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С HART OF NUCLEI

Predicted nuclear data for nucleosinthesis calculations Lutostansky Yu. S., Panov I.V N a tional Research Center "Kurchatov Institute" Institute of Theoretical and Experimental Physics, ITEP. 1. С HART OF NUCLEI. 2. DYNAMIC PROCESSES OF IMPULCE NUCLEOSYNTESIS. Superheavy nuclei.

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С HART OF NUCLEI

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  1. Predicted nuclear data for nucleosinthesis calculationsLutostansky Yu. S., Panov I.VNational Research Center "Kurchatov Institute"Institute of Theoretical and Experimental Physics, ITEP 1

  2. СHART OF NUCLEI 2

  3. DYNAMIC PROCESSES OF IMPULCE NUCLEOSYNTESIS. Superheavy nuclei β-decay fission s-process track r-process track β-decay The tracks of elements synthesis ins (slow)- andr (rapid)- processes. 3

  4. DYNAMIC PROCESSES OF IMPULSE NUCLEOSYNTESIS. Superheavy nuclei β-decay fission Cold s-process track Hot r-process track β-decay The tracks of elements synthesis ins (slow)- andr (rapid)- processes. 4

  5. DYNAMIC MODEL OF NUCLEOSYNTHESIS – 2TWO-STEP PROCESS 1. The importance of nuclear input for r-process nucleosynthesis. 2. Spontaneous-fissionwill hinder the production of elements beyond Z = 120 “Have superheavy elements been produced in nature?” I. Petermann, K. Langanke, G. Mart´ınez-Pinedo, I.V. Panov, P.-G. Reinhard, and F.-K. Thielemann. Eur. Phys. J. A (2012) 48: 122 5

  6. IMPULCE NUCLEOSYNTHESIS OF THE HEAVY NUCLEI Dynamic r-process Hot Cold NUCLEOSYNTHESIS OF THE HEAVY NUCLEI in s (slow)andr (rapid)- processes – nuclei withT1/2  1 y. ; О – T1/2 < 1 y.; + ‑ predictions. Dynamic r-process tracks. 6

  7. Nuclear physics in the r-process • Fission rates and distributions: • n-induced • spontaneous • b-delayed b-delayed n-emissionbranchings(final abundances) b-decay half-lives(progenitor abundances, process speed) • Neutron-capture rates • for A>130 in slow freeze-out • for A<130 maybe in a “weak” r-process ? n-physics ? Seed productionrates (aaa,aan, a2n, ..) Masses (Sn)(location of the path) 7

  8. METHOD: r –Process equations for the concentration calculations Concentrations n(A,Z) are changing in time(may be more than6000 equations): dn(A, Z)/dt= – (A, Z).n(A, Z) –n(A, Z).n(A, Z) + n(A+1, Z).n(A+1, Z) + + n(A–1, Z).n(A–1, Z) – n(A, Z).n(A, Z) + + (A, Z–1).n(A, Z–1) × P(A, Z–1) + (A+1,Z–1).n(A+1,Z–1) × P1n(A+1,Z–1)+ + (A+2,Z–1).n(A+2,Z–1)×P2n(A+2,Z–1) +(A+3,Z–1)n(A+3,Z–1) × P3n(A+3,Z–1)+ + (A, Z) + Ff (A, Z), n andn — rates of (n,γ) and (γ,n) -reactions,=ln2/T1/2 —-decay rate, P - probability of (A, Z) nuclide creation after –-decay of (A, Z-1) nuclide. Branching coefficients of isobaric chains - P1n, P2n, Р3ncorresponds to probabilities of one-, two- and three- neutrons emission in–- decay of the neutron-rich nuclei; the total probability of the delayed neutrons emission is the sum: Ff (A, Z)describes fission processes. Neutrino capturing processes (A, Z) 8

  9. r –process equations for the concentration calculations.Dynamic model: n/ n(A, Z)→  n/ n (A, Z, t); n(A, Z)→ n(A, Z, t) Concentrations n(A,Z, t) are changing in time(may be more than6000 equations): dn(A, Z, t)/dt = – (A, Z).n(A, Z, t) –n(A, Z, t).n(A, Z, t) + + n(A+1, Z, t).n(A+1, Z, t) + n(A–1, Z, t).n(A–1, Z, t) – n(A, Z).n(A, Z, t) + + (A, Z–1).n(A, Z–1, t) × P(A, Z–1) + (A+1,Z–1).n(A+1,Z–1,t) × P1n(A+1,Z–1)+ + (A+2,Z–1).n(A+2, Z–1, t) × P2n(A+2,Z–1) +(A+3,Z–1)n(A+3, Z–1, t) × P3n(A+3,Z–1) +Ff (A, Z) +(A, Z, t) n(t)andn(t)–rates of (n,γ) and (γ,n) –reactions; all fluxes and spectra are time depended =ln2/T1/2 —-decay rate, P - probability of (A, Z) nuclide creation after –-decay of (A,Z-1) nuclide. Branching coefficients of isobaric chains - P1n, P2n, Р3ncorresponds to probabilities of one-, two- and three- delayed neutrons emission in–- decay of the neutron-rich nuclei. Ff (A, Z)describes fission processes — spontaneous and beta-delayed fission. (A, Z) - neutrino capturing processes. 9

  10. Masses-0. Energies - Formulas Т1/2 Qβm (m = 46) Pn~ (Qn)4. 35 A. Sobiczewski PHYSICAL REVIEW C 94, 051302(R) (2016) 10

  11. Masses-1. BETA – DECAY ENERGIES (Nucl. Map General) 11

  12. Masses-1. BETA – DECAY ENERGIES (U) Calculations in “Fayans energy density functional theory –FaDF”. [S.V. Tolokonnikov, I.N. Borzov, M. Kortelainen, Yu.S. Lutostansky, and E. E. Saperstein, J. Phys. G, 42,075102 (2015)] Predictions from the Skyrme EDF HFB-17 code. [S. Goriely, N. Chamel, and J.M. Pearson, Phys. Rev.Lett. 102, 152503 (2009)] S. Goriely, M. Samyn, and J.M. Pearson (2007) Phys. Rev. C75, 064312. 12

  13. Masses-2. NEUTRON SEPARATION ENERGY (U) Calculations in “Fayans energy density functional theory –FaDF”. [S.V. Tolokonnikov, I.N. Borzov, M. Kortelainen, Yu.S. Lutostansky, and E. E. Saperstein, J. Phys. G, 42,075102 (2015)] Predictions from the Skyrme EDF HFB-17 code. [S. Goriely, N. Chamel, and J.M. Pearson, Phys. Rev.Lett. 102, 152503 (2009)] 13

  14. Masses-3. α-Decay Energies Calculations in “Fayans energy density functional theory –FaDF”. [S.V. Tolokonnikov, I.N. Borzov, M. Kortelainen, Yu.S. Lutostansky, and E. E. Saperstein, Eur. Phys. J. A, 53 (2017); 33] Predictions from the Skyrme EDF HFB-17 code. [S. Goriely, N. Chamel, and J.M. Pearson, Phys. Rev.Lett. 102, 152503 (2009)] MMM-Predictions [I. Muntian, Z. Patyk, A. Sobiczewski, Phys. At. Nucl. (2003)]. 14

  15. Masses-3+. α-Decay Energies Calculations in “Fayans energy density functional theory –FaDF”. [S.V. Tolokonnikov, I.N. Borzov, M. Kortelainen, Yu.S. Lutostansky, and E. E. Saperstein, Eur. Phys. J. A, 53 (2017); 33] Predictions from the Skyrme EDF HFB-17 code. [S. Goriely, N. Chamel, and J.M. Pearson, Phys. Rev.Lett. 102, 152503 (2009)] MMM-Predictions [I. Muntian, Z. Patyk, A. Sobiczewski, Phys. At. Nucl. (2003)]. 15

  16. ENERGIES OF FISSION BARIERS (Np) Calculations in “Fayans energy density functional theory –FaDF”. [S.V. Tolokonnikov, I.N. Borzov, M. Kortelainen, Yu.S. Lutostansky, and E. E. Saperstein, J. Phys. G, 42,075102 (2015)] Predictions from the Skyrme EDF HFB-17 code. [S. Goriely, N. Chamel, and J.M. Pearson, Phys. Rev.Lett. 102, 152503 (2009)] Efis-1 [S. Goriely, M. Samyn, and J.M. Pearson (2007) Phys. Rev. C75, 064312]. 16

  17. ENERGIES OF FISSION BARIERS (Np) Calculations in “Fayans energy density functional theory –FaDF”. [S.V. Tolokonnikov, I.N. Borzov, M. Kortelainen, Yu.S. Lutostansky, and E. E. Saperstein, J. Phys. G, 42,075102 (2015)] Predictions from the Skyrme EDF HFB-17 code. [S. Goriely, N. Chamel, and J.M. Pearson, Phys. Rev.Lett. 102, 152503 (2009)] Efis-1 [S. Goriely, M. Samyn, and J.M. Pearson (2007) Phys. Rev. C75, 064312]. 17

  18. β-Delayed processes in very neutron-rich nuclei Delayed neutron emission -(β, n) ------------------------------------ Multi-neutron β – delayed emission -(β, kn) ------------------------------------ β – delayed fission - (β,f) 7 18

  19. BETA-DELAYED PROCESSES CALCULATIONS 1. Corrections in half-life (1) where , so Т1/2 Eβm (m = 46) (2) 2. Beta-delayed neutrons emission probability (3) I(E) = S(E). f(Z, E)/ I0 , where (4) So for k = 1(one delayed neutron emission): Pn~ E4. 35(5) 3. Beta-delayed fission probability (6) Pβf~ E4  5(7) 19

  20. Beta-Strength Function of Very Neutron-Rich Nuclei • Exp. data: K. Pham, J. Jänecke, D. A. Roberts, et al., Phys. Rev. C 51, 526 (1995) • Calculations: Yu. S. Lutostansky, JETP Lett. 106, 1 (2017) 20

  21. ISOBARIC STATES MICROSCOPIC DESCRIPTION For the GT effective nuclear field, system of equations in the energetic λ-representation has the form[FFST Migdal A. B.]: G -Tselectionrules: Δ j =0;±1 Δ j =+1: j=l+1/2 → j =l–1/2 Δ j =0: j=l±1/2 → j=l±1/2 Δ j = –1: j=l–1/2 → j=l+1/2 j =l–1/2→ j =l–1/2 where nλand ελare, respectively, the occupation numbers and energies of states λ. --------------------------------------------------------------------------------------------- Local nucleon–nucleon δ-interaction Γωin the Landau-Migdal formused: Г = С0 (f0′ + g0′σ1σ2) τ1τ2 δ(r1- r2) where coupling constants of: f0′ –isospin-isospinandg0′ –spin-isospin quasi-particle interaction with L = 0. ------------------------------------------------------------------------------------ Constants f0′and g0′ are the phenomenological parameters. Matrix elementsMGT :where χλν – mathematical deductions G -T values are normalized in FFST: Effective quasiparticle charge is the “quenching” parameter of the theory. “Quenching” effect (Losing of sum rule in beta-strength) is the main in heavy nuclei ~50% 21

  22. BETA-STRENGTH FUNCTION FOR127Xe Dependence from eg 1 - Breaking line – experimental data (1999):M. Palarczyk, et. al. Phys. Rev. 1999. V. 59. P. 500; 2 –Solid red line TFFS calculations with еq= 0.9 ; 3 - Solidblackline– calculations with еq= 0.8:Yu.S. Lutostansky, N.B. Shulgina. Phys. Rev. Lett. 1991. V.67. P.430; 22

  23. BETA-STRENGTH FUNCTION FOR95,97Rb TFFS calculations: I. N. Borzov, Yu. S. Lutostansky, I. V. Panov, S. A. Fayans 23

  24. Half-lives T1/2 (ms) andPn (%) values for Rb isotopes о – experimental data; solid line — TFFS calculations; + —Phenomenological model, dotted line forT1/2 – Gross-theory. 24

  25. BETA-DELAYED NEUTRONS IN NUCLEOSYNTESIS exp Calculated abundances:1–with out (β,n)-effect; 2–with (β,n)-effect; in the relative units (Т=109 К, nn =1024 см-3). Calc.: Lutostansky Yu.S., Panov I.V., et al. Sov. J. Nucl. Phys. 1986. v.44. 25

  26. b-Decay properties T1/2, Pnb-strength properties from theoretical models, e.g. QRPA in comparison with experiments. Pn-Values Half-lives Total Error = 5.54 Total Error = 3.73 QRPA (GT) QRPA (GT) QRPA (GT+ff) QRPA (GT+ff) Total Error = 3.08 (P. Möller et al., PR C67, 055802 (2003)) Total Error = 3.52 26

  27. Half-lives T1/2 I.V. Panov, Yu.S. Lutostansky, F.-K. Thielemann. Beta-decay half-lives for the r-process nuclei. Nuclear Physics A 947 (2016) 1-11 27

  28. Half-lives T1/2 28

  29. Half-lives T1/2 I.V. Panov, Yu.S. Lutostansky, F.-K. Thielemann. Beta-decay half-lives for the r-process nuclei. Nuclear Physics A 947 (2016) 1-11 (P. Möller et al.,PR C67, 055802 (2003)) 29

  30. THE END СПАСИБО = THANK YOU

  31. EGTR – EAR MODEL DESCRIPTION - 1 Mat. model developed for the approximate solutions of equations of the FFST theory by the quasi-classical method. ----------------------------- 2 new parameters: E = EF(n) – EF(p) = Els – average energy of the spin–orbit splitting Wigner’s SU(4) super-symmetry restoration in the heavy nuclei Calculated (circles – ○) and experimental (■) dependencies of the relative energy y(x)=Δ(EGTR-EAR)/Els from the dimensionless value x=E/Els. Blue circles (●) connected by line – calculated values for Sn isotopes. Red line – calculations with eq. Els(N) = 20N–1/3 + 1.25 (MeV). 7

  32. PROCESSES OF NUCLEOSYNTESIS. The tracks of elements synthesis ins (slow)- andr (rapid)- processes.

  33. NUCLEOSYNTHESISOF THE HEAVY NUCLEI NUCLEOSYNTHESIS OF THE HEAVY NUCLEI in s (slow)andr (rapid)- processes  – nuclei withT1/2  1 y. ; ○ – T1/2 < 1 y.; + ‑ predictions.

  34. IMPULCE NUCLEOSYNTHESIS OF THE HEAVY NUCLEI Dynamic r-process NUCLEOSYNTHESIS OF THE HEAVY NUCLEI in s (slow)andr (rapid)- processes – nuclei withT1/2  1 y. ; О – T1/2 < 1 y.; + ‑ predictions. Dynamic r-process track. 5

  35. BETA–– DELAYED FISSION

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