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D amping of GDR in highly excited nuclei

Zakopane Conference on Nuclear Physics, Aug. 27 – Sep. 2, 2012. D amping of GDR in highly excited nuclei. Nguyen Dinh Dang RIKEN and INST (VINATOM).

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D amping of GDR in highly excited nuclei

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  1. Zakopane Conference on Nuclear Physics, Aug. 27 – Sep. 2, 2012 Damping of GDR in highly excited nuclei Nguyen Dinh Dang RIKEN and INST (VINATOM)

  2. I am grateful to the organizers, especially to Adam Maj, who asked me in Hanoi last year to give at this conference a talk with this title, which is one of my most favorite subjecrs. Also, it is thanks to their most kind invitation that I could visit Zakopane and the beautiful Cracow for the first time, where, standing in front of “Lady with an ermine” by Leonardo on display at Wawel castle, I finally understood what perfection is. Acknowledgments

  3. Outline • Experimental systematics on GDR’s width at T≠0 and J≠0 • Description of GDR’s width and shape within phonon damping model (PDM): • Calculation of shear viscosity of hot nuclei from GDR’s parameters • Using the lower-bound conjecture for specific shear viscosity to test experimental data on GDR’s width at T≠0 and J≠0 • Conclusions • At T≠0 • Effect of thermal pairing on the GDR width at low T • Extension of PDM to J≠0

  4. Experimental systematics • GDR built on the ground state: • First observed in 1947 (Baldwin & Klaiber) in photonuclear reactions - EWSR:60 NZ/A (1+ ζ) MeV mb, ζ is around 0.5 – 0.7 between 30 ~ 140 MeV; - EGDR ~ 79 A-1/3 MeV; - FWHM: ~ 4 – 5 MeV (≈ 0.3 EGDR) inheavy nuclei; - can be fitted well with Lorentzian or Breit-Wigner curves. • GDR in highly-excited nuclei (T ≠ 0, J ≠ 0): • First observed in 1981 (Newton et al.) in heavy-ion fusion reactions. Limitation: 1) very difficult at low T because of large Coulomb barrier, 2) broad J distribution. • Inelastic scattering of light particles on heavy targets (mainly T). Limitation: Large uncertainty in extracting T because of large excitation energy windows ~ 10 MeV. • Alpha induced fusion (2012): precise extraction of T and low J. FWHM changes slightly at T≤ 1 MeV, increases with T at 1 < T < 3 - 4 MeV. At T> 4 MeV the GDR width seems to saturate.

  5. Dependence of GDR width on T Dependence of GDR width on J To saturate, or not to saturate, that is the question. 1) Pre-equilibrium emission is proportional to (N/Z)p – (N/Z)t 2) Pre-equilibrium emission lowers the CN excitation energy Kelly et al. (1999)included pre-equilibrium (dynamic dipole) emission pTSPM

  6. Mechanism of GDR damping at T = 0 Few MeV Few hundreds keV The variance of the distribution of ph states is the Landau width GLD to be added into G (the quantal width) .

  7. GDR damping at T≠0 G = GQ + GT How to describe the thermal width?  Coupling to 2 phonons NDD, NPA 504 (1989) 143 ph + phonon coupling Bortignon et al. NPA 460 (1986) 149 90Zr 90Zr b(E1, E) (e2 fm4 Mev-1) T=0 T=0 T=1 MeV T=3 MeV T=3 MeV The quantal width (spreading width) does NOT increase with T.

  8. Damping of a spring mass system The width G should be smaller than the oscillator’s frequency w0 , i.e. upper bound, or else no oscillation is possible. If air is heated up in (a), the viscosity of air increases  b increases G increases.

  9. Phonon Damping Model (PDM)NDD & Arima, PRL 80 (1998) 4145 NB: This model does NOT include the pre-equilibrium effect and the evaporation width of the CN states p’ p p h’ h Quantal: ss’ = ph Thermal: ss’ = pp’ , hh’ h GDR strenght function:

  10. GDR width as a function of T pTSFM (Kusnezov, Alhassid, Snover) 63Cu NDD, PRC 84 (2011) 034309 AM (Ormand, Bortignon, Broglia, Bracco) FLDM (Auerbach, Shlomo) NDD & Arima, PRC 68 (2003) 044303 Tin region Tc ≈ 0.57Δ(0) 120Sn &208 Pb NDD & Arima, PRL 80 (1998) 4145

  11. Mukhopadhyay et al., PLB 709 (2012) 9

  12. Warning: TSFM does not use the same Hamiltonian to calculate every quantities such as GDR strength function (simple deformed HO) and free energy (Strutinsky’s shell correction + parametrized expansion within macroscopic Landau theory of phase transitions). A check within the SPA by using the same Hamiltonian with QQ force to calculate all quantities has shown that the width’s increase is not sufficient up to 4 MeV [Ansari, NDD, Arima, PRC 62 (2000) 011302 (R)]. 120Sn T = 0.5, 1, 2, 3, 4 MeV

  13. GDR line shape NDD, Eisenman, Seitz, Thoennessen, PRC 61 (2000) 027302 Gervais, Thoennessen, Ormand, PRC 58 (1998) R1377 PDM E* = 30 MeV E* = 30 MeV PDM E* = 50 MeV E* = 50 MeV PDM

  14. 201 Tl New experimental data : D. Pandit et al. PLB 713 (2012) 434 Exact canonical pairing gaps Baumann 1998 Junghans 2008 Pandit 2012 208Pb no pairing with pairing NDD & N. Quang Hung (2012)

  15. PDM at T≠0 & M≠0NDD, PRC 85 (2012) 064323

  16. GDR width as a function of T and M

  17. Shear viscosity η QGP at RHIC Resistance of a fluid (liquid or gas) to flow 2001: Kovtun – Son – Starinets (KSS) conjectured the lower bound for all fluids: η/s ≥ ħ/(4πkB) First estimation for hot nuclei (using FLDM): Auerbach & Shlomo, PRL 103 (2009) 172501: 4 ≤ η/s ≤ 19 KSS NDD, PRC 84 (2011) 034309:

  18. 1.3 ≤ η/s ≤ 4 ћ/(4πkB) at T = 5 MeV

  19. Specific shear viscosity η/s in hot rotating nuclei u = 10-23 MeV s fm-3

  20. Testing the recent experimentM. Ciemala et al. Acta Phys. Pol. B 42 (2011) 633 Γex ≈ 11 MeV PDM NDD, PRC 85 (2012) 064323 Γex ≈ 7.5 MeV

  21. Test by using KSS conjecture Γex ≈ 7.5 MeV By using the derived expression for η(T) and S = aT2, one finds that Γ(T=4MeV) should be ≥ 8.9 MeV (13.3 MeV) if a = A/11(A/8) to avoid violating the KSS lower-bound conjecture.

  22. Conclusions • The PDM describes reasonably well the GDR’s width and line shape as functions of temperature T and angular momentum M. • The mechanism of this dependence on T and M resides in the coupling of GDR to ph, pp and hh configurations at T≠ 0. • As a function of T: The quantal width (owing to coupling to ph configurations) slightly decreases as T increases. The thermal width (owing to coupling to pp and hh configurations) increases with T up to T ≈ 4 MeV, so does the total width. The width saturates at T ≥ 4 MeV. Pairing plays a crucial role in keeping the GDR’s width nearly constant at T≤ 1 MeV. • As a function of M: The GDR width increases with M at T ≤ 3 MeV; At T > 3 MeV the width saturates at M ≥ 60ħ for 88Mo and 80ħ for 106Sn but these values are higher than the maximal values of M for which η/s ≥ ħ/4πkB. These limiting angular momenta are 46ħ and 55ħ for 88Mo and 106Sn, respectively; • The specific shear viscosity in heavy nuclei can be as low as (1.3 ~ 4) KSS at T = 5 MeV. • The KSS lower-bound conjecture sets a lower bound for the GDR’s width. As such, it serves as a good tool for checking the validity of the GDR data at high T. Request to experimentalists to measure GDR’s widths at T< 1 MeV and T > 4 MeV

  23. Collaborators • A. Arima (Tokyo) • K. Tanabe (Saitama Univ.) • A. Ansari (Bhubaneswar) • M. Thoennensen, K. Eisenman, J. Seitz (MSU) • N. Quang Hung (TanTao Univ.)

  24. Whatis Beauty? Quid est veritas?

  25. “If the facts conflict with a theory, either the theory must be changed or the facts.” • B. Spinoza • (1632-1677)

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