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

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 E_n ~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(n, xnf)^{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(n, F)(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 E_n ≈ 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.