Thien Cung cave (Halong bay) December 2000. From right: Dao Tien Khoa, NDD, Akito Arima, Vo Van Thuan, and Nguyen Tien Dung

I thank the organizers for giving me the pleasure to present a talk here. On Monday several speakers mentioned the first ISPUN, which took place in 2002 in Halong Bay. This made me recall our visit with Prof. Akito Arima, then RIKEN president, to Vietnam in December 2000, when we proposed Dr. Dao Tien Khoa, and Dr. Vo Van Thuan, who was then the director of the INST, to organize a meeting to maintain the spirit of the first large scale international conference in nuclear physics in Vietnam, which took place in Hanoi 20 years go in March 1994. Its name was “Perspectives of Nuclear Physics in the Late Nineties”. Some participants of that conference as Peter Ring, Naftali Auerbach, Edoardo Lanza, Nguyen Van Giai are also here today.

So in 2000, on the concern of the Vietnamese side regarding the financial issue, RIKEN had supported 2 million yen. This eventually became the first IPSUN. Now RIKEN is no longer in the list of ISPUN sponsors, but I think one had better not forget its seminal contribution.

This reminiscence is particular pleasant to me with this ISPUN14, held in the city whose nick name was “Paris of the Orient”. British explorer Alfred Cunningham in 1902 called Saigon “the chief town of the French possessions in the Far East”. Now the French have long gone. Taking the bad with the good, one should not forget that this city was first erected and named as Saigon by the French in 1860s.

Citing Anatole France, the message here is : “Ne perdons rien du passé. Ce n’est qu’avec le passé qu’on fait l’avenir” (Lose nothing of the past. It is only with the past that one makes the future).

Recent achievements in the study of highly excited nuclei:

Thermal Pairing and GDR

Nguyễn Đình Đăng

1) RIKEN Nishina Center, Wako city, Japan

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

International Symposium on Unstable Nuclei (ISPUN 2014), 8 November 2014

Contents

1) Effect of thermal pairing on the GDR width:

- within the Phonon Damping Model (PDM)

- within Thermal Shape Fluctuations Model (TSFM) that includes pairing fluctuations

2) PDM for the description of GDR in hot rotating nuclei

3) Manifestation of pairing reentrance in nuclear level densities

• All the theoretical predictions are compared with the most recent experimental systematics.

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 MeVMukhopadhyay 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

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

NDD, Quang Hung, S.R. BanerjeePLB 731 (2014) 92

N. Quang Hung(TanTao U.)

Tc97

Sudhee Banerjee’s group at VECC Kolkata

Pairing effect in the TSFM on the GDR widthRhine Kumar, Arumugam, NDD, PRC 90 (2014) 044308

Total free energy at a fixed deformation = Liquid-drop energy + Nillson-Strutinsky shell correction:

,

(Indian Institute of Technology Roorkee)

Averaged cross-section

GDR Hamiltonian:

Expectation value of an observable including thermal shape and pairing fluctuations:

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

Ciemala, PhD thesis (2013)

A. MajM. Ciemala

98Mo

See alo NDD, Ciemala,Kmiecik, Maj, PRC 87 (2013)054313

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

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

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.

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

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(BARC Mumbai)

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

Nuclear level density

104Pd (prolate)

104Pd (oblate)

Conclusions

1. Thermal pairing plays an important role in quenching the GDR width at low T, leading to a nealy constant GDR width at T ≤ 1 MeV. This has been showed within the PDM and the TSFM that includes pairing fluctuations, whose predictions agree well with the most recent experimental systematics. This means the TSFM can describe correctly the GDR width at low T even in open shell nuclei if thermal pairing is properly included.

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

3. It is demonstrated that 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.