Activation analysis in vivo using 5 MeV incident neutrons

Activation analysis in vivo using 5 MeV incident neutrons

Internataonal Journal ofApphed Radtatmn and I~otopcs, 1969, Vol 20, pp 61-68 Pergamon Prem Printed m Northern Ireland Activation Analysis in vivo usi...

533KB Sizes 45 Downloads 98 Views

Internataonal Journal ofApphed Radtatmn and I~otopcs, 1969, Vol 20, pp 61-68 Pergamon Prem Printed m Northern Ireland

Activation Analysis in vivo using 5 MeV Incident Neutrons D. N E W T O N Health Physics and Medical Diwsmn, Atomic Energy Research Estabhshrnent, HarweU, Berkshum and J . A N D E R S O N , C K . B A T T Y E , S. B. O S B O R N a n d R. W . S. T O M L I N S O N King's College Hospital and Medical School, London, S.E.5

(Recewed I0 July 1968) Activauon analysts using 5 MeV mcxdent neutrons has been considered as a method for estamatmg whole-body sodaum, chlorine and calcmm an humans. ExperLments with Lrradmted phantoms have shown that adequate unfforrmty of thermal neutron act~vatmn could be achmved m most subjects, though when the incident neutron energy was reduced to 2 5 MeV, serious non-unlformxdes arose W~th 5 MeV incident neutrons, no dLfflcultaes are expected from the interfering actavit~es reduced by the fast flux when 14 MeV sources are employed. The method has been applied successfully to the analysis of small annuals. ANALYSE PAR A C T I V A T I O N I N VIVO U T I L I S A N T LES N E U T R O N S INCIDENTS DE 5 MeV O n a consider6 l'analyse par acuvatmn uuhsant les neutrons incidents de 5 MeV comme m6thode pour le dosage du sochum, du chlore et du calcmm du corps entmr dam les humains. Des experiences avec des phant6mes lrrach~s ont montr6 qu'on pouva~t achever une umformat6 sut~ante d'act~vatmn par neutrons thermiques dam la plupart des sujets, quo~que, lors de la diminution de l ' ~ e r g m neutronlque mc~dente g 2,5 MeV, d appardt de graves nonuniformit~s Avec des neutrons incidents de 5 MeV on n'attend aucune dffficult~ ~ cause des activit~s inteffdrantes qui sont indmtes par le flux rapide lorsqu'on emplom des sources de 14 MeV O n a port6 avec du succ~s la m~thode ~ 1'analyse des pedts ammaux. AHA2IH3 AHTHBAI_[HH B HATYPE, C IIPHMEHEHHEM I I O B O q H B I X HEHTPOHOB B 5 MEFA3JIEHTPOHBOJIBT ~ oHpe~e~esH~ o6mero co~epmaHs~ • qeaoBeqecRos 0praHH3Me HaTpHH, x~opa H HaJII~I~HH 6IffJI BLI~paH MeTo~ aHTHBaI~HOHHOrO aHa~maa c IIpHMeHeHHeM II050qHI,IX He~TpHoB B 5 Mera~aeHTponB0~bT.

OHU'rS[ C O6JIyqOHHHMH (I)aHTOMaMH HORaSa0"IH, qT0 B 60~IL-

mHHO'rBe c~yqaeB BOBMOH~HOlIOJIyqllT]~ ~0CTaTOqHO e~HH006pasHyXO al~rat~al~Hio Ten~oBr~x He~TpOHOB, XOTHHpH CHHH~eHtrHvHeprHH II060qHHX He~TpOHOB~0 2,5 MeragaeRTpoHso~r-T BOBHHRaJIH cep],esHwae He0~HH00()pasHH. C II060qHMMH He~tTpoxa~H V 5 Meraa~eR~pOHBO~mT He BOBHHRaOTHHHaHHX 8aTpy~HeHHtt OT HoMex, BI~8~BaOMu[X 6MCTpY~'M HOTOROM, H o r ~ a HCHOJrbvyIOTCH HCTOqHHHH B I ~ Mera~e~rpoHBoa],T. ~)TOTMeT0~ ycnemHo HpHMeH~eTc~ ~[.YlH HCII/~[TaHH~ Ha H e S o ~ , m H x H~HBOTHI~,

AKTIVIEKUNGSANALYSE I N YIVO U N T E R V E R W E N D U N G VON 5 MeV EINFALLSNEUTl%ONEN Aktlvierungsanalysenunter Verwendung von 5 IV[eVEmfalLmeutronenwerden m Erwagunggezogen als Verfahren zum Abschatzen des Natnum, Chlor mad Kalzmm ma ganzen menschhcben K6rper. Versuche mat bestrahlten Phantomen haben gezeigt, dass ausreichende Gleichmass~gke~t der thermtschen Nentronenaktiwerung in dem metsten Objekten erre~cht 61

62

D. Newton et al.

werden konnte, aber dass ernsthche Unglemhmasslgkeiten auftraten, wenn d~e Neutronenemfallsenergm auf 2,5 MeV fiel. Keme Schwiengkexten werden erwartet bel 5 MeV Emfallmeutronen von den Stortatagkeiten, die von dem schnellen Fluss bet Anwendung von 14 MeV Qpellen mduzlert werden. Das Verfahren wurde rmt Erfolg verwendet fur die Analyse yon Klemtmren. INTRODUCTION IN STUDIES prevmusly reported (1), the wholebody contents of certain elements were determined by neutron activation analysis I n those experiments, two m e n were irradiated bilaterally wath partially moderated 1 4 M e V neutrons, some of which were further degraded in the body tissues to produce neutrons of intermediate and thermal energies, and approxam a t e uniformity of thermal neutron fluence was achieved throughout the body. T h e levels of ~aNa and saC1 resultang from thermal neutron activation of the stable elements were measured by external g a m m a - r a y counting, and by c o m parison with the activities induced in an Irradiated " p h a n t o m " m a n of known composition, the amounts of sodium and chlorine present in each subject could be calculated T h e detection of 49Ca, induced in these men by thermal neutron activation of their stable 4aCa, indicated that the method nught also be applicable to the estimation of whole-body calcium. W h e n 14 M e V incident neutrons are employed, the analysis of the g a m m a - r a y spectra of the irradiated subject is complicated by the presence of other activities induced by the fast fluxt2L A further difficulty is that the same active nuclide m a y arise from nuclear reactions in different elements for example, ~tNa m a y be produced by a fast (n, p) reaction m magnesmm as well as by thermal neutron capture in stable sodium (z.s) This leads to a systematic error (of approximately 3 per cent in the ease of sodium (s)) which could only be determined accurately if the fast flux were uniform throughout the body and the amount of the target element for the fast reaction were known. These parucular difficulties could be eliminated by reducing the energy of the incident neutrons below the threshold energy for each of the interfering reactions (Table 1), i e below 0.1 MeV. B o m b a r d m e n t w~th neutrons of such low energy would lead to grossly non-uniform thermal neutron activation, and in fact it would

TABLE 1 Fast reactions likely to interfere with the determination of sodium, chlorme and calcium Reaction

Threflaold o(5 MeV) (MeV) (mb)

SVCl(n,p)STS 3 4(12 5*) SgK(n, 2n)SSK 13 1 sip(n, Qt)~AI 20 sip(n, 2n)8°P 12 4 ~aCa(n,p)44K 53 ~Ca(n, ¢¢)41Ar 28 ~aMg(n, p)~Na 47 asCl(n, 2n)a4mCl 12 7 4XK(n, ~)ssCl 01 4XK(n,p)4XAr 17

0* 0 22 0 <0 2~. <0 3~. 0 0 3 4~ 11 7++

o(149 MeV) (rob) 25 6t 115 15 25 35 165 6 30 69

Except where otherwme shown, figures for threshold energies are taken from HOWERTON{9), and cross-section data are from STEHN et al {i0). * COHEN and. WHITE (xt)

t KHURANAand HANS(1~) ++BASSet al (is) be unnecessary, since not all of the fast neutron reactions listed in T a b l e 1 present serious dlfficulues (~) I n practice, therefore, the selection of neutron energy involves a compromise between these opposing factors, having regard to the methods of generation available. For the mvestlgaUon of sodium and calcium m vzvo, CHAMBERLAIn, FP.~MUN, PETERS and PHILIP{a) used neutrons arising from the bomb a r d m e n t of lithium with 9.5 M e g protons (their neutron spectrum showed a peak at 3.5 MeV, but extendedfrom 0 1 M e V t o 8 M e g ) ; PALMER, NELP, M u ~ o and RmH ca) have experimented with neutrons of average energy 2 M e g , produced by the reaction 9Be(d, n). An advantage of these over 14 M e g neutron sources is the lower radiation dose necessary to induce a given level of activity (5) An alternative procedure would be to use 5 M e V neutrons (conveniently generated by the reaction 2H(d, n)), since it appears (Table 1) that at this energy the cross-sections for most of

Actwat,on ana/ys,s m vlvo using 5 MeV mmdent neutrons

the unwanted reactions found at 14 M e V are negligible. I n this p a p e r we report experiments dewsed to confirm this, and to examine the possibilities of using 5 M e V neutrons for the activation analysis of h u m a n subjects T h e application of the method to the estimation of sodium, chlorine and calcium in small animals is also described

M E T H O D S AND RESULTS 1 InterJenng reactwns

Several irradiations were performed to invesugate the possible influence of lnterfenng reactions on the estimation of sodium, chlorine and calcium in animal tissues Neutrons of m a x i m u m energy 5 2 M e V were generated by the reaction ZH(d, n)SHe, using 2 M e V deuterons from a V a n de Graaff accelerator incident on a deuterated titanium target 10/, thick In order to assess interference from the reaction 24Mg(n,p)24Na, samples of two aqueous solutions were irradiated simultaneously in the reLied flux produced at the centre of a water tank exposed to these neutrons One solution contamed 12 g N a N O s and 7 g M g S O v so that the relative amounts of sodium and magnesium were similar to those in the h u m a n body ~s~, the other solution contained 12 g N a N O s only T h e aaNa actlvmes induced in each sample were measured by g a m m a - r a y spectrometry, and were found to be identical within the limits of expemmental error (4-0.5 per cent) Aqueous solutions of K N O a , Ca(NOs)~, HaPO4, M g S O 4 and HC1 were irradiated in a similar manner After irradiation, each sample was placed between two sodium iodide crystal detectors, each 15 crn dia × 9 cm thick, and its g a m m a - r a y spectrum was recorded on a multi-channel analyser asC1, agCa, 42K and 27Mg, from thermal neutron capture reactions, were identified, but of the fast reaction products listed in T a b l e 1 only 2SA1 from alp(n, 0t) was detected T h e production of 4~K, 2TMg and ZSAl should not present serious difficulties in the estimation of sodium, chlorine and calcium, as their g a m m a - r a y energies are suffiemntly different from those of ~ N a , asCl and agCa.

63

2. Flux dzstnbutzon

I t was necessary to establish that the satisfactory uniforlmty of thermal neutron activation previously obtained using 1 4 M e V incident particles ~2~ could be approached with incident neutrons of lower energy T h e variation with depth of the slow flux inducing the reaction ~Na(n,~)~aNa was measured in a tank of water, approximately 30 cm cube, fabrmated from polythene 6 m m thick (Fig 1). This represented the centre section of a 30 em wide subject lying on his side, and was extended in the longitudinal direction by blocks of paraffin wax to maintain eqmhbh u m of thermal flux at the boundaries O t h e r blocks were placed behind the tank to increase the slow neutron density 5 M e V neutrons were generated by the reaction aH(d, n)SHe, as described above T h e front face of the tank was placed 100 cm from the deuterium target, in line with the deuteron b e a m , the tank was well clear of any walls, and approximately 100 em from the floor Polystyrene boxes, each contaamng 4 0 g N a N O s in 70 ml aqueous solution, were placed in the tank at various points along the axis of the beam After irradiation the ~aNa activity ofeach was measured, again using the two 15 cm dla × 9 cm thick sodium iodide crystals For comparison, two slrmlar experiments were performed using different neutron sources In the first, 2"5 M e V neutrons were generated by the reaction ZH(d,n)SHe using 2 5 0 k e V deuterons I n the second experiment neutrons of 7 M e V m a x i m u m energy were produced by the reaction aBe(d, n)l°B A thick beryllium target was b o m b a r d e d with 2.9 M e V deuterons and those neutrons emerging in line with the deuteron beam were used to irradiate the water tank at a distance of 4 m from the source For each experiment, the measured activities, relative to the peak value in each case, are shown in Fig 2. T o secure approximate uniformity of activation in a h u m a n subject, two irradiations would be necessary, with the fast flux incident on opposite sides of the body. T h e activity distribution resulting from a bilateral irradiation can be calculated from the data of Fig. 2, and it is shown in Fig 3 for a 33 cm thick p h a n t o m irradiated with 5 M e V

64

D. Newton et al.

Th.RGET

FIo. 1. The experimental arrangeincnts for investigating slow neutron flux distrtbutions (d~mcnsions m centimetres). >-

p-

100

I--

,< 'd" ¢'4

I

50

o ¢,q

,..I uJ n-

|

0 0

DISTANCE

,

,

,

10

,

20

F R O M SURFACE

OF

,

30

PHANTOM

cm

FIo. 2. Variation along the deuteron beam axm of the neutron flux inducing the reactaon ~Na(n~)S4Na. O: 5 MeV neutrons + : 2 5 McV neutrons • : 9Be (d, n) neutrons

neutrons. This distribution shows that uniformity of activation to within + 5 and - - 8 per cent of the m e a n value could be achieved in subjects of thickness up to 26 cm (allowmg for 3 . 5 c m overlying moderating materxal); approximately 90 per cent of the normal adult population would fall within this category ts~. F r o m earlier experiments with 14 M e V neutrons ~s~ a m a x i m u m non-uniformity of 4 per cent for such subjects is deduced. I t can be shown from Fig. 2, however, that lrradtatxon

with the neutrons from 9Be(d, n) or with 2"5 M c V mono-cncrgcttc neutrons would lead to appreciable non-unlformlty (up to 17 per cent of the m e a n value for a 26 c m thick subject).

3. Irradzatzon of hying animals (i) using 5 M e V mczdent neutrons. T w o llv¢ toads (Bufo Marmus) and three different mixtures of salts in aqueous solution, contaimng approximately the same proportions of bulk elements as a m m a l tissues, were irradiated.

Aa=vatmn analysts in wvo using 5 MeV mmdent neutrons Z

65

10

5 u.

Z

0

•2

u-

. ~ . ~

6

8

DISTANCE

10 FROM

12

14crn

\,+ CENTRE x L~,~E

S uJ 10

Fio. 3. Dlstributaon of the slow neutron fluence, shown as the percentage deviation fi:om the mean, m a 33 cm thack phantom lrrad. rated bilaterally with 5 MeV neutrons (calculated from Fig. 2). During irradiation, each toad was enclosed in a cylindrical polythene container which was rotated about its vertical axis while suspended in the moderating tank in a regaon where the slow flux varied hnearly along the deuteron beam axis. Each mixture was contained in a polystyrene cylinder of approximately the same volume as the vessels housing the toads and occupying the same position in the tank; as the samples were homogeneous, it was not necessary to rotate them. T h e flux necessary to produce sufficient activity during the 15 rain lrradmtions was obtained using a gas target 5 cm thick contaimng deuterium at 2 a t m pressure, which was bombarded through a 3.5/~ thick molybdenum foil window with 9/~A of 2 MeV deuterons. T h e water tank was placed in line with the deuteron beam, w~th its front face 15 cm from the centre of the target. T h e fast flux incident on the tank was approximately 5 × 10s n/cm s sec, as measured with a BF s "long" counter t~>. After irradiation, each toad or mixture was placed between the two 15 cm X 9 cm sodium ~odide detectors, positioned 8 cm apart, and gamma-ray spectra were recorded on a multichannel analyser at intervals over a period of several hr. T h e spectrum of a toad recorded 15 m m after irradiation is shown in Fig. 4. It shows prominent peaks due to 49Ca (3.10 M e V gamma-rays, 8.9 min half-life), ssC1 (1.64 and 2.16 MeV, 37min) and ~ N a (1.37 and 2.75

MeV, 15 hr). All spectra were analysed for their constituent activaties by a computer method of least squares fittang(m. " S t a n d a r d " spectra of ~gCa, SSCl and ~aNa were obtained from sources of these nuchdes measured separately m the two-crystal arrangement, and the computer calculated the proportions of these "standard" spectra which, when combined, produced the best fit, in the least squares sense, to each spectrum of an trradiated toad or mixture. T o eliminate possible contributaons from =SAI gamma-rays (1.78 MeV) in the first few spectra of each sample, the analyses were confined to the energy range 1.99-3.32 MeV. In Fig. 5 are shown the computed 49Ca and 88C1 activities, in arbitrary units, for Toad 1 as a function of tame after irradiation. T h e decay of these values corresponds satisfactorily with the accepted half-byes of ~gCa and 3sC1, which tends to confirm that none of the unwanted activitaes mentioned above interfered significantly in the analysis of the spectra. In so far as could be determined from measurements restricted to a period of several hr after irradiation, the serial values of ~ N a activity showed the expected half-hfe of 15 hr. From the computed 49Ca activities of the toads and mixtures, corrected for radioactive decay to the mid-time of lrradmtaon, the relatave amounts of calcium in each were calculated. Allowance was made for small

66

D Newton et al. ~0 x x x)'4Na

.J ul

x x

Z15

38CI

Z

. /

"r" rO

\

>

x x

G.

X

W I--

X

x~ x x )t

x

24Na

x

49Ca

x x x

Z

x

:

x x

~

xx

x

~5

xx

x

z 0 U

x

xx x x

xx x

x

x xx

x

~ x

x

~

x

x

~

x

xx x x

0

1 2

I

I

I

I

IS

20

25

30

35

McV

Fio. 4. The gamma-ray spectrum of a toad 15 nun after n'radiatlon wxth partmUy moderated 5 MeV neutrons differences m the neutron fluence xn each case as indicated by the long counter response. Similar calculations were performed in the case of chlorine and sodium, using the computed ssC1 and ~ N a data. Since the composition o f the mixtures was known, it was then possible to calculate the toads' total calcium, chlorine and sodxum contents. These are listed in Table 2, together with their statistical standard errors (i e the uncertalnlaes arising from the random nature of radioactive decay). In addition, there m a y be systematic errors, not exceeding 4 per cent, resulting from inaccuracies in positaoning the samples in the tank and in measuring the relative neutron fluences, and from possible differences In the geometrical counting efficiency when the activ-

ity in the toads and m the salt mmtures was measured. T h e relative activities induced m all three mLxtures were consistent with their known chemical constitution. Subsequently the toads were freeze-dried and digested completely in mtrtc acid, and their sodium and calcium contents were estxmated by flame photometry. T h e results are included in Table 2. Their c h l o n n e contents could not be determined chemically because of some loss during the process of digestion. (ii) Using 14 M e V mczdent neutrons. A similar experiment was performed using 1 4 M e V neutrons, produced by the reaction 8H(d, n)4He at the tritiated target o f a Cockcroft-Walton machine delivering 2 5 0 k e V deuterons. In other respects the experimental details were

Aawatton analyszs m vlvo u.nng 5 MeV madent neutrons

67

20

IO Z >G: ,.¢ "~ 5 _P m ,,v
\

38C!

49Ca

>.* IFU ,<

2

I

I

5

25

't-I

50

I

I

I

i

75

100

125

ISO

TIME AFTER IRRADIATION,

MINUTES

FIG. 5. 49Ca and ssCl activities in Toad 1, computed from gamma-ray spectra obtained at intervals after irradiation with partially moderated 5 MeV neutrons. The lines fitted to the experimental values correspond to the accepted half-hves of 8 9 m,n for 49Ca and 37.3 mm for saC1. The error hmats mdacate the stattstmal standard uncerta, nty. TABL• 2. Total sodium, chlorine and calcium in two toads, determined by activation with 5 MeV incident neutrons. Values obtained by chemacal analysm are shown in parentheses

Na, mg CI, mg Ca, mg

Toad 1

Toad 2

88 4- 2 (89 4) 90 4- 4 780 zk 70 (825)

106 4- 2

(108 0) 102 -4- 5 1450 4-80 (1450)

similar to those described above, and the results were computed in the same way The results for four toads are given m Table 3. Reliable values for their calcium contents could not be obtained, and n o n e are shown, since m most cases the decay of the computed ~gCa activities corresponded to a half-hfe shorter than the expected 8.9 rain (e g. 6 6 4- 0.5 rain for Toad A and 7.2 4- 0"4ram for one of the

mixtures) This is a t m b u t e d to the additional presence of a~S (5.1 mm), produced by the reaction sTCl (n, t9); the gamma-rays from iTS are similar m energy to those of 4aCa DISCUSSION The results of Table 2 demonstrate the accuracy of the activation method, using 5 MeV incident neutrons, as applied to small ammals This m itself does not prove that the technique can be apphed successfully to humans, since the difficuhms of ensuring uniformity of activation throughout the body are greater than with small animals, however, it does serve to show that, with 5 MeV incident neutrons, no problems are hkely to arise from activation of dements present in biological material, but overlooked in the experiments of Section I. I n Table 3, relating to activation analysis with 14 MeV incident neutrons, the sodium values agree fairly well with those obtained from chemical

68

D. Newton et al.

TAB~ 3. Total sodaum and chlorine in four toads, determined by actlvatlon With 14 MeV mcident neutrons. Sodium values obtained by chemical analysis are given in parentheses

Na, mg Cl, mg

Toad A

Toad B

Toad D

Toad E

155 4-8 (165) 150 zk 8

84 4-4 (81) 96 4- 5

68 4-3 (61)

55 4-8 (48) 55 z~ 3

analysis, though, on average, they are marginally higher, this m a y well have been due to addluonal ~ N a produced by the reactaon ~aMg(n, p). Interference with the calcium estimates, attributed to s7S produced b y 37C1(n, p), has already been mentioned. O u r investigations of the thermal flux distrlbutlon in large phantoms irradiated by 5 M e V neutrons (Section 2) have shown that, at least m principle, adequate umformaty of activation could generally be achieved O n the other hand, 2.5 M e V neutrons, and those produced at 0 deg 04) b y the 9Be(d, n) reaction, a p p e a r to be too low in energy to give acceptably umform thermal neutron activation. A further disadvantage of ~Be(d, n) as a neutron source is that the spectrum will include neutrons of energy considerably higher than the m e a n energy (e g in our experiments up to 7 MeV) so that comphcatlons from the fast reaction a7Cl(n, p)3qS zn vzvo might still be encountered, as PALMERet al ¢3~anticipate. T h e practical reahsation of the 5 M e V method for h u m a n subjects would, however, be difficult with the type of source used m these experiments T h e fast neutron b e a m produced varies both m energy and intensity with the angle of emission of the neutrons relative to the axis of the deuteron b e a m I n order to malntaan uniformity of incident flux over the length of the subject to within, say, 5 per cent of the central value, the angle subtended by the subject at the target would have to be no more than 7 deg. This would require, for a m a n 180 cm tall, a source-subject distance of 15 m and an increase in neutron output by a factor of about I00, which would not be possible math this source. Alternatively the subject might be placed along an arc centred on the target and lying m a plane normal to the deuteron b e a m Although

the flux along this are would be uniform, it would be necessary to accelerate the deuterons to more than 10 M e V to obtain 5 M e V neutrons. Again the flux available would be hmited by technical considerations at the gas target. Acknowledgements--The work we have reported depended on the co-operatxon of many of our colleagues not included m the authorship. In particular we are indebted to Dr A. T. G. Fm~ousoN of the Nuclear Physics Dwmon at A E.R.E., who arranged and supervised most of the lrradmtions.

REFERENCES 1 ANDERSONJ , (~SBORN S. B., TOMLINSON 1~ W . S , NEVV'TON I~ , RUNDO J , SALMON L. a n d SMrrH

J. W Lancet 1205, Dec. 5 (1964). 2. BATTY~C K , TOMLINSONR W S., ANVERSONJ. and OSBORNS B. In Nuclear Actwatzon Techmques m the Lzfe Saences, p 573, I A E A ,Vienna (1967). 3. PAL~ER H E , ]~ELP W. B, MUn.~NO R. and RICH C. Phys Med. Bzol. 15, 269 (1968). 4 CrL~MB~RLAINM J , FX~MmNJ. H , PETERSD. K. and PmLXPH Br Med J 581-585,June 8 (1968) 5. Internauonal Commission on Radaological Protectaon. Report of Commatee I V on Protectzon against Eledromagnetze Radzatwn above 3 MeV and Electrons, Neutrons and Protons, Pergamon Press, London (1964). 6. Internataonal Commission on Radaological Protecnon. Report of Commzttee H on PermzsszbleDose for Internal Radmt~on, Pergamon Press, London (1959). 7. HANSONA O. and MCKaBBSNJ. L Phys Rev. 72, 673 (1947). 8. SALMONL. In Radzochemzcal Methods of Analyszs, Vol. 2, p 125, I.A E.A., Vlerma (1965). 9. H O W ~ R T O N R. J. Umvem~ of Calz.forma Radzatzon Laboratory Report UCRL 5351 (1958). 10 STEHNJ R , GOLDBEROM. D., MAoum~o B. A. and WmNER-CHAs~ R Brookhaven Natzonal Laboratory Report BNL 325, Suppl. 2, "V'ol. 1 (1964) 11. COHEN A. V and WroTE P. H. Nud. Phys. 1, 73 (1956) 12 KHURANAC. S. and HANs H. S. NucL Phys. 28, 560 (1961). 13. BAss R., BINDHARDTC. and Katuo~.R K. In Progress Report on Nuclear Data Research m the Euratom Commumty. EANDC (E) 57-U, p. I. 14. Fm~ousoN A. T. G , GALa N., Mo~msoN G. C. and WHITER. E In Dzrect Interacaonsand Nuclear Reactzon Meehamsms, p 510, Gordon and Breach, New York (1963).