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Fission Product Yield Data for the Transmutation of Minor Actinide ...

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from higher fission chances [3.1.43] (i.e. from very<br />

neutron deficient U nuclei). We have demonstrated<br />

that a more detailed treatment <strong>of</strong> <strong>the</strong> observed<br />

fission cross-section as a sum <strong>of</strong> <strong>the</strong> symmetric and<br />

asymmetric fission cross-sections needs stronger<br />

contributions from higher chances, or more fissions<br />

from very neutron deficient isotopes. This situation<br />

is described by <strong>the</strong> energy dependence <strong>of</strong> <strong>the</strong><br />

asymptotic value ã f (U, A) <strong>for</strong> <strong>the</strong> a f parameter at<br />

saddle de<strong>for</strong>mations. The description <strong>of</strong> <strong>the</strong><br />

branching ratio <strong>of</strong> symmetric to all fission events<br />

needs a relative increase <strong>of</strong> <strong>the</strong> contribution <strong>of</strong><br />

symmetric fission from neutron deficient isotopes,<br />

which is achieved by <strong>the</strong> damping <strong>of</strong> triaxial<br />

rotational mode contributions at outer saddle de<strong>for</strong>mations.<br />

Fur<strong>the</strong>r refinements <strong>of</strong> <strong>the</strong> model (such as<br />

inclusion <strong>of</strong> <strong>the</strong> temperature and angular<br />

momentum dependence <strong>of</strong> fission barriers, <strong>the</strong><br />

influence <strong>of</strong> neutron shell N = 126 on <strong>the</strong> collective<br />

enhancement in <strong>the</strong> neutron channel [3.1.41], and<br />

calculation <strong>of</strong> fission barriers <strong>for</strong> symmetric and<br />

asymmetric fission modes <strong>of</strong> U nuclei with <strong>the</strong> shell<br />

correction model method [3.1.40]) would not<br />

change our main conclusions. Lowering <strong>of</strong> <strong>the</strong><br />

asymptotic value ã f <strong>of</strong> <strong>the</strong> a f parameter at saddle<br />

de<strong>for</strong>mations can be considered as reproducing <strong>the</strong><br />

lumped effect <strong>of</strong> all <strong>the</strong>se factors. We also expect<br />

that <strong>the</strong> possible vanishing <strong>of</strong> <strong>the</strong> distinction<br />

between symmetric and asymmetric valleys in <strong>the</strong><br />

energy surface at high excitation <strong>of</strong> fissioning nuclei<br />

[3.1.43] would not have much influence on <strong>the</strong><br />

calculated values because <strong>of</strong> <strong>the</strong> strong emissive<br />

fission nature <strong>of</strong> <strong>the</strong> 238 U(n,f) reaction <strong>for</strong> E n £<br />

200 MeV.<br />

Damping <strong>of</strong> <strong>the</strong> contribution <strong>of</strong> <strong>the</strong> axial<br />

collective modes to <strong>the</strong> level density <strong>for</strong> both inner<br />

and outer saddle and <strong>for</strong> equilibrium de<strong>for</strong>mations,<br />

as well as triaxial damping at super long mode outer<br />

saddle de<strong>for</strong>mations, were assumed. A consistent<br />

description <strong>of</strong> <strong>the</strong> observed fission cross-sections<br />

and <strong>the</strong> symmetric fission branching ratio <strong>for</strong> <strong>the</strong><br />

238 U(n,f) reaction was obtained on <strong>the</strong> basis <strong>of</strong> this<br />

assumption. Symmetric/asymmetric emissive fission<br />

partitioning <strong>of</strong> <strong>the</strong> 235 U(n,f), 233 U(n,f), 237 Np(n,f),<br />

232 Th(n,f) and 238 U(p,f) reaction cross-sections have<br />

been predicted. The dependence <strong>of</strong> <strong>the</strong> symmetric<br />

fission branching ratio on <strong>the</strong> target nuclide fissility<br />

is interpreted as being due to a higher contribution<br />

<strong>of</strong> lower fission chances in <strong>the</strong> case <strong>of</strong> higher target<br />

nuclide fissilities.<br />

REFERENCES TO SECTION 3.1<br />

[3.1.1] WAHL, A.C., Nuclear-charge distribution and<br />

delayed-neutron yields <strong>for</strong> <strong>the</strong>rmal-neutroninduced<br />

fission <strong>of</strong> 235 U, 233 U, and 239 Pu and <strong>for</strong><br />

spontaneous fission <strong>of</strong> 252 Cf, At. <strong>Data</strong> Nucl. <strong>Data</strong><br />

Tables 39 (1988) 1–156.<br />

[3.1.2] BROSA, U., et al., Nuclear scission, Phys. Rep.<br />

197 (1990) 167–262.<br />

[3.1.3] BROSA, U., et al., Nuclear scission, Nucl. Phys.<br />

A 502 (1989) 423–442.<br />

[3.1.4] BROSA, U., et al., <strong>Fission</strong> channels in 258 Fm, Z.<br />

Phys. A 325 (1986) 241–242.<br />

[3.1.5] BROSA, U., Sawtooth curve <strong>of</strong> neutron multiplicity,<br />

Phys. Rev. C 32 (1985) 1438–1441.<br />

[3.1.6] OHTSUKI, T., et al., Systematic variations <strong>of</strong><br />

fission barrier heights <strong>for</strong> symmetric and asymmetric<br />

mass divisions, Phys. Rev. C 48 (1993)<br />

1667–1676.<br />

[3.1.7] KONECNY, E., et al., Symmetric and asymmetric<br />

fission <strong>of</strong> Ac isotopes near <strong>the</strong> fission<br />

threshold, Phys. Lett. 45B (1973) 329–331.<br />

[3.1.8] WEBER, J., et al., <strong>Fission</strong> <strong>of</strong> 228 Ra, Phys. Rev.<br />

C 13 (1976) 2413–2420.<br />

[3.1.9] MASLOV, V.M., HAMBSCH, F.-J., Symmetric<br />

uranium neutron-induced fission, Nucl. Phys.<br />

A 705 (2002) 352–363.<br />

[3.1.10] VIVÈS, F., et al., Investigation <strong>of</strong> <strong>the</strong> fission<br />

fragment properties <strong>of</strong> <strong>the</strong> reaction 238 U(n,f) at<br />

incident neutron energies up to 5.8 MeV, Nucl.<br />

Phys. A 662 (2000) 63–92.<br />

[3.1.11] HAMBSCH, F.-J., EC Joint Research Centre,<br />

Institute <strong>of</strong> Reference Materials and Measurements,<br />

Geel, Belgium, personal communication,<br />

2001.<br />

[3.1.12] OBERSTEDT, S., et al., <strong>Fission</strong>-mode calculations<br />

<strong>for</strong> 239 U, a revision <strong>of</strong> <strong>the</strong> multi-modal<br />

random neck-rupture model, Nucl. Phys. A 644<br />

(1998) 289–305.<br />

[3.1.13] HAMBSCH, F.-J., et al., Study <strong>of</strong> <strong>the</strong> 237 Np(n,f)<br />

reaction at MeV neutron energies, Nucl. Phys.<br />

A 679 (2000) 3–24.<br />

[3.1.14] ZÖLLER, C.M., <strong>Fission</strong> Fragment Properties in<br />

<strong>the</strong> 238 U(n,f) Reaction at Incident Neutron<br />

Energies from 1 MeV to 500 MeV, Rep. IKDA-<br />

95/25, Technische Hochschule Darmstadt (1995).<br />

[3.1.15] LISOWSKI, P., et al., “Neutron cross-section<br />

standards <strong>for</strong> <strong>the</strong> energy region above 20 MeV”,<br />

in Proc. Specialists Mtg Uppsala, Sweden, 1991,<br />

OECD, Paris (1991) 177.<br />

[3.1.16] SHCHERBAKOV, O.A., et al., “Neutroninduced<br />

fission <strong>of</strong> 233 U, 238 U, 232 Th, 239 Pu, 237 Np,<br />

nat Pb, and 209 Bi relative to 235 U in <strong>the</strong> energy<br />

range 1–200 MeV”, Nuclear <strong>Data</strong> Science Technology<br />

(Proc. Int. Conf. Tsukuba, Japan, 2001), J.<br />

Nucl. Sci. Technol. 1 Suppl. 2 (2002) 230–233.<br />

39

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