target yields for 22Na and 2*Na calculated from the excitation functions measured in this work. From Fig. 5, the calculated thicktarget yield for 22Na production by 16 MeV deuterons on natural magnesium is 2.93/zCi//zA-hr. During regular commercial production of ~2Na by 16 MeV deuteron bombardment of thick natural magnesium targets, we obtain yields varying between 2.1/~Ci//zA-hr and 2.8/xCi//zA-hr, the average value for several production runs being 2.5/zCi//~A-hr. Our values are comparable to those published elsewhere [ 19]. Table 5. Thick-target yields (tzCi//zA-hr) as a function of energy for deuterons
Energy of incident deuterons (MeV)
Target element
Mg
Mg
Isotope produced
22Na
24Na
Al
~Na
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.005 0.023 0-066 0.161 0-320 0.528 0.781 1.068 1.376 1.686 1-987 2-267 2.514 2-735 2.934
0.241 3.249 11.828 26.463 47.440 73.793 105.463 141.559 0.044 177-731 211.860 0.305 2.709 248.063 297.416 12.311 362.304 37.785 454.664 87.793 578-245 170.562
18. K. Lynn Hall and W. Wayne Meinke, J. inorg, nucl. Chem. 9, 193 (1959). 19. N. N. Krasnov and P. P. Dmitriev, Atomn Energ. 21,400 (1966).
Excitation functions
3355
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6 8 I0 12 14 Deuteron Energy, MeV
16
Fig. 5. Calculated thick-target yields as a function of energy for the production of 2~Na and 24Na from deuteron-induced reactions on natural targets: I, 24Na production from magnesium; II, 24Na production from aluminium and III, =2Na production from magnesium. 102
-
I
I
0
2
4
I
I
I
I
I
I~-
10
i, i0 -I
10 - 2
6 8 I0 12 14 16 Deuteron Energy, MeV Fig. 6. Yields for constant energy dissipation on targets for ==Na (III) and =4Na (I) production from magnesium and 24Ha (H) production from aluminium.
In many cases the m a x i m u m rate of production of a given nuclide in a cyclotron does not depend on the m a x i m u m b e a m intensity, but rather on the m a x i m u m rate at which heat can be dissipated on an internal target. It is therefore
3356
H . F . ROHM et al.
important to select the beam energy which will give the maximum rate of production for a given heat dissipation on the target. This information can be derived from the thick-target yields and is given in Fig. 6. The optimum deuteron energy for the production of 2~Na on natural magnesium is thus about 15 MeV, whereas energies above 16 MeV are needed for optimum production of 24Na on magnesium and aluminium targets.
EXCITATION FUNCTIONS FOR THE 2aMg(d,a)Z2Na, Z6Mg(d,a)2aNa AND
2rAl(d,ap)24Na REACTIONS H. F. ROHM*, C. J. V E R W E Y t , J. STEYN and W. L. R A U T E N B A C H National Physical Research Laboratory and National Chemical Research Laboratory, P.O. Box 395, Pretoria, South Africa
(Received 13 March 1969) A l n t r a e t - E x c i t a t i o n functions were determined by the "stacked-foil" technique at the Pretoria 110-cm cyclotron for the ~4Mg(d,a)22Na and ~Mg(d,a)24Na reactions from 0 to 10 MeV, and the 2~AI(d,ap)24Na reaction from 0 to 16 MeV. The maximum measured cross-sections for the production of 22Na and ~4Na from magnesium were 185 mbarn (8-6 MeV) and 118 mbam (8.6 MeV) respectively. At 16.0 MeV the absolute cross-section for the production of 24Na from aluminium was 24.0 mbarn. Thick-target yields were calculated as a function of energy (0-16 MeV) for the production of 22Na and ~ N a from natural magnesium, and 24Na from aluminium. The calculated production rates of n N a and 24Na, by 16 MeV deuterons on natural magnesium, are 2.93/~Ci//zA-hr and 578-34 ~Ci//~A-hr respectively, while for production of 24Na from aluminium a value of 170.562/~Ci//~A-hr was obtained. INTRODUCTION
A c c u ~ x E excitation functions for the production of 22Na and 24Na by deuteron bombardment of magnesium and aluminium are needed: (a) to calculate the thick-target yields as functions of the incident deuteron energy, in order to optimize the commercial production of high specific activity 2ZNa and 24Na, (b) to determine the feasibility of charged-particle activation analysis of aluminium and magnesium [ 1], and (c) to use the induced 22Na and 24Na in magnesium and aluminium foils as monitors for deuteron beam intensity and energy, for instance in "stackedfoil" measurements, where aluminium catcher foils are often employed [2]. Published excitation curves for the production of ZZNa from magnesium differ by upwards of 30 per cent at the peak of the curve[3-5], while the thick-target yield for 14 MeV deuterons varies from 1-8 # Ci/mA-hr to 3.1 tzCi//~A-hr according to Irvine and Clarke [3] and to Vlasov e t al.[5], respectively. Reported crosssections for the ZrAl(d,ap)24Na reaction at 14 MeV differ by more than 80 per cent *Present address: Institut f'dr Radiochemie, Kernforschungszentrum Karlsruhe mbH, 75 Karlsruhe, Postfach 947, W. Germany. tDeceased. 1. 2. 3. 4. 5.
Enzo Ricci and R. L. Hahn, Analyt. Chem. 40, 55 (1968). A. Demildt, J. inorg, nucl. Chem. 23, 167 (1961). J.W. Irvine, Jr. and E. T. Clarke, J. chem. Phys. 16, 686 (1948). F.O. Bartell and Sheldon Softky, Phys. Rev. 84, 463 (1951). N. A. Vlasov, S. P. Kalinin, A. A. Ogloblin, V. M. Pankramov, V. P. Rudakov, N. N. Serikov and V. A. Sidorov,Atomn. Energ. 2, 169 (1957). 3345
3346
H.F.
ROHM et al.
[6-9]. Furthermore, the excitation function for the production of ~4Na from deuterons on magnesium, reported by Irvine and Clarke [3], showed a maximum at about 9 MeV and decreased with increasing energy. However, preliminary measurements at our laboratory showed a steep rise in the production of ~4Na above 1 1 MeV when a stack of magnesium foils was irradiated with deuterons. During the last decade, considerable progress has been made in techniques for the counting and absolute standardization of radioactivity, as well as in the quality of charged particle beams and beam diagnostics. Therefore, excitation functions determined at present by use of the "stacked-foil" technique should result in more accurate and reproducible measurements. We therefore remeasured the excitation curves for the production of 22Na and 24Na by deuterons on magnesium and aluminium, using the 16 MeV external beam of the Pretoria cyclotron. Special precautions were taken to ensure effective recoil collection in the catcher foils. The 4,rr-/3y coincidence counting method was used for the absolute measurement of the induced radioactivity, Since the standardization was done directly on selected target and catcher foils, possible errors introduced by chemical treatment and special source preparation were avoided. EXPERIMENTAL
(a) Preparation of the foil stacks. The stacks consisted of target foils sandwiched between appropriately chosen catcher foils to collect the recoils escaping from the targets, and absorbers which degraded the energy of the bombarding particles. The choice of recoil catcher foils was such that the reaction product induced therein by the bombarding particle differed from the reaction product of interest in the target material. Because the degraders were always of the same material as the catcher foils, corrections could be made for any Z2Na or 24Na resulting from deuteron activation of possible contamination in the catcher foils. Furthermore, in order to estimate the contribution of ~2Na or 24Na induced by fast and slow neutrons on 2aNa, target and catcher foils were stacked well beyond the range of 16 MeV deuterons. Three stacks were irradiated for each excitation function. Overlapping of the experimental points was avoided by staggering the target foils with respect to one another in the different stacks. All the pertinent information on the foils is listed in Table 1. Table 1. Material used in stacks Foil element
Inventory form
Natural Mg
Rods, 6.35 mm diam × 10 cm long Foils, 0.0005" and 0.001" thick
Natural Al
Mylar Sheets, (C, H and O - 3.5 mg/cm -2 as Polymethylmethacrylate) 6. 7. 8. 9.
Purity Spectrographically pure 99-997%
Supplier Johnson Matthey, London, England Materials Research Corporation, N e w York, U.S.A. Imperial Chemical Industries, England
E.T. Clarke, Phys. Rev. 71,187 (1947). R. E. Batzel, W. W. T. Crane and G. D. O'Kelly, Phys. Rev. 91,939 (1953). P. A. Lenk and R. J. Slobodrian, Phys. Rev. 102, 1229 (1959). G. Christaller, European Colloquium on A.V.F. Cyclotrons, Eindhoven (1965).
Excitation functions
3347
The aluminium and mylar foils were of commercial origin, whereas magnesium rods were rolled to pinhole-free foils of thickness varying from 0"3 to 2-7 mg/cm2. Because magnesium tends to workharden during rolling, these foils were rolled and annealed alternately down to the final thickness. Annealing was carried out at 330°C for about 3 hr in a vacuum oven (0.2 x 10-Storr), and the foils were then allowed to cool under vacuum. After the final anneal some foils were tested by X-ray diffraction. No preferred crystal orientation was found, which ruled out the possibility of "channelling" affecting the yield. The foils were punched into discs of diameter 2.24 cm. They fitted in a stack holder, which had an opening of diameter 2.0 cm for the beam to pass through. The foils were weighed in a humidity- and temperature-controlled room before the stacks were assembled for irradiation. The stacks used to measure 22Na production from magnesium contained aluminium catcher foils. The only way in which deuterons can produce 2~Na activity from aluminium is by either the ~7Al(d, ap2n)22Na or 27Al(d,aaH)22Na reactions, and since the incident energy of the deuteron beam was about 16 MeV neither of these reactions was energetically possible (Table 2). Table 2. Calculated Q-values, thresholds and Coulomb barriers for deuteron reactions on magnesium and aluminium leading to the production of 22Na and 24Na
Reaction
Q-Value (MeV)*
Threshold plus Coulomb barrier (MeV)
5" 16 5" 16 5.16
5" 16 10"96 22.89
24Mg(d, a)22Na ZSMg(d, otn)Z2Na
-- 5'369
26Mg(d, t~2n)22Na
- 16.464
-5"789 17-730
~Mg(d, c024Na 25Mg(d, He3)24Na 24Mg(d, 2p)24Na 25Mg(d, 2pn)24Na
2.915 -- 6-568 -- 6.957 - 14.286
-7.093 7.537 15.429
5.06 5-23 5.81 5.81
5-06 12.32 13.35 21.24
27Al(d, c~p)~4Na
-- 5.356 - 13.585 - 16-253 -- 24.735
5-752 14-591 17-457 26.567
7.97 7-20 7.81 8.13
13-72 21.79 25.27 34.70
2¢Al(d, a3H)22Na 27Al(d, ap2n)22Na
1"960
Threshold (MeV)
Coulomb barrier (MeV)t
*Calculated from 1964 atomic mass tables [ 10]. tThese values were calculated by use of the classical formula. Aluminium catcher foils could not be used in the stacks for the measurement of Z4Na production from magnesium, since 24Na is also produced by deuteron reactions on aluminium. Consequently mylar catcher foils were used in this case. For the production of 24Na from aluminium, the expected low cross-section precluded the use of mylar catchers and degrader foils. (Mylar is rather susceptible to radiation damage.) Consequently, a stack of aluminium foils only was used, in which the target foils were 3-416 mg/cm 2 thick and the degraders 6.833 mg/cm z thick. The percentage recoils escaping from aluminium foils of both the above-mentioned thicknesses was subsequently determined as a function of deuteron energy with the aid of mylar catchers in a supplementary experiment at much lower beam intensity. (b) Beam energy measurements. The energy of the cyclotron's external deuteron beam was measured by scattering it from a thin gold foil on to a semiconductor detector. A suitable aluminium absorber in front of the detector degraded the incident beam to 7.5 MeV, enabling one to use the 6.051 MeV and 8-785 MeV[I 1] a-particles from Th(B + C + C") for energy calibration. The uncertainty of the 10. J. H. E. Mattauch, W. Thiele and A. H. Wapstra, Nucl. Phys. 67, 1 (1965). 11. C. M. Lederer, J. M. Hollander and I. Perlman, Tables of Isotopes, 6 th Edn. Wiley, New York (1967).
3348
ROHM et al.
H.F.
incident energy as determined above was ___0" 1 MeV, while fluctuations in the primary beam energy during bombardment were estimated to be less than 0.2 MeV. (Taken in conjunction with the straggling in energy loss in the foils, effective energy spreads of 0.3 MeV for 10 MeV deuterons and 0-5 MeV for 4 MeV deuterons were obtained for a stack of aluminium, as calculated from range-energy tables[12]). Williamson's tables were used to calculate the energy degradation in aluminium and magnesium, and Brandt's tables [ 13] were used for mylar. The contribution of H~+ ions to the deuteron beam was checked during a scattering experiment [14] and was found to be non-existent. (c) Measurement of the integrated beam flux. The stack foils were clamped in a holder, which was located at the end of a Faraday cup assembly (Fig. 1). The base-plate, to which the holder was secured, was air-cooled, and, this cooling was found adequate for the beam currents used in this experiment. Two collimators, each 6 mm in diameter, were used to ensure a centrally-fixed beam spot on the stacks. Quadrupole lenses enabled sharp beam-focusing, resulting in 76 per cent transmission of the beam through the last collimator as measured both on the collimator and the Faraday cup.
ZnS Screen ~-Perspex-1. Foil stacks ~-- - ~ - - ~ n s u l o i o r s _ ~ (Quartz Screen)
Be°!~
A
=
I
r
Collimotors Scale:--
Fomdoy Cup
0 I0 20 CM ~
:
I
Fig. 1. Schematic representation of the experimental set-up. Before irradiating, the beam centre was checked by the ZnS screen between the two collimators and by temporarily placing a quartz screen in the stack position.
The possible contribution by secondary electrons to the beam current in the Faraday cup was investigated by applying a transverse magnetic field over the entrance of the Faraday cup and also by applying potentials of - 300 V and + 300 V to it. No effect was observed on the beam intensity under these conditions and it was therefore concluded that the effect of secondary electrons was negligible. During the irradiations of the stacks a precision integrator, working on the principle of an operational amplifier, was connected to the Faraday cup. The calibration of the current integrator was checked before and after each irradiation by using a known current for a fixed time. (d) Irradiations. All irradiations were carded out in the 0° beam port. It was not necessary to take into account beam intensity variations during the irradiations, because for each bombardment the irradiation time was short compared to the half-life of the reaction products. Table 3 gives average beam currents and irradiation times for the different stacks. Beam focus was checked between irradiations. Preliminary experiments showed that the mylar foils in the magnesium stacks could withstand beam current up to 40 x 10 -9 amp for 40 min without "burn-through" taking place. 12. C. F. Williamson, J. P. Boujot and J. Picard, Tables of Range and Stopping Power of Chemical Elements for Charged Particles of Energy 0.5 to 500 MeV No. CEA-R 3402, Saclay (1966). 13. Werner Brandt, Energy Loss of Charged Particles in Compounds. Research Rep., E. I. du Pont de Nemours, Delaware (1960). 14. G. Heymann, Private communication.
3349
Excitation functions Table 3. Beam intensities and duration of irradiation
Stack no. 1 2 3 4 5 6
Target foils
Degrader and catcher foils
Reaction
Incident deuteron energy (MeV)
Mg
AI*
24Mg(d, c022Na
16.2 -----0-1
Mg
Mylar
2eMg(d, c024Na
16.2 +--0.1
28 25 26
AI*
All"
27Al(d, otp)24Na
16-4 __+0-1
24 27
AI* Alt
Mylar
2TAl(d,ap)24Na
16.4 - 0-1
Average beam intensity (/~A)
Duration of irradiation (hr)
0.807 0.904 0-932 40-4 x 10-3 22.2 x 10-3 18.2 × 10-3
6.067 5.423 5.256 0.501 0.603 0.734
0.976 0.923 1.086
0.250 0.250 0.250
21"6 x 10-3 22.8 × 10-3
0.583 0.450
*Aluminium of 3.416 mg/cm2 thickness. tAluminium of 6.833 mg/cm2 thickness.
(e) Measurements of the activities produced (i) ~Na from magnesium. After irradiation, short-lived activities were allowed to decay for one month before relative counting and standardization of the 2"62 yr 22Na[11] commenced.Before counting the foils in a Nal(TI) well-type crystal, T-ray spectra were taken of several foils of magnesium and aluminium to verify that the only activity present was that from 22Na. During the relative counting, the electronic drift in the counting system was monitored over a period of 14 days and it was found that the maximum variation in the gain was between - 1 and + 1 per cent of the mean value. No detectable activity, outside the 3~r limit of background, was found for any of the degrader foils and magnesium foils beyond the deuteron range, and it may be concluded that 2~Na activity originating from 2SNa contamination was negligible. The amount of 22Na was measured absolutely in 20 magnesium foils from the three stacks by use of the 4*r-fiT coincidence method. Each foil was mounted between the two halves of a 41r-B proportional counter while the coincident gamma radiation was detected in a NaI(Tl) crystal. The mean beta counting efficiency was - 88 per cent, discrimination against annihilation radiation in the gamma channel was complete, and the accuracy obtained was within 1 per cent [ 15]. (ii) 24Na from magnesium. The relative counting of both the mylar and magnesium foils was carded out in a similar manner as previously described for 22Na. The activities found in the foils were 1.8 hr ~SF[I 1], 15-0 hr ~4Na[11] and 2.62 yr 22Na. Throughout the counting, these activities were followed in at least one of the most active foils from each stack. A typical decay curve obtained from one such foil is shown in Fig. 2. From the figure it may be seen that the 22Na activity is small compared to that of the 24Na induced in the magnesium. The small correction for the 22Na contribution therefore did not adversely affect the accuracy of the ~4Na measurement. Again no detectable 24Na or 22Na was recorded in the degrader foils. After the activity from lSF had decayed, I 1 target foils from the three stacks were standardized by the same method as that used for the 2~Na. The average beta counting efficiency here was 98 per cent. The accuracy obtained was 0-5 per cent. (iii) 24Nafrom aluminium. Both the relative counting and the standardization of the target foils were performed in a similar manner to that outlined in the previous section. Gamma-ray spectra from 15. J. Steyn and A. S. M. de Jesus, Coincidence Measurements on Nuclides Decaying by Electron Capture FIS 15, CSIR Special Rep., Pretoria, South Africa (1966).
3350
H.F. ' ' ' ' 1 ' ' '
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ROHM et al.
....
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- LIFE
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l l l l l l l l
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I00
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150
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250
IRRADIATION
300
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Fig. 2. Decay curve of one of the magnesium foils, showing the presence of 2.62 yr 22Na and 15-hr 24Na only. several foils in the stack showed that the only activity present was 24Na (Fig. 3). In addition, the decay of activity was followed in at least one target and degrader foil from each of the stacks for about 12 days. The slope of the decay curve showed the presence of one activity only, with a 15-0-hr halflife.
'
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'
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Excitation functions
3 3 51
(f) Percentage recoils of total activity Throughout this work meticulous care was taken to prevent the loss of activity. Thus the collection of recoils, by the catcher foils, was determined carefully in order to obtain its contribution to the total activity. (i) 22Na recoils from magnesium. 22Na recoiling in the forward direction (i.e. 2ZNa nuclei escaping from the target foil in the direction of the beam and which are collected in the adjacent aluminium catcher foil) was found to be about 28 per cent of the total 22Na activity produced in the target foils. This percentage decreased near the threshold of the (d,a) reaction on 24Mg. The average percentage recoils in the backward direction was about 0.7. For magnesium targets thicker than 2 mg/cm 2, these percentages should stay more or less constant. On the other hand, for magnesium targets thinner than 1 mg/cm z, the percentage recoils escaping out of the target foil will become more significant ll6]. (ii) 24Na recoils from magnesium. 24Na recoils escaping from the magnesium target foils in the forward direction were about 18 per cent of the total 24Na induced in each of the target foils, which varied from l to 2 mg/cm2 in thickness. One mylar foil was sufficient to stop all recoils escaping from the target foils. (iii) 24Na recoils from aluminium. In a supplementary experiment two stacks of aluminium foils with mylar catchers and degraders were irradiated at low beam intensity. The thickness of the aluminium targets in one stack was 3-416 mg/cm 2, while in the other it was 6'833 mg/cm2. (Aluminium foils of these thicknesses were used as targets and degraders, respectively, in the stacks used for the actual measurement of the 27 Al(d, ap)24N a reaction cross-section). ~4Na recoiling in the forward direction was found to vary from I l per cent of total target activity at 16 MeV to 5.1 per cent at 10 MeV, for the stack with the 3.416 mg/cm ~ target foils. For the stack with the 6.833 mg/cm 2 target foils, these percentages were 4.6 and 3-1, respectively. Thus the error in the absolute values for our cross-sections obtained with aluminium foils only should not be greater than about 6 per cent at 16 MeV and about 2 per cent at l0 MeV. Hence, it is concluded that if the recoil range of the reaction product is less than the target thickness, degraders of dissimilar material could be dispensed with (if convenient) and no serious error would result in the determination of the absolute cross-section.
RESULTS
AND
DISCUSSION
All the experimental results for the measured excitation functions are collected in Table 4. The 24Mg(d, ct)22Na reaction Figure 4 (Curve II) shows the cross-section in mbarn as function of energy. The experimental points were calculated for the (d,a) reaction on 24Mg using a value of 78.70 per cent [17] for the isotopic abundance. Table 2 lists the possible reactions leading to the production of 22Na from deuteron bombardment of magnesium, as well as the Q-values, threshold energies and Coulomb barriers of the compound nucleus for alpha particles. Thus, up to about 10 MeV only the 24Mg(d,ot)22Na reaction will contribute to the production of 22Na. The cross-section therefore strictly applies only up to about 10 MeV. At higher energies both the 24Mg(d,a)22Na and the 25Mg(d,an)Z2Na reactions can contribute. (Due to the difference in isotopic abundance between the 24Mg (78.70 per cent) and the 25Mg (10.13 per cent) isotopes in natural magnesium, it is probable that the reaction on 24Mg remains dominant up to 16 MeV.) Our results are in good agreement with that of Vlasov et al. [5]. However, it is not clear whether these authors used isotopically-pure magnesium targets above 16. J. Csikai, (Mrs.) P. Bornemesza and I. Hunyadi, Nucl. lnstrum. Meth. 24, 227 (1963). 17. W. Seelmann-Eggebert and G. Pfennig, Chart of Nuclides, 2nd Edn. Gersbach and Sohn, Miinchen (1965).
Table 4. Experimentally determined cross-sections Or) in mbarn as a function of deuteron energy (Ea) in MeV ~4Mg(d, a)~2Na 22Na activity ~Mg(d, a)24Na 24Na ~Al(d, otp)24Na Ea er activity Ea o" E2 Gr (ttCi/mg/cm2//zA.h)t (Mev) (mbarn) x 10a (Mev) (mbarn) (/~Ci/mg/cm~//zA-h)t (MeV) mbarn 16-1 16.1 16-1 15-6 15.1 14-9 14-6 14.2 13.9 13.5 13.1 12-6 12-4 12.1 11.5 11-1 10-8 10-3 10-0 9.5 8.7 8.3 7'8 7"3 6"9 6"8 5"6 4"7 4"6 4.1 2-5 1"9 0.9
79 82 77 78 86 89 97 97 109 111 123 136 151 154 145 160 167 174 172 170 190 185 179 175 176 165 144 106 111 87 23 14 3
7.99 8.26 7.81 7.88 8.71 8.99 9.74 9.83 10.96 11"21 12.41 13.73 15.17 15.50 14.61 16.12 16.86 17.60 17.31 17.17 19.27 18-57 18-13 17-58 17"81 16"62 14"48 10"67 11"21 8"72 2"36 1"41 0"27
16.2 i6.2 16.1 15.7 15.4 15.3 15"3 15" 1 14.8 14.7 14.4 14.3 14.0 13.7 13.4 13.3 13.2 12.8 12.8 12.7 12-6 12-2 11-7 11"6 11"6 11" 1 10"7 10"5 10"5 10-0 9.7 9"5 9.5 8"9 8"6 8.5 8-2 7"4 6'9 6-6 6-1 5"7 5"3 4.6 4"3 4-2 3"2 2"8 2"2
290 272 284 257 252 250 240 235 216 215 191 187 178 157 146 137 140 118 129 130 108 114 98 93 90 94 93 94 95 100 107 110 I10 118 116 114 120 112 110 108 102 98 90 79 72 72 46 31 13
5.76 5-42 5-65 5.12 5.02 4-96 4.75 4.68 4.30 4.27 3.81 3.71 3.53 3.13 2-90 2-73 2-77 2-34 2-57 2-59 2-14 2.27 1.96 1.84 1.79 1.86 1"85 1.86 1.88 1.98 2-13 2.18 2.19 2.34 2-32 2"27 2"38 2"25 2.18 2" 14 2-03 1-93 1-79 1"57 1"43 1"43 0.91 0-62 0.26
16-1 16-1 15"8 15"4 15"3 15"1 14"6 14-6 14.3 13-9 13-8 13.6 13"1 13"1 12"8 12.3 12.2 11.9 11.4 11"3 11"0 10-5,
23-8 24-2 22"0 18"3 18"6 16"1 13"3 13"3 11-3 8.6 8.4 6-9 4.8 4.5 3.4 2.0 1.8 1.2 0.6 0.5 0-3 0-1
*Energy of deuterons at centre of target foil. t/~Ci/mg/cm2//~A-hr represents the total activity of 22Na(or 24Na) produced by deuteron reactions on natural magnesium. ~tBelow 10.5 MeV the cross-section for the 27Al(d, ap)24Na reaction decreased from 0-1 mbarn to zero at 9 MeV. 3352
Excitationfunctions
3353
II1111tll I111~
°3F Ioz
0
/
°
-1T
//m
I0
s o
-
I
o
I0-! 0
5 I0 DeuterOn Energy, MeV
15
Fig. 4. A b s o l u t e excitation function curves f o r the reactions
~Mg(d,a)=4Na (I), =4Mg(d,a)"Na (II) and =~Al(d,ap)=4Na(III).
10 MeV, or calculated an effective cross-section based on the isotopic abundance of 24Mg in natural magnesium. It is difficult to give reasons for the disagreement with the other reported values [3,4], except to attribute it to possible loss of activity during the chemical treatment of the target material, to uncertainties inherent in their counting techniques, or to the possible presence of H2+ ions in cyclotron deuteron beams. In our work on the other hand, all relative activity measurements and standardizations were done on stack foils themselves, so that no chemical yield figures were required, because no chemical separations were carried out.
The 26Mg(d,a)24Na reaction Figure 4 (curve I) gives the measured cross-section as a function of energy. Table 2 gives the possible reactions leading to 24Na production. At energies below about l0 MeV only the 2~dg(d,a)~4Na reaction can contribute, and the cross-section given in mbarn applies to this reaction only. At energies above 10 MeV the 25Mg(d,aHe)24Na and 24Mg(d,2p)24Na reactions can also contribute, and the rise in the excitation curve with increasing energy beyond 12 MeV can probably be attributed to an increase in the cross-sections of these reactions with increasing deuteron energy. Our cross-sections for the (d,a) reaction from 0 to 10 MeV differ from those reported by Irvine and Clarke [3] by about 18 per cent at 8.6 MeV. They found a similar increase in yield at higher energies, but they ascribed it to a contribution of 24Na from the aluminium foils (by the 27Al(d,ap)~4Na reaction), which sandwiched their evaporated magnesium targets. They corrected for this in such a manner that their resultant excitation function showed no rise above 10 MeV. It appears that this effect may have been over-corrected, especially since our cross-sections
3354
H.F.
R(}HM et al.
for the 27Al(d, ap)24Na reaction are considerably lower than theirs in the energy range above 10 MeV (see below). Considering the work of Hall and Meinke [18], the reasons for disagreement are not clear, even though they did not take the recoils in the backward direction into account; this reflects at most a 1 per cent error in the cross-section at 9 MeV for a target of 1 mg/cm z thick. The ZrAl(d, otp)24Na reaction The excitation function for this reaction obtained with stacks of aluminium foils only is shown in Fig. 4, Curve III. I n comparison with our results, the reported values of Clarke [6] are too high by - 53 per cent at 14 MeV and those of Batzel et a/.[7] and of Lenk et a/.[8] are too low by 57 per cent at 15 MeV. The agreement with Christaller [9] is good. Thick-target yields Table 5 gives the thick-target yields for 22Na and 2*Na calculated from the excitation functions measured in this work. From Fig. 5, the calculated thicktarget yield for 22Na production by 16 MeV deuterons on natural magnesium is 2.93/zCi//zA-hr. During regular commercial production of ~2Na by 16 MeV deuteron bombardment of thick natural magnesium targets, we obtain yields varying between 2.1/~Ci//zA-hr and 2.8/xCi//zA-hr, the average value for several production runs being 2.5/zCi//~A-hr. Our values are comparable to those published elsewhere [ 19]. Table 5. Thick-target yields (tzCi//zA-hr) as a function of energy for deuterons
Energy of incident deuterons (MeV)
Target element
Mg
Mg
Isotope produced
22Na
24Na
Al
~Na
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.005 0.023 0-066 0.161 0-320 0.528 0.781 1.068 1.376 1.686 1-987 2-267 2.514 2-735 2.934
0.241 3.249 11.828 26.463 47.440 73.793 105.463 141.559 0.044 177-731 211.860 0.305 2.709 248.063 297.416 12.311 362.304 37.785 454.664 87.793 578-245 170.562
18. K. Lynn Hall and W. Wayne Meinke, J. inorg, nucl. Chem. 9, 193 (1959). 19. N. N. Krasnov and P. P. Dmitriev, Atomn Energ. 21,400 (1966).
Excitation functions
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103
~ ~ ~ ~ I ~ ~ ~ ~ I I ~ ~ ~ I
102
~
/
t.)
-o
i
.o
I
¢-i I t 0 2
4
6 8 I0 12 14 Deuteron Energy, MeV
16
Fig. 5. Calculated thick-target yields as a function of energy for the production of 2~Na and 24Na from deuteron-induced reactions on natural targets: I, 24Na production from magnesium; II, 24Na production from aluminium and III, =2Na production from magnesium. 102
-
I
I
0
2
4
I
I
I
I
I
I~-
10
i, i0 -I
10 - 2
6 8 I0 12 14 16 Deuteron Energy, MeV Fig. 6. Yields for constant energy dissipation on targets for ==Na (III) and =4Na (I) production from magnesium and 24Ha (H) production from aluminium.
In many cases the m a x i m u m rate of production of a given nuclide in a cyclotron does not depend on the m a x i m u m b e a m intensity, but rather on the m a x i m u m rate at which heat can be dissipated on an internal target. It is therefore
3356
H . F . ROHM et al.
important to select the beam energy which will give the maximum rate of production for a given heat dissipation on the target. This information can be derived from the thick-target yields and is given in Fig. 6. The optimum deuteron energy for the production of 2~Na on natural magnesium is thus about 15 MeV, whereas energies above 16 MeV are needed for optimum production of 24Na on magnesium and aluminium targets.