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The importance of excitation functions in fast neutron flux measurement
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INSTRUMENTS
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92 (I971)
533-536; © N O R T H - H O L L A N D
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Part IV. Applications to nuclear physics 533-567 T H E I M P O R T A N C E OF E X C I T A T I O N F U N C T I O N S I N FAST N E U T R O N FLUX M E A S U R E M E N T * D. C R U M P T O N , P. E. F R A N C O I S a n d S. E. H U N T
Physics Department, The University of Aston, Birmingham, U.K. T h e i m p o r t a n c e of a knowledge o f the excitation function of reaction used as m o n i t o r s for 14 M e V flux m e a s u r e m e n t s is discussed. T h e i n f o r m a t i o n on excitation f u n c t i o n s o f frequently used reactions is s u m m a r i s e d a n d s o m e n e w m e a s u r e m e n t s are reported.
1. Introduction "14 MeV" neutrons produced from the 3T(d,n)4He reaction have an energy spread depending mainly on the angle between the deuteron beam and the direction of the emitted neutrons, but also affected by the energy of the incident deuterons and by target thickness. For the much used deuteron energy of 150 keV the mean neutron energies vary from approximately 14.7 MeV in the forward direction to 13.6 MeV in the backward direction. Fast neutron fluxes are frequently measured by using monitor foils. When the comparitor technique is used or when the geometrical conditions are such that the neutrons irradiating the foil and the specimens under investigation are of well defined and equal energy, a knowledge of the excitation function of the foil is unnecessary, providing that the foil cross section at the irradiation energy is known, but these ideal conditions are seldom realised in practice. In order to obtain as high a flux as possible the foil and specimen are frequently located near the target, so that they are irradiated by neutrons having an appreciable energy spread. A knowledge of the excitation function of the foil is therefore necessary in order to estimate the appropriate mean cross section if the neutron flux is to be estimated with reasonable accuracy. In order to minimise the uncertainties it is also desirable that the excitation function of the foil and the specimen should have a similar slope. The necessity to use maximum flux may also mean that the foil and specimen have to be placed at different angles with respect to the deuteron beam, and are consequently subjected to neutrons of different mean energy. In this case correction for the foil excitation function is even more important. Over the energy range 13.6 to 14.7 MeV the cross sections of the much used 6aCu(n,2n)62Cu reaction varies by more than 25% so that errors of up to this magnitude can be introduced if the form of the excitation function is disregarded. * Proofread by the Publisher.
It is also necessary to know the form of the excitation function in order to compare absolute measurements of reaction cross sections made by different workers using slightly different neutron energies in the 14 MeV region. Measurements on reactions suitable for neutron flux measurement have been listed by Nuert and Pollehn'-) and the available data on the excitation functions up to June, 1965, and April, 1966, has been summarised by Liskien and Paulsen 2) and Jessen et al. 3) respectively. The present work summarises later work on the reactions listed by Nuert and Pollehn and reports experimental measurements made by the authors on some of these excitation functions.
2. Experimental procedure Fast neutrons were produced by irradiating thick tritiated titanium targets with 300 keV deuterons from a small Van de Graaff accelerator. After making appropriate corrections for the energy loss of the deuterons in the target and the energy spread due to the finite angle subtended by the specimen at the target, it is estimated that neutrons of mean energy 13.5 MeV were obtained in the near backward direction (q5 = 150 °) increasing to 14.9 MeV in the forward (~b = 0 °) direction. The widths of the neutron spectra at half maximum height were estimated to vary from 0.5 MeV at q5 = 0 ° to 0.3 MeV at ~b = 150 ° through a minimum value of 0.05 MeV at gb = 90 ° (EN mean = 14.14 MeV). The specimens were in the form of elemental foils, except for fluorine, where teflon foils were used. Foils of standard size and weight were mounted equidistant from the target at various angles to the deuteron beam and irradiated simultaneously. After correction for the small anisotropy of the neutron yield (6 per cent) they were assumed to be subjected to equal fluxes. Uncertainties in geometrical measurements were estimated to contribute a possible error of __+1% to the estimation of the neutron fluxes. The resulting activities for the foils were determined using a standard 3 " × 2 " NaI(Th) crystal and photomultiplier assembly coupled to a 400 channel pulse height analyser.
533 IV. A P P L I C A T I O N S
TO N U C L E A R
PHYSICS
D. CRUMPTON et al.
534
TAnLE 1 Summary of excitation function measurements on frequently used fast neutron monitoring reactions. Reaction
3.
Author
Neutron energy (MeV)
Date
Approximate slope Reference at 14.5 MeV (% MeV)
19F(n,2n)18F
Strohal et al. Csikai Bormann and Riehle Vonach et al. Shiokawa et al. Present work
1964 1966 1967 1968 1968 1970
14 13.5 13.5 13.5 13.5 13.5
27Al(n,p)ZVMg
Ferguson and AIbergotti Cuzzocrea and Perillo Partington et al. (Present work)
1967 1968 1970
12.3 -13.9 13.7 -14.7 13.5 -14.9
63Cu(n,2n)62Cu
Glover and Weigold Liskien and Paulsen Csikai Cuzzocrea and Perillo Partington et al. (Present work)
1962 1965 1966 1968 1970
13.9 12.6 13.5 13.7 13.5
-14.8 -19.6 -14.8 -14.7 -14.9
25 26 26 25 35 + 2%
24 26 8 17 18
6~Cu(n,2n)~4Cu
Prestwood and Bayhurst Paulsen and Liskien Csikai Santry and Butler Bormann and Riehle Vonach et al.
1961 1965 1966 1966 1967 1968
12 12.6 13.6 10 13.5 13.5
-20 -19.6 -14.7 -20 -15.0 -14.7
12 12 14 11 4 11
28 30 8 31 9 11
27Al(n,~)24Na
Bayhurst and Prestwood Gabbard and Kern Strohal et al. Paulsen and Liskien Hemingway et al. Bormann and Riehle Ferguson and Albergotti Vonach et al. Cuzzocrea and Perillo
1961 1962 1964 1965 1966 1967 1967 1968 1968
7 -19.8 12.5 -18 14 -14.8 12.6 -19.6 13.5 -14.8 13.7 -14.9 12.3 -13.9 13.5 -14.7 13.7 -14.7
-12 -10 -9 -9 - 10 -10 -16 -9 -5
33 15 5 35 36 9 16 11 17
~6Fe(n,p) 56Mn
Terreil and Holm Bormann et al. Santry and Butler Strohal et al. Liskien and Paulsen Cuzzocrea et al.
1958 1962 1964 1964 1965 1968
12.4 -17.9 12 -19.6 4.57-20.3 14.1 -14.7 12.6 -19.6 13.7 -14.67
-5 20 -10 + 40 - 14 -27
37 23 38 5 26 17
Excitation
function
measurements
19F(n,2n)lSF The excitation f u n c t i o n for this reaction has been m e a s u r e d in the 10-20 M e V range by several a u t h o r s 4 - ' 2 ) . O f these five 5'8'9'11'12) have m a d e a detailed study o f the 13.5-15 M e V region. All o b t a i n e d an increase in n e u t r o n cross section as the energy increased which is typical o f (n,2n) reactions in this energy region. W i t h the exception o f B o r m a n n a n d
-14.8 -14.8 -15.0 -14.7 -14.8 -14.9
34 38 24 39 33 22+ 3% - 1 4 (at 13 MeV) - 12 (at 14.2 MeV) -3_+3~
-
5 8 9 11 12
16 17 18
Riehle, the gradients expressed as a percentage of the 14.5 M e V cross section, lie between 30% and 40% M e V - 1. The results o f b o t h Strohal et al. an d Csikai show evidence o f structure in the f o r m o f a periodic v ar i at i o n in a m p l i t u d e o f a b o u t 5% and 2 0 % respectively, with the m e a n cross section increasing at 34% and 38% M e V - '. Th e present work, yielding a slope o f 2 2 % M e V - t
EXCITATION
FUNCTIONS
IN F A S T N E U T R O N
is in good agreement with the results of Bormann and Riehle o f 2 4 % MeV-1. The energy resolution was such that we did not expect to see structure. 27Al(n,p)27Mg Several measurements t3-17) have been made of this reaction in the 10-20 MeV range. The two most recent measurements, Ferguson and Albergotti 16) and Cuzzocrea and Perillo ~7) give detailed information for the energy region 12.3-14.0 MeV and 13.7-14.6 MeV respectively. Both results show signs of structure with the mean neutron energy decreasing at 14% MeV -1 at 13.0 MeV for Ferguson and Albergotti and 12% MeV-1 at 14.2 MeV for Cuzzocrea and Perillo. Our results 18) which cover the energy range 13.515.0 MeV show a much slower decrease in cross section of approximately 3% MeV -1 at 14.5 MeV. 63Cu(n,2n)62Cu This reaction cross section is used extensively as a flux monitor and m a n y s t u d i e s 8 " 1 7 ' 1 9 - 2 7 ) of the excitation function have been made. Four authors 8"17' 2+"26) have made a more detailed study in the 14-15 MeV region. Typically the cross sections increase with energy and all obtained gradients between 25% and 26% MeV-1 at 14.5 MeV. Our mea-
FLUX MEASUREMENT
535
surements tS) yielded a slope of 25% MeV -1 in good agreement with the other authors. 65Cu(n,2n)64Cu Of the studies 8'9'11'27-3t) on this reaction the majority of detailed investigations in the 13.5 MeV regionS,q, 11,28,30,31) show an increase in cross section with energy of ll%/MeV, Csikai and Bormann and Riehle again observe structure. Csikai obtained a similar gradient of about 14°/o MeV- 1 while Bormann and Riehle reported a much slower variation of 14% MeV- 1. 27Al(n,~)2+Na Several studies 5'9-11' 14-17,32-36) have been made of this reaction. Most observed a cross section decreasing with energy by about 10% MeV -1. Ferguson and Albergotti 16) obtained a gradient of about - 1 6 % MeV -1 and Cuzzocrea and Perillo 17) - 5 % MeV -1. The latter authors and Strohal et al. both observed structure. 56Fe(n,p)56Mn With the exception of Strohal et al. 15) all authors 5,17,e3,z6,37,38) resort a slight decrease in cross section between 13.5 and 14 MeV followed by a more rapid decrease of between 5°/0 MeV- 1 and 27%
o b~,p) x Cn,,~)
o A 6-15
6-, 3-s A ~A
I'C o x° ° o
o
° o
oo o
~
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oo
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I
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4'o
go
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,oo'
,~o
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,40
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,60
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200
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Fig. 1. T h e ratio o f the cross section at 15 M e V to that at 13.5 M e V for (n,p), (n,a) a n d (n,2n) reactions as a function o f m a s s n u m b e r . IV. A P P L I C A T I O N S
TO N U C L E A R
PHYSICS
536
D. CRUMPTON et al.
MeV-1. Strohal et al. find a rapidly rising cross section between 14 a n d 15 MeV. Measurements on these reactions are s u m m a r i s e d in table 1. 4. Discussion of results Appreciable discrepancies exist between reported experimental m e a s u r e m e n t s of some excitation functions (table 1) a n d clearly further work is required. The 63Cu(n,2n)62Cu reaction is most used for flux meas u r e m e n t purposes a n d has received most attention. There is a good agreement on the gradient of the excitation f u n c t i o n obtained by several authors. The relatively steep slope of the excitation curve for this reaction would n o t appear to m a k e it a good choice for n e u t r o n flux m o n i t o r i n g unless the n e u t r o n energy is well defined or the specimen u n d e r investigation has a similarly steeply rising excitation function. In order to assist in m a t c h i n g the excitation f u n c t i o n of the specimens a n d m e a s u r i n g foils the ratios of the 15 MeV a n d 13.5 MeV cross sections have been plotted as a f u n c t i o n of mass n u m b e r (fig. 1) for reactions listed by Jessen et al.3). Certain b r o a d trends in the shapes of the excitation functions appear, in spite of the incomplete experimental data. F o r low mass n u m b e r nuclei the (n,p) a n d (n,7) cross sections c o m m o n l y fall by between 10°/o a n d 30°/o between 13.5 MeV a n d 15 MeV. This fall is less m a r k e d for heavier nuclei, a n d for mass n u m b e r s above a b o u t 70 the cross sections frequently increase with energy. The (n,2n) reactions almost all have increasing cross sections between 13.5 MeV and 15 MeV a n d this increase is more m a r k e d for the lighter nuclei.
References 1) H. Nuert and H. Pollehn, Tables of cross sections of nuclear reactions in the 14-15 MeV range, E.U.R. 122e (1963). 2) H. Liskien and A. Paulsen, Cross sections for threshold reactions, E.U.R. 119e (1965). 3) p. Jessen, M. Bormann, F. Dreyer and H. Nuert, Nuclear Data I (1966) 103. 4) O. D. Brill, N. A. Vlasov, S. P. Kalinin and L. S. Sokolov, Soviet Phys. Doklady 6 (1961) 24.
5) p. Strohal, P. Kulisic, Z. Kolar and N. Cindro, Phys. Letters 10 (1964) 104. 6) M. Bormann, E. Fretwurst, P. Schehka and G. Wrege, Nucl. Phys. 63 (1965) 438. 7) j. Pisard and C. F. Williamson, Nucl. Phys. 63 (1965) 673. 8) j. Ccikai, At. Kozlem 8 (1966) 79. 9) M. Bormann and I. Riehle, Z. Physik 207 (1967) 64. 10) H. O. Menlove, K. L. Coop and H. A. Grench, Phys. Rev. 163 (1967) 1308. 11) H. K. Vonach, W. G. Vonach, H. Mi.inzer and P. Schramel, Nat. Bur. Std. Special Publ. 299, vol. II (1968). 12) T. Shickawa, M. Yagi, K. Kaji and T. Sasaki, J. Inorg. Nucl. Chem. 30 (1968) 1. 13) O. M. Hudson and I. L. Morgan, Bull. Am. Phys. Soc. 4 (1959) 97. 14) G. S. Mani, G. J. McCallum and A. T. G. Ferguson, Nucl. Phys. 19 (1960) 535. 15) F. Gabbard and B. D. Kern, Phys. Rev. 128 (1962) 1276. 16) j. M. Ferguson and J. C. Albergotti, Nucl. Phys. A98 (1967) 65. 17) p. Cuzzocrea and E. Perillo, Nuovo Cimento 54B (1968) 53. 18) D. Partington, D. Crumpton and S. E. Hunt, Analyst 95 (1970) 257. 19) j. L. Fowler and J. M. Slye, Phys. Rev. 77 (1950) 787. 20) j. E. Brolley, J. L. Fowler and L. K. Schlacks, Phys. Rev. 88 (1952) 618. 21) A. V. Cohen and P. H. White, Nucl. Phys. 1 (1956) 73. 22) j. M. Ferguson and W. E. Thompson, Phys. Rev. 118 (1960) 228. 23) M. Bormann, S. Cierjacks, R. Langkau and H. Nuert, Z. Physik 166 (1962) 477. 24) R. N. Glover and E. Weigold, Nucl. Phys. 29 (1962) 309. 2~) L. A. Rayburn, Phys. Rev. 130 (1963) 731. 26) H. Liskien and A. Paulsen, J. Nucl. Energy A/B 19 (1965) 73. z7) M. Bormann and B. Lammers, Nucl. Phys. A130 (1969) 195. 2s) R. J. Prestwood and B. P. Bayhurst, Phys. Rev. 121 (1961) 1438. 29) H. Bormann, S. Cierjacks, E. Fretwurst, K. J. Giesecke, H. Nuert and H. Pollehn, Z. Physik 174 (1963) 1. 30) A. Paulsen and H. Liskien, Nukleonik 7 (1965) 117. 31) D. C. Santry and J. P. Butler, Can. Phys. 44 (1966) 1183. 32) B. D. Kern, W. E. Thompson and J. M. Ferguson, Nucl. Phys. 10 (1959) 226. 33) B. P. Bayhurst and R. J. Prestwood, J. Inorg. Nucl. Chem. 23 (1961) 173. 34) j. M. F. Jeronymo, G. S. Mani, J. Olkowski, A. Sadeghi and C. F. Williamson, Nucl. Phys. 47 (1963) 147. 3~) A. Paulsen and H. Liskien, J. Nucl. Energy A/B 19 (1965) 907. 36) j. D. Hemingway, R. H. James, E. B. M. Martin and G. R. Martin, Proc. Roy. Soc. A 292 (1966) 180. 37) j. Terrell and D. M. Holm, Phys. Rev. 109 (1958) 2031. 38) D. C. Santry and J. P. Butler, Can. J. Phys. 42 (1964) 1030.
INSTRUMENTS
AND
METHODS
92 (I971)
533-536; © N O R T H - H O L L A N D
PUBLISHING
CO.
Part IV. Applications to nuclear physics 533-567 T H E I M P O R T A N C E OF E X C I T A T I O N F U N C T I O N S I N FAST N E U T R O N FLUX M E A S U R E M E N T * D. C R U M P T O N , P. E. F R A N C O I S a n d S. E. H U N T
Physics Department, The University of Aston, Birmingham, U.K. T h e i m p o r t a n c e of a knowledge o f the excitation function of reaction used as m o n i t o r s for 14 M e V flux m e a s u r e m e n t s is discussed. T h e i n f o r m a t i o n on excitation f u n c t i o n s o f frequently used reactions is s u m m a r i s e d a n d s o m e n e w m e a s u r e m e n t s are reported.
1. Introduction "14 MeV" neutrons produced from the 3T(d,n)4He reaction have an energy spread depending mainly on the angle between the deuteron beam and the direction of the emitted neutrons, but also affected by the energy of the incident deuterons and by target thickness. For the much used deuteron energy of 150 keV the mean neutron energies vary from approximately 14.7 MeV in the forward direction to 13.6 MeV in the backward direction. Fast neutron fluxes are frequently measured by using monitor foils. When the comparitor technique is used or when the geometrical conditions are such that the neutrons irradiating the foil and the specimens under investigation are of well defined and equal energy, a knowledge of the excitation function of the foil is unnecessary, providing that the foil cross section at the irradiation energy is known, but these ideal conditions are seldom realised in practice. In order to obtain as high a flux as possible the foil and specimen are frequently located near the target, so that they are irradiated by neutrons having an appreciable energy spread. A knowledge of the excitation function of the foil is therefore necessary in order to estimate the appropriate mean cross section if the neutron flux is to be estimated with reasonable accuracy. In order to minimise the uncertainties it is also desirable that the excitation function of the foil and the specimen should have a similar slope. The necessity to use maximum flux may also mean that the foil and specimen have to be placed at different angles with respect to the deuteron beam, and are consequently subjected to neutrons of different mean energy. In this case correction for the foil excitation function is even more important. Over the energy range 13.6 to 14.7 MeV the cross sections of the much used 6aCu(n,2n)62Cu reaction varies by more than 25% so that errors of up to this magnitude can be introduced if the form of the excitation function is disregarded. * Proofread by the Publisher.
It is also necessary to know the form of the excitation function in order to compare absolute measurements of reaction cross sections made by different workers using slightly different neutron energies in the 14 MeV region. Measurements on reactions suitable for neutron flux measurement have been listed by Nuert and Pollehn'-) and the available data on the excitation functions up to June, 1965, and April, 1966, has been summarised by Liskien and Paulsen 2) and Jessen et al. 3) respectively. The present work summarises later work on the reactions listed by Nuert and Pollehn and reports experimental measurements made by the authors on some of these excitation functions.
2. Experimental procedure Fast neutrons were produced by irradiating thick tritiated titanium targets with 300 keV deuterons from a small Van de Graaff accelerator. After making appropriate corrections for the energy loss of the deuterons in the target and the energy spread due to the finite angle subtended by the specimen at the target, it is estimated that neutrons of mean energy 13.5 MeV were obtained in the near backward direction (q5 = 150 °) increasing to 14.9 MeV in the forward (~b = 0 °) direction. The widths of the neutron spectra at half maximum height were estimated to vary from 0.5 MeV at q5 = 0 ° to 0.3 MeV at ~b = 150 ° through a minimum value of 0.05 MeV at gb = 90 ° (EN mean = 14.14 MeV). The specimens were in the form of elemental foils, except for fluorine, where teflon foils were used. Foils of standard size and weight were mounted equidistant from the target at various angles to the deuteron beam and irradiated simultaneously. After correction for the small anisotropy of the neutron yield (6 per cent) they were assumed to be subjected to equal fluxes. Uncertainties in geometrical measurements were estimated to contribute a possible error of __+1% to the estimation of the neutron fluxes. The resulting activities for the foils were determined using a standard 3 " × 2 " NaI(Th) crystal and photomultiplier assembly coupled to a 400 channel pulse height analyser.
533 IV. A P P L I C A T I O N S
TO N U C L E A R
PHYSICS
D. CRUMPTON et al.
534
TAnLE 1 Summary of excitation function measurements on frequently used fast neutron monitoring reactions. Reaction
3.
Author
Neutron energy (MeV)
Date
Approximate slope Reference at 14.5 MeV (% MeV)
19F(n,2n)18F
Strohal et al. Csikai Bormann and Riehle Vonach et al. Shiokawa et al. Present work
1964 1966 1967 1968 1968 1970
14 13.5 13.5 13.5 13.5 13.5
27Al(n,p)ZVMg
Ferguson and AIbergotti Cuzzocrea and Perillo Partington et al. (Present work)
1967 1968 1970
12.3 -13.9 13.7 -14.7 13.5 -14.9
63Cu(n,2n)62Cu
Glover and Weigold Liskien and Paulsen Csikai Cuzzocrea and Perillo Partington et al. (Present work)
1962 1965 1966 1968 1970
13.9 12.6 13.5 13.7 13.5
-14.8 -19.6 -14.8 -14.7 -14.9
25 26 26 25 35 + 2%
24 26 8 17 18
6~Cu(n,2n)~4Cu
Prestwood and Bayhurst Paulsen and Liskien Csikai Santry and Butler Bormann and Riehle Vonach et al.
1961 1965 1966 1966 1967 1968
12 12.6 13.6 10 13.5 13.5
-20 -19.6 -14.7 -20 -15.0 -14.7
12 12 14 11 4 11
28 30 8 31 9 11
27Al(n,~)24Na
Bayhurst and Prestwood Gabbard and Kern Strohal et al. Paulsen and Liskien Hemingway et al. Bormann and Riehle Ferguson and Albergotti Vonach et al. Cuzzocrea and Perillo
1961 1962 1964 1965 1966 1967 1967 1968 1968
7 -19.8 12.5 -18 14 -14.8 12.6 -19.6 13.5 -14.8 13.7 -14.9 12.3 -13.9 13.5 -14.7 13.7 -14.7
-12 -10 -9 -9 - 10 -10 -16 -9 -5
33 15 5 35 36 9 16 11 17
~6Fe(n,p) 56Mn
Terreil and Holm Bormann et al. Santry and Butler Strohal et al. Liskien and Paulsen Cuzzocrea et al.
1958 1962 1964 1964 1965 1968
12.4 -17.9 12 -19.6 4.57-20.3 14.1 -14.7 12.6 -19.6 13.7 -14.67
-5 20 -10 + 40 - 14 -27
37 23 38 5 26 17
Excitation
function
measurements
19F(n,2n)lSF The excitation f u n c t i o n for this reaction has been m e a s u r e d in the 10-20 M e V range by several a u t h o r s 4 - ' 2 ) . O f these five 5'8'9'11'12) have m a d e a detailed study o f the 13.5-15 M e V region. All o b t a i n e d an increase in n e u t r o n cross section as the energy increased which is typical o f (n,2n) reactions in this energy region. W i t h the exception o f B o r m a n n a n d
-14.8 -14.8 -15.0 -14.7 -14.8 -14.9
34 38 24 39 33 22+ 3% - 1 4 (at 13 MeV) - 12 (at 14.2 MeV) -3_+3~
-
5 8 9 11 12
16 17 18
Riehle, the gradients expressed as a percentage of the 14.5 M e V cross section, lie between 30% and 40% M e V - 1. The results o f b o t h Strohal et al. an d Csikai show evidence o f structure in the f o r m o f a periodic v ar i at i o n in a m p l i t u d e o f a b o u t 5% and 2 0 % respectively, with the m e a n cross section increasing at 34% and 38% M e V - '. Th e present work, yielding a slope o f 2 2 % M e V - t
EXCITATION
FUNCTIONS
IN F A S T N E U T R O N
is in good agreement with the results of Bormann and Riehle o f 2 4 % MeV-1. The energy resolution was such that we did not expect to see structure. 27Al(n,p)27Mg Several measurements t3-17) have been made of this reaction in the 10-20 MeV range. The two most recent measurements, Ferguson and Albergotti 16) and Cuzzocrea and Perillo ~7) give detailed information for the energy region 12.3-14.0 MeV and 13.7-14.6 MeV respectively. Both results show signs of structure with the mean neutron energy decreasing at 14% MeV -1 at 13.0 MeV for Ferguson and Albergotti and 12% MeV-1 at 14.2 MeV for Cuzzocrea and Perillo. Our results 18) which cover the energy range 13.515.0 MeV show a much slower decrease in cross section of approximately 3% MeV -1 at 14.5 MeV. 63Cu(n,2n)62Cu This reaction cross section is used extensively as a flux monitor and m a n y s t u d i e s 8 " 1 7 ' 1 9 - 2 7 ) of the excitation function have been made. Four authors 8"17' 2+"26) have made a more detailed study in the 14-15 MeV region. Typically the cross sections increase with energy and all obtained gradients between 25% and 26% MeV-1 at 14.5 MeV. Our mea-
FLUX MEASUREMENT
535
surements tS) yielded a slope of 25% MeV -1 in good agreement with the other authors. 65Cu(n,2n)64Cu Of the studies 8'9'11'27-3t) on this reaction the majority of detailed investigations in the 13.5 MeV regionS,q, 11,28,30,31) show an increase in cross section with energy of ll%/MeV, Csikai and Bormann and Riehle again observe structure. Csikai obtained a similar gradient of about 14°/o MeV- 1 while Bormann and Riehle reported a much slower variation of 14% MeV- 1. 27Al(n,~)2+Na Several studies 5'9-11' 14-17,32-36) have been made of this reaction. Most observed a cross section decreasing with energy by about 10% MeV -1. Ferguson and Albergotti 16) obtained a gradient of about - 1 6 % MeV -1 and Cuzzocrea and Perillo 17) - 5 % MeV -1. The latter authors and Strohal et al. both observed structure. 56Fe(n,p)56Mn With the exception of Strohal et al. 15) all authors 5,17,e3,z6,37,38) resort a slight decrease in cross section between 13.5 and 14 MeV followed by a more rapid decrease of between 5°/0 MeV- 1 and 27%
o b~,p) x Cn,,~)
o A 6-15
6-, 3-s A ~A
I'C o x° ° o
o
° o
oo o
~
"----><
oo
Xo • ° o
I
2'o
4'o
go
e'o MASS
,oo'
,~o
I
,40
!
,60
i
,eo
I
200
NUMBER
Fig. 1. T h e ratio o f the cross section at 15 M e V to that at 13.5 M e V for (n,p), (n,a) a n d (n,2n) reactions as a function o f m a s s n u m b e r . IV. A P P L I C A T I O N S
TO N U C L E A R
PHYSICS
536
D. CRUMPTON et al.
MeV-1. Strohal et al. find a rapidly rising cross section between 14 a n d 15 MeV. Measurements on these reactions are s u m m a r i s e d in table 1. 4. Discussion of results Appreciable discrepancies exist between reported experimental m e a s u r e m e n t s of some excitation functions (table 1) a n d clearly further work is required. The 63Cu(n,2n)62Cu reaction is most used for flux meas u r e m e n t purposes a n d has received most attention. There is a good agreement on the gradient of the excitation f u n c t i o n obtained by several authors. The relatively steep slope of the excitation curve for this reaction would n o t appear to m a k e it a good choice for n e u t r o n flux m o n i t o r i n g unless the n e u t r o n energy is well defined or the specimen u n d e r investigation has a similarly steeply rising excitation function. In order to assist in m a t c h i n g the excitation f u n c t i o n of the specimens a n d m e a s u r i n g foils the ratios of the 15 MeV a n d 13.5 MeV cross sections have been plotted as a f u n c t i o n of mass n u m b e r (fig. 1) for reactions listed by Jessen et al.3). Certain b r o a d trends in the shapes of the excitation functions appear, in spite of the incomplete experimental data. F o r low mass n u m b e r nuclei the (n,p) a n d (n,7) cross sections c o m m o n l y fall by between 10°/o a n d 30°/o between 13.5 MeV a n d 15 MeV. This fall is less m a r k e d for heavier nuclei, a n d for mass n u m b e r s above a b o u t 70 the cross sections frequently increase with energy. The (n,2n) reactions almost all have increasing cross sections between 13.5 MeV and 15 MeV a n d this increase is more m a r k e d for the lighter nuclei.
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