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Register a new userStudy of angular momentum effects in fission
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R. Vogt
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Background: The role of angular momentum in fission has long been discussed but the observable effects are difficult to quantify. Purpose: We discuss a variety of effects associated with angular momentum in fission and present quantitative illustrations. Methods: We employ the fission simulation model $mathtt{FREYA}$ which is well suited for this purpose because it obeys all conservation laws, including linear and angular momentum conservation at each step of the process. We first discuss the implementation of angular momentum in $mathtt{FREYA}$ and then assess particular observables, including various correlated observables. We also study potential effects of neutron-induced fission of the low-lying isomeric state of $^{235}$U relative to the ground state. Results: The fluctuations inherent in the fission process ensure that the spin of the initial compound nucleus has only a small influence on the fragment spins which are therefore nearly uncorrelated. There is a marked correlation between the spin magnitude of the fission fragments and the photon multiplicity. We also consider the dynamical anisotropy caused by the rotation of an evaporating fragment and study especially the distribution of the projected neutron-neutron opening angles, showing that while it is dominated by the effect of the evaporation recoils, it is possible to extract the signal of the dynamical anisotropy by means of a Fourier decomposition. Finally, we note that the use of an isomeric target, $^{235 {rm m}}$U($n_{rm th}$,f), may enhance the symmetric yields and can thus result in higher neutron multiplicities for low total fragment kinetic energy.
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A recent analysis of experimental data [J. Wilson $et. al$, Nature $mathbf 590$, 566 (2021)] found that the angular momenta of nuclear fission fragments are uncorrelated. Based on this finding, the authors concluded that the spins are therefore determined only $after$ scission has occurred. We show here that the nucleon-exchange mechanism, as implemented in the well-established event-by-event fission model $mathtt{FREYA}$, while agitating collective rotational modes in which the two spins are highly correlated, nevertheless leads to fragment spins that are largely uncorrelated. This fact invalidates the reasoning of those authors. Furthermore, it was reported [J. Wilson $et. al$, Nature $mathbf 590$, 566 (2021)] that the mass dependence of the average fragment spin has a sawtooth structure. We demonstrate that such a behavior naturally emerges when shell and deformation effects are included in the moments of inertia of the fragments at scission.
We present the first fully unrestricted microscopic calculations of the primary fission fragment intrinsic spins and of the fission fragments relative orbital angular momentum for $^{236}$U$^*$, $^{240}$Pu$^*$, and $^{252}$Cf using the time-dependent density functional theory framework. Within this microscopic approach, free of restrictions and unchecked assumptions and which incorporates the relevant physical observables relevant for describing fission, we evaluate the triple distribution of the fission fragment intrinsic spins and of their fission fragments relative orbital angular momentum and show that their dynamics is dominated by their bending collective modes, in contradistinction to the predictions of the existing phenomenological models and some interpretations of experimental data.
We investigate the angular momentum removal from fission fragments (FFs) through neutron and $gamma$-ray emission, where we find that about half the neutrons are emitted with angular momenta $ge 1.5hbar$ and that the change in angular momentum after the emission of neutrons and statistical $gamma$ rays is significant, contradicting usual assumptions. Per fission event, in our simulations, the neutron and statistical $gamma$-ray emissions change the spin of the fragment by 3.5 -- 5~$hbar$, with a large standard deviation comparable to the average value. Such wide angular momentum removal distributions can hide any underlying correlations in the fission fragment initial spin values. Within our model, we reproduce data on spin measurements from discrete transitions after neutron emissions, especially in the case of light FFs. The agreement further improves for the heavy fragments if one removes from the analysis the events that would produce isomeric states. Finally, we show that while in our model the initial FF spins do not follow a saw-tooth like behavior observed in recent measurements, the average FF spin computed after neutron and statistical $gamma$ emissions exhibits a shape that resembles a saw tooth. This suggests that the average FF spin measured after statistical emissions is not necessarily connected with the scission mechanism as previously implied.
Using a unique two-arm detector system for heavy ions (the BRS, binary reaction spectrometer) coincident fission events have been measured from the decay of $^{60}$Zn compound nuclei formed at 88MeV excitation energy in the reactions with $^{36}$Ar beams on a $^{24}$Mg target at $E_{lab}(^{36}$Ar) = 195 MeV. The detectors consisted of two large area position sensitive (x,y) gas telescopes with Bragg-ionization chambers. From the binary coincidences in the two detectors inclusive and exclusive cross sections for fission channels with differing losses of charge were obtained. Narrow out-of-plane correlations corresponding to coplanar decay are observed for two fragments emitted in binary events, and in the data for ternary decay with missing charges from 4 up to 8. After subtraction of broad components these narrow correlations are interpreted as a ternary fission process at high angular momentum through an elongated shape. The lighter mass in the neck region consists dominantly of two or three-particles. Differential cross sections for the different mass splits for binary and ternary fission are presented. The relative yields of the binary and ternary events are explained using the statistical model based on the extended Hauser-Feshbach formalism for compound nucleus decay. The ternary fission process can be described by the decay of hyper-deformed states with angular momentum around 45-52 $hbar$.
The structure effects of the fission fragments on their yields are studied within the statical theory with the inputs, like, excitation energies and level density parameters for the fission fragments at a given temperature calculated using the temperature dependent relativistic mean field formalism (TRMF). For the comparison, the results are also obtained using the finite range droplet model. At temperatures $T =1-2$ MeV, the structural effects of the fission fragments influence their yields. It is also seen that at $T = $ 3 MeV, the fragments become spherical and the fragments distribution peaks at a close shell or near close shell nucleus.
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