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

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

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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)
  131 T1/2, Pin
• Goriely et al. Astron. Astrophys. 346, 798804
  (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) 48
  Yff(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. 2004
  n-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.

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Main r-process tR 0.5 s, cycling number ncycl
(log2(Yfin/Yinit)) gt 0, 1
fission
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Model of NSM-simulation Freiburghaus et al. AJ
525 (1999)

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Y(A) during r-process with fission cycling for
NSM conditions (t-duration time of the
r-process t0 - initial composition)
Panov I., Thielemann F.-K. Astronomy Letters,
Vol. 30 (2004) 711
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motivation further data reevaluation
in the actinide and
transactinide region

1. b-delayed rates - Pbdf for
   Zlt100
2. (n,g)-rates Zlt115
3. Neutron-induced fission rates lnif lts vgt
   Zlt115
4. Spontaneous fission phenomenological models
   Zlt115
5. a-decay Zlt115
6. Mass predictions ETFSI, HFB, Thomas-Fermi Zlt115
   
7. Conclusions

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Bf lt 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 gt Sn gt 0.
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U
Cm
Fm
Z104
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lsf - Smolanchuk et al
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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, 77 x Bfexp

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Lglsf 33, 3 - 7, 77 x Bexpf
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If ltPbdf gt 50 then Ksurviv(from Z94
to Z114)0.000001
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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.
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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 (st) interaction g constant used,
included pion-exchanging mode
In our low energy case (?Epnlt 20 MeV) the second
pion-depending term is negligible. For the
isovector constants f0 and g0 selfconsistent
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 8, eq 1.0, q 1.0 ).
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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
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Pa240 -gt U240
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Pa260 -gt U260
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S ( Ig Ibdf Idn ) 1
S Ib, I(dnbdf)
S Ib, Ibdf
S Ib, Ig
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U -gt Np Beta Delayed Fission Probabilities
TFFS-calculations (beta-model)
For dashed regions, BfltEltSn Gf Gtot .
Otherwise Gf ltltGtot
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BETA - DELAYED FISSION
, where ? ? - ? ,
For BfltEltSn Gf Gtot . Otherwise
Gf ltltGtot
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Conclusionspredicted 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 lt100

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• Thank you for the attention!

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Isobaric Collective States
TFFS equations follows Lane Theory of
Nucleus K. Ikeda, S. Fujii, and J. I. Fujita
1963-1967 Gaponov Lutostansky 1972-1981
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127Xe Beta-Strength function.

The comparison of measured and predicted S? (E)
function for 127Xe
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.
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ETFSI Lglsf 50.127 - 10.145 Bf
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Pbdf Masses, barriers ETFSI Sb
quasiclassical approach on the basis of
FFST(????) Gaponov, Lutostansky, Panov 1979
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Pa
40

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• neutron-induced g and -fission rates were
  calculated on the basis of the next mass
  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

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n, ?, fission competitionPbdf
(Sn,Bf,1/(1exp(2.p (Bf-E)/hw) )
?
n
n
(Z,A)
f
b-
Qb
Sn
Sn
Bf
Bf
G.s.
(Z1,A)
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• 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?

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R-process Nuclear data I

• Beta decay lifetimes and beta-delayed neutron
  emission
• P.Moller, J.R.Nix, K.-L.Kratz. ADNDT, 66 (1997)
  131 T1/2, Pin
• (g, n) and (n, g) rates
• RauscherThielemann 2000 (Zlt84) Panov et al.
  2005 (Zgt83)
• Neutron induced fission rates
• Panov et al., AA, (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 (Zlt101)
• data for Zgt100 needed

.
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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

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6. Data for the r-process (SHE-region)

• ETFSi mass and barrier predictions for Z up to
  118
• beta-rates for Zlt118 (QRPAFRDM)
• neutron-induced fission rates up to Z115-118
  (will be published in AA) and Available at
  CDS via
• http//cdsweb.u-strasbg.fr/cgi-bin/qcat?
  J/AA
• Pbdf for 90ltZlt100 Krumlinde, Moller 1984
• qrpa (T1/2 - Kratz, Moller, Nix, NP A,
  1997)
• Pbdf for 100ltZlt110 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.

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Lg(Tsf), s
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I.Petermann, A.Arcones, A.Keliґc, K.Langanke,
G.Martнnez-Pinedo, W.Schmidt, K-H.Hix, I. Panov,
T. Rauscher, F.-K. Thielemann, N.Zinner,
NIC-2008
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HFT parametrizations, used

• Double-humped fission barrier - Strutinsky
• complete damping approximation which averages
  over transmission resonances,
• levels in the second minimum are equally spaced
• Hill-Wheeler transmission coefficient through a
  parabolic barrier
• ?A,B define the level densities above the saddle
  points A,B
• The back-shifted Fermi-gas description of the
  level density was improved by introducing an
  energy dependent level density parameter a
• The basis of experimentally known fission
  barriers was increased
• deformed optical potential
• The details are described in Rauscher
  Thielemann. ADNDT, 2000 Panov et al. NP, 2005

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R. Smolanґczuk Acta Polonica 1999
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Smolanґczuk, PHYSICAL REVIEW C VOLUME 56, 812
(1997)
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Reasons

1. Mass and fission barriers predictions up to Z
   115 (ETFSI, HFB, TF)
2. (n,?)-rates for Z lt 115
3. Neutron-induced fission rates ?nif lt? vgt
   for Zlt115
   Panov et al. AA 2010 (extension to
   Rauscher and Thielemann ADNDT 2000)
4. ?-delayed fission rates ??df for
   90ltZlt101 Panov et al. Nucl. Phys. A 2005 .
5. spontaneous fission rates ?sf - from
   phenomenological rates to macro-micro predictions
   (Sobichevski Pomorski 2007 Smolanchuk et al
   1997)
6. and motivation
7. SHE modeling in the r-process
8. reevaluate ??-delayed fission rates ??df
9. Contribution of different fission types into
   nucleosynthesis

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Beta Delayed Multy-Neutron Emission
Probability for 2n - emission
Probability for kn - emission
U, I?(U) energies and intensities in the
daughter nucleus, Wn(U, E) probability of
neutron emission
qi and qf level densities of compound and
final nucleus, ?n(?) transitivity factor
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Beta Delayed Fission Calculations
Probabilities - PЯf d
Beta Strength function
?(?) widths approximation ?(?) a?E2
Я?E3 where a