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

2. Acknowledgments 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.

4. Outline 1.Experimental systematics on GDR’s width at T≠0 and J≠0 2.Description of GDR’s width and shape within phonon damping model (PDM): 3.Calculation of shear viscosity of hot nuclei from GDR’s parameters 4.Using the lower-bound conjecture for specific shear viscosity to test experimental data on GDR’s width at T≠0 and J≠0 5.Conclusions At T≠0 Effect of thermal pairing on the GDR width at low T Extension of PDM to J≠0

5. 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; - E GDR ~ 79 A -1/3 MeV; - FWHM: ~ 4 – 5 MeV (≈ 0.3 E GDR ) in heavy 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. 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.

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

7. Mechanism of GDR damping at T = 0 The variance of the distribution of ph states is the Landau width  LD to be added into  (the quantal width)  Few hundreds keV Few MeV

8. GDR damping at T≠0  Q  T Coupling to 2 phonons NDD, NPA 504 (1989) 143 ph + phonon coupling Bortignon et al. NPA 460 (1986) 149  90 Zr T=0 T=3 MeV 90 Zr T=0 T=1 MeV T=3 MeV b(E1, E) (e 2 fm 4 Mev -1 ) How to describe the thermal width? The quantal width (spreading width) does NOT increase with T.

9. Damping of a spring mass system The width  should be smaller than the oscillator’s frequency  0, i.e. upper bound, or else no oscillation is possible. If air is heated up in (a), the viscosity of air increases  b increases   increases.

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

11. 120 Sn & 208 Pb NDD & Arima, PRL 80 (1998) 4145 NDD & Arima, PRC 68 (2003) 044303 63 Cu NDD, PRC 84 (2011) 034309 GDR width as a function of T Tin region T c ≈ 0.57Δ(0) pTSFM (Kusnezov, Alhassid, Snover) AM (Ormand, Bortignon, Broglia, Bracco) FLDM (Auerbach, Shlomo)

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

13. 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)]. 120 Sn T = 0.5, 1, 2, 3, 4 MeV

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

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

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

18. GDR width as a function of T and M

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

20. 1.3 ≤ η/s ≤ 4 ћ/(4πk B ) at T = 5 MeV 1.3 ≤ η/s ≤ 4 ћ/(4πk B ) at T = 5 MeV

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

22. Testing the recent experiment M. Ciemala et al. Acta Phys. Pol. B 42 (2011) 633 Γ ex ≈ 11 MeV Γ ex ≈ 7.5 MeV PDM NDD, PRC 85 (2012) 064323

23. Γ ex ≈ 7.5 MeV By using the derived expression for η(T) and S = aT 2, one finds that Γ(T=4 MeV) should be ≥ 8.9 MeV (13.3 MeV) if a = A/11 (A/8) to avoid violating the KSS lower-bound conjecture. Test by using KSS conjecture

24. Conclusions ① The PDM describes reasonably well the GDR’s width and line shape as functions of temperature T and angular momentum M. ② The mechanism of this dependence on T and M resides in the coupling of GDR to ph, pp and hh configurations at T≠ 0. ③ 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. ④ 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 88 Mo and 80ħ for 106 Sn but these values are higher than the maximal values of M for which η/s ≥ ħ/4πk B. These limiting angular momenta are 46ħ and 55ħ for 88 Mo and 106 Sn, respectively; ⑤ The specific shear viscosity in heavy nuclei can be as low as (1.3 ~ 4) KSS at T = 5 MeV. ⑥ 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 4 MeV

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

26. What is Beauty? Quid est veritas ?

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