Order-to-Chaos Transition in Rotational Nuclei

Transcription

1 Order-to-Chaos Transition in Rotational Nuclei I.Y. Lee, F.S. Stephens, M.A. Deleplanque, A.O. Macchiavelli, D. Ward, P. Fallon, M. Cormaz, R.M. Clark, M. Descovich, R.M. Diamond, and E. Rodriguez-Vieitez LBNL International Conference on Finite Fermionic Systems Nilsson Model 50 Years Lund, Sweden, June 14-18, 2005

2 Outline Introduction Experimental method Simulation calculation Results Summary

3 Gamma decay from fusion reaction Decay pathway E (MeV) neutrons neutron separation y energ statistical Excitation energy Spin γ-ray Spectra Discrete Continuum nds discrete ba ine yrast l Spin Statistical 40

4 Rotational and Compound Damping Wigner Unresolved continuum Poisson Nearest Neighbor Spacing Pnar rot Level mixing v ~ d rot = rotational damping width ~ Δω = compound damping width ~v Pnar = probability of decaying via the entry component = C2a,a Goals: Determine rot,, Pnar

5 Experimental methods Gammasphere at 88- Inch Cyclotron 48 Ca + 124Sn, 215 MeV Produces 168,167,166Yb 2 109, M 5 event Sorted into Eγ Eγ Subtract background using COR method Produce 1-D spectra

6 Energy correlation matrix Raw matrix Background subtracted matrix 4 kev/channel

7 Data analysis Subtract background using COR method: Ci, j Ri, j R R R i, m m l, j l l, m l, m Produce gated 1-D spectra using Shift and add method: Gate : J - J + J J SiJ Ci x, J x 4 kev/ channel Background subtracted matrix x 0 Preserve narrow features with good statistics

8 Gated one-d spectra gate Simulated spectra With one decay width =0.15 ΔEγ =0.5 ΔEγ =1.0 ΔEγ =2.0 ΔEγ The experimental spectra contain features of more than one width This is due to, among other factors, the distribution of decay pathways Require simulation with realistic physics input to understand the data

9 Simulation calculations Competitive cascade to define the conditions for emission of rays Cascade starting point Spin rs from measured spin distribution (FSS). E* -- rs from distributions to fit statistical transitions. Decay pathway E1- E, E1 from standard estimates (DV). E2 - E from measured values (FSS), E2 from gs Yb Q0 values. Yrast line determined from experimental data decay widths as functions of of E*, I rot = I (E*)1/4; theoretical estimate, (LBD). Or fitted = 0.031(E*)3/2; theoretical estimate, (LDB). 1/Pnar = 1+c(E*)3, with c fitted to the data. discrete. E* < 0.2 MeV Detector response of Gammasphere FSS: F.S. Stephens et al., Phys. Rev. Lett. 88, (2002) DV: T. Dossing and E. Vigezzi, Nucl. Phys. A587, 13 (1995) LBD: B. Lauritzen et al., Nucl. Phys. A457, 61 (1986)

10 Key parameters: Pnar, v/d A la Breit-Wigner constant level spacing = d constant ME = v Pnar 1 c ( a' ) 1 2 (v / d )2 2 a RMT BW Random Matrix Theory: <Poisson spacing> = d Gaussian ME rms = v v/d~0 ordered; Pnar~1 v/d~1 chaotic; Pnar~0

11 Inputs of simulation Excitation energy Spin Feeding (H,k) Used Yrast line discrete shape + E vs. Mγ used Fit to 1-D spectrum

12 Inputs of simulation rot v/d

13 fe rre i lat data Gate: 1.4 MeV co ed ing Determination of rot on simulation rot fit Feeding correlation

14 Results of rot Measured Matsuo et al. Lauritzen et al. M. Matsuo et al., NPA649 (1999)379c. B. Lauritzen et al., NPA457 (1986)61.

15 Determination of v/d Measured spectra Simulation E γ (Me V) v 1 d P n ar v/ d Pnar Gates: 60 kev (15 x 4 kev)

16 Distribution of γ-rays Pnar To ta RD CD Disc NCD N Disc N Total Pnar l 1 1 c (E )3

17 (E*,I) distribution of γ-rays Total Rotational Damped Spin E* (0.2 MeV/ch) E* (0.2 MeV/ch) Eγ = 1.2 MeV Compound Damped Rotational Damped Compound Damped Spin

18 E*,I distribution of γ-rays E 1 MeV Total 1.2 MeV 1 MeV 1.4 MeV 1.2 MeV 1.4 MeV Compound Damped E* (MeV)

19 Distribution of Compound damped γ-ray 1.1 MeV Eγ = 1.1 MeV 1.2 MeV 1.2 MeV Broad distribution Breit-Wigner shape Not a single Gaussian

20 Results of individual nuclei Spectra gated on discrete lines of Individual nuclei 6n 166 Yb 5n 167 Yb 4n 168 Yb 6n 5n 4n E* Measured spectra Simulation v/d

21 Summary of Results E γ (Me V) <I> Co m po u n d dam pe d <E*> (Me V) P n ar v/ d ±10 30% ±15 30% Ro t at io n al dam pe d <E*> (Me V) ro t (ke V) ±60

22 v/d and chaoticity Random matrix calculation Levels with Poissonian spacing : d Random matrix element from a Gaussian distribution : σ = v NNS v/d

23 Summary We have measured rotational damping width a value about 300(60)keV We developed a new method to study the orderto-chaos transition in rotational nuclei The purity of the rotational wavefunction was measured from energy correlation spectra The derived values of v/d, from 0.15 to 1.5, span the range from ordered to chaotic rotational motion.

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