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

2. 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.

3. 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).

4. Recent achievements in the study of highly excited nuclei: Thermal Pairing and GDR 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 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

5. 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.

6. Thermal pairing In 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 T c ≈ 0.57Δ(T=0), but remains finite even at T >> T c. 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) ( 8 th - 10th Spring seminars, 2004, 2007, and 2010 )

7. 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 B n 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

8. Phonon Damping Model (PDM) NDD & Arima, PRL 80 (1998) 4145 Quantal: ss’ = ph Thermal: ss’ = pp’, hh’ Topical conference on giant resonances, Varenna, May 1998

9. 120 Sn & 208 Pb NDD & Arima, PRL 80 (1998) 4145 Effect of thermal pairing NDD & Arima, PRC 68 (2003) 044303 Effect of thermal pairing 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)

10. New measurements at VECC (Kolkata): α induced fusion reactions 4 He + 115 In  119 Sb* at beam energies of 30, 35, and 42 MeV Mukhopadhyay et al. PLB 709 (2012) 9 New measurements at VECC (Kolkata): α induced fusion reactions 4 He + 115 In  119 Sb* at beam energies of 30, 35, and 42 MeV Mukhopadhyay et al. PLB 709 (2012) 9 pTSFM PDM  VECC data for 119 Sb Others: Data for tin region

11. Tl 201 New data at low T: D. Pandit et al. PLB 713 (2012) 434 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 208 Pb Baumann 1998 Junghans 2008 Pandit 2012 Exact canonical pairing gaps

12. Dey, Mondal, Pandit, Mukhopadhyay, Pal, Bhattacharya, De, K. Banerjee, NDD, Quang Hung, S.R. Banerjee PLB 731 (2014) 92 Dey, Mondal, Pandit, Mukhopadhyay, Pal, Bhattacharya, De, K. Banerjee, NDD, Quang Hung, S.R. Banerjee PLB 731 (2014) 92 N. Quang Hung (TanTao U.) Tc 97 Sudhee Banerjee’s group at VECC Kolkata

13. Pairing effect in the TSFM on the GDR width Rhine 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)

14. Averaged cross-section GDR Hamiltonian: Expectation value of an observable including thermal shape and pairing fluctuations:

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

17. Ciemala, PhD thesis (2013) A. Maj M. Ciemala 98 Mo See alo NDD, Ciemala, Kmiecik, Maj, PRC 87 (2013) 054313

18. Nuclear pairing reentrance was predicted 50 years ago by T. Kammuri, PTP 31 (1964) 595 Physics explanation by L.G. Moretto NPA 185 (1972) 145

19. 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.

20. FTBCS1 at T  0 & M  0 NDD & N. Quang Hung, PRC 78 (2008) 064315 QNF: FTBCS1: Pairing Hamiltonian including z-projection of total angular momentum: Bogoliubov transformation + variational procedure:

21. N=10 M  0 Pairing reentrance

22. 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). 104 Pd* J = 20ħ Is it an evidence of pairing reentrance in a finite nucleus?

23. D. Chakrabarty & V. Datar (BARC Mumbai) B.K. Agrawal & T. Agrawal (SINP Kolkata)

24. Nuclear level density

25. 104 Pd (prolate)

26. 104 Pd (oblate)

27. 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 104 Pd at finite T and J is the first experimental evidence of pairing reentrance phenomenon in a finite nucleus. 4. 104 Pd is predicted to change shape from prolate at J ≤ 30ħ to oblate at higher J.