Test of Level Density models from Nuclear Reactions

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 64Cu • 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 E - Main drawbacks – level resolution & missing levels • Counting of neutron resonances • - Main drawback – narrow ranges of excitation energy, • spin and parity ratio

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

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 En~8 MeV 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. - Main challenge is to determine ‘a’ and ‘δ’ accurately for each nucleus * H. A. Bethe, Phys. Rev. 50, 336 (1936)

9. Some models of NLD (II) • Many ideas have been suggested for a: Al-Quraishi [**] ROHR [*] 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 α = 0.1062, β = 0.00051 α = 0.1068, γ = 0.0389 * G. Rohr, Z Phys. A – Atoms and Nuclei 318, 299 – 308 (1984); ** S.I. Al-Quraishi et al, Phys. Rev. C63, 065803(2001).

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.) 6Li + 58Fe  64Cu; 7Li + 57Fe  64Cu • * Edwards Accelerator Laboratory, Ohio University, • Athens, Ohio • (2.) 18O + 64Ni  82Kr; 24Mg + 58Fe  82Sr; 24Mg + 58Ni  82Zr • * Wright Nuclear Structure Laboratory, Yale University, • New Haven, Connecticut

13. Experimental Facilities (I): Edwards Accelerator Facility

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

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

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

17. Experiments: calibration Charged Particle Energy Calibration -elastic scattering of 6Li on Gold -elastic scattering of 7Li 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: • The Coulomb radius parameter used was 1.41 fm * National Nuclear Data Center

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

24. Results: Break up study (II) • Direct break up of 6Li is into alpha and deuteron [1-4] while 7Li breaks • up into alpha-triton and alpha-deuteron-neutron components [4-6] • Sequential break up of 6Li* and 7Li* require looking up level schemes • The dominant contribution to break up • reaction among the excited levels of 6Li • is the 3+ level at 2.18 MeV [3, 4,7] Table from TUNL website (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).

25. Results: Break up Study (III) • The low energy levels of 7Li are given in the table below: Table from TUNL website • The threshold of emitting proton in sequential break up of 7Li 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 • We look at this ratio: A represent proton cross sections B could be alpha, deuteron or triton cross sections * S. N. Ghoshal, Phys. Rev. 80, 939 (1950)

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 63Ni and 60Co

29. Results: NLD (I)

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

31. Results: NLD (II)

32. Conclusion (I)

33. 6Li + 58Fe p + 63Ni 64Cu α + 60Co 7Li + 57Fe 6Li + 55Mn p + 60Co 61Ni d + 59Co n + 60Ni CONCLUSION (II) • B. M. Oginni et al., Phys. Rev. C • 80, 034305 (2009). CT with T = 1.4 MeV. • A. V. Voinov, B. M. Oginni, et al., • Phys. Rev. C 79, 031301 (R) (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 152Eu source with known activity

39. 152Eu • 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 correct for Doppler detector beam

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 78Kr

44. How decision on the γs are made

45. Summary of data obtained

46. 24Mg on 58Ni

47. 24Mg + 58Ni

48. 24Mg on 58Fe

49. 24Mg on 58Fe

50. 24Mg + 58Fe Al - Quraishi