INT October 28, 2004Mihai Horoi - Central Michigan Univ1 New Approaches for Spin- and Parity-Dependent Shell Model Nuclear Level Density Mihai Horoi, Department.

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Presentation transcript:

INT October 28, 2004Mihai Horoi - Central Michigan Univ1 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 is acknowledged

INT October 28, 2004Mihai Horoi - Central Michigan Univ2 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, (2003), PRC 69, (2004) Part II: Methods of Removal of the Center-of-Mass Spurious Contribution

INT October 28, 2004Mihai Horoi - Central Michigan Univ3 Hauser and Feshbach, Phys. Rev 87, 366 (1952)

INT October 28, 2004Mihai Horoi - Central Michigan Univ4 The Back-Shifted Fermi Gas Model for Nuclear Level Density

INT October 28, 2004Mihai Horoi - Central Michigan Univ5 A.Adams, G.Mitchell, J.F. Shriner Phys.Lett, B422, 13(1998) 26 Al sd-shell model, USD interaction

INT October 28, 2004Mihai Horoi - Central Michigan Univ6 Data: Table of Isotopes Theory: sd-shell model + USD interaction 28 Si: positive parity

INT October 28, 2004Mihai Horoi - Central Michigan Univ7 p ’s sd ’s pf ’s pf 5/2 -g 9/ Example: 76 Sr PRL 92, pf 5/2 -g 9/2 dimension 11,090,052,440 CMichSM code - m-scheme dimension 250,000,000 on one-processor machine Lanczos iterations/week

INT October 28, 2004Mihai Horoi - Central Michigan Univ8 12 particles in sd model space

INT October 28, 2004Mihai Horoi - Central Michigan Univ9 Nuclear Shell Model d = 2 (2 j + 1)

INT October 28, 2004Mihai Horoi - Central Michigan Univ10 Sum on Partitions vs Moments of the Whole Distribution 6 particles in pf 5/2 -g 9/2 New interaction A. Lisetskiy et al. PRC 2004

INT October 28, 2004Mihai Horoi - Central Michigan Univ11 12 particles in sd model space

INT October 28, 2004Mihai Horoi - Central Michigan Univ12 12 particles in sd model space

INT October 28, 2004Mihai Horoi - Central Michigan Univ13 6 particles in p-sd model space

INT October 28, 2004Mihai Horoi - Central Michigan Univ14 Exponential Convergence Method

INT October 28, 2004Mihai Horoi - Central Michigan Univ15 Exponential Convergence Method for fp-nuclei

INT October 28, 2004Mihai Horoi - Central Michigan Univ16 Exponential Convergence Method for fp-nuclei Central Michigan Shell Model (CMichSM) code Exact: MeV

INT October 28, 2004Mihai Horoi - Central Michigan Univ17 r,s,.. – orbits, not states

INT October 28, 2004Mihai Horoi - Central Michigan Univ18 Fixed J Configura tion Centroids and Widths C. Jacquemin, Z. Phys. A 303, 135 (1981)

INT October 28, 2004Mihai Horoi - Central Michigan Univ19 Shell Model vs Fixed-J Centroids and Widths Density of States 28 Si: 12 particles in sd, Tz=0

INT October 28, 2004Mihai Horoi - Central Michigan Univ20 Shell Model vs Fixed-J Centroids and Widths Density of States 28 Si: 12 particles in sd, Tz=0

INT October 28, 2004Mihai Horoi - Central Michigan Univ21 Spin Cutoff Factor Zeroth-Order: S.S.M. Wong, Nuclear Spectroscopy, Oxford 1986, p. 45, Si: 12 particles in sd, Tz=0

INT October 28, 2004Mihai Horoi - Central Michigan Univ22 Shell Model 28 Si: 12 particles in sd, Tz=0

INT October 28, 2004Mihai Horoi - Central Michigan Univ23 Shell Model 28 Si: 12 particles in sd, Tz=0

INT October 28, 2004Mihai Horoi - Central Michigan Univ24 Zeroth-Order 28 Si: 12 particles in sd, Tz=0

INT October 28, 2004Mihai Horoi - Central Michigan Univ25 Zeroth-Order 28 Si: 12 particles in sd, Tz=0

INT October 28, 2004Mihai Horoi - Central Michigan Univ26 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.

INT October 28, 2004Mihai Horoi - Central Michigan Univ27 The Center-of-Mass Problem nucl-th/

INT October 28, 2004Mihai Horoi - Central Michigan Univ28 Nuclear Shell Model N

INT October 28, 2004Mihai Horoi - Central Michigan Univ29 The Center-of-Mass Problem

INT October 28, 2004Mihai Horoi - Central Michigan Univ30 No E (MeV) Ex (MeV) J T No E (MeV) Ex (MeV) J T p-sd s-p-sd 2 particles 6 particles N = 1

INT October 28, 2004Mihai Horoi - Central Michigan Univ31 Dimensions of Nonspurious Spaces Example: s-p-sd, 6 particles J N=1(K=1) N=0 0 4 = = = = =1 0 Total 26

INT October 28, 2004Mihai Horoi - Central Michigan Univ32

INT October 28, 2004Mihai Horoi - Central Michigan Univ33 C. Jacquemin, Z. Phys. A 303, 135 (1981) Fixed J Restricted Configura tion Widths

INT October 28, 2004Mihai Horoi - Central Michigan Univ34

INT October 28, 2004Mihai Horoi - Central Michigan Univ35 N   Nonspurious Level Density

INT October 28, 2004Mihai Horoi - Central Michigan Univ36 20 Ne: 20 particles in s-p-sd-pf shell model space

INT October 28, 2004Mihai Horoi - Central Michigan Univ37 20 Ne: 20 particles in s-p-sd-pf shell model space

INT October 28, 2004Mihai Horoi - Central Michigan Univ38 20 Ne: 20 particles in s-p-sd-pf shell model space

INT October 28, 2004Mihai Horoi - Central Michigan Univ39 Nonspurious Level Density: (0+2)  

INT October 28, 2004Mihai Horoi - Central Michigan Univ40 10 B: 10 particles in s-p-sd-pf shell model space

INT October 28, 2004Mihai Horoi - Central Michigan Univ41 10 B: 10 particles in s-p-sd-pf shell model space

INT October 28, 2004Mihai Horoi - Central Michigan Univ42 Nonspurious Level Density: General

INT October 28, 2004Mihai Horoi - Central Michigan Univ43 Summary We derived explicit expressions to calculate fixed- J centroids and widths for restricted set of configurations, such N   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 N   configurations Using our method of calculating the level density for restricted set of configurations we can calculate very accurately the nonspurious level density