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Fission Barrier Height A systematic TDDFT data for nuclear fission analysis 岩田順敬 (Yoritaka Iwata) 東工大 科学技術創成研究院 (Tokyo Tech) with T. Nishikawa (Nuclear Engineering, Ltd) K. Kean (Tokyo Tech. and JAEA) S. Chiba (Tokyo Tech.) Introduction on nuclear chart Fission mechanism is studied for this region Nucleus in our scope Thermal Neutron Fission CS We have less information about the fissility BE/A Halflife 236 U Motivation ◇ Nuclear fission is one of theoreticallytheoretically difficult processes in sub-atomic physics. DifficultDifficult toto treattreat microscopicallymicroscopically HereHere wewe taketake lessless phenomenologicalphenomenological (ab-initio(ab-initio like)like) treatmenttreatment suchsuch asas TDDFTTDDFT (time-dependent(time-dependent densitydensity functionalfunctional theory).theory). ◇◇ InIn termsterms ofof fission,fission, twotwo topicstopics areare focusedfocused onon …… __ many-bodymany-body forceforce __ frictionfriction andand dissipationdissipation Fission dynamics mapped on Eq. of Motion Γ(t) :random force macroscopic Potential V Friction γ … by CHF … by TDDFT microscopic TDDFT calc. R Contents ◇ CHF for FissionFission barrierbarrier heightheight SLy4SLy4 byby Kean-Iwata-ChibaKean-Iwata-Chiba …… effectiveeffective many-bodymany-body forceforce effecteffect ◇ TDDFT + Langevin model for Friction by Nishikawa-Iwata-Chiba …… effectiveeffective dissipationdissipation includedincluded inin TDDFTTDDFT SV-basSV-bas ◇ Result Theoretical Nuclear data … provided by theoretical systematics ◇ Summary Density functional theory WHY microscopic ? ➔ Nucleon degree of freedom （ Fermi statistics ） ➔ Nucleon-nucleon interaction （ incl. spin-orbit force ） ➔Mean-field type description ➔ Coulomb force nucleus ➔ Less phenomenological Less free parameter (no free parameter for dynamics) ーーーーーー ➔TDDFT and CHF use the same functional form proton neutron Fission dynamics to refine fissility ... mapped on Eq. of Motion Γ(t) :random force macroscopic Potential V Friction γ … by CHF … by TDDFT FissilityFissility microscopic TDDFT calc. R ~ 50 ◇ CHF for FissionFission barrierbarrier heightheight FissionFission barrierbarrier heightheight byby constraintconstraint Hartree-FockHartree-Fock withwith pairingpairing (density(density dependentdependent pairing)pairing) 15 236UU ] ] V V 10 e e M M α = 1/6 [ [ E E 5 SLy4SLy4 ββ=Q=Q20 0 0 0.2 0.4 0.6 0.8 1 1.2 SinceSince thethe barrierbarrier heightheight isis examinedexamined byby β,β, onlyonly symmetricsymmetric fissionfission cancan bebe identifiedidentified ([Thr.]([Thr.] barrierbarrier heightheight becomesbecomes ratherrather higher).higher). Fission barrier height We need a reliable fission barrier inner barrier (outer barrier) Fission barrier height is 4 to 7 MeV (exp.), while they are calculated from 7 to 14 MeV (SLy4). … almost twice larger The improved interaction is necessary ! _ why are most of the Skyrme interactions so large ? _ is there any way to re-fit the Skyrme interaction ? in the corresponding part of nuclear chart Medium effect force effect Hamiltonian density of density functional theory Analogous to Alpha term: density dependent term on the fission barrier height ... Perturbation analysis for alpha-effect 15 236UU 10 α = 1/6 5 alpha value +10 % SLy4SLy4 ββ=Q=Q20 0 20 0 0.2 0.4 0.6 0.8 1 1.2 [Perturbation analysis] -10 % We examined 10 % different cases starting from Original alpha = 1/6 = 0.1666... Sensitivity of fission barrier height on alpha We have confirmed Only 10 % change of a … can contribute to … ~40% difference of fission barrier height This fact is confirmed in U-isotopes 231 to 239 Pu-isotopes 237 to 245 using SkM*, SLy4, SV-bas interactions. alpha value -10 % Alpha-perturbation theory This fact is our motivation to change alpha slightly to have a better description of fission barrier height What to change [Strategy] +10 % Also change this one to keep the total contribution as a whole term Validity of the proposed method Binding energy [MeV] Original calc (Proposed calc) Original Proposed Radius [fm] RIPL3 r_p, r_n, r_tot (r_p, r_n, r_tot) Only small deference in these values (quality is kept) Correlation between experimental and theoretical results for SLy4 and SkM* interactions ● original ● proposed Theoretical database I using substantially refined Skyrme forces …m-SLy4 m-SkM* m-SV-bas in terms of fission ◇ TDDFT + Langevin model Friction along the collision axis Process of extracting friction effect Model time evolution Duration time ~ 1.5 [10-21 s] 296116 = 296Lv symmetric fission by TDDFT R Y.Iwata and S. Heinz, CERN Proceedings 002 (2012) Averaged friction coefficient Microscopic inputs R, dR/dt : extracted ◇ TDDFT + Langevin model It should play a essential role in fission Friction along the collision axis Validity for TDDFT + 4D Langevin method 236UU This is good enough (more than expected), now we engage to calculate the other cases Linearly scaled energy-dependence ← Root-mean squared line This is not only for the U236, but for the other isotopes. Indeed ... [systematics] Linearly scaled energy-dependence N=150 120 Uranium isotopes 100 80 Friction coeff. g 60 40 N=146 120 20 100 0 Energy 1 2 3 4 5 6 807 8 9 10 11 60 40 N=142 20 120 0 100 1 2 3 4 5 6 7 8 9 10 11 80 60 40 20 0 1 2 3 4 5 6 7 8 9 10 11 [systematics] Linearly scaled energy-dependence N=152 140 Plutonium isotopes 120 100 80 Friction coeff. g 60 40 N=148 20 120 0 100 1 2 3 4 5 6 7 8 9 10 11 Energy 80 60 40 N=144 20 140 0 120 1 2 3 4 5 6 7 8 9 10 11 100 80 60 40 20 0 1 2 3 4 5 6 7 8 9 10 11 [systematics] Linearly scaled energy-dependence N=154 120 100 Curium isotopes 80 Friction coeff. g 60 N=150 40 120 20 100 0 2 3 4 5 6 807 8 9 10 11 Energy 60 40 20 N=146 0 120 2 3 4 5 6 7 8 9 10 11 100 80 60 40 20 0 2 3 4 5 6 7 8 9 10 11 [Systematics] Linearly scaled energy-dependence Modeled by ... γ = a (E/A) + b b 115 120 125 130 135 140 145 -4.5 -5 U Pu [As a physical law] [As a physical law] Cm Cf This would be the first time -5.5 Fm to show the energy a dependence of friction -6 using microscopic calculations -6.5 Statistical law found by Nishikawa-san -7 Neutron number Energy dependence is rather moderate compared to mass dependence in which Z dependence is larger than N dependence Friction along the collision axis 236U Similarity can be found in BE How does the friction behave ? Thermal Neutron Fission CS Similarity can be found in BE/A BE/A Halflife 236 U Theoretical Database II (SV-bas and more) SkM* , SLy4 calcs will follow before long. SLy4 0.58 100 98 0.54 96 A 94 / γ 0.5 0 92 0.46 1.48 1.52 1.56 1.6 1.64 N/Z The model eq. for exploring Z=120 Stochastic 1D eq. to refine the fissility Γ(t) :random force + Coulomb pot Potential V Friction γ … by CHF … by TDDFT microscopic TDDFT calc. R Summary SkM*SkM* ◇ FissionFission barrier/Potentialbarrier/Potential SLy4SLy4 (mainly(mainly byby K.K. KeanKean sansan)) … Alpha-perturbation theory SV-basSV-bas ◇ Friction (mainly by Nishikawa san) … Friction formula (depending on mass and energy) These are substituted into both _ 1D Langevin type equation (for refining fissility) _ Usual 3D and 4D Langevin equation .
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