- Slides: 27
Zakopane Conference on Nuclear Physics, Aug. 27 – Sep. 2, 2012 Damping of GDR in highly excited nuclei Nguyen Dinh Dang RIKEN and INST (VINATOM)
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.
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): l l l At T≠ 0 Effect of thermal pairing on the GDR width at low T Extension of PDM to J≠ 0 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
Experimental systematics • GDR built on the ground state: Ø First observed in 1947 (Baldwin & Klaiber) in photonuclear reactions - EWSR: 60 NZ/A (1+ ζ) Me. V mb, ζ is around 0. 5 – 0. 7 between 30 ~ 140 Me. V; - EGDR ~ 79 A-1/3 Me. V; - FWHM: ~ 4 – 5 Me. V (≈ 0. 3 EGDR) in heavy nuclei; - can be fitted well with Lorentzian or Breit-Wigner curves. • GDR in highly-excited nuclei (T ≠ 0, J ≠ 0): Ø 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. Ø Inelastic scattering of light particles on heavy targets (mainly T). Limitation: Large uncertainty in extracting T because of large excitation energy windows ~ 10 Me. V. Ø Alpha induced fusion (2012): precise extraction of T and low J. FWHM changes slightly at T≤ 1 Me. V, increases with T at 1 < T < 3 - 4 Me. V. At T> 4 Me. V the GDR width seems to saturate.
Dependence of GDR width on T To saturate, or is 1) Pre-equilibrium emission proportional to (N/Z)p – (N/Z)t not to saturate, that is the 2) Pre-equilibrium emission lowers the CN excitation energy question. Kelly et al. (1999) included pre-equilibrium (dynamic dipole) emission p. TSPM Dependence of GDR width on J
Mechanism of GDR damping at T = 0 Few Me. V Few hundreds ke. V The variance of the distribution of ph states is the Landau width GLD to be added into G (the quantal width).
GDR damping at T≠ 0 G = GQ + GT 90 Zr T=0 T=3 Me. V Coupling to 2 phonons NDD, NPA 504 (1989) 143 b(E 1, E) (e 2 fm 4 Mev-1) ph + phonon coupling Bortignon et al. NPA 460 (1986) 149 How to describe thermal width? 90 Zr T=0 T=1 Me. V T=3 Me. V The quantal width (spreading width) does NOT increase with T.
Damping of a spring mass system The width G should be smaller than the oscillator’s frequency w 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 G increases.
Phonon Damping Model (PDM) NDD & Arima, PRL 80 (1998) 4145 p’ NB: This model does NOT include the pre-equilibrium effect and the evaporation width of the CN states p p h’ h h Quantal: ss’ = ph Thermal: ss’ = pp’ , hh’ GDR strenght function:
GDR width as a function of T p. TSFM (Kusnezov, Alhassid, Snover) 63 Cu AM NDD, PRC 84 (2011) 034309 (Ormand, Bortignon, Broglia, Bracco) FLDM (Auerbach, Shlomo) NDD & Arima, PRC 68 (2003) 044303 Tin region Tc ≈ 0. 57Δ(0) 120 Sn & 208 Pb NDD & Arima, PRL 80 (1998) 4145
Mukhopadhyay et al. , PLB 709 (2012) 9
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 Me. V [Ansari, NDD, Arima, PRC 62 (2000) 011302 (R)]. 120 Sn T = 0. 5, 1, 2, 3, 4 Me. V
GDR line shape NDD, Eisenman, Seitz, Thoennessen, Gervais, Thoennessen, Ormand, 58 (1998) R 1377 PRC 61 (2000) PRC 027302 E* = 30 Me. V PDM E* = 50 Me. V PDM
201 Tl New experimental data : D. Pandit et al. PLB 713 (2012) 434 Exact canonical pairing gaps Baumann 1998 Junghans 2008 Pandit 2012 208 Pb no pairing with pairing NDD & N. Quang Hung (2012)
PDM at T≠ 0 & M≠ 0 NDD, PRC 85 (2012) 064323
GDR width as a function of T and M
Shear viscosity η Resistance of a fluid (liquid or gas) to flow QGP at RHIC 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 NDD, PRC 84 (2011) 034309:
Specific shear viscosity η/s in hot rotating nuclei u = 10 -23 Me. V s fm-3
Testing the recent experiment M. Ciemala et al. Acta Phys. Pol. B 42 (2011) 633 Γex ≈ 11 Me. V PDM NDD, PRC 85 (2012) 064323 Γex ≈ 7. 5 Me. V
Test by using KSS conjecture Γex ≈ 7. 5 Me. V By using the derived expression for η(T) and S = a. T 2, one finds that Γ(T=4 Me. V) should be ≥ 8. 9 Me. V (13. 3 Me. V) if a = A/11 (A/8) to avoid violating the KSS lower-bound conjecture.
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 Me. V, so does the total width. The width saturates at T ≥ 4 Me. V. Pairing plays a crucial role in keeping the GDR’s width nearly constant at T≤ 1 Me. V. ④ As a function of M: The GDR width increases with M at T ≤ 3 Me. V; At T > 3 Me. V 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 Me. V. 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< 1 Me. V and T > 4 Me. V
Collaborators • • • A. Arima (Tokyo) K. Tanabe (Saitama Univ. ) A. Ansari (Bhubaneswar) M. Thoennensen, K. Eisenman, J. Seitz (MSU) N. Quang Hung (Tan. Tao Univ. )
What is Beauty? Quid est veritas?
“If the facts conflict with a theory, either theory must be changed or the facts. ” B. Spinoza (1632 -1677)