Protactinium neutron-induced fission up to 200 MeV

The theoretical evaluation of 230−233Pa(n,F) cross sections is based on direct data, 230−234Pa fission probabilities and ratios of fission probabilities in first-chance and emissive fi sion domains, surrogate for neutroninduced fission. First chance fission cross sections trends of Pa are b sed on consistent description of 232Th(n,F), 232Th(n,2n) and238U(n,F), 238U(n,xn) data, supported by the ratio surrogate data by Burke et al., 20 06, for the 237U(n,F) reaction. Ratio surrogate data on fission probabilities of 232Th(6Li,4He)234Pa and232Th(6Li,d)236U by Nayak et al.,2008, support the predicted 233Pa(n, F) cross section at E n=11.5-16.5 MeV. The predicted trends of 230−232Pa(n, F) cross section up to En=20 MeV, are consistent with fissilities of Pa nuclides, extracted by 232Th(p,F) (Isaev et al., 2008) and 232Th(p,3n) (Morgenstern et al., 2008) data analysis. The excitation ene rgy and nucleon composition dependence of the transition from asymmetric to symm etric scission for fission observables of Pa nuclei is defined by analysis of p-induced fission of 232Th at Ep=1-200 MeV. Predominantly symmetric fission in 232Th(p,F) at En(p)=200 MeV as revealed by experimental branching ratios (Dujvestijn et al., 1999) is reproduced. Steep transition from asymmetric to symmetric fission with inc rease of nucleon incident energy is due to fission of neutron-deficient Pa (A ≤229) nuclei. A structure of the potential energy surface (a drop of symmetric and asymmetric fission barriers di fference (E S Y M E f AS Y M) from∼3.5 MeV to∼1 MeV) of N-deficient Pa nuclides (A≤226) and available phase space at outer fission saddles, are shown to b e responsible for the sharp increase with En(p) of the symmetric fission component contribution for 232Th(p,F) and230−233Pa(n, F) reactions. That is a strong evidence of emissive fission nature of moderately excite d Pa nuclides, reliably quantified only up to En(p)∼20(30) MeV. Predicted fission cross section of 232Pa(n,F) coincides with that of 232Th(p,F) at En(p)≥80 MeV, that means that entrance channel dependence of fission cross section with increase of nucleon incident


Introduction
Neutron-induced cross sections of 231 Pa(n,F) and 233 Pa(n,F) data [1][2][3] when complemented with surrogate fission data, measured in reactions 232 Th( 3 He,d) 233 Pa, 231 Pa(d,p) 232 Pa, 230 Th( 3 He,d) 231 Pa and 230 Th( 3 He,t) 230 Pa at excitation energies 6-11.5 MeV [4] and fission probabilities measured in [5] via reactions 232 Th( 3 He,p) 234 Pa, 232 Th( 3 He,d) 233 Pa and 232 Th( 3 He,t) 232 Pa at excitation energies 6-15 MeV pose a number of severe problems for consistent theoretical description. In an emissive fission domain data by Petit et al. [5], as well as older indirect data by Birgul et al. [6] provoke assumption of steep decrease of the first-chance fission cross sections of 233 Pa(n,F) and 231 Pa(n,F) and systematically lowered fission probabilities of relevant Pa nuclides [7]. At excitations near fission threshold surrogate data [4,5] are model-dependent [8,9]. Above emissive fission threshold the sensitivity to the angular momentum may again increase. Recently developed surrogate ratio method [10] largely removes the uncertainty, imposed by preequilibrium effects and different angular momentum spectra of excited and fissioning states in (n,F) and transfer reactions. The theoretical approach, which would be employed for the 229−233 Pa(n,F) cross section predictions, was independently supported by the ratio surrogate data [10] a e-mail: maslov@sosny.bas-net.by for the 237 U(n,F) reaction [11,12]. Recent ratio surrogate data on fission probabilities of 232 Th( 6 Li, 4 He) 234 Pa and 232 Th( 6 Li, d) 236 U by Nayak et al. [13], relevant for the E n = 11.5-16.5 MeV, support our prediction [14]. The shell effects either in fission fragments or saddle configurations define the fission observables at relatively low excitation energies U. It is generally believed that with increase of U the shell effects diminish and fission observables are dominated by the macroscopic nuclear properties. Pre-fission neutron emission decreases the excitation energy of the fissioning nuclei, which may influence the competition of the symmetric and asymmetric fission modes [15,16], decreasing the contribution of the symmetric one. At the other hand, the neutron-deficient Pa nuclides, in 232 Th(p,xnf) or 232 Pa(n,xnf) reactions, might be more susceptible to symmetric fission even at low excitations [17,18]. Interplay of these two trends would define the fission observables at higher excitations.   rect and surrogate fission data were addressed by Arthur [19], it was proved to be a consequence of the spin population differences in transfer and (n,f) reactions [19,20]. Much larger discrepancy is observed at the onset of the 233 Pa(n,nf) reaction, the σ n f data being much lower (see Fig.1). It could be traced back to oversimplified procedure of obtaining surrogate data as σ n f = σ CN × P exp f in the emissive fission domain, pre-equilibrium emission sensitivity and influence of spectroscopic properties of transition states of 233 Pa. The latter effect for o-e nuclide 233 Pa should be excluded, unlike the observed discrepancy of direct and surrogate 230 Th( 4 He, 3 He) 231 Th data for 230 Th(n,F), which might be traced back to properties of e-e nuclide 230 Th, fissioning in 230 Th(n,nf) reaction. Wide peak around E n ∼8 MeV, observed in [21], is described by lowering the negative parity octupole band of 230 Th due to the massasymmetry of outer saddle deformations [22,23]. It might be concluded that the discrepancy of surrogate [5] and direct fission data for 230 Th target nuclide above (n,nf) fission threshold is of systematic character and might be pronounced in case of Pa nuclides. Above emissive fission threshold contributions to the observed fission cross section coming from (n,xnf), x= 1, 2, 3...X, fission of equilibrated Pa nuclei, are calculated as

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For 233 Pa(n,F) emissive fission contributions σ n,xn f (E n ) are calculated using fission probability estimates of 234−x Pa nuclides from 232 Th( 3 He,d) 233 Pa [4,5], 231 Pa(d,p) 232 Pa [5] reactions. Overall consistency of 232 Th( 3 He,d) 233 Pa fissility data measured in [4,5] is demonstrated on Fig. 2. The firstchance fission probability of the 232,233,234 Pa nuclides depends mostly on the level density of fissioning and residual nuclei (see for details [24,25]. The 233 Pa(n,f) fission cross section shape of [2,3] needs extremely low contribution of the second chance fission reaction 233 Pa(n,nf) to the 233 Pa(n,F). Consequently, calculated 232 Pa(n,f) cross section would be drastically discrepant with the indirect data [4] on 232 Pa(n,f) at E n ∼0.5 -5 MeV (see Fig.2). Shape of the 233 Pa(n,F) calculated cross section, obtained by fitting 232 Pa(n,f) data by Britt and Wilhelmy [4] in E n ∼ 2-5 MeV energy range in [14] is supported by ratio surrogate data of 232 Th( 6 Li, 4 He) 234 Pa and 232 Th( 6 Li,d) 236 U by Nayak et al. [13], relevant for the E n ∼11. 5-16.5 MeV. In case of 231 Pa(n,f) reaction (see Fig.3) discrepancy of calculated cross section, based on direct data [26,27], and surrogate data is quite similar to that observed in case of 233 Pa(n,f). Data point by Birgul et al. [6] at E n ∼ 14 MeV is compatible with the surrogate data trend. That trend and data by Birgul et al. [6] could be reproduced if the contribution of the 231 Pa(n,nf) is much lower, than predicts fission probability from 230 Th( 3 He,d) 231 Pa reaction [4]. Fig. 4 compares σ n,F (E n ) of 230 Pa(n,F) with surrogate data [4]. The predicted trend of 231 Pa(n,F) cross section up to E n ∼20 MeV, which is similar to that of 233 Pa(n,F), is consistent with fissilities of Pa nuclides, stemming from consistent analysis of 232 Th(p,F) and 232 Th(p,3n) database, enlarged by new data on 232 Th(p,F) [28] and 232 Th(p,3n) [29], sensitive to CNR*09  [25]). Fit of 232 Th(p,F) and 232 Th(p,3n) cross sections data corresponds to present description of 230−233 Pa(n,F).

p+ 232 Th and n+ 231−23Pa reactions
The excitation energy and (Z,N)-dependence of the transition from asymmetric to symmetric scission of fissioning Pa nuclei are probed in 232 Th(p,F) reaction at E n(p) up to 200 MeV. That is the mass and excitation energy range where the transition to predominantly symmetric fission was observed in 232 Th(p,F) reaction [30,31]. The data on the symmetric yield r S L = σ S L pF /(σ S L pF + σ AS pF ) for 232 Th(p, F) for 232 Th(p,F) [30][31][32] are interpreted to be due to steep transition from asymmetric to symmetric fission for neutrondeficient Pa (A≤229) nuclei, predicted in [17] (see Fig.5). At E n(p) ∼200 MeV about 20 neutron-deficient nuclides might contribute to the fission observables [23], while in [17] ν pre =1-2. Symmetric/asymmetric (p(n),xnf) contributions to observed fission cross sections are largely defined by the level density parameters a f and a n for fissioning and residual nuclides and damping of the rotational modes contri- butions to the level densities and saddle asymmetries [14,23,33]. Contribution of the higher emissive fission chances 232 Th(p,xnf)/ 232 Th(p,F) becomes overwhelming with increase of E p . The energy dependence of σ S L pF is defined by the symmetry of the outer saddle of a double humped fission barrier. For 232 Th(n,F) it was found that rather thin but high axially asymmetric outer barrier (E S L f B ) corresponds to the mass symmetric fission, in contrary to the lower massasymmetric outer fission barrier (E AS f B ). The 232 Th(n,F) measured fission cross section data also could be reproduced only for the fission chances distribution, corresponding to the preferential contribution of fission of neutron deficient Th nuclides [23] (see Fig. 6). The sharing of the 232 Th(p,F) fission cross section to SL-and AS-modes is obtained for (E S L f B − E AS f B )= 1 MeV for Pa nuclides with A≤226. That leads to the increase of symmetric fission yields in 232 Th(p,F) reaction due to 232 Th(p,xnf) at E n(p) ∼50-200 MeV. The measured symmetric fission yields for E p = 20-50 MeV [32] and E p = 190 MeV [30,31] provide an unambiguous evidence for the sharp increase of r S L at E p ≥30 MeV. There is a strong evidence [17], that fission of 233−x Pa nuclei (x = 1-20) in case of 232 Th(p,F) reaction would define competition of symmetric and asymmetric fission events at E p up to 200 .0 MeV is used for Pa nuclei with N ≤135. Cross section of 232 Th(p,F) is higher than that of 232 Th(n,F) at E n(p) ≥18 MeV [23]. That means in case of p+ 232 Th interaction the fissilities of Pa nuclei are relatively higher than those of respective Th nuclei for the n+ 232 Th interaction, which influences the observed fission cross section at E n(p) ¡100 MeV. In case of 232 Th(p,F) entrance channel plays a decisive role at E n(p) ¿100 MeV. Present estimate of 232 Th(p,F) cross section differs essentially from the phenomenological estimate [34].
Prediction of the optical potential for the incident protons was based on the optical potential for incident neutrons introducing into real and imaginary potential terms isoscalar and isovector components [35], which depend on the symmetry parameter η = (N − Z)/A, only in a real volume V n R and imaginary surface W n D potential terms [11,39]. Values of V p R and W p D for incident protons are calcu-

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EPJ Web of Conferences lated as V p R = V n R + 2αγ and W p D = W n D + 2βγ, α = 16 and β = 8 values, obtained by the description of the proton and neutron scattering data for a number of medium weight nuclei [35,36]. The predicted proton absorption cross section σ p R > σ n R at E n 50 MeV is compatible [37] with the experimental data in the same way, as it was shown for the p+ 238 U interaction [38,39]. 230−233 Pa(n,F) cross sections, shown on Figs. 1-4 were calculated with fission barrier and level density parameters, fixed by p+ 232 Th interaction data analysis. It might be argued that the uncertainty of Pa(n,F) fission cross sections is similar to that of 232 Th(p,F).

Conclusion
The improved evaluation of 230−233 Pa(n,F) evaluated data is based on consistent description of fission probability data, coming from transfer reactions and p+ 232 Th interaction data base. Recent ratio surrogate data on fission probabilities of 232 Th( 6 Li, 4 He) 234 Pa by Nayak et al. [13] support the theoretical approach in case of 233 Pa(n,F) reaction. The predicted trend of 231 Pa(n,F) cross section up to E n =20 MeV, which is similar to that of 233 Pa(n,F), is consistent with fissilities of Pa nuclides, stemming from analysis of 232 Th(p,F) and 232 Th(p,3n) data. The influence of the interplay of Pa fission barriers and entrance channel on the fission observables is shown to be different in case of n(p)+ 232 Th and n(p)+ 238 U. For p+ 232 Th interaction the Pa nuclei are responsible for σ pF > σ nF at 18≤E n(p) ≤100 MeV. For 232 Pa target σ nF approaches σ pF of 232 Th at E n(p) ∼ 80 MeV. In case of nucleon-induced fission of 232 Th the entrance channel plays a decisive role at E n(p) ≥100 MeV. The prediction of 231−233 Pa fission cross sections up to E n = 200 MeV was achieved for preferential contribution of fission of neutron-deficient nuclides. The measured data on symmetric fission yield for 232 Th(p,F) are reproduced, similar increase of symmetric fission yield for 231,232,233 Pa(n,F) reaction is predicted at E n ∼50 MeV. Present estimate of 232 Th(p,F) cross section differs essentially from the phenomenological estimate [34]. Support of International Science and Technology Center (Moscow) under the Project Agreement B-1604 is acknowledged.