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New Approaches for Spin- and Parity-Dependent Shell Model Nuclear Level Density

New Approaches for Spin- and Parity-Dependent Shell Model Nuclear Level Density. Mihai Horoi , Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, USA Support from NSF grant PHY-02-44453 is acknowledged. Plan of the Talk. Part I: Methods for Shell Model NLD

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New Approaches for Spin- and Parity-Dependent Shell Model Nuclear Level Density

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  1. New Approaches for Spin- and Parity-Dependent Shell Model Nuclear Level Density Mihai Horoi, Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, USA Support from NSF grant PHY-02-44453 is acknowledged Mihai Horoi - Central Michigan Univ

  2. Plan of the Talk • Part I: Methods for Shell Model NLD • Motivation • Sum on partitions vs moments of the whole density • Exponential Convergence Method • Fixed-J Configuration Centroids and Widths • Energy-Dependent Cutoff Description • PRC 67, 054309(2003), PRC 69, 041307(2004) • Part II: Methods of Removal of the Center-of-Mass Spurious Contribution Mihai Horoi - Central Michigan Univ

  3. Hauser and Feshbach, Phys. Rev 87, 366 (1952) Mihai Horoi - Central Michigan Univ

  4. The Back-Shifted Fermi Gas Model for Nuclear Level Density Mihai Horoi - Central Michigan Univ

  5. A.Adams, G.Mitchell, J.F. Shriner Phys.Lett, B422, 13(1998) 26Al sd-shell model, USD interaction Mihai Horoi - Central Michigan Univ

  6. Data: Table of Isotopes Theory: sd-shell model + USD interaction 28Si: positive parity Mihai Horoi - Central Michigan Univ

  7. p - 102 -1960’s sd - 105 - 1980’s pf - 109 - 1990’s pf5/2-g9/2- 1010 - 2006 Example: 76Sr PRL 92, 232501 pf5/2-g9/2 dimension 11,090,052,440 CMichSM code - m-scheme dimension 250,000,000 on one-processor machine - 150 Lanczos iterations/week Mihai Horoi - Central Michigan Univ

  8. 12 particles in sd model space Mihai Horoi - Central Michigan Univ

  9. Nuclear Shell Model d = 2 (2 j + 1) Mihai Horoi - Central Michigan Univ

  10. Sum on Partitions vs Moments of the Whole Distribution 6 particles in pf5/2 -g9/2 New interaction A. Lisetskiy et al. PRC 2004 Mihai Horoi - Central Michigan Univ

  11. 12 particles in sd model space Mihai Horoi - Central Michigan Univ

  12. 12 particles in sd model space Mihai Horoi - Central Michigan Univ

  13. 6 particles in p-sd model space Mihai Horoi - Central Michigan Univ

  14. Exponential Convergence Method Mihai Horoi - Central Michigan Univ

  15. Exponential Convergence Method for fp-nuclei Mihai Horoi - Central Michigan Univ

  16. Exponential Convergence Method for fp-nuclei Central Michigan Shell Model (CMichSM) code Exact: -203.196 MeV Mihai Horoi - Central Michigan Univ

  17. r,s,.. – orbits, not states Mihai Horoi - Central Michigan Univ

  18. Fixed J Configuration Centroids and Widths C. Jacquemin, Z. Phys. A 303, 135 (1981) Mihai Horoi - Central Michigan Univ

  19. Shell Model vs Fixed-J Centroids and Widths Density of States 28Si: 12 particles in sd, Tz=0 Mihai Horoi - Central Michigan Univ

  20. 28Si: 12 particles in sd, Tz=0 Shell Model vs Fixed-J Centroids and Widths Density of States Mihai Horoi - Central Michigan Univ

  21. Spin Cutoff Factor 28Si: 12 particles in sd, Tz=0 Zeroth-Order: S.S.M. Wong, Nuclear Spectroscopy, Oxford 1986, p. 45,171 Mihai Horoi - Central Michigan Univ

  22. Shell Model <M2> 28Si: 12 particles in sd, Tz=0 Mihai Horoi - Central Michigan Univ

  23. Shell Model <M2> 28Si: 12 particles in sd, Tz=0 Mihai Horoi - Central Michigan Univ

  24. Zeroth-Order <M2> 28Si: 12 particles in sd, Tz=0 Mihai Horoi - Central Michigan Univ

  25. Zeroth-Order <M2> 28Si: 12 particles in sd, Tz=0 Mihai Horoi - Central Michigan Univ

  26. Summary of Part I • Shell Model NLD look very promising, at least up to the particle emission threshold. More comparison with experimental data necessary. • J-dependent SM NLD are very accurately described by a sum of finite range Gaussians with fixed-J centroids and widths, if one knows with good precision the energy of g.s. and yrast states. We derived explicit expression to calculate fixed-J centroids and widths. • Exponential Convergence Method (ECM) proves to be a very powerful tool for finding yrast and non-yrast energies, by doing shell model calculations in truncated model spaces. • J-dependent SM NLD are reasonably well described by spin cutoff formula with exact cutoff factor, except for higher J’s, but not very well described by spin cutoff formula with zeroth-order cutoff factor. Improvement in estimating cutoff factor requires knowledge of higher order moments. Mihai Horoi - Central Michigan Univ

  27. nucl-th/0111068 The Center-of-Mass Problem Mihai Horoi - Central Michigan Univ

  28. Nuclear Shell Model N Mihai Horoi - Central Michigan Univ

  29. The Center-of-Mass Problem Mihai Horoi - Central Michigan Univ

  30. No E (MeV) Ex (MeV) J T 1 -60.0000 0.0000 0.0000 0.0000 2 -60.0000 0.0000 0.0000 0.0000 3 -60.0000 0.0000 0.0000 0.0000 4 -59.6000 0.4000 1.0000 0.0000 5 -59.6000 0.4000 1.0000 0.0000 6 -59.6000 0.4000 1.0000 0.0000 7 -59.6000 0.4000 1.0000 0.0000 8 -59.4000 0.6000 0.0000 1.0000 9 -59.0000 1.0000 1.0000 1.0000 10 -59.0000 1.0000 1.0000 1.0000 11 -59.0000 1.0000 1.0000 1.0000 12 -59.0000 1.0000 1.0000 1.0000 13 -59.0000 1.0000 1.0000 1.0000 14 -58.8000 1.2000 2.0000 0.0000 15 -58.8000 1.2000 2.0000 0.0000 16 -58.8000 1.2000 2.0000 0.0000 17 -58.8000 1.2000 2.0000 0.0000 18 -58.8000 1.2000 2.0000 0.0000 19 -58.2000 1.8000 2.0000 1.0000 20 -58.2000 1.8000 2.0000 1.0000 21 -58.2000 1.8000 2.0000 1.0000 22 -57.6000 2.4000 3.0000 0.0000 23 -57.6000 2.4000 3.0000 0.0000 24 -57.0000 3.0000 3.0000 1.0000 25 -57.0000 3.0000 3.0000 1.0000 26 -56.0000 4.0000 4.0000 0.0000 27 0.0000 60.0000 0.0000 0.0000 No E (MeV) Ex (MeV) J T 1 -40.0000 0.0000 0.0000 0.0000 2 -39.6000 0.4000 1.0000 0.0000 3 -39.0000 1.0000 1.0000 1.0000 4 -38.8000 1.2000 2.0000 0.0000 5 -38.8000 1.2000 2.0000 0.0000 6 -37.6000 2.4000 3.0000 0.0000 7 -37.0000 3.0000 3.0000 1.0000 8 -36.0000 4.0000 4.0000 0.0000 9 -29.6000 10.4000 1.0000 0.0000 10 -29.4000 10.6000 0.0000 1.0000 11 -29.0000 11.0000 1.0000 1.0000 12 -29.0000 11.0000 1.0000 1.0000 13 -28.8000 11.2000 2.0000 0.0000 14 -28.2000 11.8000 2.0000 1.0000 15 -28.2000 11.8000 2.0000 1.0000 16 -27.0000 13.0000 3.0000 1.0000 17 -10.0000 30.0000 0.0000 0.0000 18 -9.6000 30.4000 1.0000 0.0000 19 -9.6000 30.4000 1.0000 0.0000 20 -9.0000 31.0000 1.0000 1.0000 21 -8.8000 31.2000 2.0000 0.0000 22 -8.8000 31.2000 2.0000 0.0000 23 -8.2000 31.8000 2.0000 1.0000 24 -7.6000 32.4000 3.0000 0.0000 25 0.4000 40.4000 1.0000 0.0000 2 particles 6 particles p-sd s-p-sd N = 1 N = 1 Mihai Horoi - Central Michigan Univ

  31. Example: s-p-sd, 6 particles • J N=1(K=1) N=0 • 0 4 =4 2 • 1 2+4+3=9 4 • 2 4+3+1=8 3 • 3 3+1 =4 1 • 1 =1 0 • Total 26 Dimensions of Nonspurious Spaces Mihai Horoi - Central Michigan Univ

  32. Mihai Horoi - Central Michigan Univ

  33. Fixed J Restricted Configuration Widths C. Jacquemin, Z. Phys. A 303, 135 (1981) Mihai Horoi - Central Michigan Univ

  34. Mihai Horoi - Central Michigan Univ

  35. Nhw Nonspurious Level Density Mihai Horoi - Central Michigan Univ

  36. 20Ne: 20 particles in s-p-sd-pf shell model space Mihai Horoi - Central Michigan Univ

  37. 20Ne: 20 particles in s-p-sd-pf shell model space Mihai Horoi - Central Michigan Univ

  38. 20Ne: 20 particles in s-p-sd-pf shell model space Mihai Horoi - Central Michigan Univ

  39. Nonspurious Level Density: (0+2)hw Mihai Horoi - Central Michigan Univ

  40. 10B: 10 particles in s-p-sd-pf shell model space Mihai Horoi - Central Michigan Univ

  41. 10B: 10 particles in s-p-sd-pf shell model space Mihai Horoi - Central Michigan Univ

  42. Nonspurious Level Density: General Mihai Horoi - Central Michigan Univ

  43. Summary • We derived explicit expressions to calculate fixed-J centroids and widths for restricted set of configurations, such Nhw configurations • We found recursive formulae to calculate the dimensions of nospurious spaces • We found recursive formulae for calculating exactly the nonspurious level density when one knows the level density for a restricted set of configurations, such Nhw configurations • Using our method of calculating the level density for restricted set of configurations we can calculate very accurately the nonspurious level density Mihai Horoi - Central Michigan Univ

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