Jutta Escher Nuclear Theory & Modeling Lawrence Livermore National Lab Jutta Escher Nuclear Theory & Modeling Lawrence Livermore National Lab UCRL pending 21st Winter Workshop on Nuclear Dynamics Breckenridge, Colorado February , ERD-057 Nuclear reactions with unstable nuclei and 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 C c 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 d b B* Then combine the measured decay probabilities for: B* --> c + C + … C c A a B* with the calculated cross section for forming B* in the “desired” reaction. A a “Desired” reaction 86 Kr* 85 Kr n Neutron-induced “desired” reaction 86 Kr** 86 Kr “Surrogate” reaction  ’’ D “Surrogate” reaction d b B* A a “Desired” reaction C c The cross section   for the “desired” two-step reaction a + A --> B* --> c + C can be determined indirectly with the Surrogate method. } }  

Some examples 85 Kr 86 Kr (n) (  ’) 85 Kr(n,  ) 86 Kr 234 U 235 U 236 U (n) (t,p) 235 U(n,f) 154 Gd 155 Gd 156 Gd 157 Gd (n) ( 3 He,  ) 155 Gd(n,2n) 154 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 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 process r 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 RIBFs RIBFs = 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 Synthesis of elements in the A=90 region Can we determine (n,  ) 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 C c 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 d b B* Then combine the measured decay probabilities for: B* --> c + C + … C c A a B* with the calculated cross section for forming B* in the “desired” reaction. A a “Desired” reaction 86 Kr* 85 Kr n Neutron-induced “desired” reaction 86 Kr** 86 Kr “Surrogate” reaction  ’’ D “Surrogate” reaction d b B* A a “Desired” reaction C c The cross section   for the “desired” two-step reaction a + A --> B* --> c + C can be determined indirectly with the Surrogate method. } }  

An application to actinide nuclei Younes & Britt, PRC 67 (2003) , PRC 68 (2003) m U(n,f) inferred new!  (n,f) (b) E n (MeV) Benchmark: inferred cross section compared to prior evaluation 235 U(n,f)

A major issue: Angular-momentum matching “Simple life”: Cross section for two-step process:   =   CN  (E ) . G CN  (E)   CN  (E) =  (a+A->B*) - can be calculated G CN  (E) - probability for decay into channel  = c+C, can be determined from Surrogate experiments “Real life”: Cross section for a+A -> B* -> c+C :   =  J    CN  (E,J,  ) . G CN  (E,J,  ) J - angular momentum of compound nucleus B*   CN  (E,J,  can be calculated Problem: experiments only measure P  ( E ) =  J  F  CN (E,J,  ) . G CN  (E,J,  ) --> Nuclear theory is needed to extract the individual G CN  (E,J, . A a “Desired” reaction D “Surrogate” reaction d b B* C c

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.

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

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

The effect of the J  population on the decay probabilities 91 Zr(d,p) vs. n + 91 Zr E n = 1 MeV J( 91 Zr) = 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 (  ’). 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 Extract an (n,  ) cross section from a Surrogate experiment and compare to a direct measurement, e.g. 101 Ru(n,  ). If successful, apply the technique to obtain an unknown (n,  ) cross section, e.g. 103 Ru(n,  ).

(Not to scale)  E EE Ge Clover  -electron shield 8 mm 4.7 mm  Target 24 Rings  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

Jutta Escher Nuclear Theory & Modeling Lawrence Livermore National Lab Jutta Escher Nuclear Theory & Modeling Lawrence Livermore National Lab UCRL pending 21st Winter Workshop on Nuclear Dynamics Breckenridge, Colorado February , ERD-057 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 Bernstein et al., Fall 2002 Experiment carried out in Berkeley Surrogate measurement using 157 Gd( 3 He,  ) Direct measurement 155 Gd(n,  ) 156 Gd 155 Gd(n,2n) Cross Section (mb) E n (MeV)

Developing the Surrogate technique Direct reactions to the continuum determine 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 model The CN formation cross section needs to be calculated very precisely. Identification of the final reaction product(s) Measured  -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. 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,  ) 92 Zr via 92 Zr( ,  ’  ) 92 Zr is underway. 2. Astrophysics application After establishing the validity of the method: measure and analyze a surrogate reaction for 85 Kr(n,  ) 86 Kr, for example via 86 Kr( ,  ’  ) 86 Kr. 3. Extend the applications a) Study (n,  ) in the deformed region -> possible application: 151 Sm(n,  ) 152 Sm. b) The technique is not limited to n-induced reactions -> consider (p,  ) reactions on unstable targets in the A=60-90 mass region. Implementation:

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

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

Explanation of Figures Schematic of Lee Bernstein’s Surrogate experiment at Berkeley. Remnant of a supernova. Supernovae are potential sites for r-process heavy-element synthesis. From DOE/NSF NSAC Long-range plan, 2002 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   =  J    CN  (E,J,  ) . G CN  (E,J,  ) Hauser-Feshbach “Desired” reaction C c Form the compound nucleus B* via an alternative (“Surrogate”) reaction: d + D --> b + B* The Surrogate idea: D “Surrogate” reaction d b B* Then combine the measured decay probabilities for: B* --> c + C + … C c A a B* with the calculated cross section for forming B* in the “desired” reaction. A a “Desired” reaction 86 Kr* 85 Kr n Neutron-induced “desired” reaction 86 Kr** 86 Kr “Surrogate” reaction  ’’ D “Surrogate” reaction d b B* A a “Desired” reaction C c The cross section   for the “desired” two-step reaction a + A --> B* --> c + C can be determined indirectly with the Surrogate method. } }   Direct-reaction probability: F  CN (E,J,  ) ‘Channel’ probability: P  (E) =  J  F  CN (E,J,  ). G CN  (E,J,  ) Formation cross section:   CN (E,J,  )

The Surrogate Concept   =  J    CN  (E,J,  ) . G CN  (E,J,  ) Hauser-Feshbach “Desired” reaction C c Form the compound nucleus B* via an alternative (“Surrogate”) reaction: d + D --> b + B* The Surrogate idea: D “Surrogate” reaction d b B* Then combine the measured decay probabilities for: B* --> c + C + … C c A a B* with the calculated cross section for forming B* in the “desired” reaction. A a “Desired” reaction 86 Kr* 85 Kr n Neutron-induced “desired” reaction 86 Kr** 86 Kr “Surrogate” reaction  ’’ The cross section   for the “desired” two-step reaction a + A --> B* --> c + C can be determined indirectly with the Surrogate method. } }   Direct-reaction probability: F  CN (E,J,  ) ‘Channel’ probability: P  (E) =  J  F  CN (E,J,  ). G CN  (E,J,  ) Formation cross section:   CN (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( 210 Po) [MeV] 208 Po probability 206 Pb +  209 Bi + p Spin of 210 Po Relative population 206 Pb +  209 Bi + 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. Guttormsen et al., NPA 587 (1995) 401  -energy probabilities for 163 Dy( 3 He,  2n) 160 Dy Assuming equilibrated 162 Dy 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 . P  ( E ) =  J  F  CN (E,J,  ) . G CN  (E,J,  )

Questions to be addressed