[Paper Review] Fragment Intrinsic Spins and Fragments' Relative Orbital Angular Momentum in Nuclear Fission

Bulgac, Aurel, Abdurrahman, Ibrahim+2 more|arXiv (Cornell University)|Aug 9, 2021

Nuclear physics research studies46 citations

TL;DR

This study presents the first unrestricted microscopic calculations of fission fragment intrinsic spins and relative orbital angular momentum in 236U∗, 240Pu∗, and 252Cf using time-dependent density functional theory (TDDFT). It reveals that fragment dynamics are dominated by bending collective modes, contradicting phenomenological models and challenging prior interpretations of experimental data.

ABSTRACT

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 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.

Motivation & Objective

• To provide a fully microscopic, unrestricted description of fission fragment intrinsic spins and relative orbital angular momentum in actinides.
• To resolve long-standing ambiguities in the origin of fragment angular momenta, particularly the role of collective modes.
• To challenge and replace phenomenological models based on unverified assumptions with a rigorously derived quantum many-body framework.
• To compute the triple probability distribution P(SL, SH, Λ) for fission fragments using time-evolved TDDFT wave functions.
• To clarify the dynamics of angular momentum sharing between fragments from saddle to scission, independent of ad hoc constraints.

Proposed method

• Employed time-dependent density functional theory (TDDFT) extended to superfluid systems to simulate fission dynamics from the outer saddle to scission.
• Performed triple angular momentum projection via the overlap ⟨Φ|eiβ0(JLx+JHx)eiβLJLx eiβHJHx|Φ⟩ to extract P(SL, SH, Λ).
• Used two nuclear energy density functionals (SkM∗ and SeaLL1) with a 1 fm lattice spacing and momentum cutoff pcut ≈ 600 MeV/c.
• Enforced triangle restrictions |SL − SH| ≤ Λ ≤ SL + SH via step functions △ = Θ(Λ ≥ |SL − SH|)Θ(Λ ≤ SL + SH) to preserve angular momentum conservation.
• Evolved initial wave functions from various Q20 and Q30 deformations near the outer saddle, tracking fragment separation beyond 30 fm.
• Calculated the cosine of the angle between fragment spins, cos φLH, using the Langer-corrected formula to analyze spin correlations.

Experimental results

Research questions

• RQ1 What is the microscopic origin of intrinsic spins in fission fragments, and how do they correlate with relative orbital angular momentum?
• RQ2 How do the fragment intrinsic spins and relative orbital angular momentum distribute in primary fission for 236U∗, 240Pu∗, and 252Cf?
• RQ3 To what extent are the dynamics of fission fragment angular momenta governed by bending collective modes rather than other modes like twisting or wriggling?
• RQ4 How do the results from a fully microscopic TDDFT framework compare with phenomenological models and experimental interpretations?
• RQ5 What is the role of collective modes in shaping the triple distribution P(SL, SH, Λ) in spontaneous and neutron-induced fission?

Key findings

• The orbital angular momentum distribution for 252Cf(sf) peaks at ⟨Λ⟩ = 14.7 (7.1) with SeaLL1 and 13.3 (6.5) with SkM∗, indicating substantial angular momentum transfer.
• For 236U∗, the average relative orbital angular momentum is ⟨Λ⟩ = 12.6 (6.2) with SeaLL1 and 10.9 (5.4) with SkM∗, consistent with high angular momentum transfer.
• For 240Pu∗, ⟨Λ⟩ = 12.6 (6.2) (SeaLL1) and 11.3 (5.6) (SkM∗), showing similar trends across actinides.
• The intrinsic spin distributions show ⟨SL⟩ ≈ 11.8 (5.8) and ⟨SH⟩ ≈ 11.0 (5.3) for SeaLL1 and SkM∗ in 236U∗, indicating strong spin alignment.
• The angle φLH between fragment spins is strongly correlated, with cos φLH peaking near 1, indicating that SL and SH are preferentially aligned.
• The results contradict the 'snapping rubber band' model and instead show that bending modes dominate the dynamics, not twisting or longitudinal modes.