1. Test of Level Density models from Nuclear Reactions Babatunde M. Oginni Ohio University Nuclear Seminar December 3, 2009

2. Outline Introduction - Methods of determining level densities - Some level density models - Motivations - Goals for our study The Lithium induced reactions - Edwards Accelerator Laboratory - Level densities from evaporation of 64 Cu The A = 82 compound nuclear reactions - Wright Nuclear Structure Laboratory - Some results Summary and Conclusion

3. Introduction What is Nuclear Level Density (NLD) ? E E

4. Methods of determining NLD (I) Counting of levels - Main drawbacks – level resolution & missing levels Counting of neutron resonances - Main drawback – narrow ranges of excitation energy, spin and parity ratio E

5. Methods of determining NLD (II) = with Evaporation from compound nucleus – Hauser Feshbach Theory

6. Methods of determining NLD (III) Evaporation from compound nucleus - Level densities obtained for the residual nuclei - Main drawback – contributions from other reaction mechanisms Ericson fluctuation - Level densities obtained for the compound nucleus

7. Analysis Idea 0 E n ~8 MeV E figure from http://inpp.ohiou.edu/~voinov/index.html

8. Some models of NLD (I) Fermi gas model (FG) [*] 2 assumptions – nucleons are non-interacting fermions -- single particle states are equidistant in energy. * H. A. Bethe, Phys. Rev. 50, 336 (1936) - Main challenge is to determine ‘a’ and ‘δ’ accurately for each nucleus

9. Some models of NLD (II) 9 Many ideas have been suggested for a: ROHR [*] Al-Quraishi [**] ** S.I. Al-Quraishi et al, Phys. Rev. C63, 065803(2001). a = 0.071*A + V V = 1.64 A ≤ 38 V = 3.74 38 < A ≤ 69 V = 6.78 69 < A ≤ 94 V = 8.65 94 < A < 170 a = 0.108*A + 2.4 A ≥ 170 * G. Rohr, Z Phys. A – Atoms and Nuclei 318, 299 – 308 (1984); α = 0.1062, β = 0.00051 α = 0.1068, γ = 0.0389

10. Some models of NLD (III) Constant temperature model (CT) [*] Gilbert Cameron Model [**] - combine CT and FG models. Hartree-Fock-BCS model - microscopic statistical model * A. Gilbert et al, Can. J. Phys. 43, 1248 (1965); ** A. Gilbert et al, Can. J. Phys. 43, 1446 (1965)

11. Motivations Astrophysical applications - evaluating reliable reaction rates for the production of nuclei Production cross sections of radioactive isotopes - help answer some salient questions; FRIB Fission Product Yields [*] Medical Applications * P. Fong, Phys. Rev. 89, 332 (1953); P. Fong, Phys. Rev. 102, 434 (1956)

12. Goals for study Better understanding of the NLD problem Two main projects were undertaken: (1.) 6 Li + 58 Fe  64 Cu; 7 Li + 57 Fe  64 Cu * Edwards Accelerator Laboratory, Ohio University, Athens, Ohio (2.) 18 O + 64 Ni  82 Kr; 24 Mg + 58 Fe  82 Sr; 24 Mg + 58 Ni  82 Zr * Wright Nuclear Structure Laboratory, Yale University, New Haven, Connecticut

13. Experimental Facilities (I): Edwards Accelerator Facility

14. beam Target Si 2m flight path 14 Experimental Facilities (II)

15. 64 Cu compound nucleus 6 Li 58 Fe 7 Li 57 Fe 64 Cu 63 Ni 60 Co p α + + + +

16. Experiments: particle ID Si detectors were used to detect the charged particles: TOF and Energy information. helions and tritons cannot be differentiated from each other! 6 Li – induced rxn: 23.5, 37.7, 68.0, 98.0, 142.5 and 157.5 angles 7 Li – induced rxn: 37.7, 142.5 and 157.5 angles

17. Experiments: calibration 17 Charged Particle Energy Calibration -elastic scattering of 6 Li on Gold -elastic scattering of 7 Li on Gold -elastic scattering of d on Gold -alpha source of 3 known peaks Energy = mean (channel #) + offset

18. Experiments: Optical Parameters (I) The transmission coefficients of the entrance and exit channels and the level densities of the residual nuclei are input parameters in the Hauser-Feshbach codes that were used in our calculations. Most of the optical parameters for the exit channels are well documented in the literature [*]. For the entrance channels, we made use of our elastic scattering distribution. The optical parameters for our experiments are given in the table: * National Nuclear Data Center The Coulomb radius parameter used was 1.41 fm

19. Experiment: Optical Parameters (II) We compared our data with results of calculations using the optical parameters that were obtained:

20. Results: Proton angular distribution Angular distribution of compound nuclear reaction is expected to be symmetric about 90 degree.

21. Results: particle energy distribution (I)

22. Results: particle energy distribution (II)

23. Results: Break Up Study (I) 6 Li  α + d (Q = -1.47MeV) α + n + p (Q = -3.70MeV) 5 He + p (Q = -4.59MeV) 7 Li  α + t (Q = -2.47MeV) α + d + n (Q = -8.72MeV) 5 He + d (Q = -9.61MeV) 6 He + p (Q = -9.98MeV) α + 2n + p (Q = -10.95MeV) 5 He + n + p (Q = -11.84MeV) Is the break up a 1-step process or a 2-step process ? 6 Li  6 Li*  … 7 Li  7 Li*  …

24. Results: Break up study (II) Direct break up of 6 Li is into alpha and deuteron [1-4] while 7 Li breaks up into alpha-triton and alpha-deuteron-neutron components [4-6] Sequential break up of 6 Li* and 7 Li* require looking up level schemes (1.) J. M. Hansteen et al. Phys. Rev. 137, B524 (1965); (2.) K. Nakamura, Phys. Rev. 152, 955 (1966); (3.) E. Speth et al, Phy. Rev. Lett. 24, 1493 (1970); (4.) K. O. Pfeiffer et al. Nucl. Phys. A 206, 545 (1973); (5.) D. K. Srivastava et al. Phys. Lett. B, 206, 391 (1988); (6.) V. Valkori et al. Nucl. Phys. A 98, 241 (1967); (7.) A. Pakou et al. Phys. Lett. B, 633, 691 (2006). The dominant contribution to break up reaction among the excited levels of 6 Li is the 3 + level at 2.18 MeV [3, 4,7] Table from TUNL website

25. Results: Break up Study (III) The low energy levels of 7 Li are given in the table below: Table from TUNL website The threshold of emitting proton in sequential break up of 7 Li is about 10 MeV; most of the break up will be through the α-t and α-d-n components

26. Results: Break up study (IV) In order to better understand our break up process, we use the method Goshal [*] showed about compound reactions * S. N. Ghoshal, Phys. Rev. 80, 939 (1950) A represent proton cross sections B could be alpha, deuteron or triton cross sections We look at this ratio:

27. Results: Break up study (V) We safely conclude that the protons and high energy alphas at backward angles are mostly from compound nuclear reactions. Thus we can get NLD information from protons and high energy alphas

28. Results Using this equation: we obtain the level density information of 63 Ni and 60 Co

29. Results: NLD (I)

30. Results: Particle energy distribution (III) -- GC

31. Results: NLD (II)

32. Conclusion (I)

33. CONCLUSION (II) 6 Li + 58 Fe 7 Li + 57 Fe p + 63 Ni 6 Li + 55 Mn d + 59 Co n + 60 Ni p + 60 Co 64 Cu 61 Ni α + 60 Co CT with T = 1.4 MeV. A. V. Voinov, B. M. Oginni, et al., Phys. Rev. C 79, 031301 (R) (2009). B. M. Oginni et al., Phys. Rev. C 80, 034305 (2009).

34. A = 82 Project

35. Layout of the WNSL tandem accelerator

36. Experimental Facilities (III): WNSL

37. Experimental Facilities (IV)

38. Calibration of the clover detectors We did two types of calibrations: energy and the efficiency calibrations The idea of the calibration is to move from the “known” to the “unknown” - So we made use of 152 Eu source with known activity

39. 152 Eu Within the energy range that was considered during the experiment, the source has fifteen prominent peaks with known emission probabilities

40. Artist View of the set up beam detector correct for Doppler

41. Experimental Idea (I) For even-even nuclei, most gamma rays pass through the 2 + to 0 + levels. Production cross section of the 2 + gamma is proportional to the production cross sections of the nucleus [*]. Since we know the even-even nuclei that are expected from each reaction, we use the gamma level schemes to determine the gamma energies associated with each residual nucleus. * R. P. Koopman, PhD Thesis, Lawrence Livermore Laboratory

42. Experimental Idea (II) Not all the 2 + gammas were used in the analysis RULES FOR SELECTION There must be a noticeable gamma peak at the energy corresponding to the 2 + gamma Since most of the gammas were produced in coincidence! We place a gate on each 2 + gamma peak and check for other gammas detected in coincidence; the gammas used in the analysis had at least one gamma decayed in coincidence.

43. How to decide if the γ will be used 78 Kr

44. How decision on the γs are made

45. Summary of data obtained

46. 24 Mg on 58 Ni

47. 24 Mg + 58 Ni

48. 24 Mg on 58 Fe

50. 24 Mg + 58 Fe Al - Quraishi

51. Summary I talked about the different methods of determining LDs I presented some LD models I presented the level densities that we obtained for 63 Ni and 60 Co I also presented some results from our A = 82 nuclear compound reactions A better constraint will be achieved in the Yale experiment if both the evaporated particles and gammas are detected in coincidence

52. List of Collaborators S. M. Grimes, C. R. Brune, T. N. Massey, A. Schiller, A. V. Voinov - Ohio University, Athens, OH A. S. Adekola - Triangle University Nuclear Laboratory, NC Z. Heinen - Savannah River Site, Aiken, SC D. Carter, D. Jacobs, J. O’Donnell - Ohio University, Athens, OH Andreas Heinz (Yale University) - Yale University, New Haven, CT

53. Thanks for your attention!

55. k

56. Emitted particle energy spectra

57. Taking a peep away from stability! Al - Quraishi

58. Summary of Results!

59. State & Level density Each level of spin J comprises 2J+1 degenerate states with different projections of J where = state density = level density  cumulative number of levels

60. Optical Model

61. 61 Nuclear Processes in stars and stellar explosions neutrons protons rp process r-process (SNII) r-process (SNII) s-process (AGB) s-process (AGB) Heavy-element burning (Massive stars) Heavy-element burning (Massive stars) Big Bang H(1) Fe (26) Sn (50) Pb (82) Proton-rich (SNII) Proton-rich (SNII) C(6) CNO Breakout Novae, SNIa X-ray bursts W. Tan

62. NLD NLD from neutron resonances: Levels are excited by the absorption of neutrons with zero angular momentum, the number of resonances in the energy interval is  for target nuclei  for J = 0 target nuclei F = qvB = (mv^2)/R  R = mv/qB  Radius of curvature in a magnetic field

63. NLD Rapid increase in # of levels at high energy is expected from simple thermodynamics considerations, from probability arguments and from nuclear model calculations For the thermodynamics consideration = entropy = state density

64. Energy calibration of the leaf detectors

66. Fermi-gas level-density expressions 1) Single-particle model, no many-body effects 2) Used in most statistical-model calculations.

67. Origin of the “clover”

69. Efficiency

70. Errors Two main error types we took into consideration: statistical & systematic Statistical error is the square root of the number of counts Systematic are mainly uncertainties in target thickness (15%), beam charge integration (5%) and solid angles (5%) We obtained our overall error by propagating the errors

71. Error Propagation

72. GC model The 3 model parameters, T, U x, and E 0, are determined by the requirement that the level density and its derivative are continuous at the matching point, U x. {Sum over all Energies and spins}

73. Experiment * ?? Picture of targets and Si detector 58 Ni  0.525 mg/cm 2 59 Co  0.89 mg/cm 2

74. Calibration (cont’d) Since we know what the energy associated with each peak is, we look at the spectra from each leaf detector To obtain the counts expected, we need to know the activity of the source at a certain time, the half-life of the source and the emission probabilities for each peak