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Excitation functions of (d, α) and (d, αn) reactions on tungsten
J. lnorg. I'qucl. Chem., 1961, Vol, 23. pp. 167 to 17I, Pergamon Press Ltd. Printed in Northern Ireland
EXCITATION FUNCTIONS OF (d, :,.) AND (d, z.n) REACTIONS ON T U NGS TEN A. DEMILDT* I.K.O. Oosterringdijk 18 Amsterdam; ( Received 31 May, 1961)
Abstract---The irradiation of natural tungsten with deuterons, gives rise to three radioactive tantalum species due to the following nuclear reactions: Ju4W(d, ~)l"'2Ta; ~8"W(d,~)~S~Taand ~s6W(d, ~n)~SaTa. Calculations of the reaction energies were performed, and the excitation functions of these three reactions were determined with deuterons of up to 22 MeV. The cross-sections of the three reactions have values between 3 and 0.05 millibarn. By irradiation of tungsten a whole series of nuclear reactions give rise to c a r r i e r - • e tantalum and rhenium, as well as to active tungsten isotopes. To separate the tantalum isotopes from the irradiated tungsten different chemical procedureswereelaborated./w-'~ For the tantalum formation only three reaction types can form tantalum isotopes by irradiations of tungsten with deuterons o f 22 MeV, namely: (d, :0; (d, ~n) and (d, 9_,o) reactions. Taking into account the fact that natural tungsten contains five stable isotopes, fifteen nuclear reactions could be expected, which will give tantalum isotopes. As the ~s°w isotope has a small abundance, only twelve reactions must be considered. These reactions give rise to seven tantalum isotopes, namely: 179Ta, lS°Ta, ~SWa, lS2Ta, lSaTa, lS4Ta and lSaTa. As only three isotopes were observed one could conclude that no (d, 2p) reactions occur. The following reactions were identified: ~s4W(d, ~.)lS2Ta, ls~iW(d, a)lS4Ta and 186W(d, ~.n)lS:lTa. I. M A S S - E N E R G Y B A L A N C E S OF THE C O N S I D E R E D NUCLEAR REACTIONS For the three reactions examined the energies were calculated from the theoretical data o f MARTIN In). The reaction energies were further computed by means o f the results o f the measured binding energies.l< ~1 A survey o f these data is given in Table 1. TABLE I. COMPUTED REACTION ENERGIES (MeV) Reactions
Energies computed from theoretical masses
Energies computed from the binding energies
'*4W(d, ~)'S2Ta ~s~;W((t, :~)t~Ta ts';W(d, :~n)l~aTa
1l-3 1 I" 1 5"4
-5"4
11'0
* Research Fellow 1.1.K.W. + New address: Inst. of Anal. Chem., J. Plateaustraat, 22, University of Ghent. ~ A. DEMILDTand J. HOSTE, International Atomic Energy Agency. Congress of Copenhagen, R.I.C.C./59 (Sept. 1960). 12>A. DEMILDTand J. HOSTE,Bull. Soe. Chint. Belg. 70, 145 (1961). taJ C h . N . MARTIN, Tables de Physique Nueldaire. Gauthier-Villars (1954). ~4~A. H. WAPSTRA,Physiea 21, 385 (1955). ~:~A. H. WAPSn~A,Handbuch der Physik. Vol. 1, p. 38. S. Fliigge, Berlin (1958). 167
168
A. DEMILDT
In agreement with the calculated reaction energies one can conclude that the (d, e) and the (d, an) reactions produce respectively 11 or 12 MeV and 5 MeV. Thus the three reactions could occur with energetic deuterons high enough to exceed the Coulomb barrier of the target nuclei. One can also expect that the cross sections of the (d, ~) reactions at lower energies will be considerably higher than the (d, an) reactions. 2. T H E E X C I T A T I O N F U N C T I O N S O F T H E O B S E R V E D NUCLEAR REACTIONS
T h e nuclear excitation functions (the experimental cross sections as a function of the kinetic energy of the projectiles) were determined in the following way. Stacks of tungsten foils were irradiated with the internal deuteron beam of the synchrocyclotron of Amsterdam. To obtain a collimated mono-energetic beam, the foils were
¢/ o
b
FIG. 1 a - - T h e thick-window target holder with foils; b--Position in the cyclotron; the arrows show the direction of the deuterons.
mounted in a special thick window target holder (Fig. 1), designed in the Institute for Nuclear Physical Research (I.K.O.) of Amsterdam. The incidence gap of the deuterons was quite narrow (1.5 mm) to insure a homogeneous energy. The determination of the incident deuteron energy was computed from the 27Al(d, ~p)~Na reaction, as this excitation function is accurately established.(6,7, S,9) A stack of fourteen aluminium foils (thickness: 25.80 mg cm -2) was irradiated and the 24Na activity measured by fi-counting. The disintegration rate of the irradiated foils is a measure of the cross-sections when short irradiations (t < T~/20) are used. It was thus possible to set up a relative excitation curve. The maximum energy of the deutrons was determined by computing relative excitation functions of varying maximum deuteron energy until the experimental curve fitted the standard curve. The energy losses in each foil were computed from the range-energy curves for aluminium. (1°) For the actual measurements of the tungsten cross-sections a stack of seven aluminium foils was alternated with seven tungsten foils (thickness : 57"80 mg cm-2). The maximum energy and deuteron flux were computed by absolute fi-counting of (o) E. T. CLARKE, Phys. Rev. 71, 187 (1947). (7) H. H. PH. MOEKEN,Akademisch Proefschrift, I.K.O. Amsterdam (1957). (8) R. E. BATZEL, W. W. T. CRANE and G. D. O'KELLEY; Phys. Rev. 91, 939 (1953). (9) p. A. LENK and J. SLOBODRIAN; Phys. Rev. 116, 1229 (1959). (lo) W. A. ARON, B. C. HOFFMANand F. C. WILLIAMS, U . S . A . E . C . U-663 (1949).
Excitation functions of (d, a) and (d, ~n) reactions on tungsten
169
the 2aNa activities p r o d u c e d in the a l u m i n i u m foils. The a b s o l u t e activities were measured with a calibrated G e i g e r - M t i l l e r c o u n t e r or a 4~r-proportional m e t h a n e counter. F r o m cross-sections given in the literature, the flux is c o m p u t e d , for short i r r a d i a t i o n times, f r o m the e q u a t i o n o f CLARKE and IRVINI. (n) F - 6'40 ;; 10 -:~
D A T, tll
.
(Y
F D T ~4 m ,r
integrated flux, in # A . m i n . absolute activity in disintegrations rain -~. half-life in minutes. a t o m i c weight. thickness o f the i r r a d i a t e d foils in mg cm " for a specific isotope. cross-section in mbarns. Using the same equation, the cross-sections o f the (d, ~) and the (d, ~-#0 reactions were calculated from the absolute t a n t a l u m activities in each foil, t a k i n g into account foil thickness, half-life o f the p r o d u c t nucleus a n d isotopic a b u n d a n c e . Energy losses in each tungsten foil were c o m p u t e d from the m e a n ionization potential I w 697 eV !12) using the BETHE-LIVJNGSTOXE cquationt~aL Energy losses o f the d e u t e r o n s in a l u m i n i u m were taken from ARON el a[. ll°) The results are given in Table 2 and in Fig. 2 and 3. TABI t: 2 . - - C g o s s - S E C T I O N S IN MILLIBARNS AS A FUNC31ON OF DEUTERON ENERGY
Deuteron energy
l*"W(d, 2)>Wa
>'aW(d, ~)lSeTa
>';W(d, 2n)lSaTa
21 20 9 8 7 6 5 4 13 12 II 10 9
3.05 2.90 2-65 2.30 2.10 1.70 1.30 1.08 0.90 0-62 0-29 0.16 0.05
1-25 1-22 1"08 0'85 0'70 0"57 0'46 0"32 0'21 0"13
1-15 0'97 0"67 0.52 0.35 0.22 0.13 0'075 -
-
3. D I S C U S S I O N The form o f the two excitation functions o f the (d, ~) reactions show a simihtr behaviour, the a b s o l u t e values o f the cross-sections being o f the same size. F r o m these curves it a p p e a r s that these reactions are detectable from a b o u t I0 MeV, in a g r e e m e n t with the calculated C o u l o m b barrier. The cross-sections for the ls6W(d, ~n)aSaTa r e a c t i o n are considerably smaller than for the (d, ~) reactions, particularly in the lower energy region. This is in agreement with the fact that no lsaTa was detectable from W irradiated with 12 M e V deuterons hi the cyclotron o f Louvain. ~1~ E. T. CLARKEand J. W. IRVINEJR., Phys. Rev. 66, 23l (1944). i~e~C. J. BAKKERand E. SEGRI~,Phys. Rev. 81,489 (1951). i~a, H. A. BETHEand M. S. LlVINOSTONE; Rev. :'vlod. Phys. 9, 245 (1937).
170
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Excitation functions of (d, =) and (d, ~n) reactions on tungsten
171
4, A P P E N D I X To compute the energy losses of the deuterons in each tungsten or aluminium foil, the numerical relationship between the deuteron energy and the energy losses expressed in MeV mg -1 cm -2 was used. This relationship was computed for aluminium by ARON et a1.<1% while the relation for tungsten was computed by the author ~14)using the formulas of BETHE and LIVINGSTONE~la). The following table gives the energy losses in tungsten expressed in MeV mg ~ c m e as a function of the energy. Energy
( d E / d x ) ' w l M e V mg I cm ~t
4 6 8 10 12 14 16 18 20 22 24
0.0522 0.0425 0.0360 0-0318 0.0279 0.0253 0.0229 0.0214 0.0196 0.0187 0.0173
The range-energy relation of tungsten results from a direct interpolation between the curves of silver and lead compiled by ARON et al. u°) This curve is not used as it seems to give somewhat lower accurate results than the calculations with the energy losses values. Acknowledgements--Acknowledgements are due to Prof. Dr. A. H. W. ATEN JR. and his co-workers of the 1.K.O. Amsterdam, for their hospitality. Thanks are also due to Prof. Dr. C. GROSJEAN, who computed the range-energy relations of tungsten with the IBM 610. This work was performed as part of the research programme of the "Stichting voor Fundamenteel Onderzoek der Materie (F.O.M.)" which is financially supported by the "Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek (Z.W.O.) and of the "lnteruniversitair Instituut voor Kernwetenschappen" of Belgium.
(~4~A. DEMILDT. Thesis, University of Ghent (1960).
EXCITATION FUNCTIONS OF (d, :,.) AND (d, z.n) REACTIONS ON T U NGS TEN A. DEMILDT* I.K.O. Oosterringdijk 18 Amsterdam; ( Received 31 May, 1961)
Abstract---The irradiation of natural tungsten with deuterons, gives rise to three radioactive tantalum species due to the following nuclear reactions: Ju4W(d, ~)l"'2Ta; ~8"W(d,~)~S~Taand ~s6W(d, ~n)~SaTa. Calculations of the reaction energies were performed, and the excitation functions of these three reactions were determined with deuterons of up to 22 MeV. The cross-sections of the three reactions have values between 3 and 0.05 millibarn. By irradiation of tungsten a whole series of nuclear reactions give rise to c a r r i e r - • e tantalum and rhenium, as well as to active tungsten isotopes. To separate the tantalum isotopes from the irradiated tungsten different chemical procedureswereelaborated./w-'~ For the tantalum formation only three reaction types can form tantalum isotopes by irradiations of tungsten with deuterons o f 22 MeV, namely: (d, :0; (d, ~n) and (d, 9_,o) reactions. Taking into account the fact that natural tungsten contains five stable isotopes, fifteen nuclear reactions could be expected, which will give tantalum isotopes. As the ~s°w isotope has a small abundance, only twelve reactions must be considered. These reactions give rise to seven tantalum isotopes, namely: 179Ta, lS°Ta, ~SWa, lS2Ta, lSaTa, lS4Ta and lSaTa. As only three isotopes were observed one could conclude that no (d, 2p) reactions occur. The following reactions were identified: ~s4W(d, ~.)lS2Ta, ls~iW(d, a)lS4Ta and 186W(d, ~.n)lS:lTa. I. M A S S - E N E R G Y B A L A N C E S OF THE C O N S I D E R E D NUCLEAR REACTIONS For the three reactions examined the energies were calculated from the theoretical data o f MARTIN In). The reaction energies were further computed by means o f the results o f the measured binding energies.l< ~1 A survey o f these data is given in Table 1. TABLE I. COMPUTED REACTION ENERGIES (MeV) Reactions
Energies computed from theoretical masses
Energies computed from the binding energies
'*4W(d, ~)'S2Ta ~s~;W((t, :~)t~Ta ts';W(d, :~n)l~aTa
1l-3 1 I" 1 5"4
-5"4
11'0
* Research Fellow 1.1.K.W. + New address: Inst. of Anal. Chem., J. Plateaustraat, 22, University of Ghent. ~ A. DEMILDTand J. HOSTE, International Atomic Energy Agency. Congress of Copenhagen, R.I.C.C./59 (Sept. 1960). 12>A. DEMILDTand J. HOSTE,Bull. Soe. Chint. Belg. 70, 145 (1961). taJ C h . N . MARTIN, Tables de Physique Nueldaire. Gauthier-Villars (1954). ~4~A. H. WAPSTRA,Physiea 21, 385 (1955). ~:~A. H. WAPSn~A,Handbuch der Physik. Vol. 1, p. 38. S. Fliigge, Berlin (1958). 167
168
A. DEMILDT
In agreement with the calculated reaction energies one can conclude that the (d, e) and the (d, an) reactions produce respectively 11 or 12 MeV and 5 MeV. Thus the three reactions could occur with energetic deuterons high enough to exceed the Coulomb barrier of the target nuclei. One can also expect that the cross sections of the (d, ~) reactions at lower energies will be considerably higher than the (d, an) reactions. 2. T H E E X C I T A T I O N F U N C T I O N S O F T H E O B S E R V E D NUCLEAR REACTIONS
T h e nuclear excitation functions (the experimental cross sections as a function of the kinetic energy of the projectiles) were determined in the following way. Stacks of tungsten foils were irradiated with the internal deuteron beam of the synchrocyclotron of Amsterdam. To obtain a collimated mono-energetic beam, the foils were
¢/ o
b
FIG. 1 a - - T h e thick-window target holder with foils; b--Position in the cyclotron; the arrows show the direction of the deuterons.
mounted in a special thick window target holder (Fig. 1), designed in the Institute for Nuclear Physical Research (I.K.O.) of Amsterdam. The incidence gap of the deuterons was quite narrow (1.5 mm) to insure a homogeneous energy. The determination of the incident deuteron energy was computed from the 27Al(d, ~p)~Na reaction, as this excitation function is accurately established.(6,7, S,9) A stack of fourteen aluminium foils (thickness: 25.80 mg cm -2) was irradiated and the 24Na activity measured by fi-counting. The disintegration rate of the irradiated foils is a measure of the cross-sections when short irradiations (t < T~/20) are used. It was thus possible to set up a relative excitation curve. The maximum energy of the deutrons was determined by computing relative excitation functions of varying maximum deuteron energy until the experimental curve fitted the standard curve. The energy losses in each foil were computed from the range-energy curves for aluminium. (1°) For the actual measurements of the tungsten cross-sections a stack of seven aluminium foils was alternated with seven tungsten foils (thickness : 57"80 mg cm-2). The maximum energy and deuteron flux were computed by absolute fi-counting of (o) E. T. CLARKE, Phys. Rev. 71, 187 (1947). (7) H. H. PH. MOEKEN,Akademisch Proefschrift, I.K.O. Amsterdam (1957). (8) R. E. BATZEL, W. W. T. CRANE and G. D. O'KELLEY; Phys. Rev. 91, 939 (1953). (9) p. A. LENK and J. SLOBODRIAN; Phys. Rev. 116, 1229 (1959). (lo) W. A. ARON, B. C. HOFFMANand F. C. WILLIAMS, U . S . A . E . C . U-663 (1949).
Excitation functions of (d, a) and (d, ~n) reactions on tungsten
169
the 2aNa activities p r o d u c e d in the a l u m i n i u m foils. The a b s o l u t e activities were measured with a calibrated G e i g e r - M t i l l e r c o u n t e r or a 4~r-proportional m e t h a n e counter. F r o m cross-sections given in the literature, the flux is c o m p u t e d , for short i r r a d i a t i o n times, f r o m the e q u a t i o n o f CLARKE and IRVINI. (n) F - 6'40 ;; 10 -:~
D A T, tll
.
(Y
F D T ~4 m ,r
integrated flux, in # A . m i n . absolute activity in disintegrations rain -~. half-life in minutes. a t o m i c weight. thickness o f the i r r a d i a t e d foils in mg cm " for a specific isotope. cross-section in mbarns. Using the same equation, the cross-sections o f the (d, ~) and the (d, ~-#0 reactions were calculated from the absolute t a n t a l u m activities in each foil, t a k i n g into account foil thickness, half-life o f the p r o d u c t nucleus a n d isotopic a b u n d a n c e . Energy losses in each tungsten foil were c o m p u t e d from the m e a n ionization potential I w 697 eV !12) using the BETHE-LIVJNGSTOXE cquationt~aL Energy losses o f the d e u t e r o n s in a l u m i n i u m were taken from ARON el a[. ll°) The results are given in Table 2 and in Fig. 2 and 3. TABI t: 2 . - - C g o s s - S E C T I O N S IN MILLIBARNS AS A FUNC31ON OF DEUTERON ENERGY
Deuteron energy
l*"W(d, 2)>Wa
>'aW(d, ~)lSeTa
>';W(d, 2n)lSaTa
21 20 9 8 7 6 5 4 13 12 II 10 9
3.05 2.90 2-65 2.30 2.10 1.70 1.30 1.08 0.90 0-62 0-29 0.16 0.05
1-25 1-22 1"08 0'85 0'70 0"57 0'46 0"32 0'21 0"13
1-15 0'97 0"67 0.52 0.35 0.22 0.13 0'075 -
-
3. D I S C U S S I O N The form o f the two excitation functions o f the (d, ~) reactions show a simihtr behaviour, the a b s o l u t e values o f the cross-sections being o f the same size. F r o m these curves it a p p e a r s that these reactions are detectable from a b o u t I0 MeV, in a g r e e m e n t with the calculated C o u l o m b barrier. The cross-sections for the ls6W(d, ~n)aSaTa r e a c t i o n are considerably smaller than for the (d, ~) reactions, particularly in the lower energy region. This is in agreement with the fact that no lsaTa was detectable from W irradiated with 12 M e V deuterons hi the cyclotron o f Louvain. ~1~ E. T. CLARKEand J. W. IRVINEJR., Phys. Rev. 66, 23l (1944). i~e~C. J. BAKKERand E. SEGRI~,Phys. Rev. 81,489 (1951). i~a, H. A. BETHEand M. S. LlVINOSTONE; Rev. :'vlod. Phys. 9, 245 (1937).
170
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Excitation functions of (d, =) and (d, ~n) reactions on tungsten
171
4, A P P E N D I X To compute the energy losses of the deuterons in each tungsten or aluminium foil, the numerical relationship between the deuteron energy and the energy losses expressed in MeV mg -1 cm -2 was used. This relationship was computed for aluminium by ARON et a1.<1% while the relation for tungsten was computed by the author ~14)using the formulas of BETHE and LIVINGSTONE~la). The following table gives the energy losses in tungsten expressed in MeV mg ~ c m e as a function of the energy. Energy
( d E / d x ) ' w l M e V mg I cm ~t
4 6 8 10 12 14 16 18 20 22 24
0.0522 0.0425 0.0360 0-0318 0.0279 0.0253 0.0229 0.0214 0.0196 0.0187 0.0173
The range-energy relation of tungsten results from a direct interpolation between the curves of silver and lead compiled by ARON et al. u°) This curve is not used as it seems to give somewhat lower accurate results than the calculations with the energy losses values. Acknowledgements--Acknowledgements are due to Prof. Dr. A. H. W. ATEN JR. and his co-workers of the 1.K.O. Amsterdam, for their hospitality. Thanks are also due to Prof. Dr. C. GROSJEAN, who computed the range-energy relations of tungsten with the IBM 610. This work was performed as part of the research programme of the "Stichting voor Fundamenteel Onderzoek der Materie (F.O.M.)" which is financially supported by the "Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek (Z.W.O.) and of the "lnteruniversitair Instituut voor Kernwetenschappen" of Belgium.
(~4~A. DEMILDT. Thesis, University of Ghent (1960).