Abstract <p>The angular anisotropy of the neutron emission spectra (NES) of the <sup>232</sup>Th + <i>n</i> and <sup>238</sup>U + <i>n</i> reactions is due to the angular dependence of elastic scattering, direct excitation of collective levels, and preequilibrium emission of the 1st neutron in (<i>n</i>, <i>nX</i>)<sup>1</sup> reaction, as well as collective excitations in the continuous spectrum with <i>U</i> ≈ 1~6 MeV. In the case of the prompt fission neutron spectra (PFNS), the anisotropy is caused by the anisotropy of the exclusive spectra of prefission neutrons in (<i>n</i>, <i>xnf</i>)<sup>1</sup> reactions. To correctly estimate the excitation of the <sup>232</sup>Th and <sup>238</sup>U levels in continuous spectrum with excitation energy <i>U</i> ≈ 1~6&#xa0;MeV, the coupling of the ground-state band levels with <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11496_2025_8965_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\({{J}^{\pi }}\)</EquationSource> <!--PhysPart2470123Maslov-m1--> </InlineEquation> = 0<sup>+</sup>, 2<sup>+</sup>, 4<sup>+</sup>, 6<sup>+</sup>, 8<sup>+</sup> (in the rigid rotator model) is considered, while the coupling of the γ-band levels with <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11496_2025_8965_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\({{K}^{\pi }}\)</EquationSource> <!--PhysPart2470123Maslov-m2--> </InlineEquation> = 0<sup>+</sup>, 2<sup>+</sup> and the levels of the octupole bands with <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11496_2025_8965_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\({{K}^{\pi }}\)</EquationSource> <!--PhysPart2470123Maslov-m3--> </InlineEquation> = 0<sup>–</sup> in the soft rotator model (levels with excitation energies <i>U</i> ≈ 0~1 MeV). The <sup>232</sup>Th + <i>n</i> and <sup>238</sup>U&#xa0;+ <i>n</i> NES at <i>E</i><sub><i>n</i></sub> ~6, ~12, ~14, ~18 MeV are described in detail. An adequate description of the doubly differential emission spectra and angular distributions of the (<i>n</i>, <i>nX</i>)<sup>1</sup> neutrons in the range of the continuous spectrum corresponding to excitation energies <i>U</i> ≈ 1~6 MeV of residual nuclei has been achieved. In the case of PFNS, the anisotropy of <sup>232</sup>Th + <i>n</i> and <sup>238</sup>U + <i>n</i> reactions is shown to be caused by a part of the (<i>n</i>, <i>nX</i>)<sup>1</sup> neutrons manifested in exclusive spectra of prefission neutrons, as in the <sup>239</sup>Pu(<i>n</i>, <i>xnf</i>) reaction. For <sup>232</sup>Th(<i>n</i>,&#xa0;<i>xnf</i>)<sup>1, ... <i>x</i></sup> and <sup>238</sup>U(<i>n</i>, <i>xnf</i>)<sup>1, ... <i>x</i></sup> , the PFNS demonstrate different sensitivity to (<i>n</i>, <i>xnf</i>)<sup>1</sup> neutron emission into the forward and rear hemispheres relative to the incident neutron beam. The mean energy of PFNS and (<i>n</i>, <i>xnf</i>)<sup>1</sup> neutrons depends on the neutron emission angle θ, as well as fission cross section, mean number of prompt fission neutrons and the total kinetic energy (TKE) of fission fragments (products). The exclusive spectra of (<i>n</i>, <i>xnf</i>)<sup>1, … <i>x</i></sup> neutrons at θ ~ 90° are consistent with the observed cross sections of the <sup>232</sup>Th(<i>n</i>,&#xa0;<i>F</i>)(<sup>238</sup>U(<i>n</i>, <i>F</i>)) fission reactions and <sup>232</sup>Th(<i>n</i>, <i>xn</i>)( <sup>238</sup>U(<i>n</i>, <i>xn</i>)) neutron emission reactions. For <sup>239</sup>Pu(<i>n</i>, <i>xnf</i>), the approximated distribution <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11496_2025_8965_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\(\omega (\theta )\)</EquationSource> <!--PhysPart2470123Maslov-m4--> </InlineEquation> is consistent with the <sup>232</sup>Th + <i>n</i> and <sup>238</sup>U + <i>n</i> NES at <i>E</i><sub><i>n</i></sub> ≈ 6~18 MeV. The angular anisotropy of the (<i>n</i>, <i>xnf</i>)<sup>1</sup> neutrons for <sup>232</sup>Th + <i>n</i> and <sup>238</sup>U + <i>n</i> spectra is manifested in the ratios of the mean energies of PFNS and exclusive (<i>n</i>, <i>xnf</i>)<sup>1, … <i>x</i></sup> spectra of prefission neutrons. A correlation is found between the angular anisotropy of secondary (<i>n, xnf</i>)<sup>1</sup> neutrons with the contribution of the (<i>n</i>, <i>nf</i>) emission/fission process to the observed fission cross section and NES angular anisotropy.</p>

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Anisotropy of Prompt Fission Neutron Spectra 232Th(n, F) and 238U(n, F)

  • V. M. Maslov

摘要

Abstract

The angular anisotropy of the neutron emission spectra (NES) of the 232Th + n and 238U + n reactions is due to the angular dependence of elastic scattering, direct excitation of collective levels, and preequilibrium emission of the 1st neutron in (n, nX)1 reaction, as well as collective excitations in the continuous spectrum with U ≈ 1~6 MeV. In the case of the prompt fission neutron spectra (PFNS), the anisotropy is caused by the anisotropy of the exclusive spectra of prefission neutrons in (n, xnf)1 reactions. To correctly estimate the excitation of the 232Th and 238U levels in continuous spectrum with excitation energy U ≈ 1~6 MeV, the coupling of the ground-state band levels with \({{J}^{\pi }}\) = 0+, 2+, 4+, 6+, 8+ (in the rigid rotator model) is considered, while the coupling of the γ-band levels with \({{K}^{\pi }}\) = 0+, 2+ and the levels of the octupole bands with \({{K}^{\pi }}\) = 0 in the soft rotator model (levels with excitation energies U ≈ 0~1 MeV). The 232Th + n and 238U + n NES at En ~6, ~12, ~14, ~18 MeV are described in detail. An adequate description of the doubly differential emission spectra and angular distributions of the (n, nX)1 neutrons in the range of the continuous spectrum corresponding to excitation energies U ≈ 1~6 MeV of residual nuclei has been achieved. In the case of PFNS, the anisotropy of 232Th + n and 238U + n reactions is shown to be caused by a part of the (n, nX)1 neutrons manifested in exclusive spectra of prefission neutrons, as in the 239Pu(n, xnf) reaction. For 232Th(nxnf)1, ... x and 238U(n, xnf)1, ... x , the PFNS demonstrate different sensitivity to (n, xnf)1 neutron emission into the forward and rear hemispheres relative to the incident neutron beam. The mean energy of PFNS and (n, xnf)1 neutrons depends on the neutron emission angle θ, as well as fission cross section, mean number of prompt fission neutrons and the total kinetic energy (TKE) of fission fragments (products). The exclusive spectra of (n, xnf)1, … x neutrons at θ ~ 90° are consistent with the observed cross sections of the 232Th(nF)(238U(n, F)) fission reactions and 232Th(n, xn)( 238U(n, xn)) neutron emission reactions. For 239Pu(n, xnf), the approximated distribution \(\omega (\theta )\) is consistent with the 232Th + n and 238U + n NES at En ≈ 6~18 MeV. The angular anisotropy of the (n, xnf)1 neutrons for 232Th + n and 238U + n spectra is manifested in the ratios of the mean energies of PFNS and exclusive (n, xnf)1, … x spectra of prefission neutrons. A correlation is found between the angular anisotropy of secondary (n, xnf)1 neutrons with the contribution of the (n, nf) emission/fission process to the observed fission cross section and NES angular anisotropy.