Fission Rates and Transactinide Formation in the R-Process by Igor Panov

1. Fission rates and transactinide formation in the r-process.Igor Panov

2. Subject of the talk • Fission in the R-process • Astrophysical site for the main r-process • Actinides and transactinides • Data: T1/2, Pn, (n,g), (n,f),bdf, s.f. • Renovation of data for the r-process: Purpose and motivation • Pbdf different approaches – Sb • samples of predictions • conclusions

3. Importance of fission for the r-process • Seeger, Fowler, Clayton, 1965 fission -long and short solutions • Thielemann, Metzinger, Klapdor, Zt.Phys., A309(1983) 301. Pbdf • Lyutostansky, Panov, Ljashuk Izv RAN, ser, fiz. 1990 Pbdf • P.Moller, J.R.Nix, K.-L.Kratz. ADNDT, 66 (1997) 131T1/2, Pin • Goriely et al. Astron. Astrophys. 346, 798–804 (1999)s.f. • Panov et al., Nucl. Phys. A, 718 (2003) 647. (n,fission) vs Pbdf • I.Korneev et al. NIC-2006; Astronomy Letters, 66 (2008) 131 Yff(Z,A) • Kelic, et al., Phys. Lett. B. 616 (2005) 48Yff(Z,A) • I.V. Panov, E. Kolbe, F.-K. Thielemann, T. Rauscher, B. Pfeiffer, K.-L. Kratz. NP A 747 (2005) 633 (n,fission) (n,g) Pbdf • G.Martinec-Pinedo et al, Progress in Particle and Nuclear Physics, 59 (2007) 199. (n,fission) vs Pbdf • Y.-Z. Qian, Astron. J. 569 (2002), p. L103; Kolbe, Langanke, Fuller.Phys Rev Lett. 2004n-induced fission • I. Petermann et. al. NIC-2008; G.Martinec-Pinedo et al, Progr.in Particle and Nucl. Phys.,59(2007) 199-205:(n,fission), Pbdf , s.f., n-induced f. • K. Langanke, G. Martinez-Pinedo, I.Petermann, F.K. Thielemann,PPNP 2011 (n,fission) , Pbdf , s.f., n-induced f.

4. Main r-process: tR ≥0.5 s, cycling number ncycl (log2(Yfin/Yinit)) > 0, ~1 fission

5. Model of NSM-simulation: Freiburghaus et al. AJ 525 (1999)

6. Y(A) during r-process with fission cycling for NSM conditions (t-duration time of the r-process; t=0 - initial composition) Panov I., Thielemann F.-K. Astronomy Letters, Vol. 30 (2004) 711

7. motivation: further data reevaluation in the actinide and transactinide region • b-delayed rates - Pbdf for Z<100 • (n,g)-rates Z<115 • Neutron-induced fission rates lnif ~ <s v> Z<115 • Spontaneous fission – phenomenological models Z<115 • a-decay Z<115 • Mass predictions ETFSI, HFB, Thomas-Fermi Z<115 • Conclusions

8. : Bf < Sn;: nuclei with Bf ≥ Sn; inclined crosses: nuclei with neutron binding energy predicted by the ETFSI [5] Sn ∼ 2 MeV; and dots: nuclei in which 2 > Sn > 0.

9. U Cm Fm Z=104

10. lsf - Smolanchuk et al

12. model-independent evaluations of lsf • Based on predicted Bf (G.Martinec-Pinedo): MS: Lglsf= 23.887 –8.0824 x Bf ETFSI:Lglsf= 50.127 -10.145 x Bf • Based on experimental values of Bf Lglsf= 33,3 - 7,77xBfexp

13. Lglsf= 33,3 - 7,77x Bexpf

15. If <Pbdf > ~ 50% then Ksurviv(from Z=94 to Z=114)~0.000001

18. BETA - STRENGTH FUNCTION OF NEUTRON-RICH NUCLEI In calculation of weak process connected with -decay, -absorption, -delayed processes the Beta-Strength function S(E) plays the main role. S (E) - function for neutron-rich nuclei presented on Fig.1. S(E)– function has a resonance character with high lying Gamow-Teller (GTR) and Isobaric Analog (IAR) resonanses. Lower by energy are situated the so-called “pigmy resonanses”. The GTR with low going “tail” influence strongly on the average neutrino- absorption cross-section and on the charge-exchange reactions probabilities. “Pigmy resonanses” plays the main role in the T1/2 values, -delayed neutron emission, -delayed fission and in neutron emission after neutrino- absorption process. Fig. 1 Schema of S(E) – for function for neutron-rich nuclei and -delayed processes.

19. Calculation of Beta-Strength function in TFFS theory Beta-Strength function S(E) is formed by isobaric states in the Theory of Finite Fermy Systems (TFFS) calculated solving the nuclear effective field equations of Gamov – Teller type: In this equations all types of particle-hole quasiparticle excitations are included except of l – forbidden type.For the local single quasiparticle (στ) interaction g` constant used, included pion-exchanging mode: In our low energy case (ΔEpn< 20 MeV) the second pion-depending term is negligible. For the isovector constants f0and g0selfconsistent procedure was used. Beta-Strength function S(E) was calculated using matrix elements MGT : Normalization = Sum-rule:S(E) dE = eq2 .3 . ( N - Z ). For Emax = 20 MeV and eq = 0.8 quenching value is q = 0.64(for Emax =∞, eq = 1.0, q = 1.0 ).

20. Quasiclassical Beta - Model We change sums to integrals as usual in quasiclassic and come to the equations: , where = -  , (j1-j2=1) a  1/3. b = b+ + b-  2/3

22. Pa240 -> U240

23. Pa260 -> U260

27. S ( Ig + Ibdf + Idn ) =1 S Ib, % = I(dn+bdf) S Ib, % = Ibdf S Ib, % = Ig

28. U -> Np Beta – Delayed Fission Probabilities TFFS-calculations (beta-model) For dashed regions, Bf<E<Sn Gf ~ Gtot . Otherwise Gf <<Gtot

29. BETA - DELAYED FISSION , where = -  , For Bf<E<Sn Gf ~ Gtot . Otherwise Gf <<Gtot

32. Conclusions:predicted b.d. (and probably s.f. ) Rates looks overestimated • exp. Data on superheavy • Experimentally knowen branchings of beta-deay (as well as theor. Predictions) show aveage Intensity of beta-decays into low lying states ~ 30% • QRPA – predictions Pin ~ 80% ~ Pbdf • TFFS predictions Pin~ 60% and Pbdf ~ 20% S Pin + Pbdf <100%

33. Thank you for the attention!

34. Isobaric Collective States TFFS equations follows Lane Theory of Nucleus K. Ikeda, S. Fujii, and J. I. Fujita 1963-1967 Gaponov & Lutostansky 1972-1981

35. 127XeBeta-Strength function. The comparison of measured and predicted S(E)– function for127Xe Breaking line – experimental data (1999). Solid line – TFFS calculations by Lutostansky and Shulgina (Phis. Rev. Lett. 1991). GTR and low-lying “pigmy” resonanses are well distinguished. The experimental qwenching is q = 0.54, theoretical: q = 0.64.

37. ETFSI: Lglsf = 50.127 -10.145 Bf

38. Pbdf: Masses, barriers: ETFSI Sb – quasiclassical approach on the basis of FFST(ТКФС); Gaponov, Lutostansky, Panov 1979

39. Pa

41. neutron-induced –g and -fission rates were calculated on the basis of the nextmass predictions and fission barriers: TF,ETFSI,FRDM,HFB-14 For explanation of yields in t.n.explosion: • Odd-even effect is reduced for HFB predictions • The initial composition should consist from U with admixture of some other actinides • Inversion of odd-even effect can appear due both bdf and Np (odd Z) admixture as well • Beta-delayed fission rates should be revised

42. n, , fission:competitionPbdf (Sn,Bf,1/(1+exp(2.p (Bf-E)/hw) ) γ n n (Z,A) f b- Qb Sn Sn Bf Bf G.s. (Z+1,A)

43. Can we test the fission rates on the basis of the yields measured in impulse r-process experiments (thermonuclear explosions) ? • and what we can learn from the comparison of calculated and experimental data? • Compare results based on different predictions (Masses, Bf ); • Test odd-even dependence and inversion of odd-even effect • Whether the (n,f)-rates based on predicted fission barriers can fit the observed yields? • How the b-delayed fission affect on calculated yields?

44. R-process:Nuclear data I • Beta decay lifetimes and beta-delayed neutron emission • P.Moller, J.R.Nix, K.-L.Kratz. ADNDT, 66 (1997) 131T1/2, Pin • (g, n) and (n, g) rates Rauscher&Thielemann 2000 (Z<84) Panov et al. 2005 (Z>83) • Neutron induced fission rates Panov et al., A&A, (2010) • Spontaneous fission rates (Smolanchuk et al; phenomenological models: f1(Z2/A), f2(Bf) ) • Alpha-decay rates (Sobichevsky et al) • beta-delayed fission rates Panov et al., Nucl. Phys. A, 747 (2005) 633 (Z<101) data for Z>100 needed .

45. Nuclear data II: mass and fission barrier predictions • Masses - Extended Thomas-Fermi + Strutinsky integral (ETFSI) • Y. Aboussir, J.M.Pearson, A.K. Dutta and F.Tondeur, 1995 • Fission Barriers – ETFSi • Mamdouh et al., 2001 • Masses - Myers W. D., Swiatecki W. J., 1996 • Fission Barriers Myers W. D., Swiatecki W. J., 1999 • Masses – FRDM - Moller P.,ADNDT v59 185 1995 • Fission Barriers - Myers W. D., Swiatecki W. J., 1999

46. 6. Data for the r-process (+SHE-region) • ETFSi mass and barrier predictions for Z up to 118 • beta-rates for Z<118 (QRPA+FRDM) • neutron-induced fission rates up to Z=115-118 (will be published in A&A) and Available at CDS via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A • Pbdf for 90<Z<100 – Krumlinde, Moller 1984 qrpa (T1/2 - Kratz, Moller, Nix, NP A, 1997) • Pbdf for 100<Z<110 were considered on the basis of Sb calculated in framework of TFFS(b) model • s.f. - phenomenological models or existed calculations of Smolanchuk et al.

47. Lg(Tsf), s

50. I.Petermann, A.Arcones, A.Keli´c, K.Langanke, G.Martínez-Pinedo, W.Schmidt, K-H.Hix, I. Panov, T. Rauscher, F.-K. Thielemann, N.Zinner, NIC-2008;