Nuclear charge distribution in the region of asymmetric fission of 238U by protons of energy 20–85 MeV

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NUCLEAR CHARGE DISTRIBUTION IN THE REGION OF ASYMMETRIC FISSION OF -'3"U BY PROTONS OF ENERGY 20-85 MeVJ. I... GAI.INIER and L. YAFFE Ik'partment of ('hemislry. McGill t.'ni,,,ersit~, Montreal. Quebec. Canada ( Re~eiled

2 September 1976

Abstract--Independent formation cross sections of '"'' Pm and ""Pro and cumulative formation cross section,, ol .....('e. ''Pr. "Nd. '*'Nd. "~Pm, '"Nd, '"Pro. '"Sin. '"Sin. ''Sin and '"Eu. produced in the lission of >"[ b~ proton,, of energy, 211-~'~MeV have been measured Independent cross section,, of '""Pr. '"~Pm and '"Pro ha~.c been cslim,ued from Ihe cumulative yields. From these data. charge dislriht, tior curve,,, typical of the mas,, region •~, 146= 151 ~erc ctmstructed. Fhe values of Z.,-Z,, deduced from these approached stability vdlh increa,inv hombarding energy, ~ ith a rate of displacement slov,er than that observed ,.~,ithhear} products of lower mass. l'hc full-,aidlhs at half-maximum of the charge distribution curves broaden with increasing mass. while remaining narrower lhan in the ca,,e of neighbouring lower masses, thus confirming a mass dependence. The total number of neutnms emitted during very asymmetric mass di,,ision at these energies ~.as found to be lower than in It',, asymmetric fission processes. The results have been discussed in terms of a growing contribution from direcl interaction mechani,m~.

INTROI)UCT1ON }or ;t complete description of the fission process one must consider the distribution of nuclear charge as well as mass between the fission fragments and how this is related to the nuclear structure of the fissioning nucleus and the primar,~ fragments. Radiochemical studies have yielded considerable information and much understanding in this respect. At thermal energies a great deal of the definitive work has been done by Wahl et a1[1-41 on e~'U and their results, along with others obtained in the thermal-neutron induced tission of :"U and :'~Pu, and in the spontaneous fission of :::('m and :::Cf have been summarized by t.'meza~va et a/.[5]. 'l-he measured independent yields ha',e been found to be ~.ell represented, for each mass chain investigated, by a Gaussian distributkm. The near constancy of the width of these distributions has led to lhe assumption of a universal charge distribution applicable, at thermal energies, to all mass chains[3]. Some doubt has been cast on this assumption as a tesuh of a more detailed analysis of the charge disIributitm data. Amid and Feldsteinl61 have found de\iations from the (;aussian curves attributable to oddeven eltccts. }iclds of even Z being enhanced. A good deal of information is being accumulated about fission b} medium-energ.~ (20-85MeV) protons of various fissile materials. The work of Pate et al.[7] on the fission of :':q'h was followed by similar studies of :'~tr fission18-15.27]. '"U[10.13,161, ~"-'Th[13.17-19}. 'TI20.21]. "-Np1221. and ''Pu[23] by several groups of ',,,orkers. Studies utilizing different projectiles have been carried m,l by McHugh and Michel[24] (fission of ' ' T h t~y ~x-particles of energy 20-57 MeV). and Choppin et a/.125.26] (:'>Fh and :'~U ,aith 9.5-11.5 MeV deuteronsl. Charge dispersion curves. (neutron-proton ratio, N / Z ~s ~icld) have shown thal the most probable charge. ,4,,,. shift,, tov, ards /J-stability. Z~. with increasing incident energy. Fhe variation of 7-.,. is more \~,ithtinanciaI assistance fr,,m the National Research Council of i arlada 1497

accentuated for the heavy products[8.9. 14. 16. 17. 19. 20, 22. 23] than for the light productsll(I, 18. 211. lhe full-widths at half-maximum (FWHM) of the ctlr,,es obtained in the heavy mass region remain esscntiallx constant with increasing energy up to 40-45 McV for :~U[8.9, 11, 14, 151 and '~:Th[17, 19,24], whereas there is a regular increase for targets of lower N / Z values (20. 23). On the other hand light-mass products display values of FWHM which increase only ver~ slightl', ~i~h energyl211 or do not vary[22]. For the same target and bombarding energy the charge dispersion appear,, to bc larger for light-mass products[21] than for he:t,,,, products [201. Previous studies on >~U have involved the folh)~ing mass regions: A=90-93110], 111-117115], 122-131[11[. 130-135114] and 139-14319]. The present investigation was undertaken in order to extend the work on energy dependence of charge distribution in the fissioll of >q.' by protons of 211-85 MeV energ,, to the hear\ side of lhe asymmetric mass distribution (lanthanide region). With the exception of the work b.,, Umezawa[12] in Ihe 1355 MeV energy range, there are very fc,*. experimental data available in this region. This is undouhlcdh due to the fact that complete and lengthy radiochemical separations of individual rare-earth fission producls arc incompatible with the short half-lives encountered ,n this mass region. The advent of high-resohttion Ge(1,i) detectors h.ls made possible the use of simplified chemical procedures where lanthanides ma.~ be chemically sep,,rated ',~s a group and information regarding the individual nuclides obtained on the basis of their decay properties. EXPERIMENTAl.

Irradiations "['he target foils consisted of uranium foils of natur:d composition (99.2~7c '"U). The thicknesses used depended on the half-live,, of the nuclides being investigated-134 mg/cm: for halflives greater than I hr and 54mg/cm: for shorter half-live,, =in order to hasten dissolulionl. Prior It) irradiation the uranium foil,, were cleaned with dilute HN(), rinsed ~tth di,lillcd ~ater

1498

J.L. GALINIER and L. YAFFE

ethanol, acetone and dried. The target foil was sandwiched between two similar foils to compensate for recoil losses within the master target. The reaction 6~Cu(p,pnJn'Cu was used to monitor the proton beam. The copper foil (44 mg/cm-') was placed upstream in the target stack with respect to the direction of the proton beam and separated from the assembly by a thin aluminium foil in order to protect the Cu foil from fission product contamination. The entire stack assembly (5 foils) was carefully trimmed to ensure equal exposure to the proton beam, wrapped with 10 mg/cm2 AI foil. and placed in the target holder which was attached to the end of the cyclotron probe for irradiation in the internal proton beam of the McGill synchrocyclotron. The duration of the irradiation varied from 5 to 30 min with a beam current of the order of I #A. Different beam energies were obtained at corresponding radii in the vacuum chamber. The beam energy degradation in the target was calculated from the data of Williamson and Boujot[28] to be 1.65 and 2.50 MeV at the master target for the two different uranium foils used. An average value of -+ 2 MeV was adopted throughout the bombardment range (20-85 MeV).

(b) Chemical separations Group separation of the lanthanides. The procedure adopted is based essentially on that of Hume and Martens[29]. It consisted in the isolation of the lanthanides as a group by fluoride and hydroxide precipitations. Neodymium was used as a carrier for all the lanthanides, since the solubility products of the fluorides and hydroxides of the elements ranging from Pr to Eu do not differ greatly [30]. After bombardment the uranium target foils were dissolved in 10N HNO~ in the presence of 15 mg Nd,O,, the solution diluted to 10ml with the addition of 10N HNO, and the bulk of uranium removed by solvent extraction with methyl isobutyl ketone (50 ml equilibrated with 10N HNO0. Zirconium activities were eliminated by addition of 10 mg Zr carrier and precipitation of Zr3(PO,,), by the addition of a few drops of cone H~PO,,. Similarly, 10rag each of Ba and Sr were added and the solution scavenged with BaSO., and SrSO, precipitations. The phosphate and sulphate scavenges were repeated and 3 ml cone HF added to the solution to precipitate NdF~ which was rinsed with 10ml 0.1 N HF, dissolved in I ml saturated H~BO~ solution in the presence of I ml 10N HNO, and the resultant solution adjusted to a volume of 10 ml with distilled H20. Nd(OH)~ was subsequently precipitated with 2 ml cone NH,OH and dissolved in 3 ml 10N HNO~. The hydroxide precipitate was repeated twice, the final precipitate dissolved in 1 ml 6N HCI. diluted to 10 ml with distilled H.,O. Saturated H2C20,, 115 ml) was added to precipitate the Nd2(C20,), which was coagulated by heating the solution on a water bath for 5 rain. ]'he precipitate was washed with distilled water, ethanol and ether, calcined at 800°C for 15 rain. cooled, and mounted for activity measurements. The chemical yields of neodymium were determined gravimetrically. In those cases where more rapid chemical separation was required only single scavenges were performed. The Nd(OH)~ precipitate was dissolved in 10 ml 6N HCI, transferred to a 20 ml vial which was sealed and used for activity measurements. This series of measurements was especially designed to determine the formation cross section of 12.4-rain '"Nd and the activities were normalized with respect to the proton beam. The validity of using Nd as a carrier for the lanthanides (Pr to Eu) was verified by means of tracer experiments using 'S°Pm. ~"tNd and '~Pr. It was found that the ratio of '~°Pm/'"tNd activies was equal, within statistical uncertainties, in both the processed sample and an unprocessed sample used as a reference. The ratio of '~"Pr/'"'Nd activities was about 3% lower in the processed than the unprocessed sample. In the chemical yield calculations a correction was applied to Pr yields, while those from Pm to Eu were taken as equal. Cerium separation. A rapid procedure, based essentially on the work of Glendenin et a/.[31] was used in order to isolate 14.2-rain "~Ce from the bulk of the fission products and the other lanthanides.

The uranium target was dissolved in a minimum amount of hot 10N HNO,, 30mg of Ce carrier were added and the solution carefully boiled to dryness. The residue was dissolved with I ml of Pr hold-back carrier solution (20rag Pr,OJml), adjusted to 10 ml volume with 10N HNO, and the uranium extracted with 50 ml methyl isobutyl ketone equilibrated with 10N HNO,. To the aqueous phase was added 2 ml 2M NaBrO, and the Ce'" extracted with 50 ml methyl isobutyl ketone. The middle of the extraction period (31Jsec) was taken as the removal of Ce from its precursors. The organic phase was washed twice with 10ml 9N HNO, containing a few drops of NaBrO, solution. Ce'" was backextracted into 5 ml H20 containing 2 drops 30% H202. The oxidation-reduction cycle was repeated and cerium iodate[32] precipitated with 20 ml 0.35M HIO~ in the presence of 20 mg Pr hold-back carrier. The iodate precipitate was ~.ashed with ethanol. ether, dried and mounted for activity measurements. After these were complete the yields were measured gravimetrically by igniting the precipitate to CeO: for I hr at 800°C. Since the yield of '4~Ce was determined by measurement of the '"Pr daughter it was necessary to determine Pr contamination present at the start of the measurement. Tracer experiments with '"Ce and ' ' P r showed that no measurable Pr activities follow Ce during the solvent extraction steps. The Ce(lO,), precipitation, in the absence of Pr hold-back carrier involves substantial Pr contamination. With the addition of hold-back carrier, this reduces to a reproducible value of 15% of the Pr present at the time of the iodate precipitation. However. the time interval for growth of the daughter (1 to 2rain) between the solvent extraction and iodate precipitation is so short that the correction for growth of the daughter was at most 2%. Times were accurately recorded to determine this value. Copper separation. The procedure was based on that of Kraus and Moore[33]. The copper solution was adsorbed on a Dowex-I ×8 anion-exchange column 1100-200 mesh size), the resin having been pre-equilibrated with 4.5N HCI. The column was washed with 4.5N HCI removing Zn, Co and Fe till the yellow Cu band was ready for elution. The Cu was then eluted with 1.5N HCI. the middle fraction of the band being retained. The solution was diluted to 5 rot, Cu 2" was reduced to Cu* by heating with NaHSO,, and precipitated as CuSCN by drop-wise addition of a 10% NH,SCN solution. The precipitate was digested over a water-bath, centrifuged, washed with ethanol, acetone and transferred with isopropyl ether to a tared glass vial. The ether was gently evaporated, the precipitate dried at I I0°C for 30 rain and weighed. The precipitate was finally dissolved in 10 ml cone NH,OH and ~'Cu activity determined in this form.

(c) Activity measurements and treatment of data The properties of the nuclides measured in this v,ork are shown in Table 1. The "/-radiations for the lanthanides were detected with a 30cc Ge(I.i) solid-state detector coupled to a 4096-channel pulse-height analyser. The 51 l-keV annihilatkm 3'rays of the "'Cu monitor samples were measured with a 3"x 3" NaI(TI) scintillation crystal coupled to a 40(I-channel pulse-height analyser. The resolution of the Ge(l.iJ combination was found to be 1.4% for the 122-keV line of '"Co, 0.6% for the 356-keV y-line of " B a , and 0.4% for the 570-keV line of 2"'Bi. corresponding to a full-width at half-maximum of 2.2keV. The efficiency of the detector was determined over an energy range of 100 to 2000 keV with several standard reference sources at a distance such that errors due to source geometry and summing effects are reduced to a negligible error. Efficiency ratios at various sample-detector distances used in activity measurements and effects of source geometries in the case of liquid and solid samples were determined. The activity of each nuclide was followed for several half-lives and then extrapolated to the end of bombardment by the CLSQ computer programme[36]. Counting rates were then converted to disintegration rates by correcting for chemical yields, branching ratios and detector elficiencies and formation cross sections were calculated using standard equations.

\u,.lear • Ilarge di,,tributi<,n in the regi
14oN

Table I. [)eca~. properties of the observed nuclides Radiation detected IkcVI

Emitted radiatic, n per disintegration Ref.

Mode of formation

Half-life

c~

14.2 m

"Pr "Xd

c c

24.2 m !IUNd

.... I'nl

i-:

41,3 d

550.0

11.95

"'Nd "'t'm 'Pro x,d Pm 'Sin

c ~ ~ c c c c c c (p,yn)

1.73 h :3 I h 2.68 h 12.4 h 28.4 h 46.5 h 22.2 m 9.4 h 15.2 h 12.':4 h

211.3 286.o 333.9 I I':'.l) 340io 103.2

0.27 o.026 I).71 0.40 11.21 n.28 II '73 I).211 11.14 11.38

\ uclide '"(c

Sm

Sin t-u ~('u .

453.e, From daughter 453 t~ 91.1

I04.~

204.11 373.1) 511

U.77

134]

0.'77 I).28

1341 [341 [341 1341 1351 134] 1341 [341 [341 1341 134] [341 1341

cumulati'.'e producl. ~-- independent product. i

2. ( to,,,, ,,eclions the reaction

table for

i

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i

t,:

"'( tll p.iin )'"~(.'tl IIpIMc\

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2~ ~o

45 "ql

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~,~" -0 77

X5 : Inlerpolaled

~r mh

Ref.

_x

13~1

429 4n9 _,l)

1371 1371 I371

_4 194 187

1371 137I

I?X:

1371

•

7:

¢

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-: 1,2

"I

/

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[371

1711+ 1371 162+ 137] 1"5+ 1371 157 1371 141 + 1371

l

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II

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"OO

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27.K"

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I

' Me,':

Fig. I Excitation function for the cumulative formation cro,;,,~ection~ of '"Nd. I

I

1

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I~hle ~ Whet, nol a',ailahle lhe,. u.ere interpolated fr,.',nllhe data .d Xcv, h m et c.ll~'?I

RI,:SII.TS [he measured cumulafixc formation cross sections are ~i~en in fables ?,-L I h e cross sections quoted are usualb, the re~,ull of se,,eral determinations (the number ,ff ,,uch b, shown in parentheses in the Tables) and the ~alue quoted i,, the a~erage of these determinations. Where onb one determination ~as made lhe error quoted has been calculated by using the m a x i m u m nercentage error determined from replicate measurements at other energies. In Fig. I - 4 are s h o w n those data v. hich can be compared with those of other workers. The independent formation cross section.,, are s h o w n m Table 6 and the data are s h o w n in Figs. 5-8. The independent yields of the two shielded nuclides '""'"Pro :tn,,I ""Pro ha'..e been obtained directly from the activity :'neastJrements. In the case of ' " P r and ' " P m , the moependenl cross ,,ections have been obtained by submtcting the cumulati',.e cro,,s sections of '""Ce and ' " N d from those of their daughter,;. The error on the estimated

1

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1

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Fig. 2. Excitation function for the cumulative formation cro.,,,~ection~ of "~Pm. I

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1500

J. L. GAI.INIER and L. YAFFE Table 3. Cumulative formation cross sectionst O',,,h ""Ce /:;.(MeV) NIZ = 1.5172 20 25 30 35 40 45 50 55 60 65 70 77 85

11.7:2 10.5-+2 13.8-+ 1 10.1_+2 12.3-+2 9.9-+2 5.7--+ 1.2 7.4-+ 1.5 6.4-+0.8 4.7-+0.9 4.4-~0.9 6.1--1.2 3.6-+0.4

(2) (2) (2) (1) (2) (I) (2) (11 (2) (I) (11 (1) (2)

~Pr

'"'Nd

'4"Nd

NIZ = 1.4745

NIZ = 1.4500

NIZ = 1.4833

15.2-+2 15.0-+2 20.2-+I 17.5-+2 18.7-+1 18.3-+1 17.2-+ 1 17.6-+ I 15.8-+ 1 15.6-+2 13.8-+1 13.7-+1 9.6:1.1

15.9-+2(2) 16.7_+1(2) 18.1 -+2 (1] 20.8-+2 (2) 21.0_+2(2) 18.5_+2(11 16.6_+2(1) 20.4_+3(2) 19.2_-2{2) 15.5-+2(11 13.7-+1(2) 11.8_+2(2) 11.4_+2(2)

9.40-+0.7 (21 9.50-+0.9 (2) 11.8_+ 1 (3) 12.5_+I (2) 12.1_+1 (3) 12.2_+1 (2) 13.9:1 (4) 14.0_+2 (2) 11.9-+ 1 (3) 10.7_+1 (2) 9.5-+I (2) 6.8-+0.7 (2) 6.5_+0.9(3)

(2) (11 (2) (2) (2) (2) (3) (2) (2) (1) (3) (2) (2)

+The numbers in parentheses give the number of determinations. Table 4. Cumulative formation cross sections,* o-.... ""Pm k~(MeV) NIZ = 1.4426 2(1 25 30 35 40 45 50 55 60 65 70 77 85

12.3_+1 12.4--2 15.4_+ I 16.4-+ I 16.0_+ I 16.4-+2 18.9_+2 19.0-+2 16.3-+ 2 14.7-+1 13.5-+ I 10.1-+1 9.6_+ 1.1

(2) (2) (3) (2) (3) (2) (4) (2) (3) (2) (2) (2) (3)

'"Nd

'"Pro

'5'Sin

NIZ = 1.5167

NIZ = 1.4754

NIZ = 1.4677

4.3-+0.6 {21 4.9-+0.9 (I) 5.2+0.4 (2) 5.1 -+ 1.0 {I) 5.0-+0.7 (2) 5.2_+1.0 (I) 4.8_+0.9(2) 4.8:0.9 (I) 4.3_+ 0.4 (2) 4.2_+0.7(11 4.5_+0.8(11 4.4_+0.7(2) 3.2-_0.6 (2)

7.1_+0.8(2) 7.2-+0.6 (2) 7.7-+0.9 (3) 7.9_+(I.5(2) 7.8_+ 1.1 (3) 8.1:0.7 (2) 8.5__.0.6(4) 8.3_+1.1(2) 6.7 _+1.2 (3) 6.9_+0.5(21 6.3_+0.9(2) 5.9_+0.6(21 4.2-+-0.5(3)

3.3-+0.2 (2) 5.0-+0.6 (1) 6.7-+0.9 (I) 7.2-+0.6 (2) 6.4-+0.9(11 5.9_+0.8(I)

6.0-+0.8 (2) 6.2-+0.9 (2) 4.3-+0.5 (2)

f'Fhe numbers in parentheses give the number of determinations. "Fable 5. Cumulative formation cross sections+

I

I

I

NIZ = 1.5000

N/Z= 1.5161

NIZ = 1.4921

20 25 30 35 40 45 50

2.2 -+ 0.4 (2) 2.4±0.5 (1) 3.7:0.5 (2)

1.9 _+0.3 (2) 2.7+0.6 (I) 3.5___(I.4(2)

I. 1 -'- 0.2 (2) 1.0+0.3 (1) 1.2-+0.3121

3.1-~0.3 (2)

3.2z0.5 (2)

2.3_+0.3(2) 2.2_+0.5 (I) 2.2 - 0.3 (2) 1.8-+(I.4 111 1.6--+(I.4[2)

1.8_+0.2(2) 1.8_+0.6(1) 1.9 -+0.3 (2) 1.5_+0.5(I) 1.4_+0.4(2)

1.9_+0.4 (1) 2.4+-0.5 (1) 1.7-'-0.2 (3)

1.9_+0.5(1) 1.8_+0.2(2) 1.6_+0.4(I)

1.9_+0.6II) 1.2__.(I.2(2) 1.3_+0.3(I)

3.(I ,- 0.2 (3)

55

6(1 65 70 77 85

,;The numbers in parentheses give the number of determinations. independent yields was calculated by taking the square root of the sum of the squares of the uncertainties on both cumulative yields of the "~Ce-~4~Pr and ' " N d ~"Pm pairs. This procedure provides a reliable estimate of the independent yields concerned, especially in the case of "~Pr where the activity of the same nuclide ("6Pr) was measured for each member of the pair, thus eliminating uncertainties in decay schemes and detector efficiency. An additional +- 15% was added to the uncer-

I

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I

c

21

I

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I

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;'~aU (p.f) '"/~u Co)

i

2

E,,(MeV)

I

I I 111100

; :-:2:

.......

2(Ix}

3001 I

Ep (MeV) Fig. 4 Excitation function for the cumulative formation crosssections of '~'Eu. tainty in the case of '"'Pro in the subsequent construction of the charge dispersion curves. The above procedure was not very useful in the treatment of the ~49Nd-~49Pm pair. The cumulative yields of the pair should be very close in this energy range, i.e. the independent yields of ~'gPm should be very small since it is highly neutron-deficient and the probability of its direct production at these energies should be small. Experimentally, however, the values of the cumulative cross sections of ~*gNd and "gPm show surprisingly large differences, in complete contradiction to the charge distribution systematics in this region. A set of corrected

Nuclear charge distribution in the region of asymmelric fission of ""1' h$ proton,, of energy, 20-g5 XIe\ '

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assumption that at 20 McV almost sill of the ~ield of the 149 chain is distributed over "~Nd and it', prectirsors. except for a ().{14mb contribution from '*'Pro. its determined from charge dispersion curves constructed ~ t h other independent .~ields. The estimated independent $ields of ~'"Ptn haxe been used o n h as ;l guide for definition of the charge dispersion curves ~,ith sin assigned 50% error. Charge dispersion cur~ es for the mass region A - 146151 were conqructed as a first approximation hx using the independem yield data given in Table 6. based on the method of Wah[ el al.[I 1. In the present case. no charge dispersion data exist for chains heavier than 4 - 151. It ,aas necessar~ to assume thal, in the mass range cmcred. the most probable ,,alue of N/Z and the charge disper,,ion data ~ere independent of the mass of the fission chain so thal the fractional independent yields fell on a unique curve for :.t gi,,en incident energ$. The usual constraint[43] that the fractional cumulative \.ield, foi a

i.. .

Fig. ~. Excitation function for the independent fornlati~,n ~.r,>,,~,-

I

Fig ~. t'~,citation functions for the independent formation cros,,,ectiom, of '""'" Pm and '"'Pnl

mass chain read from a summation of fractional in-

dependent ~ielcs from the charge dispersion curves had to slim to the ~'xperimentally-determined rabies, served to define the curse,, rigorously. The cumulative cross sections in the mass range . I = 146-151 have been corrected to total chain ~ield,, with the help of the,e charge dispersion curves. For masses higher than ,'1--151 no such correction ,,,.its attempted. since lhe charge dispersion determined for the lightermass products may not ;,ppl.~ in this regitm without introdnction of a possible error...'~s a result, the experimentally-determined cumulative yields fur "',~nl, ~<'Sm. ' ' S i n , and " E n ~ere used o n b as lower limits for the total chain yields of the corresponding masses. l h e present data, along ~ith those of others[t). 12. 14.41). 421 have served to provide a better definition of the heavy side of the mm, s distribution at catch incident cncrg!,. lhe portion of lhe mass distribution co,,ering the mass range 132-161 has been found to he well discribed h,. ;i

•

'

-: "

:

"

:]-."

"_"

.q2

;:2

fig. - Excitation function for the independent formation

cros,,-

,~ection,~ of "*'~Pm.

values of '*'Pro independent cross sections were generated by determining the ratio o f ' " ~ P m ( c ) / ' " " N d ( c ) in each sample produced in this series of measurements. A value of 1.304 was found at 20 MeV, which was then used as a normalization factor for all the others at higher energies. This is based on the reasonable

(iaussian distribution and the fit ~as made b~ means of the ()R(}t.S program[44]. An example for 50 Me\. incident energ.~ i,. shm~n in Fig. 9. Fractional independent yields were then obtained b~ dividing the independent yields by the relevant *oral mass .~ield, as obtained from the mas,, distribution curves at the appropriate incident energy. An average additional error of -' 10c~ arising from uncertaint~ in n3as~ ~ields ~as added to the existing limits for the xalues of the independent truss sections. The independent cross ,ections of "*" Phi have been corrected for ground-slate contribution using the results of LImezawa 1421 at thermal

1502

J. L. GALINIER and L. YAFFE Table 6. Independent formation cross sections (in mbarn) ÷ tr,, "~Pm "~Pm~ ....Pm ""Pr§ "~Pm¶ E,, (MeV) NIZ = 1.4262 NIZ = 1.4426 NIZ = 1.4590 N/Z = 1.4746 N/Z = 1.4754 20 26 30 35 40 45 50 55 60 65 70 77 85

0.15±0.04 (1) 0.12±0.03 (2) 0.16-+0.04 (2) 0.25_+0.06(1) 0.31_+0.05 (2) 0.39_+0.10(1) 0.49-+0.08 (2)

0.04±0.02 0.04 -+0.02 0.05-+0.03 0.12-+0.06 0.21 ±0.10 0.42_+0.20 0.54±0.27 0.62--'0.31 0.64±0.32 0.61±0.30 0.88_+0.44 0.97-+0.48 0.88-+0.44

0.15+_0.03 (2) 0.22 -+0.05 (2) 0.31+_0.1)4(2) 0.47_+0.12 (1) 0.80-+0.22 13) 1.20_+0.31)(1) 1.69±0.42 (11 1.50-+0.15 {4) 1.53±0.22 12} 1.49±0.18 121 1.75-+0.14 (2) 2.18-+0.17 (4) 2.54±0.23 (2)

3.5-+0.8 4.5 -+0.9 6.4-+0.7 7.4_* 1.6 6.4_+1.0 8.4_+1.8 11.5±2.5 10.2_+2.1 9.4-'-1.4 10.9±2.7 9.4_-2.(I 7.6-+1.7 6.0_+1.0

2.8_+0.5 2.3 -+0.5 2.5-+0.3 2.8_+0.6 2.8-+0.6 2.9-+{).6 3.7±0.7 3.5_~0.8 2.4_+0.5 2.7-+0.5 1.8_+0.4 1.5-+0.3 1.0-+0.2

CThe numbers in parentheses give the number of determinations. 1:Best estimated values (see text for details). §tr,,~ ('"SPr) = o'o.. ('*SPr) - o'~.~ ("~Ce)

¶o'i.,~ ('~'Pm)=O'¢.m ('~'Pm)- o'~.~ ("Nd) Table 7. Fractional independent yields used in charge dispersion curves ' '"Pm

'" ' Pm

(Tmb

'"~Pml

"~Pm

E~(MeV)

N / Z = 1.4262

NIZ = 1.4426

NIZ = 1.4590 NIZ = 1.4746 N/Z = 1.4754

20 25 30 35 40 45 50 55 60 65 70 77 85

0.0001+ 0.00001:[: 0.0002+-0.00003.-+ 0.0004__.0.0001:~ 0.0009-+0.0001:~ 0.0019_+0.0002:1: 0.0035-+0.0004~ 0.0105-,-0.0035 0.0089-+0.0027 0.0142-+0.048 0.0214-'-0.063 0.0303-+0.066 0.0468±0.138 0.0614+_0.148

0.0040_+0.0024 0.0035_+0.0021 0.0041-+0.0024 0.0095_+0.0057 0.0180_+0.0108 0.0347_+0.0208 0.0415+0.0249 0.0506-+0.0336 0.0626±0.0376 0.0554---0.0332 0.0900-+0.0540 0.1160±0.0696 0.1240±0.0744

0.019_+0.005 0.20 -'- 0.07 0.024---0.008 0.22_+0.07 0.032-+0.007 0.30_+0.06 0.046 ~ 0.016

""Pr

0.33-+0.10

0.084-+0.032 0.32-+0.08 0.122_+0.043 0.4t)-+0.12 0.1(¢.)+ 0.055 0.51+0.16 0.150±0.030 0.48±0.15 0.184_+0.044 0.53_+0.13 0.167_+0.037 0.56_+0.20 0.224_+0.041 0.53-+0.16 0.312-+0.057 0.52-+0.12 0.446-+0.084 0.46-+0.12

0.44_+0.18

0.32_+0.15 0.33_+0.12 0.35_+0.16 0.37_+0.17 0.37-+0.14 0.44-+0.20 0.44_+0.22 0.36-+0.16 0.39_+0.18 0.29-+0.17 0.27-+0.12 0.22-+0.10

¢Corrected "S'Pm data (see text for details). :~Data from Umezawa et a/.[51.

1

.

I

I

I

U(p,;)

lO

Ap = 132.4

" "*'~"

"S E

?, •

(9;

:;

i "4)

•

24~t

energies. He has found o',,,/(tr,,, + os) = 0.88 in the thermal fission of -'++U. It is reasonable to expect this ratio to increase to close to unity at medium energies since the production of the high-spin ( 6 - ) ' + " P m should be favoured over the low-spin (1 - ) '4"*'Pm. Nevertheless. a 10% correction was applied to increase the fractional independent yield value so that the value listed is certainly an upper limit. Values for fractional independent yields used in the construction of charge distribution data are shown in Table 7. Charge dispersion curves were constructed as described above and representative samples are shown in Figs. 10-12.

o L)

DISCUSSION Excitation functions

I

130

I

140 MOSS

I

I

150

160

Number

Fig. 9. Heavy side of the mass distribution resulting from the proton fission of 2~8U at 50 MeV.

The excitation functions of the independently-formed nuclides " " P m , "~Pm and '~"Pm show the classical behaviour of neutron-deficient species formed in fission at medium energies, namely a sharp rise in the excitation function with increasing energy, e.g. Fig. 6 and 7 whereas those of ' ' P r and " ' P m , which are neutron-excessive and further from the stability line reach

Nuclc;~r charge di,trihution in the region of asymmetric fission of -"~1" b,, proton,, of energy. 2 ).-8~, ~.tc\ I

I

'i

1

":/,z

i.

- • :

!

':~

t:

"

i

I '

IqL~,

~:

NlCv'

.

:,

~,/~

~r

:"

'/-

.:).

\ /

"L

\

: "'V

\,

,

\

\ •.; ,,

''"

]

!

t

,I

!

"I ¸-

it i

°

!

+['I I •.:'

• ..

I

I I •.~'

I

+.%~

".h!,

•

1

• ..: •/Z

I

I

. ~]

1~

("

I

I

• :.~

+,

N,

Fig ;U i h:ttge distribution curve :it 211Me",. Fig. 12 harge distribution curxe at ~'~ Me\

N/Z

-'.:..

-

+.-:F)B

L il. 'qi

i

A.

+

'~. ?+

.' ~__' !

",-;

".:"

''~

I%!:

+...

Fig. 13 Incident energie,, ;el which Ihe excitatiun ftmctlon,, of the fi',qon product,, ~t" "'"U re;~ch their rrlaxlma

'/7

Fig II ( haruc di,,tribution ~:t,r',e :it 511~,fex. :, maximum at about 55 MeV. e.g. Figs. 5 and 8. Friedlander et a1.[43] ha,.e pointed out the correlation I-,etween the neutron-to-proton ratio of fission products in the cesium region and the energy at which the respective excitation functions reach a peak. the peak moving to higher energies x,.ith decreasing N/Z ratio. '1he trend has also been confirmed for products in the Ba-La region (91 and the Sh region l IlL As shown in Figure 13 the present data reinforce this trend. In the cases of '"<"Pro. "'Pro. and ""Pro. ~p, u.as found to be the cuse. no maxima ,,houh.t he oh,,erv:tble within this energy region. If one extend:, the data. ;.is shown in Fig. 6. v,4th the data

of Pappa~+ ~md ,,\lstud[40] for ....Pm ,it 170MeX,. . a maximum is found ut IO0-+It) MeV ;md thi~ lit', reasonabl~ u+ell on Fig. 13. The excitation function'~ for the cumuhflivc \ ield,, (Fig. I-4) have been drawn to include data of other ',+,orkers. In most ca~.,es, the agreement, either b), duplication or b) extension of the pre',ent data ix very good. The ,,>stematics would tend to fitvour the present data. The cumulative yield', exhibit broad peak', (e.g. " Nd ;rod "+Sml in the ease of neutron-deficient nuclide,,. Neutronexces'~ nuclides, e.g. " N d shov, a virtuall,, fiat e'v._'itatitm function within experimental uncertaintie,,. lhi,, heh:tvior is strikingly different from that of lighter product,, with comparable N / Z ratio, e.g. :"'Ba, whose eros,, ,~ection

1504

J.L. GALINIER and I,. YAFFE

decreases sharply over the energy range from 20 to 85 MeV from 43 to 9mb[9]. The difference is indicative of the less prominent role played by the displacement of the most probable nuclear charge along heavy isobaric chains in the decrease of cumulative cross sections with increasing bombarding energy. This is compatible with the hypothesis of low-energy formation of heavy products.

Charge dispersion Most probable charge-Z r. From the charge dispersion curves the most probable charge Z,, was found. The most probable A,, was chosen as that of the Pm isotope closest to the peak and the corresponding value of Za taken from Coryell[45]. The results are shown in Table 8. The shift of Zp towards stability is clearly seen in Fig. 14. The variation is, however, considerably different from that found in the lighter heavy-mass region for the same energy range 20-85 MeV, viz. 0.54 units in the present work, compared with 0.83 Z units for A = 130[14], 1.14 for A = 136 and 1.02 for A = 141 [9]. In this mass region the variation is linear (very much like that for A = %), whereas in the chains mentioned above the rate of movement, above 50MeV, decreases rapidly initially. The linear decrease of ZA'Zo for A = 146-151 suggests as a first approximation that the same mechanism is 'Fable 8. Parameters of charge dispersion curves Full-width at half-maximum

Peak position E,,(MeV)

20 25 3(I 35 40 45 50 55 60 65 70 77 85

N/Z,,

A,*,

Z,,$ ZA-Z, N/Z

1.517 1.515 1.517 1.512 1.507 1.498 1.498 1.500 1.498 1.500 1.498 1.4% 1.492

153.5 153.4 153.5 153.2 152.9 152.4 152.4 152.5 152.4 152.5 152.3 152.2 152.0

63.65 63.61 63.65 63.54 63.43 63.25 63.25 63.29 63.25 63.29 63.22 63.18 63.11

2.65 2.61 2.65 2.54 2.43 2.25 2.25 2.29 2.25 2.29 2.22 2.18 2.11

0.044 0.044 0.047 0.046 0.048 0.046 0.051 0.051 0.053 0.057 0.061 0.063 0.063

Z 1.06 1.06 1.13 1.12 1.16 1.12 1.25 1.25 1.30 1.40 1.60 1.55 1.53

fCalculated from Promethium isotopic distribution :!:From Coo'ell (45)

4.o~

~

'

'

3.C

m

::

.~,

I 60

I 80

A =96

!.0 I 20

I 40

Ep (x4ov)

Fig. 14. Displacement of most probable charge from stability as a function of incident energy.

responsible for the production of these mass chains in the 20-85 MeV range. On the other hand, the fissioning species from which the products studied originate should carry less excitation energy than those giving rise to less asymmetric mass divisions, so that the primary fragments will emit fewer neutrons. This is incompatible with the assumption of a unique mechanism, namely a compound-nucleus process in the present energy range. On the contrary, it would appear that very asymmetric mass divisions would be the result of well defined low-energy deposition events arising from a compound-nucleus mechanism at low bombarding energy and direct interaction reactions above. In the light-mass region of fission products, the measurements which have been carried out on a variety of fissile targets[10, 21, 22] show that Zp is almost independent of both the incident energy and the nature of the target, thus suggesting that the variations introduced by these factors are absorbed by the heavy complementary fragment (Fig, 14). This proposition seems to be in contradiction with our results in the A = 146-151 mass region. It should be noted, however, that results in the light mass region have been obtained for A = 96 and that the complementary mass region is centered around A = 140. It appears, then. that within a few mass units ( - 6 A units), the mechanism of production of heavy fragments becomes more selective as far as excitation energy is concerned. The dual energetic aspect of fission has been clearly demonstrated at higher energy, where, in mass regions below A = 140, the charge dispersion studies of Friedlander et a1.[43] on cesium isotopic distribution up to 2.9 GeV, Yu et a1.[46] on xenon isotopic distribution at 11.5 GeV, Yu and Porile[47] for mass chain A = 131 at the same energy have revealed the existence of doublehumped charge dispersion curves. The extension of these studies to higher masses by Chu et a/.[48] at 11.5 GeV and B~ichmann[49] at 28 GeV has shown that the charge dispersion curves change from a double hump with a shallow valley in between (peak-valley ratio - 2 ) at A = 131 to a distinct separation of the two maxima (peak-valley ratio - 8 ) at A = 147 and to a single peak on the neutron-deficient side at A = 170. This very important result confirms the conclusion that different mechanisms predominate in high-energy fission and also that these mechanisms become increasingly separable with increasing asymmetry of the process. Our data indicate that this conclusion may be extended to the medium-energy range, where the only peak observed appears to be more stationary than for lighter heavy products. This conclusion has also been strengthened by recoil studies at high energy. The ranges of neutron-deficient nuclides decrease by approximately a factor of 2 compared to their values at lower energies, while those of neutron-excess nuclides remain essentially independent of bombarding energy[50-52], the change in range between these two classes of nuclides occurring rather sharply over - 2 charge units on the neutron-deficient side of stability[53]. Starzyk and Sugarman[54] have used this relative range behaviour to decompose isobaric charge dispersion curves into three individual-dispersion components corresponding to two fission mechanisms (one at low energy and one at high energy) and a nonfission process tentatively assigned to a spallation-like mechanism. The relative contributions of the two fission modes to the overall isobaric yields at 11.5 GeV reveal a

Nuclear charge di',tribution in the region of asymmetric fission of sharp decrea~,e of the low-energy contributions between mas,, 131 and mass 1471541. the estimated values being 70 and 35% rcspectively. This result is compatible with our previous conclusion. ]'he increase in bombarding energy, which causes a shift of the energy spectrum of residual ~:ascadc nuclei tov, ards higher values, therefore depletes the probabilit.~ of occurrence of low-energy deposition c'..enls and consequently the production of the heavier neutron-execs,, products. One should note. however, that neutron-excess products of masses around A = 131, ~hich are also the results of asymmetric events, and as ,,uch me generall} associated with "low-energy fission" urc lens affccted in their production by an increase in bombarding energ,, than their heavier homologues. This is an indication that the term Iov,.-energy fission has to bc taken ill ;1 broad sense an meaning fission consecutive to energy deposition events leading to excitation energies ,,ubstantialh lower than thc incident energy, but not neccssaril} low in an absolute sense. t" , Variation of N. ;Z, a,~ a ]unction o[ mass. The varialion of .k;!,7 ,,s the mass number of the fission chain is ,,hov, n in Fi,.z'. 15 at cnergie, of 30, 50 and 85 MeV. The ~ur,.e', have been constructed with the data of other ,.sorkerslS-II. 14. 15]. Wherever necessary the data hz~se been normali,'ed Io similar monitor values. The data ,,ho,a ,t gr~tdual increase in N/Z,, between ,4 = % and ~t -- 127. folh,wed b,, a sharp rise to ~ A = 133. followed l-~,. a slovs decrease i, nd a levelling off. "Fhe decrease of \','Z, with mass Stlggesls as a first approximation at least, that the average deposition energy increases with in~rcasing as~mnaetr}, conlrar.,, to the conclusions pre,ion,d,, drav. n. Hoxsexcr. this is not incompatible if it is t,,sumcd thal Ihc actual tission takes place after the .ompound or cancade nucleus has evaporated a sub,tanlial number of neutrons. The decrease beyond ~, 133 reflects the emission of pre-fission neutrons. ~alher Ihan emission front highly excited fragments. ¢,omev.'hat ,dmilar conclusions were reached by HagebO ,'t ,4155] for the light-fragment region IA =64-98) at i70 McV. l h e Io~ N/Z,. values, together with the nara~v.ne,,- of lhe charge dispersion curves were attributed ~'ithcr Iover} high z,nd well-defined energy deposition !ollov..ed b,, fission acts much faster than those occurring m Iov,-energ~, induced fission, or to a late fission act at ,,omc intermediate step in the evaporation chain folio~ing the primary nucleonic cascade.

~miati¢m '4 Z,-Z,. as , function of mass. The displacement of the most probable charge from the stability line a, a function of the mass of the fission chain is shmsn in Fig. If,. This figure has been deduced directly i

.

i

1

,,/',t

•

/11 7- "~

..

•

i

, ,,'-~.

. . -

? -~

P" ~ ....

,,, ,,', -3"-.:.:

.." •

r

,

/

....

"t, '.-

?

.1¢

-L'

/

I

v;.

~

I

"7~,,

"40

:..

!A

I

,NIl'R)

F'i~. 1" Variation of the mo,,t probable neutron-to-proton ratio •.*,ith the rna,,'., of Ihe fi,,~,ion chains for three incident energies.

by protons of energy 21)-85Me\.'

~""U

I

'\t

\'

I

-,f

,,

I'q) ~,

...-

Iv-

',\,\ ,,/.

L,k_

!½/ / - .

r.i .@

t

1 :2C

".7 ' .',

110

. ~~r' ._ ,

1

I

"qT:.

"4(-

I

A

Fig. 16. Variation of Z;-Z,. as a function of max:', A "

. .. Khan et a/.[10l: it, II, O. Sarkar and YaffellSl: ~,. IE. II). Miller and Yaffe[ll]: :tt [1. 01. Dik.{id et a/.[14J; /,. :-.L ~. Parikh ul al.[9]: ~.. ~. ~. Present Work from the preceding one (N/Z,, ~,s mass) and. again, shows a rather rapid decrease in (Z.~-Z~,) values from mass A =96 down to A = 133, followed by a slower increase up to the mass region investigated in this work. ['he decrease in (Za-Z~,) values with increasing incident energy appears to be more marked in the heavy fragment region (specially around mass A = 133). If the same mechanism of energy dissipation prevailed for ever.~ type of mass division (e.g. neutron evaporation from highly excited fragments) one would expect, at a gi,,,.'n incident energy, a monotonous decrease with increasing mass in the (Z4-Z~,)-vs-mass curves, given the configuration of the beta-stability line. The dip in the curves suggests that interactions of the protons with the l~,rget nuclide leading to high energy transfers (by a compoundnucleus type of mechanism) are reflected in the mass divisions which, after de-excitation of the fragments. give rise to heavy products in the A = 133 mass region. The less frequent fission acts yielding heavier product,, appear to be caused by processes involving much less neutron evaporation, as demonstrated b.~ the increase of (Z~-Z~) beyond mass A = 133, in spite of the fact that the beta-stability line curves towards more neumm-rich nuclides with increasing mass. This trend indicates fl~al direct interaction mechanisms leading to increasingly less excited residuvl nuclei will give rise to incrcasingb asymmetric mass divisions, and that, as alread.~ mentioned, the relatively high (Z,-Zf,) values found in the A = 152 mass region would originate from pre-fission neutron emission (cascade and pre-fission evaporation neutrons) and post-fission neutron evaporation from fragments carrying relatively low residual cxcilation energies. Variation of the full-width at half-maximum. l h c various values of the FWHM are listed in Table 8 and shown graphically in Fig. 17. along with data for . 4 %1101 and A = 136 [81. The curves for masses in the present work are much narrower than for the lighter, masses. The same trend was found by Pappas and Alstadl40] in their work at 170MeV who found a value of FWHM

1506

J.I.. GALINIER and 1.. YAFFE

"OC'

_~ 3 c z ~4

>. zc

A.135

.r

.....

~C:

T ..... 4to_ °

h ._

. .o.ir

-

~ - t l

•

•

... •

A='b2

I 20

l 42'

I 6") :l:

I H:;

<)

IS"

~Me',' :

Fig. 17. Full-width at half-maximum of charge dispersion c u r v e % as a function of incident, energy.

I "TK"

I "4.}

150

160

,5,

Fig. 19. Variation of the heavy side of the cumuhuive mass distribution as a function of different energies.

"..-.. ......... .. //~ <~ ..~

i r / f

x x -.,

.~ . .

x

.......

<.

.. - ./

i*~ • al. "~

~,\", %# x

•

T~lq

I 100

_~_.

'.2

"¢,..,'

',,,'.~)H~

I

I 120

i

MASS

(A

i 14C

I "60

units)

Fig. 18. Variation of the full-width at half-maximum as a function of the mass of the fission chains for three incident energies. approximately equal to 2.2 Z units for A = 140 and ~ 2.8 Z for A = 100-140. This narrow curve also corresponds to that found in the complementary mass region A = 64-98[55]. The trend of decreasing FWHM with fission product mass was also observed by Parikh et al.[9]. The data by various workers, as a function of A, are plotted in Fig. 18. A maximum is evident at A = 132, difficult to explain since it might be expected that if there were a directing influence of the 82-neutron shell, it should have provoked the reverse effect. Heavy wing of the mass distribution. In Fig. 19 is shown the variation of the heavy wing of the mass distribution with incident proton energy. The peaks shift towards the lighter mass side while the yields at the maximum increase monotonically by a factor of approx. 2 as the incident energy increases. The half-width at halfmaximum undergoes a slight increase from 11 to 13 mass units. Both these phenomena are consistent with the onset of symmetric fission accompanied by the filling up of the valley of the mass distribution at lower energies. Baba et aL[41] have shown that, in the energy range 13-55 MeV, the overall mass distribution can be decomposed into three Gaussian components, corresponding to two wings and a symmetric component centered on the valley according to the method proposed by Ford[561. By integrating over the theoretical Gaussian distributions they were able to observe a steep rise in the total fission cross section (from 0.22 to 1.45 barn between 18.2 and 35.2 MeV), followed by a slower increase up to 55 MeV. A similar analysis, performed with the aid of data by Stevenson et al.[39] in the 10-340MeV bombarding

energy range reveals a levelling off at a plateau of 1.5 barn. This result, combined with the fact that the yield of the maximum of the heavy-mass peak increases (from 36 to 71 rob) in the 20-85 MeV region, and the integrand of the symmetric component increases markedly from 55 mb at 20 MeV to 430 mb at 54.1 MeV[41] is consistent with the decrease at higher mass yields that is noticed in the present work.

Neutron emission McHugh and Michel[241 have proposed that one can obtain the rate of change in neutron emission as a function of energy by a study of the variation of Z, with energy, viz. &:/6E = (~Z,,16E)d(6Z, I~A),.

(1)

Coryell el a1.[45] have shown that (6Z,,/SAb..-~ 05Z.J6A)=0.38. More recently Dik'~i~ et al. have experimentally determined (SZ,,/6A)~ = 0.38-'-0.02 for isobaric studies along various mass chains. The quantity (6Z;,/(SE), was obtained by a linear least-squares fit of the present data normalized to A = 152. Excitation energies used were those of Dik~,i~ et al.[14], obtained by using the Vegas Stepno code[57] followed by Monte Carlo evaporation[58, 59]. Intermediate values of the excitation energies were interpolated. These are shown in Table 9. The plot of Z,,vs E* was found to be linear with a slope of 0.0208 McV ', a value substantially lower than that found in the region A = 131-135. 0.027 MeV ~[14], and 0.048MeV ~ in the region A=111-1171151. Satisfactory agreement is obtained with the value of 0.0195 reported by Nethaway[60] from a compilation of data in the region A - 1 4 8 - 1 6 0 for excitation energies up to 21.5 MeV for fissioning nuclei of A = 233 to 254. The number of post-fission neutrons, t o. has been calculated on the assumption that

~Sv,IaE = av;,/6E + ~v,ISE

(2)

where h and I refer to heavy and light fragments

Nuclear charge distribution in the region of asymmetric fission of :'"U by protons of energy 21~85 Me\ respectively, and vdvt was chosen equal to 2. The latter assumption is supported by the work of Cheifetz et al.[61} who reported an experimentally-measured ratio of 2.2 for the mass split 1.5 in the 155 MeV proton-induced fission of '~gU. Bishop et a/.[62] have reported ratios from 1.12 to 1.34 for similar mass splits in the 11.522 MeV proton energy region, the ratio increasing with energy. The number of post-fission neutrons is given in Table 9. Table 9. Total number of neutrons emitted in the asymmetric fission of ="U E,,(MeV) < E * > (MeV) v,+ v~.~ ~',§ A = 1521~,/~,, = 2) uT¶ A = 152 A = 131-13511 ,4 : 111-117¢*

30

4~}

50

60

70

85

26.7 32.1 35.8 43.4 45.4 53.9 0.29 0.45 0.59 0.61 11.74 0.81 1.12 1.h3 2.16 2.60 3.09 3.63 2.19 3.60 4.26 3.90

2.64 2.94 3.56 3.73 4.43 4.72 5.69 6.77 7.56 8.87 S.s0 6.56 7.83 8.68 10.19 5.10 6.70:~- 8.20 9.60

+Prefission cascade neutrons. SPrefission evaporated neutrom,. §Post-fission neutrons. ¢ffotal number of neutrons. IIAfter Dik~i,2 et al.[14}. ttAfter Sarkar[15}. StE,, ..: 55 MeV. (E*~ = 39.f, MeV. The number of pre-fission neutrons (cascade z,, and evaporated v~.) was calculated by the use of the codes previously mentioned[57-59], using a level-density parameter of a = A/20 and a radius parameter to= 1.5 fm. The total number of neutrons emitted (vp + v, + vF) is given in Table 9, along with corresponding values for A = 131-135 (14) and A = 111-117 (15). It is evident that an increase in asymmetry is translated into a decrease in number of neutrons emitted. This result was predictable from the lower value of dZpldE and is in accord with the hypothesis that highly asymmetric splits are induced by low-deposition energy cascades. It is true that, in the calculations, average excitation energies were used to determine the number of post-fission neutrons. However, the calculation then overestimates the number of emitted neutrons and does not modify the conclusions drawn from the experimentally-observed variation of dZ° with energy. Acknowledgements--The authors wish to express their thanks to Dr. S. K. T. Mark, Director of the Foster Radiation Laboratory. McGill University, for his read', co-operation and to Mr. R. H. Mills for operating the cyclotron. REFERENCES

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