(A)symmetry of Fission in the. 74 Z 90, A 205 Region.

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1 (A)symmetry of Fission in the 74 Z 9, A 2 Region. P. Möller (LANL) and J. Randrup (LBL) Collaborators on this and other projects: W. D. Myers, H. Sagawa (Aizu), S. Yoshida (Hosei), T. Ichikawa(YITP), A. J. Sierk(LANL), A. Iwamoto (JAEA), S. Aberg (Lund), R. Bengtsson (Lund), S. Gupta (IIT, Ropar), and many experimental groups (e. g. K.-L. Kratz (Mainz), H. Schatz (MSU),A. Andreyev(University of West Scotland),... ) More details, figure files, papers, data on This is our new web site! The previous private one maintained locally was killed after more than 1 years in existence. The new one is officially managed by our laboratory computer people, although we program all the web pages (mostly by me). 1

2 My presentation will have 4 themes: T H E M E S To calculate yields accurate potential-energy surfaces are absolutely necessary Accuracy includes height of saddles and ridges as well as their location in a high-dimensional space Benchmarking of yield model on nuclei from Th to Fm. Application to neutron-deficient Hg region.

3 M exp M th (MeV) Mass Models Compared to AME23 HFB(Sly4): σ =.11 (MeV) µ = 2.94 (MeV) FRLDM(22): σ =.72 (MeV) µ =.3 (MeV) Neutron Number N

4 1 1 SKM* M exp M th (MeV) 1 σ = 7.33 (MeV) µ = 3.93 (MeV) Neutron Number N

5 Proton Number Z E γ (MeV) Effect of Axial Asymmetry on Nuclear Mass 18 Ru (3+) (4+) 2+ γ band + GS band 2(+) Neutron Number N Gd GS band γ band (8+) Pt GS band (+) 3+ γ band 4+ 2+

6 M exp M th (MeV) Mass-model error with γ correction for 71 nuclei with E γ >.2 MeV σ =.381 MeV µ =.19 MeV Mass-model error without γ correction for 71 nuclei with E γ >.2 MeV σ =.77 MeV µ =.42 MeV Nucleon Number A Mass-model error with ε 3 correction for 78 nuclei with E ε3 >.2 MeV σ =.38 MeV µ =.168 MeV Mass-model error without ε 3 correction for 78 nuclei with E ε3 >.2 MeV σ = 1.16 MeV µ = 1.32 MeV Nucleon Number A

7 6 4 New Masses in Audi 23 Evaluation, Relative to 1989, Compared to Theory FRLDM (1992) M exp M calc (MeV) σ 164 =.779 MeV σ 29 =.68 MeV Neutrons from β-stability 6 New Masses in Audi 23 Evaluation, Relative to 1989, Compared to Theory 4 FRDM (1992) M exp M calc (MeV) σ 164 =.669 MeV σ 29 =.462 MeV Neutrons from β-stability

8 Energy Release Q α (MeV) Neutron Number N α-decay of RIKEN exp. (24) OTHER exp. FRDM (1992) FRLDM (1992) HFB8 (Goriely) HFB2 (Goriely) Proton Number Z

9 6 3 12X 18 Scale 1. (MeV) 4 γ Axial Asymmetry Spheroidal Deformation ε 2

10 From: Nucl. Phys A469 (1987) 1 Fragment Elongation σ (Units of R ) 1..7 Family of shapes considered Distance between Mass Centers r (Units of R )

11 Fragment Elongation σ (Units of R ) From: Journ. Phys. G: Nucl. Part. Phys. 2 (1994) 1681 Potential energy for 28 Fm E (MeV) Distance between Mass Centers r (Units of R )

12 Dam building flips waterflow across new saddle 6 Imaginary Water-Flow Strategies Energy: E(I,J,K,L,N) Wetness: IW(I,J,K,L,N) (Wet=1,Dry=) 4 Other 3 2 Retaining wall prevents backflow Fission Direction

13 1 Saddle Search Strategies Illustrated α Θ

14 One-Dimensional Paths Saddle point Function Value Θ

15

16 1 Saddle Search Strategies Illustrated α Θ Graphics by Peter Möller

17 Five Essential Fission Shape Coordinates d ε f1 ε f2 M1 M2 Q 2 4 Q 2 ~ Elongation (fission direction) 3 α g ~ (M1-M2)/(M1+M2) Mass asymmetry 1 ε f1 ~ Left fragment deformation 1 ε f2 ~ Right fragment deformation 1 d ~ Neck grid points 36 3 unphysical points 9 32 physical grid points

18 1 22 Fm 97 Nuclear Inertia B r (Units of µ) 1 Cranking (dynamic) Cranking (static) Semi-empirical Irrotational Reduced mass µ Distance between Mass Centers r (Units of R ) Figure 37

19 Physical Review C 13 (1976) 229

20 Fission Barrier and Associated Shapes for 228Ra Asymmetric mode Symmetric mode Separating ridge Graphics by Peter Möller Potential Energy (MeV) Nuclear Deformation (Q2 / b)(1/2) 1

21 Yield Y(Z f ) (%) Calc. (6.84 MeV) Exp. 239 Pu(n,f) Calc. (Ignatyuk lev. dens.) (all panels) 24 Pu Calc. (6.4 MeV) Exp. 23 U(n,f) 236 U 2 2 Calc. (6.4 MeV) Exp. 233 U(n,f) 234 U Calc. (11. MeV) Exp. 234 U(γ,f) 234 U Yield Y(Z f ) (%) Fragment Charge Number Z f Fragment Charge Number Z f

22 Yield Y(Z f ) (%) D space (Tot. min.) (all panels) Calc. (6.84 MeV) Exp. 239 Pu(n,f) 24 Pu Calc. (6.4 MeV) Exp. 23 U(n,f) 236 U 2 2 Calc. (6.4 MeV) Exp. 233 U(n,f) 234 U Calc. (11. MeV) Exp. 234 U(γ,f) 234 U Yield Y(Z f ) (%) Fragment Charge Number Z f Fragment Charge Number Z f

23 Triple No of Elongation Grid Points: 133 Points in Q 2 in all Panels 2 Calc. 239 Pu(n,f) 24 Pu Calc. 23 U(n,f) 236 U 2 Yield Y(Z f ) (%) Calc. 233 U(n,f) 234 U Calc. (11. MeV) Exp. 234 U(γ,f) 234 U Yield Y(Z f ) (%) Fragment Charge Number Z f Fragment Charge Number Z f

24 Mass Yield (%) Exp. 2 Fm(n,f) 26 Fm Charge Number Z

25 Charge Yield (%) Exp. (n,f) 26 Fm Charge Number Z 7 26 Fm Mass Yield (%) Exp. (n,f) Mass Number A

26 Yield Y(A f )(%) Calc. (6.38 MeV) Exp. 2 Fm(n,f) 26 Fm Fragment mass number A f

27 Yield Y(A f )(%) Yield Y(A f )(%) Calc.(7 MeV) Calc.(7 MeV) 27 Fm(n,f) 26 Fm D Brownian motion 28 Fm D Brownian motion Calc.(7 MeV) Calc.(7 MeV) Fm(n,f) 26 Fm 4D Scission surface R sc =1. fm 28 Fm 4D Scission surface R sc =1. fm Fragment Mass Number A f Fragment Mass Number A f

28 Folded-Yukawa potential T 1/2 = 1.74 (s) Ti Hg+e ε 2 =-.13 ε 4 =.1 ε 6 =.1 n =.99 MeV p =.1 MeV (L-N) λ n =34.88 MeV λ p =32. MeV a=.8 fm. Gamow-Teller Strength 2.. B f Q EC 1 1 Excitation Energy (MeV)

29 Thu Sep 21 18:6:18 MDT 26 Graphics Art by Peter Moller Hg 1 Scale.2 (MeV) 4 4 Axial Asymmetry γ Spheroidal Deformation ε 2

30 2 Hg 1 QEC Ridge Sym. Trough ss io n Ba rri er 1 Fi. Valle Asym Potential Energy (MeV) 174 y Nuclear Deformation (Q2/b)(1/2) 12

31 2 Hg n sio Fis 1 g Rid e QEC rri e Ba n Fi ss io y. Valle Valley r 1 Asym Sym. Potential Energy (MeV) Nuclear Deformation (Q2/b)(1/2) 12

32 2 e 1 Sym. 1 ier Ba rr Fis s ion ey Vall QEC Valley m. Asy Potential Energy (MeV) Hg Ridg Nuclear Deformation (Q2/b)(1/2) 12

33 8 6 Calc. (E * = B f + 2 MeV) Calc. (E * = 2 MeV) Calc. (E * = 4 MeV) 174 Hg 176 Hg 4 2 Yield Y(A f ) (%) Hg 18 Hg Fragment Mass Number A f

34 Charge Yield Y(Z f ) (%) Rn Fragment Charge Number Z f

35 C O N C L U S I O N S First generation model describes actinide yields from Th to Fm with unexpected (to me) accuracy. Hg yields are somewhat more roughly described, but lack of data inhibits precise understanding of deviations, (if any). Most experimental yield is subbarrier. Interesting energy dependence obtained for 174 Hg, symmetric yield increases with decreasing energy. Studies of entire isotope chains indicates transition from asymmetric below approximately A = 2 to symmetry beyond. Highly variable behavior below Pb. Future enhancements?: What s beyond Brownian shape motion? Odd-even effects and (Z, N) yields. Experimental tests of predictions in region below Pb HIGHLY desirable.

36 M E T R O P O L I S The simplicity of the algorithm nobly stands aside the complexity of the problems it successfully treats.