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Alex Brown UNEDF Feb-22-2008 Strategies for extracting optimal effective Hamiltonians for CI and Skyrme EDF applications.

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Presentation on theme: "Alex Brown UNEDF Feb-22-2008 Strategies for extracting optimal effective Hamiltonians for CI and Skyrme EDF applications."— Presentation transcript:

1 Alex Brown UNEDF Feb-22-2008 Strategies for extracting optimal effective Hamiltonians for CI and Skyrme EDF applications

2 Alex Brown UNEDF Feb-22-2008 sd pf

3 Alex Brown UNEDF Feb-22-2008 77 gs BE and 530 excited states, 137 keV rms B. A. Brown and W. A. Richter, Phys. Rev. C 74, 034315 (2006). Number of data for each nucleus

4 Alex Brown UNEDF Feb-22-2008 3 spe 63 tbme for the sd-shell

5 Alex Brown UNEDF Feb-22-2008 Starting Hamiltonian Renormalized NN

6 Alex Brown UNEDF Feb-22-2008 Sigma_th = 100 keV

7 Alex Brown UNEDF Feb-22-2008

8 About 5 iterations needed

9 Alex Brown UNEDF Feb-22-2008

10

11

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13 rms for the 608 levels rms for the tbme USDA 30 USDB 56 Linear combinations of two-body matrix elements

14 Alex Brown UNEDF Feb-22-2008 USDA 170 keV rms

15 Alex Brown UNEDF Feb-22-2008 USDB 137 keV rms

16 Alex Brown UNEDF Feb-22-2008 USDA ground state energy differences MeV theory underbound oxygen beyond N=16 all unbound

17 Alex Brown UNEDF Feb-22-2008 USDA 170 keV rms for 608 levels 290 keV rms for tbme (4.1% of largest)

18 Alex Brown UNEDF Feb-22-2008 USDB 137 keV rms for 608 levels 376 keV rms for tbme

19 Alex Brown UNEDF Feb-22-2008 USD 150 keV rms for 380 levels 450 keV rms for tbme

20 Alex Brown UNEDF Feb-22-2008 A few notes Need a realistic model for the starting and background Hamiltonians What do we use for undetermined linear combinations? starting Hamiltonian or Hamiltonian from previous iteration Not obvious that the same (universal) Hamiltonian should apply to all sd-shell nuclei – probably a special case – we now know that other situations (like O vs C) require an explicit change in the TBME due to changes coming from core-polarization of difference cores.

21 Alex Brown UNEDF Feb-22-2008 TBME depend on the target nucleus and model space Comparison of 24 O (with proton p 1/2 ) and 22 C (without p 1/2 )

22 Alex Brown UNEDF Feb-22-2008 USD G Effective spe for the oxygen isotopes

23 Alex Brown UNEDF Feb-22-2008 A tour of the sd shell on the web

24 Alex Brown UNEDF Feb-22-2008 Positive parity states for 26 Al

25 Alex Brown UNEDF Feb-22-2008 Positive parity states for 26 Mg

26 Alex Brown UNEDF Feb-22-2008 g s p = 5.586 g s n = -3.826 g l p = 1 g l n = 0

27 Alex Brown UNEDF Feb-22-2008 g s p = 5.586 g s n = -3.826 g l p = 1 g l n = 0

28 Alex Brown UNEDF Feb-22-2008 g s p = 5.586 g s n = -3.826 g l p = 1 g l n = 0 g s p = 5.586 g s n = -3.826 g l p = 1 g l n = 0

29 Alex Brown UNEDF Feb-22-2008 g s p = 5.127 g s n = -3.543 g l p = 1.147 g l n = -0.090

30 Alex Brown UNEDF Feb-22-2008 g s p = 5.586 g s n = -3.826 g l p = 1 g l n = 0

31 Alex Brown UNEDF Feb-22-2008 g s p = 5.127 g s n = -3.543 g l p = 1.147 g l n = -0.090

32 Alex Brown UNEDF Feb-22-2008 sd pf

33 Alex Brown UNEDF Feb-22-2008 jj44 means f 5/2, p 3/2, p 1/2, g 9/2 orbits for protons and neutrons

34 Alex Brown UNEDF Feb-22-2008 USDA 170 keV rms for 608 levels 290 keV rms for tbme (4.1% of largest)

35 Alex Brown UNEDF Feb-22-2008 Why do we need to modify the renormalized G matrix for USD Is the renormalization adequate Difference between HO and finite well Effective three-body terms Real three-body interactions

36 Alex Brown UNEDF Feb-22-2008 Skyrme parameters based on fits to experimental data for properties of spherical nuclei, including single-particle energies, and nuclear matter. A New Skyrme Interaction for Normal and Exotic Nuclei, B. A. Brown, Phys. Rev. C58, 220 (1998). Displacement Energies with the Skyrme Hartree-Fock Method, B. A. Brown, W. A. Richter and R. Lindsay, Phys. Lett. B483, 49 (2000). Neutron Radii in Nuclei and the Neutron Equation of State, B. A. Brown, Phys. Rev. Lett. 85, 5296 (2000). Charge Densities with the Skyrme Hartree-Fock Method, W. A. Richter and B. A. Brown, Phys. Rev. C67, 034317 (2003). Tensor interaction contributions to single-particle energies, B. A. Brown, T. Duguet, T. Otsuka, D. Abe and T. Suzuki, Phys. Rev. C 74, 061303, (2006). Neutron Skin Deduced from Antiprotonic Atom Data, B. A. Brown, G. Shen, G. C. Hillhouse, J. Meng and A. Trzcinska, Phys. Rev. C76, 034305 (2007).

37 Alex Brown UNEDF Feb-22-2008 Data for Skx BE for 16 O, 24 O, 34 Si, 40 Ca, 48 Ca, 48 Ni, 68 Ni, 88 Sr, 100 Sn, 132 Sn and 208 Pb with “errors” ranging from 1.0 MeV for 16 O to 0.5 MeV for 208 Pb rms charge radii for 16 O, 40 Ca, 48 Ca, 88 Sr and 208 Pb with “errors” ranging from 0.03 fm for 16 O to 0.01 fm for 208 Pb About 50 Single particle energies with “errors” ranging from 2.0 MeV for 16 O to 0.5 MeV for 208 Pb. Constraint to FP curve for the neutron EOS

38 Alex Brown UNEDF Feb-22-2008 Skx - fit to these data Fitted parameters: t 0 t 1 t 2 t 3 x 0 x 1 x 2 x 3 W W x (extra spin orbit term) t 0s (isospin symmetry breaking) Vary α by hand (density dependence) minimum at α = 0.5 (K=270) t 0 t 0s t 1 t 2 t 3 x 0 and W well determined from exp data x 3 constrained from neutron EOS W x x 1 and x 2 poorly determined

39 Alex Brown UNEDF Feb-22-2008 Skx - fit to all of these data Fit done by 2p calculations for the values V and V+epsilon of the p parameters. Then using Bevington’s routine for a “fit to an arbitrary function”. After one fit, iterate until convergence – 20-50 iterations. 10 nuclei, 8 parameters, so each fit requires 2000-5000 spherical calculations. Takes about 30 min on the laptop. Goodness of fit characterized by CHI with best fit obtained for “Skx” with CHI=0.6

40 Alex Brown UNEDF Feb-22-2008 Skx - fit to all of these data Single-particle states from the Skyrme potential of the close-shell nucleus (A) are associated with experimental values for the differences -[BE(A) - BE(A-1)] or = -[BE(A+1)-BE(A)] based on the HF model The potential spe are typically within 200 keV of those calculated from the theoretical values for -[BE(A) - BE(A-1)] or = -[BE(A+1)-BE(A)] No time-odd type interactions, but time-odd contribution to spe are typically not more than 200 keV (Thomas Duguet)

41 Alex Brown UNEDF Feb-22-2008

42 Displacement energy requires a new parameter

43 Alex Brown UNEDF Feb-22-2008 Rms charge radii

44 Alex Brown UNEDF Feb-22-2008 Skx Skyrme Interaction

45 Alex Brown UNEDF Feb-22-2008 Skx Skyrme Interaction

46 Alex Brown UNEDF Feb-22-2008 Skx Skyrme Interaction

47 Alex Brown UNEDF Feb-22-2008 Neutron EOS related to neutron skin -- x 3 How can we constrain the neutron equation of state? We know the proton density from electron scattering The neutron skin is S = R_p – R_n where R are the rms radii

48 Alex Brown UNEDF Feb-22-2008

49 For Skxtb α t = -118, β t = 110 For Skxta α t = 60, β t = 110 For Skx α t = 0, β t = 0

50 Alex Brown UNEDF Feb-22-2008 Skx – fit to single-particle energies

51 Alex Brown UNEDF Feb-22-2008 Skx with G matrix tensor CHI jumps up from 0.6 to 1.5 due to spe

52 Alex Brown UNEDF Feb-22-2008 normal spin-orbit tensor terms

53 Alex Brown UNEDF Feb-22-2008

54 0.25 0.20 0.15 S (fm) K=200 MeV for nuclear matter incompressibility Phys. Rev. C 76, 034305 (2007). Skx for charge density diffuseness and neutron skin

55 Alex Brown UNEDF Feb-22-2008 122 Zr S BE (fm) (MeV) 0.15 -928.6 0.20 –931.3 0.25 –934.2

56 Alex Brown UNEDF Feb-22-2008 S (fm) = 0.12 0.16

57 Alex Brown UNEDF Feb-22-2008 Neutron matter effective mass can constrain x 1 and x 2

58 Alex Brown UNEDF Feb-22-2008 Phys. Rev. C 76, 034305 (2007).

59 Alex Brown UNEDF Feb-22-2008 28 O 34 Si 42 Si 48 Ca 24 O

60 Alex Brown UNEDF Feb-22-2008 Skxta/b: Skx with the inclusion of the rho+pi tensor in fits to spe, BE and radii, B. A. Brown, T. Duguet, T. Otsuka, D. Abe and T. Suzuki, Phys. Rev. C 74, 061303(R) (2006).. Z=8

61 Alex Brown UNEDF Feb-22-2008 Skxta/b: Skx with the inclusion of the rho+pi tensor in fits to spe, BE and radii, B. A. Brown, T. Duguet, T. Otsuka, D. Abe and T. Suzuki, Phys. Rev. C 74, 061303(R) (2006).. Z=8

62 Alex Brown UNEDF Feb-22-2008 Skxta/b: Skx with the inclusion of the rho+pi tensor in fits to spe, BE and radii, B. A. Brown, T. Duguet, T. Otsuka, D. Abe and T. Suzuki, Phys. Rev. C 74, 061303(R) (2006).. N=16

63 Alex Brown UNEDF Feb-22-2008 In 28 O the d 3/2 is bound by 0.2 MeV

64 Alex Brown UNEDF Feb-22-2008 Skxta/b: Skx with the inclusion of the rho+pi tensor in fits to spe, BE and radii, B. A. Brown, T. Duguet, T. Otsuka, D. Abe and T. Suzuki, Phys. Rev. C 74, 061303(R) (2006).. N=20

65 Alex Brown UNEDF Feb-22-2008 N=20

66 Alex Brown UNEDF Feb-22-2008 N=28

67 Alex Brown UNEDF Feb-22-2008 N=28

68 Alex Brown UNEDF Feb-22-2008

69 114 Sn to 115 Sb proton spectroscopic factors

70 Alex Brown UNEDF Feb-22-2008

71 32 Cl 33 Ar p 32 Cl(p,gamma) 33 Ar Rp-process path Experiment needed to get energy of states in 33 Ar to 5 keV accuracy. Theory needed to get proton decay widths to ground and excited states of 32 Cl and gamma widths for 33 Ar 32 P 33 P R. R. C. Clement et al., Phys. Rev. Lett. 92, 172502 (2004) H. Schatz, et al., Phys. Rev. C 72, 065804 (2005) Role of excited state in other nuclei - Janina Grineviciute

72 Alex Brown UNEDF Feb-22-2008 Full pf space for 56 Ni with GXPF1A Hamiltonian (order of one day computing time) M. Horoi, B. A. Brown, T. Otsuka, M. Honma and T. Mizusaki, Phys. Rev. C 73, 061305(R) (2006).

73 Alex Brown UNEDF Feb-22-2008 e p =1 e n =0

74 Alex Brown UNEDF Feb-22-2008 e p =1.37 e n =0.45

75 Alex Brown UNEDF Feb-22-2008 e p =1.37 e n =0.45e p =1.10 e n =0.68

76 Alex Brown UNEDF Feb-22-2008 e p =1 e n =0

77 Alex Brown UNEDF Feb-22-2008 e p =1.37 e n =0.45

78 Alex Brown UNEDF Feb-22-2008 |g a /g v |=1.26

79 Alex Brown UNEDF Feb-22-2008 |g a /g v |=0.97

80 Alex Brown UNEDF Feb-22-2008 Nuclear Structure Theory - Confrontation and Convergence (AI) Ab initio methods with NN and NNN (CI) Shell model configuration interactions with effective single-particle and two-body matrix elements (DFT) Density functionals plus GCM… My examples with Skyrme Hartree-Fock (Skx) Cluster models, group theoretical models ….. Good – most “fundamental” Bad – only for light nuclei, need NNN parameters, “complicated wf” Good – applicable to more nuclei, 150 keV rms, “good wf” Bad – limited to specific mass regions and E x, need effective spe and tbme for good results Good – applicable to all nuclei Bad – limited mainly to gs and yrast, 600 keV rms mass, need interaction parameters Good – simple understanding of special situations Bad – certain classes of states, need effective hamiltonian Each of these has its own computational challenges

81 Alex Brown UNEDF Feb-22-2008 USDB ground state energy differences MeV theory underbound

82 Alex Brown UNEDF Feb-22-2008

83

84

85 PRL98, 102502 (2007) RIKEN PRL99 1125012 (2007) NSCL Theory has 10 eV width

86 Alex Brown UNEDF Feb-22-2008 Mihai Horoi Thomas Duguet Werner Richter Taka Otsuka D. Abe T. Suzuki Funding from the NSF Collaborations

87 Alex Brown UNEDF Feb-22-2008 Monopole interactions

88 Alex Brown UNEDF Feb-22-2008 Monopole interaction changes

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