Jutta Escher Nuclear Theory & Modeling Lawrence Livermore National Lab Jutta Escher Nuclear Theory &...

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


86Kr*

85Krn

Neutron-induced“desired” reaction

86Kr**

86Kr


αα’ D


db

B*

Aa


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


Cc

Do we have any indication that this method might work?


d + D --> b + B*

The Surrogate idea:

D


db

B*


B* --> c + C + …

Cc

Aa

B*


Aa


86Kr*

85Krn


86Kr**

86Kr


αα’ D


db

B*

Aa


Cc



a + A --> B* --> c + C


} }

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


D


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+


En = 1 MeV J(91Zr) = 5/2+

JE & C. Forssén

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.







The effect of the J population on the decay probabilities


En = 1 MeV J(90Zr) = 0+

C. Forssén & JE







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+





C. Forssén & JE

J populations

Decay probabilities



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





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





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



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


Cc


d + D --> b + B*

The Surrogate idea:

D


db

B*


B* --> c + C + …

Cc

Aa

B*


Aa


86Kr*

85Krn


86Kr**

86Kr


αα’ D


db

B*

Aa


Cc



a + A --> B* --> c + C


} }

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


Cc


d + D --> b + B*

The Surrogate idea:

D


db

B*


B* --> c + C + …

Cc

Aa

B*


Aa


86Kr*

85Krn


86Kr**

86Kr


αα’The cross section α for the


a + A --> B* --> c + C


} }

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

Jutta Escher Nuclear Theory & Modeling Lawrence Livermore National Lab Jutta Escher Nuclear Theory &...

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