Nuclear reactions with unstable nuclei and the Surrogate

Nuclear reactions with unstable nuclei and the Surrogate reaction technique Jutta Escher Nuclear Theory & Modeling Lawrence Livermore National Lab “Surrogate Nuclear Reactions”: The LLNL team: A program to develop the experimental L. Ahle, L. theoretical Bernstein, and J. Burke, J. Church, framework for determining sections of F. Dietrich, J. Escher, cross C. Forssén, reactions unstable nuclei; with a … focus on V. on Gueorguiev, R. Hoffman, applications to astrophysics 21 st Winter Workshop on Nuclear Dynamics Breckenridge, Colorado February 5 - 12, 2005 UCRL pending 04 -ERD-057 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.

The Surrogate concept The cross section s c for the “desired” two-step reaction } } a + A --> B* --> c + C c can be determined indirectly with the Surrogate method. b a n A 85 Kr “Desired” reaction Neutron-induced “desired” reaction C The Surrogate idea: Form the compound nucleus B* via an alternative (“Surrogate”) reaction: d + D --> b + B* Then combine the measured decay probabilities for: B* --> c + C + … with the calculated cross section forming B* in the “desired” reaction. b ’ 86 Kr** B* B* D D 86 Kr “Surrogate” reaction 86 Kr* c The method was used in the 70 s - in a very simplistic manner - to obtain (n, f) cross section estimates. We are exploring new applications of the Surrogate idea. d d

Some examples 85 Kr(n, g)86 Kr (n) 235 U(n, f) 85 Kr 86 Kr ( , ’) (n) 234 U 235 U 236 U (t, p) 155 Gd(n, 2 n)154 Gd (n) (3 He, ) 154 Gd 155 Gd 156 Gd 157 Gd

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 There is a large number of unstable isotopes. The physics associated with unstable nuclei is not very well understood. • Radioactive ion beam facilities (RIBFs) • Indirect methods for obtaining structure and reaction information • Reactions in inverse kinematics • Etc.

The origin of the heavy elements “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] Unresolved issues… Cat’s eye nebula • site of the r process? multiple sites? ss e s c s o e r p oc r s rp • details of the supernova mechanism? • mixing processes in red giants rp pr oc es s Remnant of a supernova = ‘playground’ of RIBFs = Radioactive Ion Beam Facilities Understanding the origin of the heavy elements requires knowledge of reactions on unstable nuclei! • role of other processes? Fascinating connections between nuclear physics and astrophysics!

Possible application of the Surrogate technique: s-process branch points Important s-process branch point nuclei Synthesis of elements in the A=90 region Can we determine (n, g) cross sections for s-process branch points via Surrogate reactions? Table: Jeff Blackmon, Presentation at “Nuclear Reactions on Unstable Nuclei, ” Asilomar, 2004

The Surrogate concept The cross section s c for the “desired” two-step reaction } } a + A --> B* --> c + C c can be determined indirectly with the Surrogate method. b a n A 85 The Surrogate idea: D D 86 Kr Kr “Desired” reaction Neutron-induced “desired” reaction C b ’ 86 Kr** B* B* “Surrogate” reaction 86 Kr* c Form the compound nucleus B* via an alternative (“Surrogate”) reaction: d + D --> b + B* Then combine the measured decay probabilities for: B* --> c + C + … with the calculated cross section forming B* in the “desired” reaction. Do we have any indication that this method might work? d d

An application to actinide nuclei 235 U(n, f) s(n, f) (b) 235 m. U(n, f) inferred new! Benchmark: inferred cross section compared to prior evaluation Younes & Britt, PRC 67 (2003) 024610, PRC 68 (2003) 034610 En(Me. V)

A major issue: Angular-momentum matching “Simple life”: Cross section for two-step process: sac = sa. CN (E ). GCNc(E) s CN (E) = s(a+A->B*) - can be calculated GCNg(E) - probability for decay into channel g = c+C, can be determined b from Surrogate experiments D a A “Desired” reaction B* d “Surrogate” reaction C “Real life”: c Cross section for a+A -> B* -> c+C : sac = SJ, p sa. CN (E, J, p). GCNc(E, J, p) J - angular momentum of compound nucleus B* s CN (E, J, p) can be calculated Problem: experiments only measure Pc (E) = SJ, p Fd. CN (E, J, p ). GCNc(E, J, p) --> Nuclear theory is needed to extract the individual GCNc(E, J, p).

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 Jp population of the compound nucleus following the direct reaction. We study the dependence of the Jp 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.

The role of the target spin 90 Zr(d, p) En = 1 Me. V JE & C. Forssén vs. n +90 Zr J(90 Zr) = 0+ 91 Zr(d, p) En = 1 Me. V vs. n +91 Zr J(91 Zr) = 5/2+

The effect of the Jp population on the decay probabilities 90 Zr(d, p) Jp populations En = 1 Me. V vs. n +90 Zr J(90 Zr) = 0+ Decay probabilities C. Forssén & JE

The effect of the Jp population on the decay probabilities 91 Zr(d, p) Jp populations En = 1 Me. V vs. n +91 Zr J(91 Zr) = 5/2+ Decay probabilities C. Forssén & JE

Observations So far, we find: • The Jp population in the intermediate nucleus is significantly different for the ninduced and the (d, p) reaction. • The (d, p) results do not depend much on the angle of the outgoing proton. • Different Jp populations lead to very different decay probabilities. • The spin of the original target nucleus plays an important role. Next steps: • Study the Jp population in the intermediate nucleus for other reaction mechanisms. In particular, we are interested in (a, a’). 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, g) cross section from a Surrogate experiment and compare to a direct measurement, e. g. 101 Ru(n, g). • If successful, apply the technique to obtain an unknown (n, g) cross section, e. g. 103 Ru(n, g).

Setup for a benchmark experiment Ge Clover From: J. Church, N Division, LLNL (July 2004) d-electron shield E DE g Target g 8 mm (Not to scale) 24 Rings q Segmentation allows geometric particle correlations 8 Sectors f 4. 7 mm From: J. Burke, N Division, LLNL (Dec 2004) Berkeley 2005

Synopsis Reactions with unstable nuclei 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. Idea Determining reaction cross sections indirectly via Surrogate Nuclear Reactions. This requires some development, both in nuclear theory and in experimental techniques. Implementation • 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.

Surrogate nuclear reactions An indirect method for determining reaction cross sections Jutta Escher Nuclear Theory & Modeling Lawrence Livermore National Lab The LLNL team: L. Ahle, L. Bernstein, J. Burke, J. Church, F. Dietrich, J. Escher, C. Forssén, V. Gueorguiev, R. Hoffman, … 21 st Winter Workshop on Nuclear Dynamics Breckenridge, Colorado February 5 - 12, 2005 UCRL pending 04 -ERD-057 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.

Cross Section (mb) A test case in the rare-earth region Surrogate measurement using 157 Gd(3 He, a) Direct measurement 155 Gd(n, g)156 Gd En(Me. V) 155 Gd(n, 2 n) Bernstein et al. , Fall 2002 Experiment carried out in Berkeley En(Me. V)

Developing the Surrogate technique • Direct reactions to the continuum determine the Jp population of the compound nucleus following the direct reaction. • How do the differences in Jp population influence the decay probabilities? Low-energy n-capture will be dominated by sand p-waves while direct reactions populate a wide range of Jp. • Accurate optical model The CN formation cross section needs to be calculated very precisely. • Identification of the final reaction product(s) Measured g-ray intensities need to be converted to CN decay -> requires a proper description of the structure of the residual nucleus. • Non-equilibrium effects The formation of an equilibrated system is a crucial ingredient of the Surrogate Technique. The validity of assumption needs to be tested. Implementation: 1. Benchmarking in the spherical region Carry out a Surrogate experiment in the A=90 region and compare the extracted cross section to a direct measurement. Analysis of 91 Zr(n, g)92 Zr via 92 Zr( , ’ g)92 Zr is underway. 2. Astrophysics application After establishing the validity of the method: measure and analyze a surrogate reaction for 85 Kr(n, g)86 Kr, for example via 86 Kr( , ’ g)86 Kr. 3. Extend the applications a) Study (n, g) in the deformed region -> possible application: 151 Sm(n, g)152 Sm. b) The technique is not limited to n-induced reactions -> consider (p, g) reactions on unstable targets in the A=60 -90 mass region.

The Surrogate technique in its infancy the mass~90 region Early studies (t, ) (n, ) H. C. Britt and J. B. Wilhelmy, private communication Conclusion: A comprehensive theory effort is required! (3 He, t) 91 Zr(3 He, t)91 Nb* and 92 Mo(t, a)91 Nb* as Surrogates for 90 Nb(n, )91 Nb* -> p + 90 Zr

Selecting a benchmark case: The advantages of a Surrogate for n + 90 Zr • Detailed comparison with P. Garrett’s GEANIE results possible -> information on individual g’s! • Reasonable direct (n, g) results available 90 Zr(n, g) versus 91 Zr(n, g) The advantages of a Surrogate for n + 91 Zr • Better direct (n, g) results available • Statistical treatment more accurate • g-cascade simplified in 92 Zr

Explanation of Figures Remnant of a supernova. Supernovae are potential sites for r-process heavy-element synthesis. From DOE/NSF NSAC Long-range plan, 2002 Schematic of Lee Bernstein’s Surrogate experiment at Berkeley. From “Opportunities in Nuclear Astrophysics” Town Meeting at Notre Dame, 1999

s process branch points From: Jeff Blackmon, Presentation at “Nuclear Reactions on Unstable Nuclei, ” Asilomar, 2004

The Surrogate Concept The cross section s c for the “desired” two-step reaction } } a + A --> B* --> c + C c can be determined indirectly with the Surrogate method. a n A b b 85 Kr “Desired” reaction Neutron-induced “desired” reaction C The Surrogate idea: Form the compound nucleus B* via an alternative (“Surrogate”) reaction: d + D --> b + B* Then combine the measured decay probabilities for: B* --> c + C + … with the calculated cross section forming B* in the “desired” reaction. ’ 86 Kr** B* B* D D 86 Kr d d “Surrogate” reaction 86 Kr* c Direct-reaction probability: Fd. CN(E, J, p) ‘Channel’ probability: Pc(E) = SJ, p Fd. CN(E, J, p). GCNc(E, J, p) Formation cross section: s CN(E, J, p) s c = SJ, p s CN (E, J, p). GCNc(E, J, p) Hauser-Feshbach

The Surrogate Concept The cross section s c for the “desired” two-step reaction } } a + A --> B* --> c + C c can be determined indirectly with the Surrogate method. a b n A 85 Kr “Desired” reaction Neutron-induced “desired” reaction C The Surrogate idea: Form the compound nucleus B* via an alternative (“Surrogate”) reaction: d + D --> b + B* Then combine the measured decay probabilities for: B* --> c + C + … with the calculated cross section forming B* in the “desired” reaction. ’ B* B* 86 Kr** D 86 Kr d “Surrogate” reaction 86 Kr* c Direct-reaction probability: Fd. CN(E, J, p) ‘Channel’ probability: Pc(E) = SJ, p Fd. CN(E, J, p). GCNc(E, J, p) Formation cross section: s CN(E, J, p) s c = SJ, p s CN (E, J, p). GCNc(E, J, p) Hauser-Feshbach

Different reactions, same results? Even a compound nucleus remembers constants of motion! Grover & Nagle, Phys. Rev. 134 (1964) B 1248 209 Bi E(210 Po) [Me. V] +p +a 206 Pb +a Relative population 206 Pb 209 Bi 208 Po probability 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? Spin of 210 Po +p

Exploring the limitations of the method Central point Formation 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. -energy probabilities for 163 Dy(3 He, 2 n)160 Dy With pre-equilibrium contributions Assuming equilibrated 162 Dy Guttormsen et al. , NPA 587 (1995) 401

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 Jp population of the compound nucleus following the direct reaction. We study the dependence of the Jp population on the reaction mechanism, angle, and energy. Pc (E) = SJ, p Fd. CN (E, J, p ). GCNc(E, J, p) • How do the differences in Jp 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 Jp.

Questions to be addressed