Photofission cross sections of several nuclei with mono-energetic gamma rays

Nuclear Physics 3 4 (1962) 439---456, ~ ) North-Holland Publ,sk,ng Co, Amsterdam Not to be reproduced by photoprmt or microfilm without wmtten permlsmon from the pubhsher

P H O T O F I S S I O N C R O S S S E C T I O N S OF S E V E R A L N U C L E I WITH MONO-ENERGETIC GAMMA RAYS J R H U I Z E N G A , K M C L A R K E *, J E G I N D L E R a n d R V A N D E N B O S C H

A~gonne Nat,onal Laboratory, Argonne, Ill*no~s it" R e c e i v e d 12 D e c e m b e r 1961 G a m m a r a y s of 6 14, 6 91 a n d 7 12 M e V p r o d u c e d b y t h e Ft*(p, ~7,)O l* r e a c t i o n were u s e d to i n d u c e h e a v y e l e m e n t fission T h e p h o t o f l s s l o n cross sections of T h 2st, U 23s, U is6, U uS, U *st, U 2to a n d N p u* for a 7 0-MeV a v e r a g e g a m m a r a y e n e r g y (a mLxture of t h e 6 91a n d 7 12-MeV g a m m a r a y s ) a r e 9, 15, 28, 33, 52, 44 a n d 45 m b , r e s p e c t i v e l y T h e cross s e c t i o n for p r o d u c i n g Mo .9 f r o m U 2.8 wath 7 0-MeV g a m m a r a y s is 1 1 m b T h e 7 0-MeV p h o t o n a b s o r p t i o n cross s e c t i o n of h e a v y nuclei is d e t e r m i n e d to be 604-20 m b F r o m this

Abstract:

cross s e c t i o n o n e d e d u c e s t h a t t h e g a m m a r a y s t r e n g t h f u n c t i o n Fo]D for h e a v y nuclei a t 7 0 M e V xs (2 5 4 - 0 8) X 10 -4 T h e v a r i a t i o n m t h e photoflssxon cross sections wath 6 14-MeV p h o t o n s for nuclei m w l n c h p h o t o n e u t r o n e m i s s i o n is e n e r g e t i c a l l y f o r b i d d e n is i n t e r p r e t e d m t e r m s of r e s o n a n c e a b s o r p t i o n T h t s r e s u l t s f r o m t h e h n e w i d t h of t h e 6 14-MeV p h o t o n s (O 16 recoils s t o p p e d p r i o r t o t h e e m i s s i o n of t h e 6 14-MeV ~, ray) b e i n g of t h e s a m e o r d e r of m a g m t u d e as t h e a v e r a g e s p a c i n g b e t w e e n levels of t h e s a m e s p i n in t h e c o m p o u n d n u c l e u s

1. I n t r o d u c t i o n The dependence of photoflssion cross sections on energy and the target nucleus at energies approaching the fission "threshold", has amportant knphcatxons for the fission process The problem has taken on added slgmflcance in recent collective model interpretations a. 3) of photoflsslon phenomena at low energies Among the m a n y ways of inducing a nucleus to undergo nuclear fission, excitation b y low-energy photons of discrete energy is one of the simpler processes. In this instance, the absorption of 6 and 7 MeV radiation b y very heavy nuclei (Z _~ 88) leads to excitation energies of the order of the nucleon binding energies, and relatively simple forms of nuclear behavlour are to be expected Moreover, photon excltatlon provides an alternative means of examining compound nuclei at excitation energies in the vicinity of the fission threshold as opposed to excitation via slow neutron capture of (d, p-f) deuteron stripping reactions The earliest work on the photoflsslon of actimde elements b y photons of chscrete energy near the fission threshold was reported independently b y two groups of workers s, 4) as early as 1941 A later report was made b y a tbard t P r e s e n t a d d r e s s D e p a r t m e n t of P h y s i c s , T h e J o h n H o p k i n s U n i v e r s i t y , B a l t i m o r e , M a r y l a n d t t T h i s p a p e r is b a s e d o n w o r k p e r f o r m e d u n d e r t h e a u s p i c e s of t h e U S A t o m i c E n e r g y C o m m i s s i o n P r e h m m a r y r e s u l t s were r e p o r t e d b y Huxzenga et al t0) 439

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group 5) in 1955. Subsequent Investigations by other workers using bremsstrahlung spectra to Induce hsslon indicated that some type of " s t r u c t u r e " existed s. 7) in the photohsslon excitation functions for the nucleldes Th 23~ and U ~ss in the energy interval between the fission threshold and about 7 MeV. Further, these same even nuclei showed remarkably large angular anlsotroples s, 9) for fission fragment emission at low-energies In the odd-mass nucleus U ~35, however, this behavlour was absent Apart from any phenomenologlcal interpretatlon, there exists the lmphcatlon t h a t the cross sections for photohsslon in even nuclei near threshold m a y be significantly correlated with the spin state of the excited nucleus in its transition over the saddle point A Bohr has suggested that the photohsslon of an even nucleus near the fission threshold should occur predominantly via a single or, at most, a small number of welldefined low-lying states of the compound nucleus m its saddle point conhguratlon If one assumes electric dipole absorption, the compound nucleus for an even target is always produced in a (1--) state In the Bohr prescription, the lowest hSSlOn channel at the saddle point is an odd-parity (1--) state similar to the observed low-energy (1--) state of even nuclei These states represent a collective mode of excitation associated with asymmetric vibrations in the shape of the nuclear surface lo) At higher excitation energies other channels of the (1--) type representing intrinsic nuclear excitation become available Such a correlation with odd-parity states in the saddle point configuration further implies that the level spacing of the (1--) states m a y be reflected in the observed low-energy photohsslon cross sections The present article describes experiments extending the original work of two of the authors li. 12) Photoflsslon cross sections at 6 1 and 7 0 MeV are reported for the seven nucleldes Th 23~, U ~34, U ~3s and U 2ss (even), U ~33 and U 235 (oddneutron) Np ~87 (odd-proton)

2. E x p e r i m e n t a l Procedure 2 1 GENERAL ARRANGEMENT Photohsslon of heavy element targets was Induced with mono-energetlc gamma rays which were produced by proton bombardments of fluoride targets Protons of variable energy were accelerated In the Argonne 4-MeV Van de Graaff generator The heavy-element targets were contained In a cancellation ionization chamber of 2~-geometry The spectrum and intensity of the gamma radiation incident upon the fissionable targets were monitored by a high resolution scmtlllatlon spectrometer employing an antlcolncldence 13) annulus Both the fission chamber and the scintillation spectrometer were mounted on the axis of the incident proton beam such that the gamma beam traversed first through the fission chamber and then into the gamma ray detector The external beam windows and internal electrodes of the fission

PHOTOFISSION CROSS SECTIONS

441

chamber were such that any attenuation of the transmitted gamma beam was neghglble The hSSlOn chamber was located as close to the gamma ray source (fluoride target) as physically possible In this arrangement the fissionable sample intersected the gamma ray beam with a geometry of 4 24 × 10-* × 4a The central NaI crystal of the scintillation spectrometer subtended a sohd angle to the gamma ray source of 8 882 × 10-6× 4a in collimated geometry Mono-energetlc gamma rays of 6 14, 6 91 and 7 12 MeV were obtained from the F19(p, aT)O 16 reaction These radiations represent the well-known groundstate transitions 14,15) from excited states in O ls Thin calcium fluoride targets of about 190-keV thickness to 1 88 MeV protons were employed in the investigation reported here In the earher work of two of the authors i1,1~), thick fluoride targets were employed Such targets are less favourable with respect to the gamma-ray intensity ratios to be discussed The gamma rays used in the present experiments were obtained by bombarding thin fluoride targets with either 1 56 or 2 10 MeV protons At the lower bombarchng energy, the predominant gamma ray component is the 6 14 MeV hne At the higher proton bombarding energy the 6 91 and 7 12 MeV gamma ray group is in greater abundance Estimates of the individual intensities of the 6 91 and 7 12 MeV gamma rays could be obtained in our experimental arrangement, however, no advantage was taken of this posslblhty The actual gamma ray intensity ratios, 1(6 14)/1(7 0) (where hereafter 1(7 0) represents the intensity sum I(6 9 1 + 7 12)), obtained at the two proton bombarding energies, differed by a factor of 22 Direct use was made of this large difference m the gamma ray intensity ratio in obtaining absolute photofisslon cross sections with 6 14 and 7 0 MeV gamma rays 2 FISSION C H A M B E R The hsslon chamber employed is a modified version of a type first described by Baldwin and Klalber le) It consists basically of a cancellation-type ionization chamber of 2~ geometry filled with methane at 1 atm pressure In common with previous designs 1s,17), it contained three electrodes arranged so as to form two adjacent parallel-plate Ionization chambers of approximately equal capacitance The central electrode served as a signal electrode and was capacltatlvely coupled to the grid of the first tube of a preamplifier To mlmmize alpha pulse pile-up from alpha-active target nucleldes and hence to enhance the resolving power of the fission chamber, the latter was operated as an electronpulse counter The three successive electrodes ,were operated at increasing positive potentials to achieve a proper potential gradient in the beam direction One high-voltage electrode was movable with respect to the middle electrode so that the capacitance between these two electrodes could be varied over a small range This feature permitted essentially complete balancing of the ionization produced In the two adl acent ionization region s for radiation passmg through both

442

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The heavy element samples were made an integral part of the ground potential electrode when in counting position Five samples were mounted on a wheel such that each sample, in turn, could be made a part of the electrode b y a "rotation" operat]on which suitably positioned each new sample The ionization chamber is illustrated in fig 1 The target matelaals were coated on 0 010 cm thick platinum backing foils b y a technique described elsewhere :s) The coatings were all about 1 mg/cm 2 thick In practice the alpha-active samples were uncolhmated wluch made for imperfect cancellation of non-fission pulses Alpha noise from this source, however, was barely detectable below a total alphaactivity level of about 108 disintegrations per mm The flSSlOn chamber was operated without benefit of a sample collimator for two reasons 1) not to reduce appreciably the observed (7, fission) counting rate and 2) to assure that the observed counting rates were, to a good approximation, a measure of the total number of fissions occurring, 1 e , independent of any amsotropy In the fission angular chstrlbutlon The output signal from the central electrode of the fission chamber was amphfled b y a combination preamplifier and stacked cathode-follower amphfler after which the signal was handled b y standard electronic techtuques The fission pulse-height distribution was obtained through a 10channel chscrlmlnator which allowed for variation in the relative positions of individual channels as well as the position of all channels with respect to pulse-height These features permitted the location of the aerly channels

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F i g 2 F i s s i o n f r a g m e n t p l a t e a u s o b s e r v e d for t h e r m a l n e u t r o n b s m o n of U " tlncknesses

s a m p l e s of v a r i o u s

PHOTOFISSION CROSS SECTIONS

443

lU the very " t a l l " of the alpha particle dlstnbutlons and made it possible to obtain definite fission "plateaus " Since the heavy element samples were relatively tluck and the discrimination against alpha particle pileup was incomplete, the fission plateaus were rather short, especially for the most alpha active targets In fig 2, fission plateaus are plotted for U ~Ss samples of various thicknesses The fissions were produced b y neutrons from a Ra-Be source embedded in paraffin Each plateau is obtained in a single run with the 10-channel discriminator For calibration and performance monitoring purposes, the output from a precision exponential pulse generator could be coupled to feed artificial pulses through the grid of the hrst tube of the preamplifier In tlus manner, the discriminator output could be checked chrectly in terms of an input signal to the grid of the preamplifier 2 3 GAMMA R A Y S P E C T R O M E T E R

The spectrum and flux of the high-energy gamma quanta were measured with a sodium Iodide scintillation spectrometer employing an antlcomcldence annulus Such a detector combines the desirable feature of good detection efficiency w~th good resolution The construction and performance of this 50 000

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F i g 3 G ~ m m a r a y s p e c t r a f r o m t h e Fl°(p, a ? ) O is r e a c t i o n The g a m m a r a y s p e c t r o m e t e r cons l s t e d of a c e n t r a l NaI(T1) c r y s t a l 6 1 c m in d l a m e t e r a n d 15 2 c m l o n g e n v e l o p e d b y a l a r g e h o l l o w c y l i n d e r of NaI(T1) w l ~ c h w a s o p e r a t e d in a n t l c o m c l d e n c e w i t h t h e m a r e c r y s t a l T h e d a s h e d h u e s h o w s t h e r e s u l t of r u n 203 w i t h Ep ~ 1 56 MeV a n d 10 10 b e a m i n t e g r a t o r cycles T h e full h u e s h o w s t h e r e s u l t of r u n 204 w i t h Ep = 2 10 MeV a n d 3 44 b e a m i n t e g r a t o r cycles

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spectrometer has been described in the recent literature 13). It consists of a principal detecting crystal of NaI (TI), 6 1 cm in diameter by 15 2 cm long, enveloped by a hollow cylinder of NaI(T1) in antlcolncldence with the main crystal The dimensions of the latter crystal are 20 3 cm outer dlam by 6 4 cm Inner dlam by 30 5 cm long For gamma rays of 6 and 7 MeV, such a scintillatlon spectrometer completely suppresses the peaks associated with the escape of the two quanta from annn~ilatlon events following pair production Likewise the one 511 keV quantum escape peak is markedly reduced and the general Compton background decreases by a factor of 5 over that for the crystal without the antIcoincldence feature The radiation incident on the main crystal was colhmated by a 3 492 cm dlam hole in a 10 2 cm thick bismuth block The r-ray spectra obtained by bombarding the CaF2 target with 1 56 and 2 10 MeV protons are displayed in fig 3 For protons of bombarding energy 1 56 MeV the 6 14 MeV gamma rays have the larger yield while 2 10 MeV protons give predominantly 7 0 MeV gamma rays 2 4 HEAVY-ELEMENT

SAMPLES

Excepting Th ~32 and N p 237 which are mono-isotopxc, the samples employed consisted of separated isotopes The enrichment of the uranium isotopes exceeded 93 % in all cases The isotopic content of the uranium targets is given in table 1 Of the separated isotopes, U 238, U 234 and U 238 were subjected to radio-chemical purification via ether extraction is) The thorium was initially in the form Th(N03)4" 4H20 (Baker's C P grade) and was used without further purification TABLE 1 I s o t o p m c o n t e n t of u r a m u m t a r g e t s m m a s s p e r c e n t 233

U z" U 234 U "s U "6 U "s

98 33

234

0 93 0 0

010 44 022 07

235

0 4 99 4 0

0127 87 94 62 04

236

94 77

238

1 1 0 0 99

53 69 038 54 96

The samples were in the form of oxide films of about 1 mg/cm ~ This thickness was necessitated by two considerations, a) typically low (7, fission) cross sections of the order of a few tens of mllhbarns or less, and b) the relatively low-photon intensities The thickness of each sample was determined both by alpha counting and by weighing Quantitative counting was achieved under conditions of reduced geometry to eliminate the self-absorption effect in thick samples The agreement between sample masses as determined by both

PHOTOFISSION

CROSS

445

SECTIONS

methods was quite close To ascertain the degree of uniformity of the heavyelement samples, a surface mapping of the alpha activity was performed on two ~epresentatlve samples The alpha activity in both cases was found to be uniform to within about Jz 4 ~/o 2 5 SELFABSORPTION CORRECTION FOR FISSION FRAGMENTS As the ranges of fission fragment recoils are so short, I e, the maximum range of fission recoils in UsOs IS approximately I0 0 mg/cm2, self absorption corrections to the fission counting of thick samples are important Thls correction IS obtained empirically The fission counting rate per mg of U236 oxide at zero blas, RM°, is obtained from fig 2 These extrapolated values are plotted as a function of total mass of the sample as in fig 4 From this figure, the hypo41 I,,~ E,.J

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Fig 4 E x p e r i m e n t a l h s s l o n c o u n t i n g rates p e r m g of sample a t zero bias are p l o t t e d as a function of the m a s s of the s a m p l e These d a t a were collected for t h e r m a l n e u t r o n fission of U ~85, and are used for the d e t e r m i n a t i o n of the fission f r a g m e n t self-absorption correctmn

thetical fission countmg rate per mg of oxide at zero mass, Ro °, m a y be found b y extrapolation The ratio R~°/Ro ° is then a measure of the self-absorption of U z35 oxides for fisslon fragments, i e , (self-absorption) = 1-- (Rzg°/Ro°). All samples used in the photoflsslon experiments were deposited uniformly, each weighing from 11 to 12 mg For lsotroplc emission of the fission fragments and sample masses of 11 5 rag, the correction for self-absorption IS about 7 Self-absorption corrections det er m m e d from fig * should be v a h d for all samples used as targets with the possible exception of thorium and n e p t u n m m For these two targets differences in oxide composition a n d / o r atomic number from uranium oxide m a y cause a slight deviation from the self-absorption calculated in the empirical manner described

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446

2 6 FISSION AND GAMMA COUNTING

The normal operating procedure consisted of making a simultaneous fission and gamma count for a specified period These counts were also related to the charge cycle of a current integrator which was used to monitor the proton beam current To mlmmxze the effect of unknown "fluctuations", the counting intervals, 1 e , the number of beam integrator cycles, were kept short Each sample was counted for a sufficient number of intervals to give the desired statistical accuracy Since the gamma ray detector Intercepted only a very small fraction of the gamma rays passing through the fissionable sample, the calculation of the gamma ray Intensities on the fissionable sample required, in addition to the sohd angles of the fissionable sample and gamma ray detector, information about the anlsotroples of the gamma rays The gamma ray counting rates were compared for a fixed sohd angle at 0 ° and 61 ° to the proton beam direction for proton bombarding energies of 1 56 and 2 10 MeV The results of these measurements are summarized in table 2 TABLE 2 A n g u l a r d i s t r i b u t i o n s of 6 14 a n d 7 0 (6 91:~7 l l ) M e V g a m m a r a y s f r o m F1°(p, c~7) r e a c t m n w i t h C a F s t a r g e t described in t e x t Gamma ray Proton energy (MeV) (MeV)

1(0°)]1(61")

(b]a) a)

6 14

1 56 2 10

1 11±002 1 1 0 ~ 0 09

0 15~-0 03 0 19::1:0 13

70

1 56 2 10

1 ll::LO 14 1 21 ::t:O 09

0 15:[:0 19 0 29=L0 14

a) A n g u l a r d i s t r i b u t i o n IS a s s u m e d to be of t h e f o r m W(O) = a + b cosl0

The gamma ray counter and fissionable sample were both placed at 0 ° to the proton beam direction Since the fissionable sample subtended a solid angle of only 0 0424 × 4~, rather large gamma ray anlsotroples would lead to only minor corrections in the Integrated flux calculated on the basis of the 0° gamma ray count and the assumption of lsotroplc distribution If the gamma rays have an angular distribution given by W(O) = a+b cos20 with b/a = 1, the integrated gamma ray flux will be 4 °/o smaller than that calculated on the basis that the gamma rays have an lsotroplc distribution The measured values of the gamma ray amsotroples which are given in table 2 are so small t h a t the error in the gamma ray Intensity Impinging on the target calculated with the assumption of gamma ray lsotropy is neghglble ( < 1 % ) 2 7 BACKGROUND

MEASUREMENTS

Among the principal sources of background other than alpha noise that might contribute to the observed fission counting rate were a) natural background

PHOTOFISSION CROSS SECTIONS

447

rate, 1 e , spontaneous fission of the heavy-element samples, and b) neutroninduced fission of the target nuclei For the case of U 238, the nuclelde with the shortest spontaneous fission half-hfe 19) among those mveshgated, the contrlbutlon to the observed fission rates was neghgible Beam contamination due to neutrons was potentially the most serious source of background In photonuclear experiments, It is always difficult to establish conclusively that the number of neutron-induced fissions is very small compared to the number of photohsslons An estimate of the number of neutron-induced fissions produced b y fast neutrons generated within the heavyelement target by (7, fission) reactions can be made from a) the geometry, b) known (n, fission) cross sections and c) an assumed value for the total number of neutrons produced per photohssion On this basis, the number of (n, fission) events coming from this source was calculated to be neghglble Neutroninduced fissions arising from photoneutrons (7, n) generated within a heavyelement target were also estimated to be unimportant The extent of neutron-induced fission due to neutrons entering the fission chamber was determined by attenuation experiments in which the intensity of the fission-producing radiation was varied by interposing various absorbing materials (lead and Iron) between the photon source and the fission chamber The fissionable nucleldes used were U 235 and U 23e The former Isotope has large resonance neutron-capture cross sections in both the thermal and epithermal regions, the latter Isotope will fission only under fast neutron ( > 300 keV) lrrachatIon The results of the absorption measurements Inchcate 1,) t h a t the fission counting rate was decreased In a manner analogous to that expected for the attenuation of high-energy electromagnetic radiation. In Iron, whose Isotopes all have neutron-binding energies ,o) exceechng that of the high-energy gamma quanta used, the observed ratio of the fission counts to the gamma ray count was independent of the thickness of iron absorber On the basis of this evidence, it was concluded that neutron-induced fission b y neutrons in the thermal-, epithermal- and "fast"-energy regions made no significant contribution to the observed fission rate Further, neglecting the background from this source probably Introduced an uncertainty which was much smaller than ordinary statlstical errors in counting 2 8 GAMMARAYS WITH ENERGY GREATER THAN 7 MeV High energy (E~ > 7 MeV) gamma ray contamination of the 6 and 7 MeV photon beam m a y arise from the F19(p, 7)Ne 2° reaction and the high-energy excited states of O le produced in the F19(p, 0tT)Ole reaction The 8 87 MeV level in oxygen de-excites chiefly 21) by a gamma ray cascade via the 6 14 MeV level. Employing the upper hmlt on the Intensity of the 2 73 MeV gamma ray deduced from the present experiment and the literature value of the branching ratlo between the 2 73 and 8 87 MeV gamma rays give an upper

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limit to the intensity ratio 18 87/(I614+I70) of 10-3 Only at the higher proton energy of 2 10 MeV is it energetically possible to populate the 9 58 and 9 85 MeV levels in 016 Some estimates of the yield of gamma rays with energy greater than 7 MeV have been reported 32, 23) for selected resonances in the reactions of protons on fluorine A measure of the intensity of 8 to 16 MeV gamma rays were experimentally determined in our detector arrangement with the antlcolncldence annulus With a 1 56 MeV proton bom bardm ent the maximum excitation energy of Ne 2° is 14 3 MeV The registered counts at energy greater than 14 3 MeV give a measure of the background No photopeaks were observed for 7 rays of energy greater than 7 12 MeV The intensity of gamma rays in the 9 to 14 MeV energy region is at least a factor of 1000 less than the intensity of the gamma rays in the 6 and 7 MeV energy region If one assumes therefore t hat the cross section with the high energy gamma rays is 500 mb, the contribution of the high energy cross section to a 10 mb low-energy cross section is less than 5 ~o In the hght of these estimates, no corrections have been made in the photoflsslon cross sections for possible contamination of the 6 and 7 MeV photon beam with high energy gamma rays

3. Experimental Results The first loading of the fission chamber contained the samples of T h ~32, U 23s, U 236 and U 23s, and, in addition, a blank platinum foil comparable to the backing foils for the fissionable samples Each sample mcludmg the blank was counted for only a few charge cycles in succession The sample wheel was rotated, therefore, approximately five times in collecting the fission data at each proton energy The second loading contained a blank, U 2a6, U 234, U 233 and Np 237 samples A s um m a r y of the fission fragment counting data is given in table 3 The total number of fission counts collected at each proton bombardIng energy ranged from 400 to 2500 The gamma r ay spectra shown in fig 3 were analysed for the total number of 6 14 and 7 0 MeV gamma rays produced per charge cycle These are listed in table 6 for each of the two proton bombarding energies Gamma ray intensities were calculated 34) b y evaluating the parameters A, and ~, from the gamma ray spectra b y a modified chl-squared minimum calculation The gamma ray photopeaks are assumed to be Gausslan in shape and characterized b y A, which represents the am pht ude of the 7 ray with mean energy E , and a, which IS a measure of the peak width The Intensity of gamma r a y , at energy E is given b y A, exp E--(E--E,)2/~,2J The Integrated intensity of the full energy peak of gamma r a y , is A ~,~½ The photofractlon efflclencies of the 6 1 cm × 15 2 cm crystal with a colhmated beam of ~ rays with diameter of 3 492 cm are calculated b y the procedure of Miller and Snow 35)

PHOTOFISSION

449

CROSS SECTIONS

TABLE 3 Photoflssion c o u n t i n g rates of several h e a v y nucleldes a t two p r o t o n energies

Sample

Loading

T h ~s~

i 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2

U ~a8 U 23s U za6

U 234 U 2a3 1Np237

Elemental m a s s (mg)

10 60 1026 9 54 9 50

9 70 9 71 9 94

Proton energy (MeV)

Charge cycles

1 56 2 10 1 56 2 10 1 56 2 10 1 56 2 10 1 56 2 10 1 56 2 10 1 56 210 1 56 2 10

90 30 75 25 60 15 75 20 75 20 60 20 60 20 45 15

Fissions a) p e r charge cycle

5 I1 4-0 28 29 92-4-1 29 678±038 42 674-1 79 9 634-0 48 86 174-3 36 16 324-0 64 78 084-2 81 14 835=0 73 82 3 2 ± 3 29 8 034-0 52 1 2 9 0 4-6 1 10 105=0 66 1133 4-56 17 154-0 91 1 2 5 6 5=50

(Ep ~ 1 56) (Ep = 2 10)

0 171 4-0 012 0159

q-0011

0 112 4-0 007 0 209 4-0 011 0 180 4-0 012 0 06224-0 0050 0 08914-0 0073 0 1374-0 009

G a m m a r a y s are p r o d u c e d in t h e F1D(p, c¢7)Ole reaction a) These values result w h e n the necessary c o r r e c t m n s are a p p h e d to the original data, 1 e , fission plateau e x t r a p o l a t e d to zero bias a n d a c c o u n t is t a k e n of the fission f r a g m e n t self-absorption ( ~ 7 °/o) An a p p r o x i m a t e e s t i m a t e of the observed fission counts, and hence an estimate of the c o u n t m g error, c a n be o b t a i n e d b y m u l t i p l y i n g the fissions p e r charge cycle b y the n u m b e r of charge cycles The error which is listed also c o n t a i n s a factor for the u n c e r t a i n t y introduced b y e x t r a p o l a t i n g the fission p l a t e a u to zero bias b) The q u a n t i t y h s t e d in the last c o l u m n is the ratio of the fissions p e r charge cycle at Ep = 1 56 to those a t Ep = 2 10

TABLE 4 G a m m a r a y p h o t o p e a k intensities p e r charge cycle Proton energy (MeV) 1 56 2 10

1(6 14)

I ( 7 0)

6700±200 69004-150

1900~100 409005=570

The g a m m a r a y detector s u b t e n d e d a solid angle of 8 832 × 10 -8 × 4z~ G a m m a r a y s are produced in the FX'(p, ~ , ) O le reaction I n order to c o n v e r t the values in the table to the n u m b e r of g a m m a r a y s strlkang the fissionable target, one has to (1) m u l t i p l y each e n t r y b y the ratio of the g e o m e t r y of t h e fissionable sample to the g e o m e t r y of the V r a y detector (in all cases 4 80 × 103) and (2) divide each e n t r y b y the a p p r o p r i a t e p h o t o f r a c t l o n efficmncms (product of absolute crystal effmIency a n d t h e p h o t o p e a k to t o t a l ratio) F o r our blaI a r r a n g e m e n t in which a colhmated b e a m of 3 492 cm d i a m e t e r strikes a c r y s t a l of 6 1 cm chameter a n d 15 2 cm long, the p h o t o f r a c t l o n effIclencles 36) are 0 2055=0 006 a n d 0 1 8 9 ± 0 006 for 6 14 and 7 0 MeV ~, rays, respectively The errors m the photofractaon effxclencles include o n l y statistical u n c e r t a i n t i e s and do not include s y s t e m a t m errors In the cross sections for the v a r i o u s interaction processes of ~' r a y s with N a I

450

J R HUIZENGA et

al

The photoflsslon cross section ratio for 7 0 and 6 14 MeV gamma rays is given b y U7 0/a6 14 =

(e 6 14/e 7 0)

1 -- ( F / F ' ) ( X ' . 1,/I. 14) [ ( F / F ' ) (I' 7 o/I614)-- (I7

o/Ie 14)]'

(1)

where F/F' is the ratio of fission counts per charge cycle at proton bombarding energies of 1 56 and 2 10 MeV (given In the 7th column of table 3), I s 14 and 170 are the gamma r a y photopeak intensities per charge cycle (given in table 4) of the 6 14 and 7 0 MeV gamma rays at proton bombarding energy of 1 56 MeV, I'614 and 1' 7 o are similar quantities at proton bombarding energy of 2 10 MeV and e614 and e~o are the photofractlon t efflclencles in our geometry The quantities needed for a calculation of the cross section ratio for a particular nuclelde are ratios of experimental numbers The geometry of the y ray counter and the sohd angle subtended by the fissionable sample in the y ray beam do not enter the calculation Likewise, the result is rather insensitive to the photopeak efflclencles of the 7 rays as it enters only in the denominator of eq (1) as a ratio of e614/e70 For y rays so close in energy the ratio is close to unity, and in our particular arrangement it was 1 085 The values of the photoflsslon cross section ratios, which were calculated for seven targets b y inserting data of tables 3 and 4 into eq (1), are summarized in column 2 of table 5 In prmclple the calculation of the photoflsslon cross TABLE 5 P h o t o f l s s i o n cross sections o b t a i n e d w i t h m o n o - e n e r g e t l c g a m m a r a y s f r o m t h e Fl°(p, a 7 ) O 16 reaction Target T h ~sz U ~as U :3e U ~s5 U zs~ U 233 N p ~s~

a~ o/a6 a, 1 004-0 1 124-0 0 804-0 2 064-0 10 0 4-5 3 244-0 1 434-0

13 15 10 33 0 79 21

a, 0(mb)

a6 i , ( m b )

9± 3 154- 5 284- 9 334-10 524-16 444-14 45+14

94- 3 134- 4 35-t-ll 164- 5 5+_~° 134- 4 314-10

Bn(MeV ) a) 6 6 6 5 6 5 6

34 04 40 24 77 90 76

Ef (MeV) b) 5 5 5 5 5 5 5

5 3 2 5 1 4 3

s) F r o m t h e c o m p i l a t i o n of ref 20) b) F r o m t h e c o m p i l a t i o n of ref 26)

section ratio depends on the fission fragment anlsotropy Since we are counting the fission fragments in 2~ geometry, the anlsotropy can only affect the fission fragment self-absorption correction The fission fragment self-absorption correction discussed in sect 2 5 was made for thermal neutron fission of U 2a5 which is lsotroplc Gamma r a y induced fission of an even target which proceeds t P h o t o f r a c t l o n efficiency is defined as t h e p r o d u c t of t h e a b s o l u t e c r y s t a l efflcaency a n d p h o t o p e a k - t o - t o t a l ratio

P H O T O F I S S I O N CROSS SECTION'S

451

by a dipole interaction will give a greater intensity of fragments in a direction perpendicular rather than parallel to the beam If the fission fragment angular distribution is gaven by W(O) = a + b sm~0, where 0 is the angle between the ? ray beam and the fission fragment, the assumption of lsotropy in our chamber (2~ geometry) will underestimate the fission intensity by approximately only 4 ~o wath a b[a value of 1000 With an even target, quadrupole fission will give a correction in the opposite direction The size of the correction even for large amsotroples is again negligible in a 2~ chamber The phot~hssion cross section ratios of U ~34 and U ~8 have been corrected for the effect of the 5 ~o isotopic impurities The absolute values of the photofiss~on cross sections at 6 14 and 7 0 MeV which are given in columns 4 and 3, respectively, of table 5 are calculated from the folkwlng equations

F = 4 8 x 103NE(I6 14/E614)o'014+

(17 o/e7 0)0"701,

F' ---- 4 8 × 10aNI (1'61,1e014)0"614+ (I'7 0187 0)0"701,

(2) (3)

where N is the number of target atoms per cm 2, while the factor of 4800 is the ratio of geometries subtended b y the fissionable target and gamma ray detector, and the other symbols have the same meaning as in eq (1) The most favourable condition for the determination of individual photoflsslon cross sectmns by the simultaneous solution of eqs (2) and (3) results when the ratios 161JI7o and 1' 61JI'7 o are very different In the reported experimental arrangement the ratio

(xo 1JX,.o)/(I'O.lJX'

.o) is

o

The uncertainties in the absolute photoflsslon cross sections are considerably larger than those in the cross section ratios This is due to the uncertainties in the additional parameters which must be known to evaluate the absolute cross section In an Independent experiment a thick target (6 6 g/cm 2) of U328sOs was bombarded with the gamma rays produced in the F19(p, ~?)016 reaction with 2 10 MeV protons The nuclelde Mo °9 was radlochemlcally isolated and counted b y standard techniques The Initial counting rate of the molybdenum sample was 70 counts per rain and the activity decayed with the characteristic 2 8-day half-hfe of Mo ~9 The cross section for producing Mo g9 from U 2as with the ? rays produced in the F19(p, ~7)O ~" reaction with Ep = 2 10 MeV is 1.14~0 30 mb At this proton energy approximately 85 % of the ? ray Intensity is of 7 0 MeV energy (see table 4), although the photoflsslon cross sections of U ~ss with 6 14 and 7 0 MeV gamma rays are approximately the same With a photofission cross section of 15 mb for U 23s, the Mo 99 is formed in 7 6 % yaeld with 7 0 MeV gamma rays This is to be compared to a Mo 99 yaeld of 6 1 % In the thermal neutron fission 27) of U ~a5 for which one expects a comparable yield

452

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R

HUIZENGA et al

4. Discussion of Experimental Results Preliminary to the discussion of photonuclear absorption cross sections, it should be emphasized t hat the lifetimes of the gamma rays produced in the F19(p, ~y)O is reaction fall into chstlnct categories The half-lives 2s) of the 6 91 and 7 12 MeV levels (collectively called the 7 0 MeV rachation throughout the paper) are 8 × 10-15 and 7× 10-15 sec, respectively Gamma rays are emitted from these levels predominantly while the recoiling 016 nucleus is In motion This results In a Doppler width of the order of 102 keV The level spacing per spin state at 7 0 MeV of excitation energy IS of the order of a few eV Consequently, the energy spread of the 7 0 MeV photon beam is very broad compared to the spacing of levels with the same spin in the compound nucleus The same conclusion cannot be made for the 6 14 MeV photons The half-hfe 2s) of the 6 14 MeV level is 6 × 10-l~ sec The stopping time of the 0 is recoils is of the order of 10-I2 sec. Therefore, a large percentage of the recoils is stopped before de-excitation of the 6 14 MeV level The expected Doppler width for a 6 14 MeV gamma r ay from a system at thermal energy is approximately 10 eV The total photonuclear absorption cross section of a particular nucleide m a y be considered equal to the sum of the cross sections b y which the excited nuclelde is de-excited For h e a v y nucleides (Z _~ 90) excited with 6 14 or 7 0 MeV gamma rays, fission competes favourably with other modes of de-excitation The total photonuclear absorption cross section ae(y) m ay then be represented b y

e(7) --

(4)

where a(v.v, ~, a(v.n), and a~v.t~ are the cross sections for de-excitation b y reemission of one or a cascade of gamma rays, by neutron emission and by fission, respectively De-excitation b y charged particle emission is omitted from eq (4) because of its large Inhibition b y Coulomb forces The photofissIon cross section IS related to the photon absorption cross section by

=

),

(5)

where F. represents the width or probability for each specific de-excitation process Values of F~/Fv deduced from neutron capture reactmns of transthorlum nuclei indicate that the fismon width is rapidly increasing 29) as the excitation energy increases from 5 5 to 7 0 MeV The thermal neutron fission to activation ratio a0) for U 2a5 (excitation energy of compound nucleus U 2a~ is 6 4 MeV) is 5 3 + 0 3 and for U ~aa (excitatmn energy of compound nucleus U 2aa is 6 8 MeV) is 9 8 + 0 4 The magnitude of F~/Fv for U ~aa increases with increasing neutron energy st) and reaches 13 5 for 1 MeV neutrons From such experiments one concludes t h a t at 7 0 MeV the fission widths for these nuclei are

PHOTOFISSION CROSS SIgCTIONS

453

considerably larger than their radiation widths The total radiation width is essentially independent of the compound nucleus spin 3,,33) and excitation energy 33) in the energy region 6 to 7 MeV The radiation widths for transthorium nucleydes 3,) at excitation energies equal to their neutron binding energies are approximately 0 03:~0 01 eV The neutron blnchng energies of U 234 and Np 23~ are each 6 8 MeV The value /'f for these nucleldes is expected to be very much larger than Fn for 7 0-MeV photon absorption Electric dipole photon absorption in U 234 produces a 1 excited state The ground and first two excited states of the (7, n) reaction product U 233are { + , ~ + and ~ + , respectively Neutron emission to the ground state of U 23z can proceed with p wave neutrons, while neutron decay to the first two excited states requires an angular momentum of l = 3 Consequently, these transitions are strongly retarded It is known that for excitation energies of even several MeV above the neutron threshold, the values 36) of Fn/Fr for U 2~ and Np 237 do not exceed approximately unity The above mentioned considerations make it possible to estimate the 7 0 MeV photon absorption cross sections ae(7) of U 2~ and Np 237 The photo~lSsion cross sections a~,r~ are 5 2 i 1 6 and 4 5 + 1 4 mb, respectively The radiation cross sections ac~,~'~ are of the order of 5 mb The photoneutron emission cross sections ac~,n~ of these targets with 7 0 MeV photons are estimated to be negligible It IS concluded, therefore, that at(y) for heavy element targets lrrachated with 7 0 MeV y rays IS 6 0 i 2 0 mb This experimental cross section is in very good agreement with one of 52 mb calculated for 7 0 MeV photons on heavy elements from the expressmn 36) at(r) = 5 2 mb(E/7 MeV)(0 01A)~

(6)

In the derivation of this equation it is assumed that (1) the total integrated cross section in the giant resonance IS given by the sum rule 3~), (2) the giant resonance is a Lorentz line .~7), (3) the peak of the giant resonance occurs at an energy equal to 80 A-½ and (4) the full width of the giant resonance at half-maximum intensity IS 5 MeV In an energy i n t e r v a l / I E containing n levels, it is also possible to relate 3~) the average cross section for dipole rachation to the gamma ray strength function ro[D by the relation

ac (r) -----~2~2[(2Ie+ 1)/(2Ig+ 1)]

(FolD),

(7)

where I e and Ig are the spins of the excited and ground states, -P0 is the average width of the elastic gamma ray and D = ,4E/n For E~ = 7 MeV, one has ~zz~2 = 7 84 × 104 mb For spin zero target nuclei, it is therefore possible to deduce unambiguously the gamma ray strength function from the measured 7 0 MeV photon cross sections The derived value of (2 5:J=0 8)× 10-4 for F0/D IS in good agreement wlth estimates 3s) of this q u a n t i t y from neutron capture experiments

4:54

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R HUIZENGA et a~

T h e n e u t r o n binding energies of T h ~82, U 2as, U 23s, U 235 a n d U 233 range from 5 2 to 6 4 MeV and p h o t o n e u t r o n emzsslon in these targets m a y be appreciable. I n the case of the o d d - n e u t r o n targets like U 233, however, the residual nucleus following n e u t r o n emission is even a n d intrinsic levels are unavailable until the pairing energy gap is exceeded The p h o t o n e u t r o n emission cross section for o d d - n e u t r o n nuclei p r o b a b l y does not become appreciable until the p h o t o n e n e r g y exceeds the n e u t r o n binding energy b y at least 1 MeV This m a y account for the observation t h a t the photofzsslon cross section of U z33 IS app r o x i m a t e l y equal to t h a t of U 234 W i t h the 6 14 MeV p h o t o n s the n e u t r o n binding energies for most of the nucleldes are large enough to forbid n e u t r o n emission In these cases the flsszon cross section can be represented b y

o'(~,~) = [ G / ( G + F ~ ) I ~ c ( ~ )

(s)

The r a d i a t i o n widths F~ for the various h e a v y nucleldes excited to 6 14 MeV are e x p e c t e d to be n e a r l y the same T h e observed variation in the 6 14 MeV photofzsszon cross sections (table 5) must therefore reflect variations either In Ft or ae(7) of the targets Variations are expected in the values of a(r,f) for a series of similar targets (such as U .3~, U 236 and U 238) which are i r r a d i a t e d with the 6 14 MeV g a m m a rays for the following reason The D o p p l e r - b r o a d e n e d 6 14 MeV line has a w i d t h of a p p r o x i m a t e l y 10 eV which is c o m p a r a b l e to the spacing between levels of the same spin at 6 MeV of excitation e n e r g y F o r dipole absorption In an even t a r g e t one is interested in the spacing between 1-- states F r o m the average level spacing 34) for h e a v y nuclei excited to energies comparable to n e u t r o n blnchng energies, one calculates t h a t the average spacing of 1 - levels in even nuclei excited to 6 14 MeV is a b o u t 10 eV Since the w i d t h of the 6 14 MeV g a m m a r a y hne is so small, the m a g n i t u d e of ae(7) m a y d e p e n d on the a m o u n t of overlap of the g a m m a r a y with the resonance Small variations in a(~, t) for a series of even isotopes m a y also be a c c o u n t e d for b y variations in Ft Although the even isotopes of u r a n i u m have the same fission thresholds (possibly decreasing s h g h t l y with decrease in A) and the same fission states avmlable at the saddle point for either electric dipole or quadrupole g a m m a r a y absorption, some information exists from which it can be inferred t h a t the e n e r g y of the (1--, K = 0) level at the saddle point is changing The Information which IS available comes from the equlhbr l u m d e f o r m a t i o n where the (1--, K ---- 0) level has a m a x i m u m energy t T m ~ If the same is above the ground state for nuclei with 142 n e u t r o n s ~02,~4~J true for the saddle deformation, the lowest energy (1--) fissioning state m a y v a r y in energy from nucleus to nucleus and have a m a x i m u m for U ~s4 In the light of possible resonance absorption of t h ~ 6 14 MeV 7 ray, it is not meaningful to compare these cross sections with those derived from * See for e x a m p l e ref 3~)

PHOTOFISSION CROSS SECTIONS

455

bremsstrahlung experiments The photoflsslon cross section observed with 7 0 MeV gamma rays are consistent wlth previous bremsstrahlung data However, no bremsstrahlung cross section data s) of sufficient accuracy are available from the analysis of fission yaelds for comparison with the present results Photoflsslon cross sections of Th *s2 and U 2s8 have previously been measured wath the F19(p, 0w)O:s gamma rays by several groups s-5) However, the mixture of 6 14 and 7 0 MeV gamma rays was different in each case from the ratios in the present work Since the a~,t~ cross sections are raLher Independent of energy for Th 2s2 and U 238 in the energy interval reported the average cross section for the 6 and 7 MeV gamma rays of the early workers gives a measure of the degree of agreement with the present results H a x b y et al 4) obtained photoflsslon cross sections of 1 7 and 3 5 mb for Th *s* and U 2ss, respectively, Hartley 5) reported respective values of 4 4 and 8 7 mb Considering the errors inherent In the 7 ray monitoring equipment of the prevxous workers, the agreement wtth the present results is satisfactory We wish to t h a n k J R Wallace and the operating crew of the Van de Graaff for the proton bombardments It is also a pleasure to acknowledge C. C Trail and S Raboy for the use of their anticolncldence spectrometer and computer program We are also indebted to K F l y n n for assistance in the Mo 99 chemical separation The authors thank P Axel for helpful suggestions and discussion

References 1) A Bohr, m Proc I n t Conf on the Peaceful Uses of Atomxc Energy, Geneva, August 1955 (Umted Nations, New York, 1956) Vol 2, p 151 2) D L Hill and J A Wheeler, Phys Rev 89 (1953)1102 3) B Arakatsu, Y Uernura, M Sonada, S Shlmlzu, K Klmura and K Muracka, Proc Phys Math Soc J a p a n 25 (1941) 440 4) R O Haxby, W E Shoupp, W E Stephens and W H Wells, Phys Rev 59 (1941) 57 5) W H Hartley, P h D Thesis, Umverslty of Pennsylvama, 1955 (unpubhshed) 6) J E Gmdler, J R Hmzenga and R A Schmltt, Phys Rev 104 (1956)49.5 7) R A Schmltt and R B Duffleld, Phys Rev 105 (1957) 19.77 8) E J Wmhold and I Halpern, Phys Rev 103 (1956)990 9) A P Baerg, R M Bartholomew, F Brown, L K a t z and S B Kowalskl, Can J Phys 37 (1959) 1418 10) S A E Johansson, Nuclear Physics 22 (1961)529 11) K M Clarke and J R Hmzenga, Bull Am Phys Soc II, 2 (1957)377A 12) K M Clarke, P h D Thesls, Pennsylvama State Umverslty, Umvermty Park, Pennsylvama, 1958 (unpubhshed), Argonne National Laboratory Report ANL-5853 1Thesis), July (1958) 13) C C Trail and S Raboy, Rev Scl I n s t r 30 (1959)425 14) F A l z e n b e r g a n d T Laumtsen, Revs Mod Phys 27 (1955)77 15) J P Elhott, Proc Roy Soc 242 (1957)57 16) G G Baldwin and G S Klalber, Phys Rev 71 (1947)3 17) H M Sterner and J A Jungerman, Phys Rev 101 (1956)807 18) E K Hyde, The actmlde elements, National Nuclear Energy Series, Dlwslon IV, Vol 14A (McGraw-Hill Book Company, Inc , New York, 1954) chapt 15, pp 568--70

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