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Nuclear reactions with unstable nuclei and the Surrogate reaction technique

Nuclear reactions with unstable nuclei and the Surrogate reaction technique. Jutta Escher Nuclear Theory & Modeling Lawrence Livermore National Lab.

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Nuclear reactions with unstable nuclei and the Surrogate reaction technique

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  1. Nuclear reactions with unstable nucleiand the Surrogate reaction technique Jutta Escher Nuclear Theory & Modeling Lawrence Livermore National Lab “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 LLNL team: L.Ahle, L. Bernstein, J. Burke, J. Church, F. Dietrich, J. Escher, C. Forssén, V. Gueorguiev, R. Hoffman, … 21st Winter Workshop on Nuclear Dynamics Breckenridge, Colorado February 5 - 12, 2005 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. UCRL pending 04-ERD-057

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

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

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

  5. Cat’s eye nebula s process r process Remnant of a supernova = ‘playground’ of RIBFs rp process RIBFs = Radioactive Ion Beam Facilities 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… • site of the r process? multiple sites? • details of the supernova mechanism? • mixing processes in red giants • role of other processes? Fascinating connections between nuclear physics and astrophysics! Understanding the origin of the heavy elements requires knowledge of reactions on unstable nuclei!

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

  7. The cross section sac for the “desired” two-step reaction a + A --> B* --> c + C can be determined indirectly with the Surrogate method. D D a’ A A A a 86 Kr n 85 Kr d d } } a a a “Surrogate” reaction “Surrogate” reaction “Desired” reaction “Desired” reaction “Desired” reaction “Surrogate” reaction c a Neutron-induced “desired” reaction 86 Kr** B* B* B* 86 Kr* The Surrogate idea: b b c c 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 + … C C C with the calculated cross section for forming B* in the “desired” reaction. The Surrogate concept Do we have any indication that this method might work?

  8. 235U(n,f) new! 235mU(n,f) inferred Benchmark: inferred cross section compared to prior evaluation s(n,f) (b) En(MeV) An application to actinide nuclei Younes & Britt,PRC 67 (2003) 024610, PRC 68 (2003) 034610

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

  10. 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?

  11. 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.

  12. 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 The role of the target spin

  13. 90Zr(d,p) vs. n +90Zr En = 1 MeV J(90Zr) = 0+ Jp populations Decay probabilities C. Forssén & JE The effect of the Jp population on the decay probabilities

  14. 91Zr(d,p) vs. n +91Zr En = 1 MeV J(91Zr) = 5/2+ Jp populations Decay probabilities C. Forssén & JE The effect of the Jp population on the decay probabilities

  15. Observations • So far, we find: • The Jp 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 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. 101Ru(n, g). • If successful, apply the technique to obtain an unknown (n,g) cross section, e.g. 103Ru(n, g).

  16. 8 Sectors f 24 Rings q Ge Clover d-electron shield E DE g Target g 4.7 mm 8 mm (Not to scale) Setup for a benchmark experiment From: J. Church, N Division, LLNL (July 2004) Berkeley 2005 From: J. Burke, N Division, LLNL (Dec 2004) Segmentation allows geometric particle correlations

  17. 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.

  18. Appendix

  19. 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, … 21st Winter Workshop on Nuclear Dynamics Breckenridge, Colorado February 5 - 12, 2005 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. UCRL pending 04-ERD-057

  20. 155Gd(n,g)156Gd Cross Section (mb) En(MeV) Cross Section (mb) 155Gd(n,2n) En(MeV) A test case in the rare-earth region Surrogate measurement using 157Gd(3He,a) Direct measurement Bernstein et al., Fall 2002 Experiment carried out in Berkeley

  21. Implementation: 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,g)92Zr via 92Zr(a,a’ g)92Zr is underway. 2. Astrophysics applicationAfter establishing the validity of the method: measure and analyze a surrogate reaction for 85Kr(n,g)86Kr, for example via 86Kr(a,a’ g)86Kr . 3. Extend the applicationsa) Study (n,g) in the deformed region -> possible application: 151Sm(n,g)152Sm. b) The technique is not limited to n-induced reactions -> consider (p,g) reactions on unstable targets in the A=60-90 mass region. Developing the Surrogate technique • Direct reactions to the continuumdetermine 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 s- and p-waves while direct reactions populate a wide range of Jp. • Accurate optical modelThe 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 effectsThe formation of an equilibrated system is a crucial ingredient of the Surrogate Technique. The validity of assumption needs to be tested.

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

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

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

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

  26. The cross section sac for the “desired” two-step reaction a + A --> B* --> c + C can be determined indirectly with the Surrogate method. D D a’ A A A a 86 Kr n 85 Kr d d } } a a a “Surrogate” reaction “Surrogate” reaction “Desired” reaction “Desired” reaction “Desired” reaction “Surrogate” reaction c a Neutron-induced “desired” reaction 86 Kr** B* B* B* 86 Kr* The Surrogate idea: b b c c 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 + … C C C with the calculated cross section for forming B* in the “desired” reaction. The Surrogate Concept Direct-reaction probability:FdCN(E,J,p) ‘Channel’ probability: Pc(E)=SJ,pFdCN(E,J,p).GCNc(E,J,p) Formation cross section:saCN(E,J,p) sac = SJ,psaCN(E,J,p). GCNc(E,J,p) Hauser-Feshbach

  27. The cross section sac for the “desired” two-step reaction a + A --> B* --> c + C can be determined indirectly with the Surrogate method. D a’ A A a 86 Kr n 85 Kr d } } a a “Surrogate” reaction “Desired” reaction “Desired” reaction “Surrogate” reaction c a Neutron-induced “desired” reaction 86 Kr** B* B* 86 Kr* The Surrogate idea: b c 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 + … C C with the calculated cross section for forming B* in the “desired” reaction. The Surrogate Concept Direct-reaction probability:FdCN(E,J,p) ‘Channel’ probability: Pc(E)=SJ,pFdCN(E,J,p).GCNc(E,J,p) Formation cross section:saCN(E,J,p) sac = SJ,psaCN(E,J,p). GCNc(E,J,p) Hauser-Feshbach

  28. 209Bi + p Grover & Nagle,Phys. Rev. 134 (1964) B1248 206Pb + a 208Po probability 206Pb + a Relative population 209Bi + p E(210Po) [MeV] Spin of 210Po Different reactions, same results? 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?

  29. a-energy probabilities for 163Dy(3He,a2n)160Dy With pre-equilibrium contributions Assuming equilibrated 162Dy Guttormsen et al.,NPA 587 (1995) 401 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.

  30. 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.

  31. Pc(E)=SJ,p FdCN(E,J,p ).GCNc(E,J,p) Developing the Surrogate reaction technique… • Direct reactions to the continuumdetermine 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. • 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.

  32. Questions to be addressed

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