Jutta EscherNuclear Theory & Modeling
Lawrence Livermore National Lab
Jutta EscherNuclear Theory & Modeling
Lawrence Livermore National Lab
UCRL pending
21st Winter Workshop on Nuclear DynamicsBreckenridge, Colorado
February 5 - 12, 2005
155Gdn157Gd 3He
α
156 **Gd
“(n,γ)”
156Gd*
(3He, αγ)
“(n,2n) ”
154Gd*
(3He, α2nγ)
“(n,n’)”
155Gd*
(3He, αnγ)
04-ERD-057
Nuclear reactions with unstable nucleiand the Surrogate reaction technique Nuclear reactions with unstable nucleiand the Surrogate reaction technique
The LLNL team:L.Ahle, L. Bernstein, J. Burke, J. Church,
F. Dietrich, J. Escher, C. Forssén,V. Gueorguiev, R. Hoffman, …
This work is carried out under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. Funding is provided by the LDRD program at LLNL.
“Surrogate Nuclear Reactions”: A program to develop the theoretical and experimental framework for determining cross sections of reactions on unstable nuclei; with a focus on applications to astrophysics
The Surrogate concept
The method was used in the 70s - in a very simplistic manner - to obtain (n,f) cross section estimates.
“Desired” reaction
Cc
We are exploring new applications of the Surrogate idea.
Form the compound nucleus B* via an alternative (“Surrogate”) reaction:
d + D --> b + B*
The Surrogate idea:
D
“Surrogate”reaction
db
B*
Then combine the measured decay probabilities for:
B* --> c + C + …
Cc
Aa
B*
with the calculated cross section for forming B* in the “desired” reaction.
Aa
“Desired” reaction
86Kr*
85Krn
Neutron-induced“desired” reaction
86Kr**
86Kr
“Surrogate”reaction
αα’ D
“Surrogate”reaction
db
B*
Aa
“Desired” reaction
Cc
The cross section α for the
“desired” two-step reaction
a + A --> B* --> c + C
can be determined indirectlywith the Surrogate method.
} }
α
Some examples
85Kr 86Kr
(n)
(αα’)
85Kr(n,γ)86Kr
234U 235U 236U
(n)
(t,p)
235U(n,f)
154Gd 155Gd 156Gd 157Gd
(n) (3He,α)
155Gd(n,2n)154Gd
Unstable nuclei and the Surrogate technique
Challenges and opportunities for nuclear reaction theory
• Direct reactions to the continuum
• Equilibration process of a highly excited nucleus (Interplay of statistical and direct reaction theory)
• Non-equilibrium decays
• Optical models away from stability
• Level densities away from stability
• Extrapolations
• Structure and reaction physics
• Large-scale computing
Experimental challenges
• Radioactive ion beam facilities (RIBFs)
• Indirect methods for obtaining structure and reaction information
• Reactions in inverse kinematics
• Etc.
There is a large number of unstable isotopes. The physics associated with
unstable nuclei is not very well understood.
The origin of the heavy elements
rp p
roce
ss
r pro
cess
s process
s process
“How were the elements from iron to uranium made?” -- one of the ‘Eleven Science Questions for the New Century’ [Connecting Quarks with the Cosmos, Board on Physics and Astronomy, National Academies Press, 2003]
Remnant of a supernova
Cat’s eye nebula
Fascinating connections between nuclear physics
and astrophysics!
Unresolved issues…
• site of the r process? multiple sites?
• details of the supernova mechanism?
• mixing processes in red giants
• role of other processes?
= ‘playground’
of RIBFsRIBFs = Radioactive Ion Beam Facilities
Understanding the origin of the heavy elements requires knowledge of reactions on unstable nuclei!
Possible application of the Surrogate technique:s-process branch points
Kr
Rb
Sr
86848382
85
88878684
89Y
929190Zrs-processpath
93Nbunstablenucleus
96959492Mor-processnucleus
Tcp nucleus
9896Rustablenucleus
β-
β+
?
(n,γ)
(γ,n)
Synthesis of elements in the A=90 region
Can we determine (n,γ) cross sections for s-process branch
points via Surrogate reactions? Table: Jeff Blackmon, Presentation at “Nuclear Reactions on Unstable Nuclei,” Asilomar, 2004
Important s-process branch point nuclei
The Surrogate concept
“Desired” reaction
Cc
Do we have any indication that this method might work?
Form the compound nucleus B* via an alternative (“Surrogate”) reaction:
d + D --> b + B*
The Surrogate idea:
D
“Surrogate”reaction
db
B*
Then combine the measured decay probabilities for:
B* --> c + C + …
Cc
Aa
B*
with the calculated cross section for forming B* in the “desired” reaction.
Aa
“Desired” reaction
86Kr*
85Krn
Neutron-induced“desired” reaction
86Kr**
86Kr
“Surrogate”reaction
αα’ D
“Surrogate”reaction
db
B*
Aa
“Desired” reaction
Cc
The cross section α for the
“desired” two-step reaction
a + A --> B* --> c + C
can be determined indirectlywith the Surrogate method.
} }
α
An application to actinide nuclei
Younes & Britt,PRC 67 (2003) 024610,PRC 68 (2003) 034610
235mU(n,f) inferred
new!
(n,
f) (
b)
En(MeV)
0.0
0.5
1.0
1.5
2.0
0.0 0.5 1.0 1.5 2.0 2.5
En (MeV)
Cramer et al. ENDF/B-VI Younes et al.
Benchmark: inferred cross section compared to prior evaluation
235U(n,f)
A major issue: Angular-momentum matching
“Simple life”:
Cross section for two-step process: α = αCN
(E ). GCN(E)
αCN
(E) = (a+A->B*) - can be calculatedGCN
γ(E) - probability for decay into channel γ= c+C, can be determined from Surrogate experiments
“Real life”:
Cross section for a+A -> B* -> c+C : α = J αCN
(E,J,). GCN(E,J,)
J - angular momentum of compound nucleus B*α
CN(E,J, can be calculated
Problem: experiments only measure P (E) = J FCN
(E,J,). GCN(E,J,)
--> Nuclear theory is needed to extract the individual GCN(E,J,.
Aa
“Desired” reaction
D
“Surrogate”reaction
db
B*
Cc
Even a compound nucleus remembers constants of motion!
A compound nucleus can often be formed in two (or more) ways. How do the constants of motion differ in the different entrance channels?
How do these differences impact the observed cross sections?
Populating the intermediate nucleus
• Direct reactions to the continuum……determine the J population of the compound nucleus following the direct reaction.
We study the dependence of the J population on the reaction mechanism, the structure of the (direct-reaction) target, the energy of the intermediate nucleus, and the angle of the outgoing particle.
0
0.2
0.4 0
0.2
0.4
0.6
1 3 5 7 9 11 13
1 3 5 7 9 11 13
J populations in
91 * Zr from90 ( , )Zr d p
=7.0E MeV
=7.2E MeV
=7.3E MeV
=7.7E MeV
=8.2E MeV
=7.0E MeV
=7.2E MeV
=7.3E MeV
=7.7E MeV
=8.2E MeV
2J
θ=120o=+1
=-1
0
0.2
0.4 0
0.2
0.4
0.6
1 3 5 7 9 11 13
1 3 5 7 9 11 13
J populations in
91 * Zr from90 ( , )Zr d p
=7.0E MeV
=7.2E MeV
=7.3E MeV
=7.7E MeV
=8.2E MeV
=7.0E MeV
=7.2E MeV
=7.3E MeV
=7.7E MeV
=8.2E MeV
θ=90o
2J
=+1
=-1
0
0.2
0.4 0
0.2
0.4
0.6
1 3 5 7 9 11 13
1 3 5 7 9 11 13
J populations in
91 * Zr from90 ( , )Zr d p
=7.0E MeV
=7.2E MeV
=7.3E MeV
=7.7E MeV
=8.2E MeV
=7.0E MeV
=7.2E MeV
=7.3E MeV
=7.7E MeV
=8.2E MeV
2J
θ=50o
=-1
=+1
The role of the target spin
90Zr(d,p) vs. n +90Zr
En = 1 MeV J(90Zr) = 0+
91Zr(d,p) vs. n +91Zr
En = 1 MeV J(91Zr) = 5/2+
JE & C. Forssén
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
The effect of the J population on the decay probabilities
90Zr(d,p) vs. n +90Zr
En = 1 MeV J(90Zr) = 0+
C. Forssén & JE
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
J populations
Decay probabilities
The effect of the J population on the decay probabilities91Zr(d,p) vs. n +91Zr
En = 1 MeV J(91Zr) = 5/2+
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
C. Forssén & JE
J populations
Decay probabilities
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Observations
So far, we find:
• The J population in the intermediate nucleus is significantly different for the n-induced and the (d,p) reaction.
• The (d,p) results do not depend much on the angle of the outgoing proton.
• Different J populations lead to very different decay probabilities.
• The spin of the original target nucleus plays an important role.
Next steps:
• Study the J population in the intermediate nucleus for other reaction mechanisms. In particular, we are interested in (αα’). Work in progress.
• Study the associated decay probabilities.
• Carry out a benchmark experiment. Experiment planned to take place in Berkeley at the end of February 2005.
• Extract an (n,γ) cross section from a Surrogate experiment and compare to a direct measurement, e.g. 101Ru(n, γ).
• If successful, apply the technique to obtain an unknown (n,γ) cross section, e.g. 103Ru(n, γ).
(Not to scale)
γ
E E
Ge Clover
-electron shield
8 mm 4.7 mm
γ
Target
24 Rings θ
Segmentation allows geometric particle correlations
From: J. Church,N Division, LLNL (July 2004)
Setup for a benchmark experiment
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
From: J. Burke,N Division, LLNL (Dec 2004)
8 Sectors
Berkeley 2005
Synopsis
Determining reaction cross sections indirectly via Surrogate Nuclear Reactions. This requires some development, both in
nuclear theory and in experimental techniques.
• Promising examples (e.g. actinide fission).• Differences in the production of the intermediate nucleus and their
effect on the decay probabilities need to be better understood.• Theoretical and experimental efforts at LLNL address this issue;
a benchmark study is underway.• Nuclear physics is moving towards radioactive ion beams; the
Surrogate method could become a useful technique.
play a crucial role for nuclear physics and astrophysics. A large number of nuclear reactions cannot be determined with current techniques.
Reactions on short-lived radioactive nuclei provide a major challenge.
Reactions with unstable nuclei
Implementation
Idea
Jutta EscherNuclear Theory & Modeling
Lawrence Livermore National Lab
Jutta EscherNuclear Theory & Modeling
Lawrence Livermore National Lab
UCRL pending
21st Winter Workshop on Nuclear DynamicsBreckenridge, Colorado
February 5 - 12, 2005
155Gdn157Gd 3He
α
156 **Gd
“(n,γ)”
156Gd*
(3He, αγ)
“(n,2n) ”
154Gd*
(3He, α2nγ)
“(n,n’)”
155Gd*
(3He, αnγ)
04-ERD-057
Surrogate nuclear reactions - An indirect method for determining reaction
cross sections
Surrogate nuclear reactions - An indirect method for determining reaction
cross sections
The LLNL team:L.Ahle, L. Bernstein, J. Burke, J. Church,
F. Dietrich, J. Escher, C. Forssén,V. Gueorguiev, R. Hoffman, …
This work is carried out under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. Funding is provided by the LDRD program at LLNL.
A test case in the rare-earth region
155Gdn157Gd 3He
α
156 **Gd
“(n,γ)”
156 Gd*
(3He, αγ)
“(n,2n) ”
154 Gd*
(3He, α2nγ)
“(n,n’)”
155 Gd*
(3He, αnγ)
Bernstein et al., Fall 2002
Experiment carried out in Berkeley
Surrogate measurement using 157Gd(3He,α)Direct measurement
155Gd(n,γ)156Gd
155Gd(n,2n)
Cro
ss S
ecti
on (
mb
)C
ross
Sec
tion
(m
b) En(MeV)
En(MeV)
Developing the Surrogate technique
• Direct reactions to the continuumdetermine the J population of the compound nucleus following the direct reaction.
• How do the differences in J population influence the decay probabilities?Low-energy n-capture will be dominated by s- and p-waves while direct reactions populate a wide range of J.
• Accurate optical modelThe CN formation cross section needs to be calculated very precisely.
• Identification of the final reaction product(s)Measured γ-ray intensities need to be converted to CN decay -> requires a proper description of the structure of the residual nucleus.
• Non-equilibrium effectsThe formation of an equilibrated system is a crucial ingredient of the Surrogate Technique. The validity of assumption needs to be tested.
1. Benchmarking in the spherical regionCarry out a Surrogate experiment in the A=90 region and compare the extracted cross section to a direct measurement. Analysis of 91Zr(n,γ)92Zr via 92Zr(α,α’ γ)92Zr is underway.
2. Astrophysics applicationAfter establishing the validity of the method: measure and analyze a surrogate reaction for 85Kr(n,γ)86Kr, for example via 86Kr(α,α’ γ)86Kr .
3. Extend the applicationsa) Study (n,γ) in the deformed region -> possible application: 151Sm(n,γ)152Sm. b) The technique is not limited to n-induced reactions -> consider (p,γ) reactions on unstable targets in the A=60-90 mass region.
Implementation:
The Surrogate technique in its infancy -the mass~90 region
91Zr(3He,t)91Nb* and92Mo(t,α)91Nb*
as Surrogates for90Nb(n,)91Nb* -> p + 90Zr
H.C. Britt and J.B. Wilhelmy, private communication
(n, )
(3He,t)
(t,α)Earlystudies
Conclusion: A comprehensive theory effort is required!
Selecting a benchmark case: 90Zr(n,γ) versus 91Zr(n,γ)
1 10 1001
10
100
Cross section (barns)
Incident energy (keV)
1975 Boldeman 1965 Kapchigashev
90Zr(n,γ)
The advantages of a Surrogate for n + 90Zr• Detailed comparison with P. Garrett’s GEANIE results possible -> information on individual γ’s!• Reasonable direct (n,γ) results available
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
The advantages of a Surrogate for n + 91Zr• Better direct (n,γ) results available• Statistical treatment more accurate • γ-cascade simplified in 92Zr
Explanation of Figures
155Gdn157Gd 3He
α
156 **Gd
“(n,γ)”
156 Gd*
(3He, αγ)
“(n,2n) ”
154 Gd*
(3He, α2nγ)
“(n,n’)”
155 Gd*
(3He, αnγ)
Schematic of Lee Bernstein’s Surrogate experiment at Berkeley.
Remnant of a supernova.Supernovae are potentialsites for r-processheavy-element synthesis.
From DOE/NSF NSACLong-range plan, 2002
From “Opportunities in Nuclear Astrophysics” Town Meeting at Notre Dame, 1999
s process branch points
Isotope Half-lifeRIA
intensity(109 pps)
79Se 1.1x106 y 2085Kr 10.7 y 8086Rb 19 d 80089Sr 50 d 194Nb 2x104 y 1
103Ru 39 d 1106Ru 367 d 5110Ag 250 d 10115Cd 44 d 90114In 50 d 90121Sn 50 y 120123Sn 130 d 150124Sb 60 d 1125Sb 2.8 y 3127Te 109 d 1129Te 34 d 20133Xe 5.2 d 200134Cs 2.1 y 2000135Cs 2x106 y 3000141Ce 33 d 500143Pr 14 d 800147Nd 11 d 80147Pm 2.62 y 80151Sm 90 y 10
Isotope Half-lifeRIA
intensity(109 pps)
153Sm 1.9 d 20152Eu 13 y 40154Eu 8.6 y 30155Eu 4.9 y 4153Gd 241.6 d 20160Tb 72 d 1163Ho 4570 y 400169Er 9.4 d 30
170Tm 128.6 d 100171Tm 1.92 y 100177Lu 6.7 d 1179Ta 1.7 y 1181Hf 42 d 30182Hf 9x106 y 10182Ta 114 d 1185W 75.1 d 2186Re 2.0 y 1191Os 15 d 2192Ir 74 d 1193Pt 50 y 1198Au 2.7 d 1203Hg 47 d 100204Tl 3.77 y 1
205Pb 1.5x107 y 1
From: Jeff Blackmon,Presentation at “Nuclear Reactions on Unstable Nuclei,” Asilomar, 2004
The Surrogate Concept
α = J αCN
(E,J,). GCN(E,J,)
Hauser-Feshbach
“Desired” reaction
Cc
Form the compound nucleus B* via an alternative (“Surrogate”) reaction:
d + D --> b + B*
The Surrogate idea:
D
“Surrogate”reaction
db
B*
Then combine the measured decay probabilities for:
B* --> c + C + …
Cc
Aa
B*
with the calculated cross section for forming B* in the “desired” reaction.
Aa
“Desired” reaction
86Kr*
85Krn
Neutron-induced“desired” reaction
86Kr**
86Kr
“Surrogate”reaction
αα’ D
“Surrogate”reaction
db
B*
Aa
“Desired” reaction
Cc
The cross section α for the
“desired” two-step reaction
a + A --> B* --> c + C
can be determined indirectlywith the Surrogate method.
} }
α
Direct-reaction probability:
FCN(E,J,)
‘Channel’ probability:
P(E) = J FCN(E,J,).GCN
(E,J,)
Formation cross section: αCN(E,J,)
The Surrogate Concept
α = J αCN
(E,J,). GCN(E,J,)
Hauser-Feshbach
“Desired” reaction
Cc
Form the compound nucleus B* via an alternative (“Surrogate”) reaction:
d + D --> b + B*
The Surrogate idea:
D
“Surrogate”reaction
db
B*
Then combine the measured decay probabilities for:
B* --> c + C + …
Cc
Aa
B*
with the calculated cross section for forming B* in the “desired” reaction.
Aa
“Desired” reaction
86Kr*
85Krn
Neutron-induced“desired” reaction
86Kr**
86Kr
“Surrogate”reaction
αα’The cross section α for the
“desired” two-step reaction
a + A --> B* --> c + C
can be determined indirectlywith the Surrogate method.
} }
α
Direct-reaction probability:
FCN(E,J,)
‘Channel’ probability:
P(E) = J FCN(E,J,).GCN
(E,J,)
Formation cross section: αCN(E,J,)
Different reactions, same results?
A compound nucleus can often be formed in two (or more) ways. How do the constants of motion differ in the different entrance channels?
How do these differences impact the observed cross sections?
Even a compound nucleus remembers constants of motion!
Grover & Nagle,Phys. Rev. 134(1964) B1248
E(210Po) [MeV]
208 P
o pr
obab
ilit
y
206Pb + α
209Bi + p
Spin of 210Po
Rel
ativ
e po
pul
atio
n
206 P
b +
α
209Bi + p
Exploring the limitations of the method
Central pointFormation and decay of a true compound nucleus are independent of
each other. The Surrogate method assumes that the intermediate nucleus is in a compound state, i.e. equilibrated, before it decays.
Guttormsen et al.,NPA 587 (1995) 401
α-energy probabilities for163Dy(3He,α2n)160Dy
Assuming equilibrated 162Dy
With pre-equilibrium contributions
A thorough study of the Surrogate technique…
…raises many interesting nuclear physics questions:
• Optical model: How do the optical model parameters change as one moves away from stability? What are the fundamental limitations of the optical model?
• Level densities: Major improvements necessary (level densities needed in various energy ranges, for various deformations,...)! How do level densities change as one moves away from stability?
• Extrapolations of reaction cross sections: Experimental limitations will require models to extrapolate to low energies
• Descriptions of multi-particle transfers
• Models for fission
• Etc.
Developing the Surrogate reaction technique…• Direct reactions to the continuum
determine the J population of the compound nucleus following the direct reaction. We study the dependence of the J population on the reaction mechanism, angle, and energy.
• How do the differences in J population influence the decay probabilities?Low-energy n-capture will be dominated by s- and p-waves while direct reactions populate a wide range of J.
0
0.2
0.4 0
0.2
0.4
0.6
1 3 5 7 9 11 13
1 3 5 7 9 11 13
J populations in
91 * Zr from90 ( , )Zr d p
=7.0E MeV
=7.2E MeV
=7.3E MeV
=7.7E MeV
=8.2E MeV
=7.0E MeV
=7.2E MeV
=7.3E MeV
=7.7E MeV
=8.2E MeV
2J
θ=120o=+1
=-1
0
0.2
0.4 0
0.2
0.4
0.6
1 3 5 7 9 11 13
1 3 5 7 9 11 13
J populations in
91 * Zr from90 ( , )Zr d p
=7.0E MeV
=7.2E MeV
=7.3E MeV
=7.7E MeV
=8.2E MeV
=7.0E MeV
=7.2E MeV
=7.3E MeV
=7.7E MeV
=8.2E MeV
θ=90o
2J
=+1
=-1
0
0.2
0.4 0
0.2
0.4
0.6
1 3 5 7 9 11 13
1 3 5 7 9 11 13
J populations in
91 * Zr from90 ( , )Zr d p
=7.0E MeV
=7.2E MeV
=7.3E MeV
=7.7E MeV
=8.2E MeV
=7.0E MeV
=7.2E MeV
=7.3E MeV
=7.7E MeV
=8.2E MeV
2J
θ=50o
=-1
=+1
P (E) = J FCN
(E,J,). GCN(E,J,)
Questions to be addressed