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Physics Letters B 581 (2004) 56-61

www. elsevier. com/locate/physletb

Actinide symmetric/asymmetric nucleon-induced fission up to

200 MeV

V.M. Maslov

Joint Institute of Nuclear and Energy Research, "Sosny", 220109 Minsk, Belarus Received 22 August 2003; received in revised form 4 November 2003; accepted 25 November 2003

Editor: V. Metag

Abstract

The fission cross sections of the symmetric SL-mode and the asymmetric lumped (S1 + S2)-mode of the 235U(n, F),

237Np(n, F) and 238U(p, F) reactions are calculated up to En = 200 MeV within a statistical model. For each fissioning nuclide, emerging in (n, xnf) reactions, a separate triaxial outer fission barrier is assumed for the SL-mode. To reproduce the measured

branching ratio of symmetric and asymmetric fission events, strong contribution of fission from neutron-deficient nuclei is assumed. Damping of the contribution of triaxial collective modes to the level density at the SL-mode outer saddle seems to be essential for the description of the branching ratio. The sensitivity of the calculated branching ratio to the fissility of the target nuclide and the incident particle is investigated. © 2003 Published by Elsevier B.V.

1. Introduction

In neutron-induced fission of actinides, the contribution of the symmetric or superlong (SL) fission mode [1,2] increases with the excitation energy [3-7]. At incident neutron energies En > 6 MeV, pre-fission neutrons might be emitted, before the fissioning nuclide reaches the outer saddle point. We will call them pre-saddle. This peculiarity considerably complicates the interpretation of fission observables. A number of nuclides might contribute to the fission observables, about ~ 20 for the 238U(n, xnf) fission reaction at En ~ 200 MeV [8]. In other words, an ensemble of nuclides, which emerge after emission of x pre-saddle neutrons, contributes to the symmet-

E-mail address: maslov@sosny.bas-net.by (V.M. Maslov).

ric and asymmetric fission. The branching ratio of symmetric fission events to the total observed fission events rsym = tfnFSL/(°nFSL + ^nF(S1+S2)) was obtained for 238U(n,F) by Zoller et al. [9] at En up to ~ 500 MeV. The values of rsym were obtained from the deduced yield distributions of primary fission fragments and their average total kinetic energies (TKE) as a function of mass. Description of the branching ratios rsym by Zoller et al. [9] up to En ~ 200 MeV favors the major contribution to the observed fission cross section of fission chances with a larger number of pre-saddle neutrons [8]. With increasing fissility of the target nuclide this number might be somewhat lower. We will apply the same approach, which was previously used for the description of the cross section and the branching ratio of symmetric/asymmetric fission of the observed 238U(n, F) reaction, to which either first chance 238U(n, f) and emis-

0370-2693/$ - see front matter © 2003 Published by Elsevier B.V. doi:10.1016/j.physletb.2003.11.062

sive fission 238U(n, xnf) reactions contribute, to describe measured fission cross sections in the reactions 235U(n,F), 237Np(n, F) and 238U(p,F). In particular, we will predict the 235U(n,F)sym, 237Np(n, F)sym and 235U(n,F)asym, 237Np(n, F)asym fission cross sections. Simultaneous analysis of 238U(n, F) and 238U(p, F) reaction cross sections would help to investigate the dependence of observed fission cross sections on the projectile.

2. Statistical model

We assume that the fission fragments are emitted from a chain of U(Np) nuclei after pre-equilibrium (PE) emission and evaporation of neutrons [10]. We do not take into account charged-particle emission, for justification see the discussion in [8]. A coupledchannels model, fitting the 238U total fission cross sections [11] up to En ~ 200 MeV is employed. The contribution of the SL-mode anFSL to the observed fission cross section, originating from (n, xnf) fission reactions, was calculated using the fission probability PfsLx(U) for symmetric fission of the fissioning xth nucleus,

^nFSL(En) = ^nfSL(En)

X Umax

+ ££ f wJ+i(U)pJL(x+i)(U)du, (1) ---1 J

x=1 Jn

Wjn(U) is the population of the (x + 1)th nucleus at excitation energy U after emission of x neutrons. The excitation energy Umax is defined by incident neutron energy En and energy removed by pre-saddle evaporated neutrons. The modeling of the first-chance fission cross section anfSL is described elsewhere [7]. The lumped contribution of the asymmetric fission standard 1 (S1) and standard 2 (S2) modes is defined in an analogous way.

The nuclear level density p(U, J,n) is represented as factorized contribution of quasiparticle and collective states [12]. The quasiparticle level densities Pqp(U,J,n) were calculated with the phenomenolog-ical model of Ignatyuk et al. [13] as

where Krot(U, J) and Kvib(U) are the factors of rotational and vibrational enhancement. At saddle and ground-state deformations Krot(U) is defined by the symmetry class, adopted from shell-model calculations [2,14,15]. At inner saddle we assume axial symmetry for neutron numbers N < 144 and triaxial shape for N > 144. At outer saddle triaxiality is assumed for mass symmetric mode, while axial shape is assumed for the mass asymmetric mode. For more extensive discussions see [2,7,8] and references therein. At excitations U > Ur, damping of rotational modes was anticipated [16]. Damping of rotational modes contribution to the nuclear level density p(U, J, n) might be different for axially symmetric and triaxial nuclei [17],

Krsoytm(U) = K - 1) F(U) + 1,

^asym (

KZr(U) = - 1 )F(U) + l), (4)

F(U) = (1 + exp(U - Ur)/dr) 1.

P(U, J, n) = Krot(U)Kvib(U)Pqp(U,J, n)

Here, ff|2 and a2 are the spin-distribution parameters. The mass asymmetry for the S 1(S2)-modes at the outer saddles doubles the rotational enhancement factors as defined by Eqs. (3), (4). Shell effects in the level density are modeled with the dependence of the a -parameter on the shell correction SW as recommended by Ignatyuk et al. [13]: a(U) = a(1 + SWf(U)/(U)). The value of the asymptotic an-parameter a n is defined by fitting to the neutron-resonance spacing (Dobs) or by systematics. We assume an = af, then the af/an ratio depends on values of SWf(n), taken from [18] (SWn) and [19] (SWf).

3. Analysis

The total fission cross section anF = anFSL + ffnF(S1+S2) depends on the contributions of both terms. These contributions strongly depend on the asymptotic value af(A) of the af parameter of the fissioning nuclei, while the branching ratio rsym depends both on the contributions of fission chances and the damping of the contribution of the triaxial collective modes to the nuclear level density (see Eqs. (4), (5) for the SL fission mode [8]. The contributions of fission chances to the observed fission cross section anF are affected by decreasing the asymptotic value of the af parameter

with energy as

( (U — 20\1/4\ 5f(t/, A) = 5f(A)i 1 - 0.1 f—— J J. (6)

This expression was obtained by consistent description of observed Th, U and Pu fission cross sections [20] as well as branching ratio r sym for238U(n, F) reaction [8]. The heights of the outer fission barrier B of the SL mode for 239U and 236U fissioning nuclides were derived to be higher than those of the asymmetric modes, i.e., (E®sl - EffiS1(S2)) - 3.5 MeV, while h&>BSL = 2.25 MeV [7]. The contributions of lighter U nuclides via (n, xnf) reactions to the observed symmetric fission might be obtained assuming for each of them the same difference of the outer barriers for the symmetric SL and the asymmetric fission S1(S2) modes, the shell-correction values being defined as (^WfBSL — ¿WfBS1(S2)) — 3.5 MeV, assuming ^^fBS1(S2) — 0.6 MeV [19]. The assumption that the difference of mass-symmetric and mass-asymmetric fission barriers do not vary with the neutron number might seem too crude (see Schmidt et al. [21], however, we believe that weak isotopic dependence of (EfBSL — EfBS1(S2)) could be compensated by slight variation of asymptotic value of the af parameter (see Eq. (6)). The inner and outer fission-barrier parameters of uranium for the double-humped fission-barrier model [22], relevant for the saddle asymmetries, predicted by SCM calculations [14] for asymmetric fission, were defined in [23,24]. This simple systematics of level-density and fission-barrier parameters for U nuclides allowed to reproduce the observed 235U(n, F) fission cross section [25]. The same approach works in the case of neutron-induced fission of 237Np target nuclides.

It might be anticipated that further sophistication of the model, i.e., inclusion of the temperature and angular momentum dependence of fission barriers and shell corrections, influence of neutron shell N = 126 on collective enhancement in neutron channel [17], or use of calculated with SCM method [2] fission barriers for symmetric and asymmetric fission modes of U nuclei, would not change pattern of emissive fission contributions. Lowering of asymptotic value af of af parameter at saddle deformations might be considered as reproducing lumped effect of all these factors. We anticipate also that because of strong emissive fission nature of 238U(n, f) reaction for En <

235U FISSION CROSS SECTION

zf O H

an 1 en

CO O DC O

10 100 NEUTRON ENERGY,MeV

Fig. 1.

200 MeV, vanishing of the distinction of symmetric and asymmetric valleys at high excitation of fissioning nuclei [26] would not be much pronounced.

Fig. 1 shows the calculated symmetric 235U(n, F)sym, asymmetric 235U(n, F)asym and symmetric + asymmetric 235U(n, F) fission cross sections for the energy-dependent asymptotic af(U, A) of af parameter (Eq. (6)). The set of solid curves shows the 235U(n, F)sym and 235U(n, xnf)sym cross sections, while the dashed lines show those for the asymmetric neutron-induced fission of 235U target nuclide.

Fig. 2 shows the symmetric 237Np(n, F)sym, asymmetric 237Np(n, F)asym and symmetric + asymmetric 237Np(n, F) fission cross sections. The lines on Fig. 2 have the same meanings as on Fig. 1. The sum of the calculated 237Np(n, F)sym and 237Np(n, F)asym reaction cross sections (dash-dotted line) is quite compatible with the observed fission cross section [27] up to En - 200 MeV. The data by Hambsch et al. [3] for the symmetric fission yield are also reproduced.

In case of the proton-induced fission reaction 238U(p,F), the observed fission reaction cross section could be calculated using the fission-barrier and level-density parameters of Np nuclei, obtained by fitting

Fig. 2.

the 237Np(n, F) fission cross section. It might be anticipated that 238U(p, xnf) reactions give the dominant contribution to the observed fission cross section. The sum of 238U(p, F)sym and 238U(p, F)asym cross sections is compared with the measured data on Fig. 3.

The relative contributions of o^p™ and a^™ to the observed fission cross section anF could be controlled by comparing the calculated branching ratio rsym with the measured data by Zoller et al. [9] (see Fig. 4) for the 238U(n, F) reaction and with the measured data below the fission threshold by Hambsch [5] for 238U(n, f), Vives et al. [4] for 235u(n, f) and Hambsch et al. [3] for 237Np(n, f). The relative contributions of fission chances with low and high number of pre-fission neutrons have a major influence on the energy dependence of rsym at En > 25 MeV. When the energy-dependent asymptotic af(A) of af parameter is employed (see Eq. (6)), higher chances make a predominant contribution to the observed fission cross section, and damping of triaxial collective modes contribution (see Eqs. (4), (5)) at outer symmetric fission saddle allows to reproduce the measured data by Zoller et al. [9] for 238U(n,F) at En > 10 MeV. Below the fission threshold there is a systematic

Fig. 3.

SYMMETRIC FISSION BRANCHING RATIO

1 F-^-...........:

0.001 —^-—........

10 100

NEUTRON ENERGY, MeV

Fig. 4.

difference of branching-ratio data by Hambsch [5] for 238U(n, f) and Vives et al. [4] for 235U(n, f).

The calculated branching ratios r sym for 235U(n, F) and 238U(n, F) reactions are different around the

235'238U(n, nf) reaction thresholds. A strong dip is observed for the 238U(n, F) reaction, a similar dip of lower amplitude is predicted for the 235U(n,F) reaction. These peculiarities are due to different contributions of (n, F)asym and (n, F)sym reactions because of higher fission thresholds of the symmetric fission modes as compared with those of asymmetric fission. At incident neutron energies En > 25 MeV, symmetric fission makes the higher contribution to the observed fission cross section in the case of the 235U(n,F) reaction, but the lowest in the case of 238U(n, F). This might be explained by different emissive fission contributions to the (n, F)asym and (n, F)sym reactions. The branching ratio for the 238U(p, F) reaction is not much different from that of the 238U(n, F) reaction at incident nucleon energies En(p) > 50 MeV At lower energies, i.e., 15 < En(p) < 50 MeV, the difference is due to the different contributions of emissive fission reactions to the observed proton- and neutron-induced fission cross sections. In summary, different shapes of branching ratios rsym for the 237Np(n, F), 235U(n, F), 238U(n,F) and 238U(p, F) reactions for En < 90 MeV might be attributed to the higher contribution of lower fission chances in case of higher target nuclide fissil-ity, for higher energies En > 90 MeV they do not differ much.

4. Conclusions

The damping of the contribution of axial collective modes to the level density at the inner and the outer saddles and at equilibrium deformations as well as triaxial damping at the outer saddle deformations of the SL-mode, produce symmetric/asymmetric emissive fission partitioning of 238U(n, F) based on the consistent description of the observed fission cross section and the symmetric/asymmetric fission branching ratio. The estimate of asymptotic level density parameter af(A) of the fissioning nuclei is equivalent to the more fission events at lower intrinsic excitation energies (which is due to pre-fission neutron emission), or more fission events from neutron-deficient U nuclei, i.e., from higher fission chances. Triaxial damping at the outer saddle of the SL mode is equivalent to less symmetric fission events at higher excitation energy and more symmetric fission from neutron-deficient isotopes, as compared with the "no triaxial damping"

case. The dependence of the symmetric fission branching ratio on the fissility of the target nuclide as well as on the incident particle is demonstrated. It would be of much interest to estimate the probability of symmetric fission in the 235U(n, F) reaction [28] as a function of internal excitation energy of the fissioning nuclei in the emissive fission domain. For this we should calculate the exclusive 235U(n, x nf) reaction neutron spectra for x ~ 20. This will be done as an extension of the present work.

Acknowledgements

This work was supported by the International Science and Technology Center under the Project B-404 "Actinide Nuclear Data Evaluation", Funding Party Japan, and the International Atomic Energy Agency under Research Contract RC9837.

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