238U Photofission in the Energy Region of the Giant Dipole

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ISSN 1063-7788, Physics of Atomic Nuclei, 2014, Vol. 77, No. 7, pp. 824–833. c Pleiades Publishing, Ltd., 2014. Original Russian Text c B.S. Ishkhanov, A.A. Kuznetsov, 2014, published in Yadernaya Fizika, 2014, Vol. 77, No. 7, pp. 871–881. NUCLEI Theory

238UPhotoﬁssion in the Energy Region of the Giant Dipole Resonance B. S. Ishkhanov1), 2)* andA.A.Kuznetsov2)** Received August 14, 2013; in ﬁnal form, January 24, 2014

Abstract—238Uphotofission is studied in the region of nuclear excitation energies that extends up to 20 MeV. Independent photofission-fragment yields and cumulative photofission-fragment yields after the emission of fast neutrons are measured by gamma-spectroscopy methods. The mass distributions of photofission fragments are obtained at the endpoint bremsstrahlung energies of 19.5, 29.1, 48.3, and 67.7 MeV. A comparative analysis of the behavior of the symmetric and asymmetric modes of photon- induced fission as a function of the average excitation energy of the fissioning nucleus is performed. The integrated yield of 238Uphotofission is calculated, and the evaluated cross sections for photofission and for photoneutron reactions are discussed. DOI: 10.1134/S1063778814070084

1. INTRODUCTION a nucleus and perform a comparison with other studies where the authors performed the respective Investigation of the mass distribution of fission calculation. fragments furnishes important information about the Here, we analyze mass distributions on the basis dependence of the fission-barrier parameters on the of the multimode-fission model [1, 2], where one excitation energy of the fissioning nucleus, about the interprets a mass distribution as the sum of con- formation of fragment masses at the instant of the tributions of various fission modes—specifically, a break of the neck between fission fragments, about symmetric mode (SL) and two asymmetric modes the change in the potential-energy surface in re- (STI and STII) associated with an enhanced yield sponse to symmetric and asymmetric nuclear defor- of fission products featuring N =82 and N =88 mations, and about fission dynamics. From the mass neutrons. The predictions of the multimode-fission distribution of fission fragments, one can also deter- model were confirmed in experimental investigations mine the number of neutrons escaping from fission of mass distributions of fragments originating from fragments and its dependence on the fragment mass neutron- and proton-induced fission. A calculation and, hence, on the fragment excitation energy. of the contributions from various fission modes to Although photofission, along with neutron-indu- the mass distribution of photofission fragments was ced fission, has been studied for several decades, new performed in [3] at two accelerator energies. Without reliable data on the mass distributions of photofission quantitative calculations, the existence of contribu- fragments are necessary. First, this is because the tions from various fission modes was highlighted majority of experiments devoted to studying photofis- in [4]. In the present study, we perform for the first sion were performed in beams of bremsstrahlung time a simultaneous analysis and a comparison of photons. The use of different converter targets for the behavior of the symmetric and asymmetric modes producing photons in such experiments prevents a of photofission induced by bremsstrahlung photons comparison and an accurate interpretation of the in the region of excitation energies of the 238U results of experiments performed under different nucleus between 5 and 20 MeV. The results obtained conditions. These problems can partly be allevi- in this way are compared with the predictions of ated by using the concept of the average excitation the multimode-fission model for the dependence of energy of a nucleus irradiated with photons from individual fission modes on the excitation energy of the bremsstrahlung spectrum. In the present study, the fissioning nucleus. we calculate the average excitation energy for such

1)Moscow State University, Moscow, 119991 Russia. 2. EXPERIMENTAL PROCEDURE 2)Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, 119991 Russia. The induced-activity method in which the ra- *E-mail: [email protected] dioactivity of ﬁssion fragments formed in the target **E-mail: [email protected] under study upon its irradiation with a bremsstrah-

824 238U PHOTOFISSION IN THE ENERGY REGION OF THE GIANT DIPOLE RESONANCE 825 lung-photon beam from an accelerator is analyzed [5] is used to measure the yield of fragments originating e– Target under from 238Uphotofission. This method makes it pos- study sible to determine, in a single experiment, the yield Electron of several fission fragments in the chain of decay of accelerator Bremsstrahlung target Transportation of the nuclear isobars, and this improves substantially the irradiated target to the accuracy of the results. detector The experiment being discussed was performed in a beam of bremsstrahlung photons from the RTM- 70 racetrack microtron of the Skobeltsyn Institute Germanium γ spectrometer of Nuclear Physics at Moscow State University [6]. Electrons were accelerated to a maximum energy of Irradiated 70 MeV and were then used as an efficient source target of bremsstrahlung with a variable endpoint energy of photons in the range from 15 to 70 MeV [7]. A Fig. 1. Layout of the experimental setup used. target from a natural mixture of uranium isotopes was exposed to a beam of bremsstrahlung photons immediately upon decay. Depending on the way in generated by a braking target bombarded with a flux which a specific nucleus arose, it is possible to deter- of monochromatic electrons from an accelerator rated mine an independent or an cumulative reaction yield. to an energy T (see Fig. 1). The bremsstrahlung tar- The gamma-activation procedure makes it possible get 2.5 mm thick was manufactured from tungsten. to measure the yields of isotopes whose half-life is The target under study was prepared by sputtering longer than a few minutes. Therefore, one calcu- uranium onto an aluminum disk. Since the con- 238 lates the yields of photofission-fragment production centration (in percent) of U(99.27%)inanatural after the emission of fast neutrons. Experimental mixture of uranium isotopes is much higher than the 235 data on the charge distribution of fission fragments concentration of U(0.72%), all of the results given indicate that their most probable charge in the chain 238 below refer to U photodisintegration. The activity of decay of nuclear isobars is shifted by several units of photofission fragments stopped in the aluminum from the stablest nucleus toward neutron-rich nuclei. substrate was detected. Four irradiation runs at the It follows that, for the majority of the isotopes, the accelerated-electron energies of 19.5, 29.1, 48.3, and procedure used permits determining only the cumu- 67.7 MeV were performed. lative yield, which takes into account both the direct The residual-activity spectra of the irradiated ura- production of a specific nucleus in the fission process nium sample were measured by a detector from high- and its production via the decay of the whole chain of purity germanium with an efficiency of 30%.The parent nuclear isobars to it. The cumulative yield Y1 energy-resolution of the detector was 0.9 keV for the was calculated by the formulas photon-energy of 122 keV and 1.9 keV for the photon N10λ1 energy of 1.33 MeV. The detector was surrounded Y1 = − , (1) − e λ1t1 by lead and copper shields, whereby the background (1 ) conditions of the measurements were substantially S improved. The detection efficiency was determined N10 = − − − − , k (e λ1(t2 t1) − e λ1(t3 t1)) with the aid of 133Ba, 137Cs, 60Co, 241Am, and 152Eu 1 calibrations sources. All measurements started in where N10 is the number of radioactive nuclei at the approximately two minutes after the completion of instant of termination of irradiation; S is the photo- irradiation. The yields of various isotopes were cal- peak area over the measurement time; t1 is the irra- culated on the basis of an analysis of the spectra and diation time; t2 is the instant of start of the measure- measurement of the intensity of the peaks of total ment; t3 is the instant of completion of irradiation; λ1 absorption of photons emitted in the decay of product is the isotope-1 decay constant; k1 is a coefficient that radioactive isotopes [8]. is equal to the product of the detector efficiency, the addition coefficient, and the photon yield for cascade gamma transitions. 3. CALCULATION OF THE The independent daughter-nucleus yield, which is PHOTOFISSION-PRODUCT YIELD the number of nuclei of a specific isotope produced Nuclei produced upon fission are related to each directly upon fission, can be determined in those cases other by a decay chain. Each radioactive nucleus in where the yield of parent nuclear isobars is known. the chain may originate directly from the decay pro- The independent yield Y2 of the production of a nu- cess or arise via β− decays of parent nuclei produced cleusonlyviaphotofission is determined from the

PHYSICS OF ATOMIC NUCLEI Vol. 77 No. 7 2014 826 ISHKHANOV, KUZNETSOV cumulative yield Y1 of the production of the parent where ZF and AF are, respectively, the charge and nucleus by the formulas mass numbers of the fissioning nucleus; ZUCD is the most probable charge based on the assumption that λ2N20 Y2 = − (2) the ratio of the numbers of protons and neutrons in 1 − e λ2t1 − − light and heavy fission fragments is identical to that − λ1t1 − − λ2t1 − λ2(1 e ) λ1(1 e ) in the fissioning nucleus [11]; and ΔZp is the charge Y1 −λ t , (λ2 − λ1)(1 − e 2 1 ) polarization calculated on the basis of the systematics presented in [12]. The plus and minus signs S refer to, respectively, a light and the complementary N20 = −λ2(t2−t1) −λ2(t3−t1) heavy fragment, and ν and ν are the numbers k2(e − e ) L H − − − − of neutrons emitted by, respectively, a light and the N λ N λ (e λ1(t2 t1) − e λ1(t3 t1)) + 10 1 − 10 2 , complementary heavy fragment. These numbers can −λ (t −t ) −λ (t −t ) λ2 − λ1 λ2 − λ1 (e 2 2 1 − e 2 3 1 ) be estimated as [13] − where λ1 and λ2 are, respectively, the isotope-1 and νL =0.531ν +0.062(AL + 143 AF ), (5) isotope-2 decay constants; Y is the cumulative yield 1 − of isotope-1 production; Y2 is the independent yield of νH =0.531ν +0.062(AH 143), isotope-2 production via fission; and N and N are 10 20 where AH and AL, are respectively, the heavy- and the numbers of, respectively, nuclei 1 and nuclei 2 at light-fragment mass number and ν is the average the instant of completion of irradiation. number of fission neutrons. The yield of isotopes that have a given mass num- In [4, 14, 15], it was shown that, in the excitation- ber A can be determined as the cumulative yield of − energy region extending up to 30 MeV, the width of long-lived nuclei lying at the end of the chain of β the charge distribution is weakly dependent on the decays of isobaric nuclei with this mass number or excitation energy of the fissioning nucleus. For 238U as the sum of independent yields of nuclei having this photofission, the width of the charge distribution is mass number. The yield of isotopes having a given C ≈ 0.8 [15]. For 238U fission, the chain of decays mass number A is the total yield of nuclear isobars and the charge distribution of nuclear isobars with produced upon photofission. Because of the emission mass number A =97 are given in Figs. 2 and 3, of delayed neutrons, the sum of independent yields of respectively. One can see that, in order to determine isotopes in the decay chain is not exactly equal to the the total yield of nuclear isobars with mass number cumulative yield. The yields of individual photofission A =97,itissufficient to determine the cumulative products can be estimated with the aid of the charge yield of production of the zirconium isotope 97Zr in distribution—that is, with the aid of the dependence 40 the chain of decays of A =97isobaric nuclei. In the of the yields of individual photofission products on the 238 charge Z in the chain of nuclear-isobar decays. case of U fission at the accelerated-electron energy of 29.1 MeV, the relative cumulative yield measured experimentally for the production of this zirconium 97 ± 4. CHARGE DISTRIBUTION isotope is CY(40Zr)=0.130 0.004, while the inde- OF PHOTOFISSION PRODUCTS pendent yield of production of the respective niobium 97 ± The charge distribution of photofission products is isotope is IY(41Nb)=0.00057 0.00046. approximated by a Gaussian functions as [9] The systematics used to determine the charge distribution of fission fragments was compiled on the MY(A) 2 IY(A, Z)= √ exp[−(Z − Zp) /C]dZ, (3) basis of data on neutron- and proton-induced fission. πC Figure 4 shows the chain of decays of nuclear isobars where IY(A, Z) is the independent yield of the photofis- with mass number A = 134. The procedure used sion product that has given values of A and Z, makes it possible to determine the cumulative yield of 134 MY(A) is the total yield of isotopes that has this 52 Te nuclei and the independent yield of production 134 mass number, Zp is the most probable charge in the of 53 I nuclei via fission. In Fig. 5, the fractional 134 charge distribution, and C is the width of the charge independent yield of production of 53 I iodine nuclei distribution. is given as a function of the average excitation energy The most probable charge Zp in each chain of of the fissioning nucleus. The fractional independent isobaric nuclei can be calculated on the basis of the yield FIY(A, Z) is defined as the ratio of the inde- relations [10] pendent yield of production of nuclei belonging to a (A, Z) Z = Z ± ΔZ , (4) specificsort,IY , to the total yield of the decay p UCD p chain for the same mass number, MY(A)—that is, ZUCD =(ZF /AF )(A + νL,H), FIY(A, Z)=IY(A, Z)/MY(A). The maximum of the

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(3/2+)

97 3/2(+) 169.9 ms 36Kr 97 Rb β– 37 n

25.1 % + 1/2 426 ms n 97 β– 38Sr 0.005%

– <20% (27/2 ) IT >80% β– 142 ms

+ (9/2) – 1.17 s IT <0.7% β (1/2–) 0 3.75 s 97 β– n 39Y 0.055% (3.75 s) <0.08% (1.17 s) 1/2+ 16.91 h 97 β– 40Zr IT 1/2– 743.35 52.7 s 9/2+ 0 72.1 min 97 β– + 41Nb 5/2 97 42Mo

Fig. 2. Chain of decays of isobaric nuclei whose mass number is A =97[16]. charge distribution at a low excitation energy in the in photofission decreases exponentially as soon as chain of isobaric nuclei with mass number A = 134 the endpoint energy of the bremsstrahlung spectrum 134 corresponds to the even–even magic nucleus of 52 Te. becomes higher than 10 MeV. In response to the increase in the excitation energy Nuclear fragments formed as the results of fission of the 238U nucleus from 6 to 16 MeV, the fractional are highly neutron-rich objects. Therefore, they are independent yield of production of the odd iodine iso- unstable against β− decay. In the case where the ex- 134 − tope 53 I grew by a factor of 2.5 from 10 to 25% of citation energy of the nucleus formed upon β decay the mass yield of production of A = 134 nuclei. Small is higher than the neutron-separation energy, delayed deviations from the charge distribution are observed neutrons escape from fission fragments. For different because of the even–odd effect in fission—that is, chains of isobaric nuclei, the number of delayed neu- because of an enhanced yield of products containing trons is markedly different. The number of delayed an even number of protons or neutrons. As was neutrons can be assessed by evaluating the convo- shown in [4], the magnitude of the even–odd effect lution of the charge distribution and the probability for the emission of a delayed neutron in the decay of

aspecific nucleus. After the emission of a delayed FY(Z) (per 100 fission events) Efiss, MeV 1.5 175 neutron, the nucleus being considered becomes a link of a different, A = A − 1, mass chain of β− decays. 170 This entails an increase in the measured cumulative yield of the A = A − 1 chain and, accordingly, its 1.0 165 decrease for the A chain. In deriving the total mass yields, we have therefore taken into account in the 160 present study the contributions of delayed neutrons. 0.5 155 5. RESULTS AND DISCUSSION 0 150 The cross sections for photoneutron reactions in 35 36 37 38 39 40 41 42 the energy range extending up to 20 MeV were mea- Z sured in several experiments [19, 20]. Figure 6 shows the cross sections for 238Uphotofission induced by Fig. 3. Charge distribution of 238Uphotofission prod- beams of monochromatic photons [19, 20], evaluated ucts with mass number A =97 at the accelerated- cross sections [21], and cross sections calculated with electron energy of 29.1 MeV: (closed boxes) independent yield (IY), (open triangles) cumulative yield of isotope the aid of the TALYS code [22]. In the total pho- production (CY), and (closed circles) reaction energy. toabsorption cross section [19] σ(γ,tot), one can see

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134 β– 49In

65% 0+ 1.12 s n 134 β– 50Sn 17% (7–) 10.23 s 0.091% (10.23 s) β– n (0–) 0.78 s 134 51Sb β– 0+ 41.8 min 134 – 52Te β 2.3% (8)– IT 316.4997.7% β– 3.60 min (4)+ 0 52.5 min 134 53I β– 7– IT1965.5 290 ms 0+ 0 134 54Xe

Fig. 4. Chain of decays of isobaric nuclei with mass number A = 134 [16]. two maxima, at E(1) = 10.77 MeV and at E(2) = nels of the (γ,F)=(γ,fiss)+(γ,n fiss) fission re- 13.80 MeV. The splitting of the giant resonance into action. The photofission reaction was pinpointed two maxima is due to the ground-state deformation by detecting signals from three or more neutrons in of the 238U nucleus. The first and second maxima coincidence. Because of problems associated with manifest themselves primarily in, respectively, the neutron-multiplicity sorting, different partial cross (γ,n) and the (γ,2n) reaction channel. In exper- sections of photoneutron reactions were obtained in iments with beams of monochromatic photons [19, different laboratories. Such a situation around cross 20], the separation of the (γ,n) and (γ,2n) reac- sections for photonuclear reactions accompanied by tion channels was based on an analysis of delayed- neutron emission was observed for a large set of tar- neutron energy spectra measured by the coincidence get nuclei. Figure 6 displays a glaring discrepancy method at various distances from the target being between the experimentally measured cross sections, studied. The same method was used to detect chan- as well as between them and the cross sections calculated theoretically. Photofission cross sections can be determined directly by detecting fission fragments FIY(134I) as such. 0.30 The gamma-activation procedure makes it pos- 0.25 sible to determine the relative yields of the reaction 238U(γ,n)237U and the reaction of 238Uphotofis- 0.20 sion. The ratio of the total yield of the reaction 238U(γ,F) to the yield of the reaction 238U(γ,n)237U 0.15 provides information about the ratio of the integrated 0.10 cross sections for these reactions induced by photons of the bremsstrahlung spectrum. Within the 0.05 gamma-activation procedure, each fission product is accurately identified by the respective gamma-ray 0 5 10 15 20 lines. In contrast to the case of the detection of 〈E (T)〉, MeV delayed neutrons and their multiplicity sorting, there exc are no ambiguities here. However, systematic ef- Fig. 5. Fractional independent yield (FIY) of the pro- fects associated with determining the shape of the 134 bremsstrahlung spectrum are possible. The average duction of 53 I iodine nuclei as a function of the average excitation energy of the 238U nucleus according to (open excitation energies Eexc of the fissioning nucleus, the triangles) [17], (open boxes) [18], and (closed circles) our ratios Yγ,F /Yγ,n of the yields of photofission and the present study and (open circles) according to calculations photoneutron reaction according to the evaluated da- based on the systematics from [12]. ta from [21], and the ratios Yγ,F /Yγ,n obtained in our

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σ, mb 180

120

0 5 10 15 20 25 Eγ, MeV

Fig. 6. Cross sections for 238Uphotofission that were measured in experiments reported in (open triangles) [19] and (open boxes) [20], (closed diamonds) evaluated cross sections from [21], and (dashed curves) cross sections calculated with the aid of the TALYS code [22]. present study are given in Table 1 versus the endpoint was taken from evaluated nuclear data [21]. The energy T of the bremsstrahlung spectrum. bremsstrahlung spectrum was calculated with the aid In order to compare the fission-product yields ob- of the GEANT4 code [23]. tained under different irradiation conditions, we made Table 1 shows that the ratios of the yields de- use of the concept of the average excitation energy of termined in the present study agree well with the the fissioning nucleus. In the case of bremsstrahlung yields obtained on the basis evaluated nuclear data photons, the average excitation energy of the fission- from [21]. With the aid of bremsstrahlung-photon ing nucleus, Eexc(T ), was calculated by the formula beams, one can measure the dependence of cross sections for photonuclear reactions on the accelerated- T 0 EN(T,E)σγ,F (E)dE electron energy, and this permits estimating inte- Eexc(T ) = , (6) T N(T,E)σ (E)dE grated reaction yields and testing cross sections mea- 0 γ,F sured by different methods and with the aid of different where N(T,E) is the number of bremsstrahlung pho- sources. tons of energy E at the accelerated-electron energy From an analysis of the yields of fission prod- T and σγ,F (E) is the photofission cross section at ucts, we obtained mass distributions of photofission the photon energy E.Thephotofission cross section products at four values of the endpoint energy of the bremsstrahlung spectrum: T =19.5, 29.1, 48.3, and 67.7 MeV. By way of example, Fig. 7 shows the Table 1. Average excitation energy Eexc(T ) of the fis- mass distribution of fission fragments at one of these sioning nucleus versus the accelerated-electron-beam en- values, 29.1 MeV. Table 2 gives mass yields per 100 ergy, ratio Yγ,F /Yγ,n of the integrated yields of the reac- fission events at four accelerator energies. In order to tion of 238Uphotofission and the photonuclear reaction obtain these mass distributions of fission fragments, accompanied by the emission of one neutron according we have analyzed 40 chains of decays of isobaric nu- to evaluated data from [21], and values obtained in our clei produced in the fission process. The yield of each present study for this ratio versus the average excitation isotope was determined from the maximum number of energy Eexc(T ) of the nucleus gamma transitions [24]. An analysis of mass distributions provides a vast Y /Y Y /Y T ,MeV Eexc(T ) , γ,F γ,n γ,F γ,n body of information about the fission process, in- MeV [21] (our study) cluding photofission cross sections, the number of 19.5 11.9 ± 0.3 0.583 0.547 ± 0.034 fast fission neutrons, the ratio of the symmetric- and asymmetric-fission yields, and the magnitude of the 29.1 13.7 ± 0.3 0.743 0.748 ± 0.046 even–odd effect. Analyzing mass distributions, we 48.3 14.4 ± 0. 0.789 0.724 ± 0.046 can determine the branching ratios for various fission ± ± modes, and this provides information as to how the 67.7 15.6 0.3 0.836 0.838 0.047 fissioning nucleus traverses the fission barrier.

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FMY(A) (per 100 fission events) the reaction involving the emission of one neutron. 7 At high energies, the reaction channel in which the 6 emission of one neutron is followed by the fission of a nucleus with mass number A − 1 becomes open. 5 The threshold for fission preceded by the emission of 238 4 one neutron from the U nucleus is 12 MeV [19]. After neutron emission, there occurs the fission of the 3 237U product nucleus, which has the lower excitation 2 energy 237 238 − bind 238 − 1 Eexc( U)=Eexc( U) En ( U) Tn, (7) 0 bind 238 80 100 120 140 160 where En is the neutron binding energy in the U A nucleus and Tn is the kinetic energy of the emitted neutron. In the multimode-fission model, the mass dis- Fig. 7. Approximation by five Gaussian functions for the tribution is interpreted as the sum of the contri- mass distribution of fragments originating from 238U fission induced by bremsstrahlung photons whose endpoint butions from the symmetric and asymmetric fission energy is 29.1 MeV: (points) experimental data, (dashed modes. Each fission mode corresponds to the passage curve) STI asymmetric component, (dash-dotted curve) through the fission barrier of specificshape.For STII asymmetric component, (thin solid curve) SL (sym- each fission mode, the yield is described in the form metric) component, and (thick solid curve) total mass of a Gaussian function. However, it is impossible yields FMY(A) per 100 fission events. to approximate the shape of the mass distributions by using only three Gaussian functions (two fission In the multimode-fission model [1, 2], the resulting modes). For this, one needs five Gaussian functions mass distribution of fission fragments is treated as the (three fission modes). In addition to broad maxima at result of the competition between collective modes, A ≈ 139 and A ≈ 96, the mass distribution exhibits which leads to asymmetric and symmetric disintegra- narrower maxima in mass-number regions around tion into fragments. Starting from the first studies A = 134 and A = 101. Asymmetric fission modes devoted to the fission of nuclei, the mass distribution are associated with the N =82and N =88neutron was interpreted as a superposition of the contribu- shells of fragments for, respectively, the STI and the tions from two fission modes, symmetric and asym- STII mode. metric [25]. The ratio of asymmetric- and symmetric- The total yield of fragments whose mass number is fission yields (peak/valley) is defined as the ratio of A is given by the expression the yields of nuclear isobars at the maximum and Y (A)=Y (A)+Y (A)+Y (A) (8) minimum of the mass distribution of fission frag- SL STI STII ments. The results of various experiments [14, 26– (A − A¯ )2 = K exp − SL 30] for the symmetric and asymmetric fission modes SL 2σ 2 SL in bremsstrahlung-photon beams are shown in Fig. 8 − ¯ − 2 versus the average excitation energy of the fissioning (A ASL DSTI) + KSTI exp − nucleus. The results obtained in our present study 2σ2 STI comply with the general trend toward the enhance- (A − A¯ + D )2 ment of the symmetric mode as the excitation energy + K exp − SL STI STI 2σ2 grows. The symmetric mode becomes three to four STI ¯ 2 times stronger with respect to the asymmetric mode (A − ASL − DSTII) 238 + K exp − as the average excitation energy of the U nucleus STII 2σ2 increases from 12 to 16 MeV. This complies with STII (A − A¯ + D )2 the idea that the role of shell effects becomes less + K exp − SL STII , pronounced as the excitation energy of nuclei grows. STII 2 2σSTII The ratio of the asymmetric- and symmetric- fission yields decreases exponentially in the excitation- where the Gaussian function parameters KSL, KSTI, energy range from 6 to 12 MeV,whereupon (at higher and KSTII and σSL, σSTI,andσSTII are, respectively, energies) this ratio remains virtually unchanged. The the amplitudes and widths of the symmetric (SL) and ¯ reason behind this behavior is that, at low excitation two asymmetric (STI and STII) fission modes; ASL energies of the nucleus being considered, it may is the most probable mass value for the symmetric ¯ ¯ either undergo fission or become a participant of fission mode; ASL − DSTI and ASL + DSTI are the

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Table 2. Mass distribution for 238Uphotoﬁssion (per 100 ﬁssion events)

Y (A) ± dY (A) A T =19.5 MeV T =29.1 MeV T =48.3 MeV T =67.7 MeV 84 0.62 ± 0.15 0.79 ± 0.19 0.44 ± 0.13 1.14 ± 0.32 85 1.21 ± 0.08 1.13 ± 0.07 1.01 ± 0.03 1.33 ± 0.06 87 1.70 ± 0.10 1.58 ± 0.10 1.31 ± 0.09 1.66 ± 0.13 88 1.99 ± 0.09 2.07 ± 0.07 1.94 ± 0.06 2.08 ± 0.11 89 3.54 ± 0.49 2.49 ± 0.27 2.49 ± 0.34 3.25 ± 0.49 91 4.69 ± 0.07 4.36 ± 0.11 4.49 ± 0.08 3.98 ± 0.13 92 5.17 ± 0.34 5.14 ± 0.28 4.68 ± 0.17 4.86 ± 0.20 93 5.15 ± 0.22 5.27 ± 0.39 5.08 ± 0.29 5.31 ± 0.46 94 5.36 ± 0.51 5.45 ± 0.46 5.71 ± 0.69 97 5.64 ± 0.13 5.68 ± 0.16 5.88 ± 0.55 5.73 ± 0.12 99 5.83 ± 0.05 6.01 ± 0.08 5.89 ± 0.03 5.54 ± 0.06 101 5.82 ± 0.69 5.93 ± 0.46 5.90 ± 0.40 5.59 ± 0.52 104 3.38 ± 0.26 3.57 ± 0.21 3.12 ± 0.22 3.62 ± 0.33 105 2.88 ± 0.10 2.90 ± 0.12 2.59 ± 0.14 3.09 ± 0.13 107 1.08 ± 0.14 1.01 ± 0.12 1.06 ± 0.14 1.62 ± 0.30 112 0.21 ± 0.04 0.40 ± 0.07 0.64 ± 0.14 0.64 ± 0.08 113 0.21 ± 0.08 0.43 ± 0.17 0.52 ± 0.12 0.57 ± 0.22 115 0.22 ± 0.09 0.46 ± 0.07 0.57 ± 0.04 0.58 ± 0.06 117 0.33 ± 0.06 0.48 ± 0.09 0.61 ± 0.08 0.70 ± 0.08 123 0.32 ± 0.04 0.48 ± 0.05 0.43 ± 0.05 0.77 ± 0.08 127 0.65 ± 0.09 1.06 ± 0.28 1.07 ± 0.09 0.92 ± 0.10 128 0.90 ± 0.12 1.16 ± 0.10 1.10 ± 0.12 1.05 ± 0.12 129 1.34 ± 0.09 1.52 ± 0.12 1.42 ± 0.08 1.45 ± 0.12 130 2.19 ± 0.13 131 3.83 ± 0.12 3.18 ± 0.14 3.82 ± 0.07 3.72 ± 0.11 132 5.04 ± 0.05 4.56 ± 0.06 5.08 ± 0.04 4.87 ± 0.06 133 6.61 ± 0.15 6.29 ± 0.15 6.30 ± 0.17 5.82 ± 0.25 134 6.85 ± 0.28 6.64 ± 0.26 6.51 ± 0.12 6.30 ± 0.47 135 6.33 ± 0.15 6.33 ± 0.18 5.82 ± 0.11 6.07 ± 0.41 138 5.77 ± 0.46 5.97 ± 0.32 5.82 ± 0.44 139 5.99 ± 0.14 5.94 ± 0.13 5.38 ± 0.22 5.69 ± 0.18 140 5.71 ± 0.41 5.26 ± 0.55 5.43 ± 0.22 5.29 ± 0.57 141 4.89 ± 0.26 5.22 ± 0.21 5.24 ± 0.38 142 4.87 ± 0.41 4.87 ± 0.32 4.35 ± 0.14 4.49 ± 0.55 143 4.51 ± 0.08 4.21 ± 0.09 3.34 ± 0.06 4.18 ± 0.11 146 3.27 ± 0.37 2.97 ± 0.23 2.49 ± 0.24 3.28 ± 0.36 149 1.24 ± 0.11 1.41 ± 0.20 1.09 ± 0.14 1.24 ± 0.23 151 0.73 ± 0.12 0.56 ± 0.10 0.59 ± 0.11 0.46 ± 0.10

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p/ Ymode, % 103 103

Jacobs [14], Schmitt [26] Present work Naik [27], Jacobs [28] 2 Jacobs [29], Chattopadhyay [30] 10 102

101

101 100

100 10–1 5 10 15 20 25 5 10 15 20 25 〈 〉 〈 〉 Eexc(T) , MeV Eexc(T) , MeV

Fig. 8. Ratio of the asymmetric- and symmetric-fission Fig. 9. Contributions of various fission modes (Ymode) yields (p/v)for238Uphotofission as a function of the to the mass distribution in 238Uphotofission versus average excitation energy Eexc(T ) of the fissioning nu- the average excitation energy of the fissioning nucleus cleus. (Eexc(T )): (open triangles, boxes, and circles) contributions of, respectively, the STII, STI, and SL fission modes according to calculations on the basis of the mass most probable masses of a light and the complemen- distribution from [14] and (closed triangles, boxes, and circles) respective fission-mode contributions calculated tary heavy fragment in the STI asymmetric fission on the basis of the mass distribution obtained in our ¯ ¯ mode; and ASL − DSTII and ASL + DSTII are the most present study. The yields of the modes were normalized probable masses of a light and the complementary to 100 fission events: YSL + YSTI + YSTII = 200%. heavy fragment in the STII asymmetric fission mode. The dependences of the contributions of the var- 6. CONCLUSIONS 238 ious modes to the photofission of the isotope U From our investigation, we have derived the inde- on the excitation energy of its nucleus were obtained pendent and cumulative yields of isotopes produced for the first time. In order to analyze the fission upon the fission of the isotope 238U. We have per- modes, we used data obtained in the present study formed a detailed analysis of the production of each and in [14]. Figure 7 shows the approximation of nuclear isobar via fission and obtained the mass dis- the mass distribution by five Gaussian functions for tributions of products originating from the photofis- the case of 238U fission induced by bremsstrahlung sion induced by bremsstrahlung photons at four val- photons whose spectrum has the endpoint energy of ues of the accelerated electron energy. We have 29.1 MeV. shown that, as the excitation energy of the 238Unu- cleus grows from 6 to 16 MeV, the role of shell effects Three fission modes were discovered in all of the becomes less significant. measured mass distributions. The contributions of the various fission modes (areas under the respective A simultaneous analysis and a comparison of the Gaussian curves) are shown in Fig. 9 versus the ex- behavior of the symmetric and asymmetric modes of 238 citation energy of the 238U nucleus. A simultaneous U fission induced by photons were performed for analysis of available data reveals that the contribution the first time. The dependence of the contributions of of the mode responsible for symmetric fission to frag- the three fission modes on the excitation energy of the 238 ments grows rather fast as the excitation energy of the U nucleus was obtained for the first time as well. 238U nucleus becomes higher. The contribution of the STI asymmetric mode, which is associated with REFERENCES the N =82 spherical neutron shell, decreases fast. 1. U. Brosa, S. Grossmann, and A. Muller,¨ Phys. Rep. The contribution of the STII asymmetric mode, which − 197, 167 (1990). is associated with the N =86 88 deformed neutron 2. M. C. Duijvestijn, A. J. Koning, and F.-J. Hambsch, shell, remains virtually unchanged. Our results also Phys. Rev. C 64, 014607 (2001). confirm the behavior of the fission barriers for the var- 3. N. A. Demekhina and G. S. Karapetyan, Phys. At. ious fission modes at various compound-nucleus ex- Nucl. 71, 27 (2008). citation energies [1, 2] that was obtained from data on 4. S. Pomme,´ E. Jacobs, K. Persyn, et al., Nucl. Phys. A the neutron-induced fission of the isotope 238U [12]. 560, 689 (1993).

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