Transcript Влияние массового распределения осколк

Fission rates and transactinide
formation in the r-process.
Igor Panov
Subject of the talk
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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
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
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T1/2, 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) 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.
Main r-process: tR ≥0.5 s, cycling number ncycl (log2(Yfin/Yinit)) > 0, ~1
fission
Model of NSM-simulation: Freiburghaus et al. AJ 525 (1999)
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
motivation:
further data reevaluation in the actinide and
transactinide region
1.
b-delayed rates - Pbdf for Z<100
2. (n,g)-rates
3.
Z<115
Neutron-induced fission rates
lnif ~ <s v>
Z<115
4. Spontaneous fission – phenomenological models Z<115
5.
a-decay
Z<115
6. Mass predictions ETFSI, HFB, Thomas-Fermi Z<115
7. Conclusions
: 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.
U
Fm
Cm
Z=104
lsf - Smolanchuk et al
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
Lglsf = 33, 3 - 7, 77 x Bexpf
If
<Pbdf > ~ 50% then
Ksurviv(from Z=94 to Z=114)~0.000001
BETA - STRENGTH FUNCTION OF NEUTRON-RICH NUCLEI
In calculation of weak process connected with b-decay, n-absorption, b-delayed processes the
Beta-Strength function Sb (E) plays the main role. Sb (E) - function for neutron-rich nuclei
presented on Fig.1.
Sb (E)– function has a resonance
character with high lying GamowTeller (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 crosssection and on the charge-exchange
reactions probabilities. “Pigmy
resonanses” plays the main role in the
T1/2 values, b-delayed neutron
emission, b-delayed fission and in
neutron emission after neutrinoabsorption process.
Fig. 1 Schema of Sb (E) – for function for neutron-rich nuclei and b-delayed processes.
Calculation of Beta-Strength function in TFFS theory
Beta-Strength function Sb (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:
2
4


2 2 dn -2  q
2 -2 
g 0 эф  g 0 - e q f 
 

(
1

q
) 
2
d

m
R
1

q



In our low energy case (ΔEpn< 20 MeV) the second pion-depending term is negligible. For the
isovector constants f0 and g0 selfconsistent procedure was used. Beta-Strength function Sb (E)
was calculated using matrix elements MGT :
C
Г (E)
Sb (E) 
i
Emax
Normalization = Sum-rule:
M

2
N
 S (E) dE = e
b
q
2 .3 . (
2
i
( Ei )
( Ei - E ) 2  Г 2 ( E ) / 4
N - Z ).
0
For Emax = 20 MeV and eq = 0.8 quenching value is q = 0.64 (for Emax = ∞, eq = 1.0, q = 1.0 ).
Quasiclassical Beta - Model
We change sums to integrals as usual in quasiclassic and come to the equations:
1
g0


E  E ls
E - E ls
E
a
b 
b
 - E ls
  E ls
, where  =  -  ,
(j1-j2=1)
a   R l2 (r )bll  l1l2
b    R l1l2 b(l1l) 2 l1l2
a  1/3.

1
b   1  (2A) -1/ 3
3
b = b+ + b-  2/3
E N - Z

E ls
A

Pa240 -> U240
Pa260 -> U260
S  Ig + Ibdf + Idn ) =1
S Ib, %  Idn+bdf)
S Ib, % = Ibdf
S Ib , % = Ig
U -> Np Beta – Delayed Fission Probabilities
TFFS-calculations (beta-model)
For dashed regions, Bf<E<Sn
Gf ~ Gtot . Otherwise Gf <<Gtot
BETA - DELAYED FISSION
E  E ls
E - E ls
E

a
b 
b 
 - E ls
  E ls
g0
1
a   R l2 (r )bll  l1l2
b    R l1l2 b(l1l) 2 l1l2
For
Bf<E<Sn
Otherwise
Qb
Pbf 

0
Gf ~ Gtot .
Gf <<Gtot
 f (Z, Qb - E)Sbi (E)
i
Qb
Гf
dE
Г tot
i
f
(
Z
,
Q
E
)
S

b
b ( E )dE

0 i
, where  =  -  ,
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%
Thank you for the attention!
Isobaric Collective States
TFFS equations follows
Lane Theory of Nucleus
K. Ikeda, S. Fujii, and J. I. Fujita 1963-1967
Gaponov & Lutostansky 1972-1981
127Xe
Beta-Strength function.
The comparison of measured and predicted Sb (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.
ETFSI: Lglsf = 50.127 - 10.145 Bf
Pbdf: Masses, barriers: ETFSI Sb – quasiclassical approach on
the basis of FFST(ТКФС); Gaponov, Lutostansky, Panov 1979
Pa
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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
n, g, fission: competition
Pbdf (Sn,Bf,1/(1+exp(2. (Bf-E)/h) )
γ
n
(Z,A)
n
f
b-
Qb
Bf
G.s.
Sn
Bf
Sn
(Z+1,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
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2.
3.
4.
calculated and experimental data?
Compare results based on different predictions
(Masses, Bf );
Test odd-even dependence and inversion of oddeven 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?
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
Rauscher&Thielemann 2000 (Z<84) Panov et al. 2005 (Z>83)
• Neutron induced fission rates
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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)
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data for Z>100 needed
Nuclear data II: mass and fission
barrier predictions
1. Masses - Extended Thomas-Fermi + Strutinsky
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integral (ETFSI)
– Y. Aboussir, J.M.Pearson, A.K. Dutta and F.Tondeur, 1995
Fission Barriers – ETFSi
– Mamdouh et al., 2001
2. Masses - Myers W. D., Swiatecki W. J., 1996
• Fission Barriers Myers W. D., Swiatecki W. J., 1999
3. Masses – FRDM - Moller P., ADNDT v59 185 1995
• Fission Barriers - Myers W. D., Swiatecki W. J., 1999
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
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(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.
Lg(Tsf), s
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;
HFT – parametrizations, used:
• Double-humped fission barrier - Strutinsky
• complete damping approximation which averages
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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 51
R. Smolan´czuk Acta Polonica 1999
Smolan´czuk, PHYSICAL REVIEW C VOLUME 56, 812 (1997)
Reasons:
1.
Mass and fission barriers predictions up to Z ~ 115 (ETFSI, HFB, TF)
2.
(n,g)-rates for Z < ~ 115
3.
Neutron-induced fission rates
lnif ~ <s v> for Z<115
Panov et al. A&A 2010 (extension to Rauscher and Thielemann ADNDT 2000)
4.
b-delayed fission rates lbdf
for 90<Z<101
Panov et al. Nucl. Phys. A
2005 .
5.
spontaneous fission rates: lsf
- from phenomenological rates to macro-micro
predictions (Sobichevski & Pomorski 2007; Smolanchuk et al 1997)
6.
7.
and motivation:
SHE modeling in the r-process
8.
reevaluate b-delayed fission rates lbdf
9.
Contribution of different fission types into nucleosynthesis
Beta – Delayed Multy-Neutron Emission
Probability for 2n - emission:
Qb
i
ijl
  f (Z  1, Qb - E)Sb (E)W2 (E n , E m )dE
P2 n 
B2 n ijlm
Qb
  f (Z  1, Qb - E)Sb (E)dE
i
0 i
Probability for kn - emission:
Pkn 
Qb Qkn
  Ib (U)Wn (U, E)dUdE
Bkn 0
U, Ib(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,
Тn(Е) — transitivity factor
Tn (E)q f ( U - E - Bn )
Wn ( U, E)  U-B
n
 Tn (E' )q f (U - E'-Bn )dE'2q i (U)Г g (U)
0
Beta – Delayed Fission Calculations
Qb
Probabilities Pβf d:
Pbf 
  f (Z, Qb 0
i
Qb
E)Sbi (E)
Гf
dE
Г tot
i
f
(
Z
,
Q
E
)
S
b
b ( E )dE

0 i
CN
M i2 (E i )

2 i
Beta Strength
function:
Sb (E) 
# Г(Е) widths approximation:
Г(Е) = α·E2 + β·E3 + …
Г( E )
Г 2 (E)
(E i - E) 
4
2
where α ≈ 1/εF and β « α, so we used only the first term.
# As Гf « Гn so neutron emission dominates when this energetically possible.
# Sub-barrier fission probabilities in the daughter nucleus are small to gamma
decay of exited states (barrier was taken in standard parabolic form).
# Main dependence of Pβf is from barrier energy Bf but not from barrier
thickness or form.