Mass Yield Distributions and Fission Modes in Photofission of 238U

238 1 Mass yield distributions and ﬁssion modes in photoﬁssion of U below 20 MeV

2 S. S. Belyshev, B. S. Ishkhanov, A. A. Kuznetsov, and K. A. Stopani 3 Lomonosov Moscow State University, Department of Physics, 4 Skobeltsyn Institute of Nuclear Physics, Moscow, 119991 Russia 5 (Dated: February 17, 2015)

238 6 Photon activation technique is used to obtain photofission mass distributions of U after ir- 7 radiation in a bremsstrahlung beam with end-point energies 19.5, 29.1, 48.3, and 67.7 MeV. The 8 weights of the symmetric (SL) and asymmetric (STI and STII) modes in the mass distributions of 238 235,238 9 photofission of U and neutron-induced fission of U at the average excitation energies of up 10 to 20 MeV are calculated on the basis of the obtained results and other available data. The weight 11 of the SL mode increases by about an order of magnitude as the average excitation energy increases 12 from 8.5 to 17 MeV, while the weight of the STI mode decreases by 2 times, and the weight of 238 13 the STII mode slightly increases. It is shown that the peak-to-valley ratios in photofission of U 235 14 and neutron-induced fission of U are very close across almost the whole studied energy range. A 15 similar conclusion is made concerning the behavior of asymmetric and symmetric fission modes in 238 235 238 16 photofission of U and neutron-induced fission of U and U.

17 I. INTRODUCTION

18 Fission is one of the most studied nuclear processes. However, there are still areas where new and reliable data 19 are needed both for fundamental nuclear science and applied developments. One of these areas is the problem 20 of accurate model description of fragment mass distributions in photon-induced fission, or photofission. Among 21 the examples of its practical importance one can name subcritical nuclear reactor designs (accelerator driven 22 systems), that rely on the spallation reaction triggered by high energy protons [1, 2], and a gamma-ray emission, 23 which often follows this reaction, can trigger photofission and affect functioning of the reactor. Another possible 24 practical application is the transmutation and re-processing of nuclear waste in photonuclear reactions using 25 high-intensity photon beams where the photofission process also plays an important role [3, 4]. Availability of 26 reliable data on cross sections and mass distributions of photofission is also desirable for development of highly 27 intense impulse sources of fast neutrons based on electron accelerators [5, 6]. 28 Since full experimental data are not available in the whole range of nuclear masses and photon energies, model 29 simulations are often used in practical applications [7, 8]. For the purpose of refinement of numeric calculations 30 the most important experimental input for the models comes from the parameters of the fission barrier at 31 different excitation energies. The primary source of this information are distributions of fission fragments, 32 which directly reflect the stage of formation of the fragment masses, as well as the behavior of the potential 33 energy surface under symmetric and asymmetric nuclear deformations which ultimately result in fission. 34 Theoretical calculations of the potential energy surface in the multi-dimensional deformation space during 35 fission show that the transition from the initial excited state to the point of scission into two fragments can 36 be accomplished along several different trajectories, corresponding to distinct valleys on the potential energy 37 surface [9, 10]. Each of these trajectories forms a fission barrier, which is double-humped in the case of actinide 38 nuclei. Within the multimodal fission model (MM-RNRM [9]) the potential energy valleys correspond to fission 39 modes and the resulting mass distribution is understood as a sum of contributions from three different fission 40 modes: the symmetric SL mode and the asymmetric modes STI and STII. The contribution of each mode is 41 determined by the probability of tunneling through the potential barrier of the particular mode, and, hence, 42 on the shape and height of the barrier, the number of transition states, and their energies above the barrier. 43 Predictions of the multimodal model agree with the experimental mass distributions of neutron- and proton- 44 induced fission. The main factor determining the shape of the fission barrier of asymmetric modes in the 45 model [9] is the nuclear shell structure, in the form of the shell corrections [11]. The amount of shell effects 46 depends on the nuclear temperature during fission [12], and the temperature dependence is introduced by means 47 of the so-called shell effects damping function. Exponential damping of the shell effects, which is considered 48 in [13], leads to gradual vanishing of the asymmetric modes at higher excitation energies and the rate of damping 49 is determined by the damping energy parameter E0 ≈ 15 MeV. Based on the analysis of charge distributions of 50 fission fragments a different value is suggested in [14], E0 ≈ 60 MeV. 51 The shape and the width of the valley on the potential energy surface between the second saddle point and the 52 point of scission into fragments affect the stiffness (and, thus, the width of the distribution) of the corresponding 53 fission mode, and, therefore, can be analyzed using the fragment distributions. In neutron-induced fission the 54 properties of fission modes were studied for the actinide nuclei in [15]. Systematic relationships for yields of 55 fission products in neutron- and proton-induced fission of heavy nuclei and a parameterization of fission product 56 yields as a function of the fissioning nucleus and the excitation energy were obtained in [16]. 57 A consistent description of the dependence of the fission modes on the excitation energy in photofission has 58 not yet been published. There are only few works where contributions of different components of the mass 59 distributions were estimated. Contributions of fission modes in the mass distribution were calculated in [17] at 2

60 two energies of the electron accelerator (50 MeV and 3.5 GeV). The presence of different fission modes is pointed 61 at in [18], though no quantitative estimates are given. Contributions of the fission modes were estimated in [19] 62 using bremsstrahlung photons with end-point energies from 6 to 10 MeV. 238 63 In the present work the photon activation technique is used to measure photofission mass distributions of U 64 using bremsstrahlung with end-point energy 19.5, 29.1, 48.3, 67.7 MeV. Using the obtained results and available 65 data from other works [17, 18, 20–22] the relative contributions of fission modes in the excitation energy range 238 66 from 8.5 to 17 MeV are obtained. The behavior of photofission modes of U is compared to the behavior of 235 238 67 the modes of the neutron-induced fission of U from [15, 23, 24] and U from [24, 25] and the results of the 238 68 systematics [16] for neutron-induced fission of the U compound nucleus.

69 II. EXPERIMENTAL TECHNIQUE

70 A. Experimental setup

238 71 The photon activation technique was used to measure photofission fragment yields from U. The experi- 72 mental setup and the data analysis procedures are described in [26–29]. The experiment was performed using 73 bremsstrahlung radiation produced by the 70 MeV race-track microtron of the Skobeltsyn Institute of Nuclear 74 Physics of the Moscow State University [30] at the electron energies T = 19.5, 29.1, 48.3, and 67.7 MeV. A −2 75 0.2-mm-thick aluminum disk (100 mm in diameter), onto which a 1-mg cm -thick film of natural uranium 76 was deposited, was used as a target. The target was irradiated by bremsstrahlung radiation produced by the 77 electron beam. A 2.2-mm-thick tungsten target was used as a bremsstrahlung converter. Each irradiation took 78 3 ÷ 7.5 hr at the average beam current of about 10 nA. After each irradiation series of gamma-ray spectra of 79 induced activity were measured using an HPGe detector with relative efficiency 30% and energy resolution of 80 0.9 keV at 122 keV, 1.9 keV at 1.33 MeV. Each series of spectrum acquisitions was started within 2 min after 81 the corresponding irradiation and lasted for several days to several weeks. After acquisition the spectra were 82 analyzed and yields of different isotopes were calculated from the time dependence of the peak areas.

83 B. Data analysis

84 The nuclei produced as a result of fission are interconnected by chains of decays. Each unstable nucleus can − 85 be produced both in fission and as a result of β -decays of other members of the chain. The activation technique 86 allows to measure the yields of isotopes with half lives of several minutes and greater. Thus, only fragment 87 yields after prompt neutron emission are obtained. For majority of the isotopes the employed technique allows 88 to determine only the cumulative yield, which includes its production both in fission and in decays of the whole 89 chain of the parent isobar nuclei. 90 The cumulative yield of a fission fragment Ycum was calculated using the following expression:

N0λ Ycum = , (1) (1 − e−λtrad )

91 where λ is the decay constant, trad is the duration of the irradiation, and N0 is the number of the nuclei in 92 the target at the end of the irradiation. N0 was determined from the areas of corresponding photopeaks in the 93 measured gamma-ray spectra: S 1 N0 = , (2) k e−λ(t1−trad) − e−λ(t2−trad)

94 where S is the area of the peak, summed over the measured spectra, t1 and t2 denote the times when the 95 measurement started and ended, k is a coefficient equal to the product of the detector efficiency at the peak’s 96 energy, the relative intensity of the spectral line, and the true coincidence correction factor. Generally, for 97 different peaks of the same decaying fragment the yields were obtained in this way independently, and a weighted 98 average was calculated subsequently. Two typical spectra of the uranium target after irradiation at T = 99100 29.1 MeV with corresponding photopeaks of fission fragments are shown in Fig. 1. 101 When the independent yield could be calculated (i.e., the decays of parent nuclei of the chain were visible 102 in the spectra), the differential equations describing accumulation and decay of the mass chain elements were 103 analytically solved, and the resulting solutions were used to fit the experimental decay curves. As an example 104 we show the expressions, that were used to obtain independent yields for chain with 3 elements, described by a 105 decay scheme “isotope 1 → isotope 2 → isotope 3”:

−λ1t −λ2t λ2N20 λ2(1 − e rad ) − λ1(1 − e rad ) Y2 = −λ t − Y1 −λ t , (3) 1 − e 2 rad (λ2 − λ1)(1 − e 2 rad ) 3 I Nb Zr 95 m 135 95 Nb Pa I 97 Zr

10000 I Te+ 97 234 134 Sb 132 m 134 Ru + I La 128 I+ Te 105 134 142 I Sr 134 133 Sr 91 Ru 132 Sb+ I 91 m Sr Y Y 105 743 keV 658.1 keV I 129 91 132 92 I 1001 keV Te Sb + + Sb 847.0 keV 134 Kr + 836.8 + keV Kr 135 133 129 88

1000 724.4 keV 884.1 keV 641.3 keV Sr + 954.5 + keV Sr 766.5 keV 92 667.7 keV 1024.3 keV 749.8 keV 676.4 keV 812.8 keV 652.6 keV 772.6 keV 934.4 keV 914.6keV 1072.5 keV 912.7 keV 834.8 keV 1038.8 keV 953.3 keV

100 Counts

600 700 800 900 1000 1100

Energy (keV)

Figure 1. (Color online) Gamma-ray spectra of induced activity of uranium target after irradiation at T = 29.1 MeV, summed over 10 hours. From top to bottom: (1) measurement 1 hr after irradiation; (2) measurement 3 days after irradiation.

106 where Y2 is the independent yield of the second isotope of the chain, Y1 is the cumulative yield of the ﬁrst 107 isotope, obtained using Eq. (1), λ1 and λ2 are the corresponding decay constants, and N20 is the number of 108 nuclei of the second isotope at the end of the irradiation, which is determined as follows:

S N λ N λ (e−λ1(t1−trad) − e−λ1(t2−trad)) N = + 10 1 − 10 2 · , (4) 20 −λ (t −t ) −λ (t −t ) −λ (t −t ) −λ (t −t ) k2(e 2 1 rad − e 2 2 rad ) λ2 − λ1 λ2 − λ1 (e 2 1 rad − e 2 2 rad )

109 where N10 is the number of nuclei of the first isotope, which is obtained similarly to Eq. (2), and k2 is calculated 110 for the second isotope analogously to k. 111 By definition the mass yield YMY(A) is a sum of independent yields of all isotopes of the isobaric chain with 112 the given mass number A, or the cumulative yield of the long-lived isotope at the end of the chain. 113 Direct determination of the summed yield of fission fragments with a given mass number A from the sum 114 of yields of all elements of the mass chain was not possible (due to a very long- or short-lived decay, or due 115 to absence of detectable gamma lines), and the following procedure was used to estimate the mass yields from 116 the charge number distribution. The charge number distribution of photofission products with a given mass 117 number A can be approximated using the Gaussian function [31]:

2 YMY(A) − (Z−ZP ) YIY(A, Z) = √ e C , (5) πC

118 where YIY(A, Z)is the independent yield of the photoﬁssion product with the given A and Z, YMY(A) is the 119 mass yield of the isotopes with the mass number A, Zp is the most probable charge number of the nuclei from 120 the given mass chain, C is the width of the charge number distribution. The YMY(A) value was determined 121 from available independent and cumulative yields by normalizing the observed points to expression (5). 122 The most probable charge number Zp was calculated for each chain of isobar nuclei using the expressions [32]:

Zp = ZUCD ± ∆Zp,ZUCD = (ZF /AF )(A + νL,H ), (6)

123 where ZF = 92 and AF = 238 are the charge and mass numbers of the initial nucleus, ZUCD is the most probable 124 charge number, determined from the assumption that the ratio of neutrons to protons in ﬁssion fragments is the 125 same as in the initial nucleus [33], and the charge polarization ∆Zp was calculated from the systematics [16]. 126 The “+” and “−” signs denote, respectively, the heavy and the light fragments. νL and νH are the numbers 127 of prompt neutrons emitted from the light and heavy fragments, estimated as described in [34]. As shown in 4

0.3

I) 0.25 134 ( 0.2 FIY Y 0.15

0.1 Pommé 1993 De Frenne 1984 Fractional yield 0.05 Present work Systematics (Wahl 2002) 0 5 10 15 Average excitation energy 〈E*〉 (MeV)

134 238 Figure 2. Relative independent yield of the 53 I isotope as a function of the average excitation energy of U: (dots) present work; Pomm´e1993: [36]; De Frenne 1984: [37]; empty dots (Wahl 2002) represent relative independent yield of 134 the 53 I isotope calculated from the systematics [16] for neutron- and proton-induced ﬁssion.

128 works [21, 35, 36], for excitation energies less than 30 MeV the width of the charge number distribution shows 238 129 only a slight dependence on its value. For photofission of U the width of the charge number distribution 130 C ≈ 0.8 [35]. 131 An example of determination of fission fragment yields is shown in Fig. 2. Our technique allows to determine 134 134 132 the cumulative yield of the 52 Te isotope and the independent yield of the 53 I isotope. Figure 2 shows the relative 134 133 independent yield of the 53 I isotope as a function of the average excitation energy of the nucleus. By definition, 134 the fraction independent yield YFIY(A, Z) is equal to the isotope’s independent yield YIY(A, Z) normalized by 135 the total yield YMY(A) of the decay chain with the given mass number: YFIY(A, Z) = YIY(A, Z)/YMY(A). At 136 low excitation energies the most probable charge number of the mass chain with A = 134 corresponds to the 134 238 137 even magic 52 Te. As the excitation energy of U increases from 6 to 16 MeV the relative independent yield 134 138 of the odd iodine isotope 53 I increases by 2.5 times, from 10% to 25% of the total mass yield. The obtained 139 results are in agreement with the predictions of the systematics [16], which is based on the experimental data 140 on neutron- and proton-induced fission. 141 As the final step to obtain the mass yields one has to take into account the effect of delayed neutron emission. 142 Our technique allows to start measurements of the radioactivity of the fission products in about several minutes 143 after the irradiation. By this moment almost all delayed neutrons are already emitted, which results in a 144 shift of the cumulative yields. The number of emitted delayed neutrons depends on the particular mass chain. 145 The relative number of delayed neutrons can be estimated by folding the charge number distribution with the 146 probability of delayed neutron emission from a particular nucleus. The delayed neutron correction increases the 147 observed mass yield YMY(A) due to emission of delayed neutrons from the neighboring mass chain A + 1, while 148 emission of delayed neutrons by the A chain itself results in a decrease of the observed mass yield. X X ∆YMY(A) = YIYi(A + 1,Zi) · Wd(A + 1,Zi) − YIYi(A, Zi) · Wd(A, Zi), (7) i i

149 where Wd(A, Zi) is the probability of a delayed neutron emission by a given isotope (A, Zi), YIYi(A, Zi) is the 150 independent yield of the (A, Zi) isotope. 238 151 As a result of the analysis the mass distributions of fragments of photofission of U were obtained at four 152 values of the bremsstrahlung end-point energy T = 19.5, 29.1, 48.3, 67.7 MeV. The obtained mass yields are 238 237 153 normalized to the yield of the photoneutron reaction U(γ, n) U. 154 To compare the obtained fission product yields with results of other experiments the average excitation ∗ 155 energies of the initial nucleus were calculated. The average excitation energy hE i of the fissioning nucleus was 156 calculated using the following expression:

T R N(T,E)σγ,F (E)EdE hE∗(T )i = 0 , (8) T R N(T,E)σγ,F (E)dE 0

157 where N(T,E) is the bremsstrahlung photon spectrum, T is the electron accelerator energy (i.e., the end-point 158 energy of the bremsstrahlung spectrum), σγ,F (E) is the photoﬁssion cross section at the photon energy E. The 159 bremsstrahlung spectrum for each accelerator energy was calculated using the GEANT4 [38] package. The 5

Table I. Experimental mass yields in photoﬁssion of 238U. Relative mass yields are normalized to the yield of the 238 237 U(γ,n) U reaction at the corresponding energy. Fraction mass yields YFMY are given per 100 ﬁssion reactions, i.e. P YFMY = 200. A 3 10 × relative mass yield YMY/Y (γ, n) Fraction mass yield YFMY A 19.5 MeV 29.1 MeV 48.3 MeV 67.7 MeV 19.5 MeV 29.1 MeV 48.3 MeV 67.7 MeV 84 1.90 ± 0.45 2.94 ± 0.71 1.62 ± 0.49 5.01 ± 1.41 0.62 ± 0.15 0.79 ± 0.19 0.44 ± 0.13 1.14 ± 0.32 85 3.69 ± 0.25 4.18 ± 0.24 3.72 ± 0.10 5.81 ± 0.24 1.21 ± 0.08 1.13 ± 0.07 1.01 ± 0.03 1.33 ± 0.06 87 5.17 ± 0.32 5.86 ± 0.35 4.81 ± 0.32 7.27 ± 0.57 1.70 ± 0.10 1.58 ± 0.10 1.31 ± 0.09 1.66 ± 0.13 88 6.08 ± 0.67 7.69 ± 0.52 7.12 ± 0.79 9.13 ± 0.83 1.99 ± 0.22 2.07 ± 0.14 1.94 ± 0.22 2.08 ± 0.19 89 10.80 ± 1.50 9.25 ± 1.01 9.15 ± 1.26 14.25 ± 2.14 3.54 ± 0.49 2.49 ± 0.27 2.49 ± 0.34 3.25 ± 0.49 91 14.31 ± 1.59 16.17 ± 0.83 16.49 ± 0.30 17.44 ± 1.28 4.69 ± 0.52 4.36 ± 0.22 4.49 ± 0.08 3.98 ± 0.29 92 15.77 ± 1.03 19.06 ± 1.05 17.19 ± 0.62 21.32 ± 0.89 5.17 ± 0.34 5.14 ± 0.28 4.68 ± 0.17 4.86 ± 0.20 93 15.71 ± 2.50 19.55 ± 3.03 18.64 ± 1.06 23.30 ± 2.02 5.15 ± 0.82 5.27 ± 0.82 5.08 ± 0.29 5.31 ± 0.46 94 16.34 ± 1.55 20.24 ± 1.72 25.03 ± 3.03 5.36 ± 0.51 5.45 ± 0.46 5.71 ± 0.69 97 17.19 ± 0.40 21.07 ± 0.58 21.58 ± 2.04 25.11 ± 0.53 5.64 ± 0.13 5.68 ± 0.16 5.88 ± 0.55 5.73 ± 0.12 99 17.76 ± 0.14 22.31 ± 0.31 21.62 ± 0.12 24.31 ± 0.28 5.83 ± 0.05 6.01 ± 0.08 5.89 ± 0.03 5.54 ± 0.06 101 17.75 ± 2.11 22.01 ± 1.72 21.65 ± 1.48 24.51 ± 2.30 5.82 ± 0.69 5.93 ± 0.46 5.90 ± 0.40 5.59 ± 0.52 104 10.31 ± 0.79 13.24 ± 0.77 11.46 ± 0.81 15.87 ± 1.45 3.38 ± 0.26 3.57 ± 0.21 3.12 ± 0.22 3.62 ± 0.33 105 8.77 ± 0.54 10.75 ± 1.61 9.50 ± 0.51 13.57 ± 0.57 2.88 ± 0.18 2.90 ± 0.43 2.59 ± 0.14 3.09 ± 0.13 107 3.29 ± 0.42 3.73 ± 0.43 3.90 ± 0.52 7.11 ± 1.33 1.08 ± 0.14 1.01 ± 0.12 1.06 ± 0.14 1.62 ± 0.30 112 0.64 ± 0.11 1.61 ± 0.27 1.93 ± 0.31 2.79 ± 0.36 0.21 ± 0.04 0.43 ± 0.07 0.52 ± 0.09 0.64 ± 0.08 113 0.64 ± 0.09 1.61 ± 0.42 1.90 ± 0.45 2.50 ± 0.56 0.21 ± 0.03 0.43 ± 0.11 0.52 ± 0.12 0.57 ± 0.13 115 0.66 ± 0.12 1.72 ± 0.26 2.09 ± 0.36 2.54 ± 0.24 0.22 ± 0.04 0.46 ± 0.07 0.57 ± 0.10 0.58 ± 0.06 117 0.62 ± 0.13 1.77 ± 0.33 1.94 ± 0.28 2.70 ± 0.35 0.20 ± 0.04 0.48 ± 0.09 0.53 ± 0.08 0.62 ± 0.08 123 0.72 ± 0.09 1.79 ± 0.19 2.10 ± 0.17 2.99 ± 0.36 0.34 ± 0.03 0.48 ± 0.05 0.57 ± 0.05 0.68 ± 0.08 127 1.99 ± 0.27 3.93 ± 1.03 3.92 ± 0.32 4.04 ± 0.44 0.65 ± 0.09 1.06 ± 0.28 1.07 ± 0.09 0.92 ± 0.10 128 2.75 ± 0.36 4.30 ± 0.35 4.05 ± 0.44 4.60 ± 0.53 0.90 ± 0.12 1.16 ± 0.10 1.10 ± 0.12 1.05 ± 0.12 129 4.07 ± 0.53 5.63 ± 0.73 5.22 ± 0.63 6.34 ± 1.08 1.34 ± 0.17 1.52 ± 0.20 1.42 ± 0.17 1.45 ± 0.25 130 8.12 ± 1.36 2.19 ± 0.37 131 11.67 ± 1.47 11.79 ± 2.12 14.01 ± 1.26 16.31 ± 1.22 3.83 ± 0.48 3.18 ± 0.57 3.82 ± 0.34 3.72 ± 0.28 132 15.35 ± 0.15 16.94 ± 0.23 18.66 ± 0.14 21.36 ± 0.28 5.04 ± 0.05 4.56 ± 0.06 5.08 ± 0.04 4.87 ± 0.06 133 20.15 ± 0.46 23.36 ± 0.55 23.13 ± 0.64 25.52 ± 1.09 6.61 ± 0.15 6.29 ± 0.15 6.30 ± 0.17 5.82 ± 0.25 134 20.89 ± 0.86 24.65 ± 0.97 23.90 ± 0.44 27.62 ± 2.06 6.85 ± 0.28 6.64 ± 0.26 6.51 ± 0.12 6.30 ± 0.47 135 19.31 ± 0.46 23.50 ± 0.68 21.36 ± 0.39 26.61 ± 1.78 6.33 ± 0.15 6.33 ± 0.18 5.82 ± 0.11 6.07 ± 0.41 138 17.58 ± 1.39 22.17 ± 1.17 21.35 ± 1.60 5.77 ± 0.46 5.97 ± 0.32 5.82 ± 0.44 139 18.27 ± 0.42 22.04 ± 0.48 19.75 ± 0.82 24.95 ± 0.81 5.99 ± 0.14 5.94 ± 0.13 5.38 ± 0.22 5.69 ± 0.18 140 17.42 ± 1.24 19.51 ± 2.03 19.93 ± 0.81 23.22 ± 2.50 5.71 ± 0.41 5.26 ± 0.55 5.43 ± 0.22 5.29 ± 0.57 141 14.91 ± 2.09 19.37 ± 2.71 22.97 ± 1.66 4.89 ± 0.68 5.22 ± 0.73 5.24 ± 0.38 142 14.85 ± 1.78 18.08 ± 1.17 15.97 ± 0.50 19.70 ± 2.42 4.87 ± 0.58 4.87 ± 0.32 4.35 ± 0.14 4.49 ± 0.55 143 13.75 ± 0.25 15.64 ± 0.34 12.26 ± 0.24 18.33 ± 0.49 4.51 ± 0.08 4.21 ± 0.09 3.34 ± 0.06 4.18 ± 0.11 146 9.97 ± 1.14 11.02 ± 0.85 9.15 ± 0.88 14.37 ± 1.58 3.27 ± 0.37 2.97 ± 0.23 2.49 ± 0.24 3.28 ± 0.36 149 3.79 ± 0.33 5.23 ± 0.74 4.00 ± 0.51 5.45 ± 1.01 1.24 ± 0.11 1.41 ± 0.20 1.09 ± 0.14 1.24 ± 0.23 151 2.21 ± 0.37 2.08 ± 0.37 2.17 ± 0.39 2.02 ± 0.44 0.73 ± 0.12 0.56 ± 0.10 0.59 ± 0.11 0.46 ± 0.10

160 photoneutron and photofission reaction cross sections were measured in several experimental works [39–41]. We 161 used the evaluated photofission cross section from Ref. [42], which was obtained from the experimental cross 162 sections and which takes into account shortcomings of the neutron multiplicity sorting technique employed 238 163 in experimental measurements. It has been shown in [43] that under 20 MeV the fissility of U obtained 164 experimentally is in agreement with the one determined using the evaluation [42]. The procedure of calculation 165166 of the average excitation energy is illustrated schematically in Fig. 3. ∗ 167 The bremsstrahlung energies shown above correspond to the following average excitation energies: hE i = 168 11.9 ± 0.3, 13.7 ± 0.3, 14.4 ± 0.3, 15.6 ± 0.3 MeV.

169 III. DISCUSSION OF THE RESULTS

238 170 The fraction mass yield distributions YFMY(A) of photofission fragments of U per 100 photofission reactions, 171 defined as

YMY(A) YFMY(A) = 200 × P , (9) YMY

172 for the end-point energies of bremsstrahlung T = 19.5, 29.1, 48.3, 67.7 MeV are shown in table I. 6

100 180 )

-1 160 -1 10 140 120 10-2 100 80 10-3 60 Cross section (mb) 10-4 40 20 Bremsstrahlung spectrum (MeV 10-5 0 0 10 20 30 40 50 60 70 Photon energy (MeV)

Figure 3. (Color online) Evaluated cross section of the photoﬁssion reaction on 238U ([42], right axis) and simulated bremsstrahlung spectra at T = 19.5, 29.1, 48.3, 67.7 MeV (left axis) used to calculate the average excitation energies of photoﬁssion.

238 173 Figure 4 shows the same data in graphical form as a function of the average excitation energy of U. A 174 comparison of the obtained distributions with available photofission data from other works based on the activa- 175176 tion technique with similar electron beam energies is shown in Fig. 5. The shape of the final mass distributions 177 depends on competition of collective modes, which lead to either symmetric or asymmetric formation of fission 178 fragments [44, 45]. This behavior is a result of nuclear shell effects, which experience damping as the nuclear 179 excitation energy increases, and is often illustrated by the energy dependence of the peak-to-valley ratio, i.e. the 180 ratio between the maximum and the minimum of the mass distribution. Figure 6 shows the peak-to-valley ratio 181 p/v as a function of the average excitation energy obtained in this work and in [21, 22, 45–48] for photofission 238 235 238 182 of U, and in [24, 49] and [25, 50–55] for fission of, respectively, U and U, induced by monoenergetic 183 neutrons. 184 Since there is no standardized way of calculation of the peak-to-valley ratio, the values reported in the cited 185 works could not be used directly, and instead we re-analyzed the mass distributions from these works. Two 186 forms of the p/v ratios were calculated: (p/v)1 is the ratio of the average yield of A = 133 and A = 134 mass 187 chains to the average yield of the A = 115 and A = 117 mass chains; and (p/v)2 is the ratio of the A = 140 188 and the A = 115 mass chains (as the most commonly and reliably measured in majority of publications). 189 The results of the calculations are shown in Tables II, III and IV. In addition, for the sake of unification in 238 190 each case of photofission of U we re-calculated the average excitation energy according to Eq. (8), using the 191 bremsstrahlung spectra calculated with GEANT4 for the experimental parameters of each work. 192 As seen from Fig. 6, our results generally agree with the general tendency of increasing contribution of the 193 symmetric fission mode as the excitation energy increases. The value of the peak-to-valley ratio decreases 194 exponentially when the excitation energy increases in the range from approximately 6 to 15 MeV, but at higher 195 energies the ratio decreases less rapidly. This behavior can be explained by the fact that at lower excitation 196 energies only fission (γ, fiss) and neutron emission (γ, n) are possible, and as the energy increases the reaction 197 channel of neutron emission and subsequent fission (γ, n fiss) becomes open (the so-called second chance fission). 238 198 In [39] it has been shown that the energy threshold of the latter reaction in U is about 12 MeV. After emission 237 199 of a neutron the resulting U nucleus undergoes fission at a lower excitation energy:

∗0 237 ∗ 238 238 E ( U) = E ( U) − Bn( U) − Tn (10)

238 200 (where Bn is the neutron separation energy of U, Tn is the kinetic energy of the outgoing neutron), effectively 201 contributing a larger value of the peak-to-valley ratio. 238 202 The behavior of the peak-to-valley ratio is similar for photofission of U and neutron-induced fission of 235,238 203 U. The only region where the ratio of asymmetric and symmetric fission is systematically different in 238 204 both (p/v)1 and (p/v)2 is from 12 to 15 MeV for the neutron-induced fission of U, while at other energies 205 the difference is not so consistent. This can probably be connected to different fissilities and neutron separation 206 energies of the compound nuclei. The energy threshold of fission with a preceding neutron emission (γ, n fiss) 239 207 is lower for the odd-even U compound nucleus, and thus the second-chance fission process is more important 238 208 in neutron-induced fission of U. 238 209 Further analysis of the mass distributions of photofission of U is focused on the structure which can be 210 seen at the peaks of the distribution at lower excitation energies of the compound nucleus (of the order of the 211 fission barrier height). According to [9] the presence of relatively narrow maxima corresponding to the mass 212 numbers A ≈ 134 and A ≈ 101 in addition to the main peaks at A ≈ 139 and A ≈ 96 is a manifestation of 213 the asymmetric mode STI which leads to formation of a spherical fragment with N ≈ 82 and a corresponding 7

Table II. Peak-to-valley ratio p/v in photoﬁssion of 238U

∗ T , MeV hE i, MeV Y (133) Y (134) Y (140) Y (115) Y (117) (p/v)1 (p/v)2 Ref. 10 7.38±0.29 6.44±0.80 9.00±0.72a 6.78±0.90 0.102±0.012 0.046±0.002 104.4±11.3 66.5±11.8 [48] 9.7 8.07±0.33 6.60b 5.7±0.2 0.033±0.004 0.027±0.007 220.0±29.6 172.7±21.8 [45] 11.5 8.47±0.26 7.69±0.22 8.11±0.31a 5.40±0.22 0.095±0.022 0.074±0.006 93.4±12.8 56.8±13.4 [22] 13.4 9.49±0.23 7.44±0.27 8.41±0.22a 4.83±0.24 0.165±0.028 0.154±0.023 49.7±5.8 29.3±5.2 [22] 12 9.57±0.30 6.80±0.34 6.88±0.23 6.10±0.20 0.075±0.007 0.087±0.011 84.4±7.3 81.3±8.0 [21] 15 10.24±0.21 6.79±0.33 8.08±0.29a 5.12±0.23 0.190±0.028 0.188±0.023 39.4±3.9 26.9±4.1 [22] 17.3 11.12±0.20 6.81±0.21 8.14±0.30a 4.93±0.14 0.284±0.016 0.263±0.023 27.3±1.6 17.4±1.1 [22] 15 11.27±0.24 6.34±0.37 6.87±0.25 5.91±0.20 0.172±0.021 0.171±0.024 38.5±3.8 34.4±4.4 [21] 15.5 11.74±0.23 6.60b 5±0.1 0.173±0.010 38.2±2.2 28.9±1.8 [45] 19.5 11.94±0.26 6.61±0.15 6.85±0.28 5.71±0.41 0.216±0.038 0.202±0.041 32.2±4.4 26.5±5.0 this work 20 12.91±0.25 6.30±0.35 6.84±0.22 5.59±0.20 0.270±0.025 0.281±0.031 23.8±1.9 20.7±2.1 [21] 25 12.93±0.25 6.60b 5.32 5.54 0.475 12.5±0.0 11.7 [47] 21.3 13.08±0.26 6.60b 4.9±0.1 0.268±0.010 24.6±0.9 18.3±0.8 [45] 30 13.29±0.26 5.93 5.48 0.522 11.4±0.0 10.5 [47] 25 13.33±0.26 6.31±0.32 6.59±0.33 5.39±0.22 0.334±0.032 19.3±2.0 16.1±1.7 [46] 35 13.53±0.27 6.90 5.45 4.97 0.529 11.7±0.0 9.4 [47] 29.1 13.69±0.30 6.29±0.15 6.64±0.26 5.26±0.55 0.464±0.069 0.477±0.088 13.7±1.7 11.3±2.1 this work 40 13.78±0.28 6.58 5.15 0.542 12.1 9.5 [47] 30 13.92±0.30 6.10±0.31 6.43±0.21 5.62±0.18 0.444±0.036 0.446±0.045 14.1±1.0 12.7±1.1 [21] 48.3 14.45±0.30 6.30±0.17 6.51±0.12 5.43±0.22 0.568±0.097 0.530±0.077 11.7±1.3 9.6±1.7 this work 48 15.37±0.34 6.20 5±0.3 0.510±0.020 0.500±0.020 12.3±0.3 9.8±0.7 [45] 67.7 15.60±0.34 5.82±0.25 6.30±0.47 5.29±0.57 0.580±0.055 0.616±0.081 10.1±0.9 9.1±1.3 this work 70 17.23±0.35 5.84±0.30 6.12±0.27 5.33±0.17 0.695±0.052 0.737±0.064 8.57±0.56 7.7±0.6 [21] 100.3 19.71±0.38 6.60b 5.3±0.1 0.718±0.030 0.690±0.020 6.21±0.21 7.4±0.3 [45] 301.3 21.49±0.40 6.60b 4.8±0.2 1.350±0.050 1.040±0.040 3.53±0.12 3.6±0.2 [45] a Refs. [22, 48, 55] give yields of the A = 134 mass chain for two gamma-ray energies of 134Te. We used the weighted average value of these. b In [45] the yield of A = 133 was obtained from the A = 99 measurement.

Table III. Peak-to-valley ratios p/v in neutron induced ﬁssion of 238U

∗ Tn, MeV hE i, MeV Y (133) Y (134) Y (140) Y (115) Y (117) (p/v)1 (p/v)2 Ref. 1.5 6.31 7.15±0.22 8.12±0.40 6.01±0.18 0.0102±0.0014 748.5±105.1 589.2±82.8 [51] 1.5 6.31 825±165c [52] 2.0 6.81 7.12±0.21 7.78±0.37 6.10±0.13 0.0121±0.0017 615.7±88.3 504.1±71.6 [51] 2.0 6.81 452±90.4c [52] 3.0 7.81 238±47.6c [52] 3.0 7.81 7.37±0.82 8.19±0.84 6.16±0.13 0.057±0.010 136.5±26.1 108.1±19.1 [53] 3.72 8.53 6.98±0.29 8.60±0.21a 5.68±0.29 0.038±0.006 0.030±0.004 227.7±24.2 149.6±24.8 [55] 3.9 8.71 6.95±0.25 7.76±0.42 6.17±0.48 0.0340±0.0050 216.3±32.6 181.5±30.2 [51] 3.9 8.71 129±25.8c [52] 4.8 9.61 89±17.8c [52] 5.42 10.23 6.84±0.21 7.82±0.19a 5.93±0.21 0.074±0.018 0.059±0.013 110.2±18.5 80.1±19.7 [55] 5.5 10.31 6.77±0.20 7.00±0.50 5.61±0.15 0.077±0.011 89.4±13.2 72.9±10.6 [51] 6.0 10.81 6.13±0.93 5.38±0.40 0.124±0.011 49.4±8.8 43.3±5.1 [25] 6.9 11.71 7.10±0.19 7.24±0.86 5.40±0.18 0.134±0.018 53.5±7.9 40.3±5.6 [51] 7.1 11.91 6.84±0.92 5.35±0.40 0.121±0.007 56.7±8.4 44.3±4.3 [25] 7.7 12.51 7.04±0.20 7.02±0.43 5.69±0.14 0.191±0.032 36.8±6.3 29.8±5.0 [51] 7.75 12.56 6.82±0.24 7.75±0.19a 6.01±0.26 0.202±0.037 0.166±0.021 39.6±4.7 29.8±5.6 [55] 8.1 12.91 6.71±0.98 5.15±0.42 0.135±0.011 49.7±8.2 38.1±4.3 [25] 9.1 13.91 6.31±1.01 4.98±0.48 0.191±0.016 33.1±6.0 26.1±3.4 [25] 10.09 14.90 6.50±0.18 7.30±0.22a 5.45±0.23 0.338±0.039 0.279±0.063 22.4±2.7 16.1±2.0 [55] 13.0 17.81 8.8±0.88 [52] 14.8 19.61 5.68±0.51 6.35±0.30 4.54±0.40 0.870±0.150 0.800±0.160 7.2±1.0 5.2±1.0 [50] 14.8 19.61 5.73±0.37 5.49±0.45 0.970±0.150 5.8±0.9 [54] 15.0 19.81 6.5±0.65c [52] 16.4 21.21 5.8±0.58c [52] 17.7 22.51 6.8±0.68c [52] Y (99) + Y (140) c In [52] only the ratio is given. 2Y (115) 8

8 8

exp

STI

6 6 STII

SUM

29.1 MeV 19.5 MeV 4 4

2 2 Fractional mass yield (pci/fis)

0 0

80 90 100 110 120 130 140 150 160 80 90 100 110 120 130 140 150 160

8 8 A A

6 6

67.7 MeV 4 4

48.3 MeV

2 2 Fractional mass yield (pci/fis)

0 0

80 90 100 110 120 130 140 150 160 80 90 100 110 120 130 140 150 160

A A

238 Figure 4. (Color online) Fraction mass yields (YFMY) of photofission of U and results of fitting the distributions with five Gaussian curves at bremsstrahlung end-point energies 19.5, 29.1, 48.3, and 67.7 MeV: experimental data (squares), asymmetric component STI (dashed curve), asymmetric component STII (dotted curve), symmetric component SL (solid curve), sum of the components (dashed-dotted curve).

Table IV. Peak-to-valley ratios p/v in neutron induced ﬁssion of 235U

∗ Tn, MeV hE i, MeV Y (133) Y (134) Y (140) Y (115) Y (117) (p/v)1 (p/v)2 Ref. 0 6.55 6.70 7.87 6.22 0.013 0.013 574.9 494.3 [24] 0.17 6.72 6.63±0.28 6.98±0.67 6.45±0.34 0.011±0.002 613.1±126.9 581.1±120.2 [49] 0.6 7.10 6.69±0.29 7.73±1.38 6.3±0.25 0.019±0.003 382.1±77.1 333.9±60.4 [49] 1.0 7.55 6.92±0.3 6.23±0.28 0.022±0.003 311.7±48.7 280.6±43.9 [49] 2.0 8.55 6.37±0.27 7.84±1.04 6.11±0.24 0.057±0.009 125.5±21.9 107.9±17.5 [49] 4.0 10.55 6.47±0.28 6.66±0.50 5.82±0.24 0.111±0.022 59.1±12.1 52.4±10.7 [49] 5.5 12.05 6.34±0.27 6.45±0.96 5.66±0.24 0.311±0.044 20.6±3.3 18.2±2.7 [49] 6.3 12.85 6.11±0.26 6.57±2.47 5.6±0.23 0.355±0.056 17.8±4.5 15.8±2.5 [49] 7.1 13.65 6.22±0.27 7.18±1.66 5.51±0.22 0.377±0.056 17.8±3.4 14.6±2.2 [49] 8.0 14.55 5.95±0.26 6.43±1.29 5.3±0.2 0.422±0.067 14.7±2.8 12.6±2.0 [49] 14.7 21.25 5.53 5.72 4.53 1.09 1.07 5.2 4.1 [24]

214 light fragment. The pre-neutron mass distributions measured in [18, 19, 56] also show analogous fine structure 215 around the A = 134 mass number. It is seen from Figs. 4 and 5 that this effect experiences damping as the 216 excitation energy of the initial nucleus increases and it practically disappears when the excitation energy is 217 greater than approximately 15 MeV. This behavior of the asymmetric mode STI as a function of the excitation 218 energy was theoretically described in [9, 12]. Another nuclear effect, which may result in different yields of 219 fragments with neighboring masses at the peaks of the mass distribution, is the even-odd effect, which also 220 experiences damping with the increase of the nucleus’ excitation energy [36], but we see no direct signs of its 221 contribution in other regions of Fig. 4.

222 The obtained mass distributions were decomposed into the components of the multimodal model of ﬁssion [9, 223 10]: the asymmetric STI mode, corresponding to the N = 82 magic number, the asymmetric STII mode, 224 corresponding to the deformed shell N = 86 ÷ 88, and the symmetric SL mode. For each mode the distribution 9

100000

30 MeV 10000 (× 104)

29.1 MeV 1000 (× 103)

20 MeV 100 (× 102)

19.5 MeV Fractional mass yield (pci/fis) 10 (× 10)

15 MeV 1

0.1 80 100 120 140 160 Mass number

Figure 5. Comparison of the mass yield distributions of photoﬁssion at bremsstrahlung end-point energies T from 15 to 30 MeV. From top to bottom: (1) T = 30 MeV, hE∗i = 13.9 MeV (Ref. [21]); (2) T = 29.1 MeV, hE∗i = 13.7 MeV (this work); (3) T = 20 MeV, hE∗i = 12.9 MeV (Ref. [21]); (4) T = 19.5 MeV, hE∗i = 11.9 MeV (this work); (5) T = 15 MeV, hE∗i = 10.2 MeV (Ref. [22]).

1000 1000 238U (γ, F), this work 238U (γ, F), this work 238U (γ, F) 238U (γ, F) 238U (n, F) 238U (n, F) 235U (n, F) 235U (n, F) 100 100

Peak-to-valley 10 Peak-to-valley 10

1 1 5 10 15 20 25 5 10 15 20 25 Average excitation energy 〈E*〉 (MeV) Average excitation energy 〈E*〉 (MeV)

238 Figure 6. (Color online) Peak-to-valley ratios (p/v)1 (left) and (p/v)2 (right) for photofission of U (dots, stars) and neutron-induced fission of 235U (squares) and 238U (triangles) as a function of the average excitation energy hE∗i. Photofission data from this work (dots) and Refs. [21, 22, 45–48] (stars), neutron-induced fission for 238U from Refs. [25, 50–55], for 235U from Refs. [24, 49].

225 of fragment masses is described as a Gaussian function. The total yield of fragments with a given mass number 10

Table V. Contributions of the fission modes into the mass distributions as a function of the excitation energy of the fissioning nucleus hE∗i in photofission and neutron-induced fission of 238U (not marked) and 235U. T , MeV hE∗i, MeV STI STII SL Reaction Ref. 6.12 5.66 52.87 ± 6.44 147.13 ± 7.64 (γ, F ) [18] 7.33 6.23 48.07 ± 6.29 151.93 ± 7.25 (γ, F ) [18] 9.31 7.19 41.57 ± 5.25 158.43 ± 7.21 (γ, F ) [18] 11.5 8.47± 0.26 40.49±7.32 158.73±8.77 0.78±0.98 (γ, F ) [22] 13.4 9.49± 0.23 47.39 ±10.33 150.58 ±11.92 2.03 ±2.45 (γ, F ) [22] 12 9.57± 0.30 47.35 ± 5.19 151.74 ± 5.91 1.22 ± 0.62 (γ, F ) [21] 15 10.24± 0.21 37.67 ±6.43 159.87 ±7.40 2.47 ±1.52 (γ, F ) [22] 15 11.27± 0.24 37.37 ± 4.41 160.37 ± 5.50 2.71 ± 1.04 (γ, F ) [21] 19.5 11.94± 0.26 34.18 ± 7.00 162.01 ± 10.20 3.81 ± 1.36 (γ, F ) this work 20 12.91± 0.25 37.12 ± 5.01 158.35 ± 6.84 5.15 ± 2.47 (γ, F ) [21] 29.1 13.69± 0.30 27.15 ± 5.17 165.29 ± 7.64 7.56 ± 1.97 (γ, F ) this work 30 13.92± 0.30 28.83 ± 4.34 159.85 ± 8.36 10.90 ± 6.46 (γ, F ) [21] 48.3 14.45± 0.30 24.95 ± 5.21 166.21 ± 9.76 8.83 ± 3.22 (γ, F ) this work 67.7 15.60± 0.34 22.44 ± 5.65 168.03 ± 8.88 9.53 ± 3.95 (γ, F ) this work 70 17.23± 0.35 22.84 ± 2.32 164.46 ± 4.24 13.33 ± 2.75 (γ, F ) [21] 14.7 21.25 8.08±1.98 172.04±7.96 19.88±8.63 235U(n, F ) [24] 6.0 10.81 48.45±14.68 148.86±15.42 2.69±0.68 (n, F ) [25] 7.1 11.91 52.51±13.17 143.73±17.66 3.76±0.65 (n, F ) [25] 8.1 12.91 48.82±13.18 147.19±16.51 3.99±0.72 (n, F ) [25] 9.1 13.91 46.25±11.34 147.06±16.68 6.68±2.16 (n, F ) [25] 14.7 19.51 19.24±2.97 152.27±9.20 28.49±12.82 (n, F ) [24] 3500 50 16.1 ± 10.8 129.7 ± 19.3 54.1 ± 27.8 (γ, F ) [17, 20]

226 A is described by the following relationship:

2 (A − ASL) Y (A) = YSL(A) + YSTI(A) + YSTII(A) = KSL exp − 2 + 2σSL 2 2 (A − ASL − DSTI) (A − ASL + DSTI) +KSTI exp − 2 + KSTI exp − 2 + 2σSTI 2σSTI 2 2 (A − ASL − DSTII) (A − ASL + DSTII) +KSTII exp − 2 + KSTII exp − 2 , (11) 2σSTII 2σSTII

227 where the Gaussian parameters KSL,KSTI,KSTII, σSL, σSTI, σSTII are the amplitudes and widths of the sym- 228 metric (SL) and asymmetric (STI, STII) fission modes, ASL is the most probable fragment mass number for the 229 symmetric mode, ASL −DSTI,ASL +DSTI are the most probable mass numbers of the light and heavy fragments 230 of the asymmetric mode STI, ASL − DSTII,ASL + DSTII are the most probable mass numbers of the light and 231 heavy fragments of the asymmetric mode STII. Restoration of mode probabilities from the post-neutron distri- 232 bution can be negatively influenced by the shifting and widening effects in the peaks of the distribution caused 233 by emission of prompt neutrons. To estimate possible errors from these effects we also performed fits with ver- 234 sion of Eq. (11) with independent parameters of the light and heavy branches of asymmetric modes. The mode 235 weights obtained in this way were nearly identical to the results of Eq. (11), albeit with larger uncertainties. 236 Figure 4 shows the results of least-squares approximation of the obtained mass distributions using expres- 237 sion (11). 238 The obtained data make it possible to discuss the dependence of the fission modes on the average excitation 239 energy. Ref. [57] presented experimental yields of fragments with mass numbers A = 134, 139, 143 as a function 238 240 of the excitation energy in photofission of U. The A = 134 yield decreases from 9% to 6% as the excitation 241 energy increases from 6 to 20 MeV, while the yields of fragments with A = 139, 143 practically do not change 242 within error boundaries. Although this behavior gives general description of the energy dependence of the 243 contribution of asymmetric modes STI and STII, it does not provide quantitative estimates of probabilities 238 244 of the modes. Furthermore, it is shown in the works that analyzed the photofission modes of U [19] and 235 245 neutron-induced fission of U [15, 23], that the width of the STI mode is approximately two times less than the 246 width of STII, and, hence, it not enough to compare just the yields of specific mass chains, i.e. the amplitudes 247 of the modes, but one has to take into account the areas of the corresponding distributions. Only one work, 248 namely Ref. [17], contains calculation of contributions of fission modes into the mass distribution, while in other 249 works on photofission such analysis has not been made. [18] merely points at the presence of three distinct 250 fission modes in the experimental data. In [19] the contributions of the fission modes are estimated from the 251 mass-energy spectra of the fragments of fission induced by bremsstrahlung radiation at electron accelerator 252 energies from 6 to 10 MeV. 238 253 To analyze the contribution of photofission modes of U we used our data and the data from Refs. [17, 18, 20– 11

254 22], where the average excitation energy was re-calculated using Eq. (8). In all of these works the post-neutron 255 mass distributions were obtained, i.e. the distributions after emission of prompt neutrons. The experimental 256 mass distributions were decomposed into Gaussian functions, and,√ as stated by Eq. (11), the contributions, 2 257 or weights, of each mode were obtained in each case as W = K 2πσ , where K and σ correspond to the 258 parameters of the mode. In addition, the mode weights were also obtained from mass yield distributions of 238 235 259 neutron-induced ﬁssion of U [24, 25] and U [23, 24].

STII

100

STI Mode yield (pci/fis)

0.1 5 10 15 20 Average excitation energy 〈E*〉 (MeV)

Figure 7. (Color online) Contributions (weights) of different fission modes in photofission of 238U and neutron-induced fission of 235U as a function of the average excitation energy hE∗i: (circles) contributions of the STII, STI, SL modes of photofission of 238U calculated from mass distributions obtained in the present work and in works [17, 18, 20–22], (stars) contributions of the STII, STI, SL modes of neutron-induced fission of 235U from [15, 23, 24], and (squares) 238U [24, 25]. Mode yields are normalized per 100 fission reactions: YSL + YSTI + YSTII = 200%.

260 Presence of three fission modes has been found in all of the measured and analyzed mass distributions at the ∗ 261 excitation energies hE i > 10 MeV. Table V lists the obtained contributions of the fission modes at different ∗ 262 mean excitation energies hE i. At lower excitation energies the weight of the symmetric SL mode is expected 263 to be less than 1% and no decays with mass numbers 110 < A < 127 were detected in [18] in post-neutron 264 distributions using the activation technique. At the same time in both works [18, 19] using the double energy 265 technique a small contribution of symmetric fission is observed in the pre-neutron distributions. The analysis 266 of the obtained data shows that the contribution of the symmetric fission mode increases by about an order of 267 magnitude as the excitation energy increases from 8.5 to 17 MeV. The contribution of the asymmetric mode 268 STI, related to the spherical neutron shell N = 82 drops in about two times in the same energy range. The 269 contribution of the asymmetric mode STII, related to the deformed neutron shell N = 86 ÷ 88 increases.

270 It has been shown previously from the analysis of the peak-to-valley ratios, that the ratio of asymmetric and 271 symmetric fission decreases exponentially as the excitation energy increases. However, this dependence as is 272 is probably not a direct reflection of the behavior of shell effects in this range of the excitation energy of the 273 fissioning nucleus. This can be seen from the behavior of the two asymmetric modes which both appear due to 274 the shell correction component of the fission barrier, and only one of these modes disappears with the increase 275 of the excitation energy. 238 276 It has been shown above that the ratio between asymmetric and symmetric fission for photofission of U 235,238 277 and fission of U induced by monoenergetic neutrons are very close. In addition to the data from Table V, 278 in the following comparison of the relative contributions of modes in photon- and neutron-induced fission we 279 used the data from [15], where the relative contributions of the modes were obtained up to the excitation energy 280 of 12 MeV. For comparison of the fission modes in the whole studied energy range we used the fission product 281 systematics in proton- and neutron-induced fission from [16]. Figure 7 shows the relative contributions of fission 238 235,238 282 modes during photofission of U and neutron-induced fission of U. Curves denote results of calculation 283 of fission of a compound nucleus of uranium with A = 238, according to the systematics from [16]. It is seen 238 235,238 284 that the energy dependence of modes in photofission of U and neutron-induced fission of U is identical, 285 which is a common but not general behavior: e.g., there is a very pronounced difference in energy dependencies 12

286 of peak-to-valley ratios of thorium isotopes [57]. It is also important that the percieved scatter of the points 287 in Fig. 7 is significantly less than in the case of the peak-to-valley ratios making the tendencies more clearly 288 revealed. 289 The behavior of the STI mode, which is related to the N = 82 shell and the structure of the mass distribution 290 around A = 134 agrees with the experimental data up to the excitation energy 17 MeV. However, one has to 291 bear in mind that the systematics of Ref. [16] is composed in such a way that the STI contribution is zero at the 292 energy E = 22 MeV, and there are only two experimental values of the contribution of modes around 20 MeV 235 238 293 (for U (n, F) and U (n, F)). It is seen that from 12 to 20 MeV the STI contribution in neutron-induced 238 239 238 294 fission of U corresponding to the odd U compound nucleus is larger than in photofission of U and 235 295 neutron-induced fission of U, as noted above during discussion of the peak-to-valley ratios. 296 At higher excitation energies (the last row of table V) there is a noticeable difference between the contributions 297 of fission modes in photon- and neutron-induced fission. It follows from the systematics [16] that above 25 MeV 298 there is no contribution of the STI mode. However, it is seen from the experimental results of [17, 20] that 299 this mode is still present at 50 MeV. This behavior is further confirmed by measurements of the ratio of the 238 300 asymmetric and symmetric channels [58]. According to the results of Ref. [59] the neutron-induced fission of U 301 is dominated by asymmetric fission at least up to 200 MeV, however, the STI contribution at neutron energies 302 of about 50 MeV (estimated using the described procedure) does not exceed 2%. Theoretical calculations of 303 photofission probabilities at intermediate energies [60] suggest a rather different process of formation of final 304 mass distributions due to hadron photoproduction cascades at the initial stage of photoabsorption.

305 IV. CONCLUSIONS

238 306 Photon activation technique was used to obtain photofission mass distributions of U in a bremsstrahlung 307 beam with end-point energies 19.5, 29.1, 48.3, and 67.7 MeV. The weights of the symmetric (SL) and asymmetric 238 308 (STI and STII) modes in the mass distributions of photofission of U at the average excitation energies of up 309 to 20 MeV are calculated on the basis of the obtained results and other available data. 310 Since the yield of each fission mode is determined by the probability of tunneling through a fission barrier, 311 the observed distinctive behavior of the fission modes is an evidence of presence of three minimal trajectories, 312 or three distinct fission barriers on the potential energy surface. 313 Damping of the shell effects results in an increase of the contribution of the symmetric mode SL, which 314 increases by about an order of magnitude as the excitation energy increases from 8.5 to 17 MeV. 315 The weights of the asymmetric modes STI and STII and their energy dependence are noticeably different. 316 This difference also implies substantially different shapes of the barriers for these fission modes. 317 The behavior of the asymmetric modes is anti-correlated. The contribution of the STI mode decreases by 318 about 2.5 times from 5 to 17 MeV, the contribution of the STII mode slightly increases. This may be interpreted 319 as an indication that the minima of the potential energy surface that correspond to asymmetric fission split 320 before the saddle point, directly after the second potential well. The opposite behavior of the asymmetric 321 modes can indicate not only different values of the shell corrections, but also of different dependencies of the 322 shell corrections on the excitation energy, i.e. different shell effects damping functions.

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