Damping of GDR in highly excited nuclei

Nguyen Dinh Dang

RIKENand

INST (VINATOM)

Zakopane Conference on Nuclear Physics, Aug. 27 – Sep. 2, 2012

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≠02. Description of GDR’s width and shape within phonon damping

model (PDM):

3. Calculation of shear viscosity of hot nuclei from GDR’s parameters4. Using the lower-bound conjecture for specific shear viscosity to

test experimental data on GDR’s width at T≠0 and J≠05. Conclusions

At T≠0 Effect of thermal pairing on the GDR width at low T Extension of PDM to J≠0

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) 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.

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

To saturate, or not to saturate,

that is the question.

pTSPM

Mechanism of GDR damping at T = 0

The variance of the distribution of ph states is the Landau width GLD

to be added into G (the quantal width) .

Few hundreds keV

Few MeV

GDR damping at T≠0G = GQ + GT

Coupling to 2 phonons NDD, NPA 504 (1989) 143

ph + phonon couplingBortignon et al. NPA 460 (1986) 149

90Zr

T=0

T=3 MeV

90Zr

T=0

T=1 MeV

T=3 MeV

b(E1

, E) (

e2 fm

4 Mev

-1)

How to describe the thermal width?

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 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.

Phonon Damping Model (PDM)NDD & Arima, PRL 80 (1998) 4145

p’

p

hh’

h

p

 2 GDRqTQ E=G+G=GQuantal: ss’ = ph Thermal: ss’ = pp’ , hh’

 .122 ww

w

wqGDR

qq E

S+

=

GDR strenght function:

NB: This model does NOT include the pre-equilibrium effect and the evaporation width of the CN states

120Sn & 208 PbNDD & Arima, PRL 80 (1998) 4145

NDD & Arima, PRC 68 (2003) 044303

63CuNDD, PRC 84 (2011) 034309

GDR width as a function of T

Tin region

Tc ≈ 0.57Δ(0)

pTSFM (Kusnezov, Alhassid, Snover)

AM(Ormand, Bortignon, Broglia, Bracco)

FLDM(Auerbach, Shlomo)

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 MeV [Ansari, NDD, Arima, PRC 62 (2000) 011302 (R)].

120SnT = 0.5, 1, 2, 3, 4 MeV

NDD, Eisenman, Seitz, Thoennessen, PRC 61 (2000) 027302Gervais, Thoennessen, Ormand, PRC 58 (1998) R1377

E* = 30 MeV

E* = 50 MeV

E* = 30 MeV

E* = 50 MeV

GDR line shape

PDM

PDM

PDM

Tl201

New experimental data :D. Pandit et al. PLB 713 (2012) 434

NDD & N. Quang Hung (2012)

no pairingwith pairing

208Pb

Baumann 1998Junghans 2008Pandit 2012

Exact canonical pairing gaps

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

GDR width as a function of T and M

Shear viscosity ηResistance 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/(4πkB)

First estimation for hot nuclei (using FLDM): Auerbach & Shlomo, PRL 103 (2009) 172501:

4 ≤ η/s ≤ 19 KSS

QGP at RHIC

1.3 ≤ η/s ≤ 4 ћ/(4πkB) at T = 5 MeV

Specific shear viscosity η/s in hot rotating nuclei

u = 10-23 MeV s fm-3

Testing the recent experimentM. Ciemala et al. Acta Phys. Pol. B 42 (2011) 633

Γex ≈ 11 MeV

Γex ≈ 7.5 MeV

PDM

NDD, PRC 85 (2012) 064323

Γex ≈ 7.5 MeV

By using the derived expression for η(T) and S = aT2, 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

Conclusions① 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 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;

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< 1 MeV and T > 4 MeV

Collaborators

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

What is Beauty? Quid est veritas?

“If the facts conflict with a theory, either the theory must be changed

or the facts.”

B. Spinoza (1632-1677)