11th International Spring Seminar On Nuclear Physics, Ischia, May 12 – 16, 2014

Thermal pairing and hot GDR

Nguyen Dinh Dang1) RIKEN Nishina Center, Wako city, Japan

2) Institute for Nuclear Science & Technique, Hanoi – Vietnam

Plan

• What is thermal pairing?• Effect of thermal pairing on the GDR width at low T• First experimental evidence of pairing reentrance a finite nucleus• Damping of GDR at finite T and J• Viscosity of hot nuclei• Conclusions

Thermal pairingIn finite systems such as nuclei large thermal fluctuations smooth out the sharp superfluid-normal (SN) phase transition. As the result, pairing does not collapse at Tc ≈ 0.57Δ(T=0), but remains finite even at T >> Tc.

This has been shown within the following approaches:

1) Fluctuations of pairing field (Moretto, 1972)2) SPA (Dang, Ring, Rossignoli, 1992)3) SM (Zelevinsky, Alex Brown, Frazier, Horoi, 1996)4) MBCS (Dang, Zelevinsky, 2001)5) FTBCS1 (Dang, Hung, 2008)6) Exact solutions of pairing problem embedded in the GCE, CE, and MCE (Dang, Hung, 2009) (8th - 10th Spring seminars, 2004, 2007, and 2010)

Decaying scheme of a highly-excited compound nucleus

1) GDR photons are emitted in the early stage in competition with neutrons. 2) When E* becomes lower than Bn slower γ transitions take place. 3) Most of the angular momentum is carried off at the final stage of the decay by quadrupole radiation.

1

2

3

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

 2 GDRqTQ E

Quantal: ss’ = ph Thermal: ss’ = pp’ , hh’

Topical conference on giant resonances, Varenna, May 1998

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

Effect of thermal pairing

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)

New measurements at VECC (Kolkata): α induced fusion reactions 4He + 115In 119Sb*

at beam energies of 30, 35, and 42 MeV.Mukhopadhyay et al. PLB 709 (2012) 9

pTSFM

PDM

VECC data for 119SbOthers: Data for tin region

Tl201

New data at low T:D. Pandit et al. PLB 713 (2012) 434

NDD & N. Quang Hung PRC 86 (2012) 044333

no pairing

with pairing

208Pb

Baumann 1998Junghans 2008Pandit 2012

Exact canonical pairing gaps

Tc97

Dey, Mondal, Pandit, Mukhopadhyay, Pal, Bhattacharya, De, K. Banerjee,

NDD, Quang Hung, S.R. Banerjee

PLB 731 (2014) 92

N. Quang Hung(TanTao U.)

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

Ciemala, PhD thesis (2013)

A. MajM. Ciemala(Krakow)

98Mo

Nuclear pairing reentrance was predicted 50 years agoby T. Kammuri, PTP 31 (1964) 595

Physics explanation by L.G. MorettoNPA 185 (1972) 145

FTBCS1 at T0 & M0NDD & N. Quang Hung, PRC 78 (2008) 064315

QNF:

FTBCS1:

Pairing Hamiltonian including z-projection of total angular momentum:

Bogoliubov transformation + variational procedure:

,ˆˆ' MNHH

N=10 M 0

Pairing reentrancePairing reentrance

Uranium rhodium germanium (URhGe) becomes superconducting in a strong magnetic field.

Discovery of reentrance of superconductivity in metal (2005)

The sample at Grenoble High Magnetic Field Laboratory (CNRS) was cooled down below its critical temperature (290 mK) and the magnetic field was raised to 2 T. The sample's superconducting properties vanished. However, when the magnetic field was raised to 8 T, the superconducting behavior reappeared. The critical temperature at that field strength increased to about 400 mK. The sample retained the superconducting state until 13 T.

Lévy, Sheikin, Grenier, Huxley, Science 309 (2005) 1343.

Enhancement of nuclear level densities at finite T and J

Experiments were carried out at BARC (2006 – 2010) at energies of carbon beam 40 – 45 MeV. The proton spectra in coincidence with a γ-ray multiplicity detector array show broad structures, which can be fitted using the statistical model by multiplying the phenomenological nuclear level densities by an enhancement function dependent on excitation energy and angular momentum (Datar, Mitra, and Chakrabarty).

104Pd*J = 20ħ

Is it an evidence of pairing reentrance in a finite nucleus?

D. Chakrabarty & V. Datar(Mumbai)

B.K. Agrawal & T. Agrawal (Kolkata)

Nuclear level density

104Pd (prolate)

104Pd (oblate)

Shear viscosity h

y

u

Unit: 1 P (poise) = 0.1 Pa.s = 1 g / (cm.s)1cP = 1mPa.s = 0.001 Pa.snamed after Poiseuille (1797 – 1869)

Substance T (ºC) h (cP)

AirWaterHoneyPitchNucleusLead glassQGP

1820

~ 20-273~ 5004×1012

0.021

2,000 – 10,000230,000,000,000

(1 – 3) ×1012 ~1014

~1014

= 1/ f h is called fluidity

Using string theory, P. Kovtun, D.T. Son and A. Starinets (KSS), PRL 94 (2005) 111601, conjectured that the value

is the universal lower bound for all fluids.

Lower bound for /h s

P. Kovtun D.T. Son A. Starinets(U. Victoria) (U. Chicago) (Oxford U)

Quark-Gluon Plasma

Experimental data from the RHIC (BNL) and LHC (CERN) have revealed that thematter formed in ultrarelativistic heavy-ion (Au-Au with √sNN= 200 GeV, T>Tc~175 MeV,and Pb-Pb with √sNN= 5.4 TeV) collisions is a nearly perfect liquid with extremely low

specific viscosity: /s = (1.5 ~ 2.5) KSS.

h / s in Hot Nuclei

I) Calculations using FLDM: N. Auerbach & S. Shlomo

PRL 103 (2009) 172501

One of fundamental explanations of giant resonance damping remains the friction term(viscosity) of neutron and proton fluids → Viscosity can be extracted from the GR.

They found h/s = (4-19) KSS for heavy, (2.5 – 12.5) KSS for light nuclei.

Shortcomings:

1) the GDR width does not agree with experimental systematic at high T; 2) The entropy S = 2aT with constant level density parameter a; 3) Large uncertainties.

(Tel-Aviv U) (Texas A&M U)

By using the Green-Kubo relation, which expresses h in terms of correlation functions of shear stress tensors:

and the fluctuation-dissipation theorem, one obtains

with

This exact formula relates the linear transport coefficient of any system (in a non-equilibrium or local thermodynamic equilibrium) to fluctuations in global thermodynamic equilibrium

(such as thermal noise of electric and heat currents, collective vibrations, etc.)

NDD, PRC 84 (2011) 034309

Derivation of h/s from the GDR width and energy at T≠0

Shear viscosity of hot nuclei

A) By using Breit-Wigner distribution:

B) By using Lorentz distribution:

Entropy density

Fermions Bosons

Nj = 2j+1 , (upper sign) Nj = 1 , (lower sign)

Conclusions

1. The PDM prediction that thermal pairing compensates the smoothing of Fermi surface as T increases, leading to a nealy constant GDR width at T ≤ 1 MeV, has been confirmed by all latest experimental data.

2. The PDM successfully describes the GDR in hot rotating nuclei as well.

3. The enhancement of level densities found in 104Pd at finite T and J is the first experimental evidence of pairing reentrance phenomenon in a 　　 finite nucleus.

4. 104Pd is predicted to change shape from prolate at J ≤ 30ħ to oblate at higher J.

5. The specific shear viscosity of hot nuclei is (1.3 – 4) KSS at T = 5 MeV, that is almost the same as that of QGP, (1.5 – 2.5) KSS at T~ 175 MeV.