Recent achievements in the study of highly excited nuclei

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).
International Symposium on Unstable Nuclei (ISPUN 2014), 8 November 2014
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
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
Thermal pairing
In finite systems such as nuclei large thermal fluctuations smooth out the sharp superfluidnormal (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:
Fluctuations of pairing field (Moretto, 1972)
SPA (Dang, Ring, Rossignoli, 1992)
SM (Zelevinsky, Alex Brown, Frazier, Horoi, 1996)
MBCS (Dang, Zelevinsky, 2001)
FTBCS1 (Dang, Hung, 2008)
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.
Phonon Damping Model (PDM)
NDD & Arima, PRL 80 (1998) 4145
( )
Pq E = å Fs( ) Fs'( )
f s - f s'
E - Es' + Es
g q (w ) = ÁmPq (w ± ie ) .
Quantal: ss’ = ph
Thermal: ss’ = pp’ , hh’
Topical conference on giant resonances, Varenna, May 1998
  Q  T  2 q EGDR 
GDR width as a function of T
(Kusnezov, Alhassid, Snover)
NDD, PRC 84 (2011) 034309
(Ormand, Bortignon, Broglia, Bracco)
(Auerbach, Shlomo)
Effect of thermal pairing
Tin region
NDD & Arima, PRC 68 (2003) 044303
Tc ≈ 0.57Δ(0)
120Sn & 208 Pb
NDD & Arima, PRL 80 (1998) 4145
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
 VECC data for 119Sb
Others: Data for tin region
New data at low T:
D. Pandit et al. PLB 713 (2012) 434
Exact canonical pairing gaps
Baumann 1998
Junghans 2008
Pandit 2012
no pairing
with pairing
NDD & N. Quang Hung PRC 86 (2012) 044333
Dey, Mondal, Pandit, Mukhopadhyay, Pal,
Bhattacharya, De, K. Banerjee,
NDD, Quang Hung, S.R. Banerjee
PLB 731 (2014) 92
Sudhee Banerjee’s group at VECC Kolkata
N. Quang Hung
(TanTao U.)
Pairing effect in the TSFM on the GDR width
Rhine Kumar, Arumugam, NDD, PRC 90 (2014) 044308
(Indian Institute of Technology Roorkee)
Total free energy at a fixed deformation = Liquid-drop energy + Nillson-Strutinsky shell correction:
Averaged cross-section
GDR Hamiltonian:
Gi » 0.026Ei1.9
Expectation value of an observable including thermal shape and pairing fluctuations:
PDM at T≠0 & J=M≠0
NDD, PRC 85 (2012) 064323
Ciemala, PhD thesis (2013)
See alo NDD, Ciemala,
Kmiecik, Maj, PRC 87 (2013)
M. Ciemala
A. Maj
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
Discovery of reentrance of superconductivity in metal (2005)
Uranium rhodium germanium (URhGe) becomes superconducting in a strong magnetic field.
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 T0 & M0
NDD & N. Quang Hung, PRC 78 (2008) 064315
H '  H   Nˆ   M
Pairing Hamiltonian including z-projection of total
angular momentum:
M = å mk (ak++ ak + - akak- ) .
Bogoliubov transformation + variational procedure:
N = 2åêvk2 + (1- 2vk2 )(nk+ + nk- )ú
D k = D + dD k ,
D = Gå uk vk D k ,
M = å mk (nk+ - nk- )
dD k = Guk vk dN k2 D k ,
uk2 =
D k = 1- nk+ - nk- ,
Ek = (e k¢ - l - Gvk2 )2 + D 2k
dN = n (1- n ) + n (1- n
1 æ e k¢ - l ö 2 1 æ e k¢ - l ö
÷ , vk = ç1÷
Ek ø
Ek ø
ek¢ = ek +
å( u
- vk2' ) A k+ A k+' + A k+ A k '
Pairing reentrance
Pairing reentrance
Enhancement of nuclear level densities at finite T and J
J = 20ħ
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).
Is it an evidence of pairing reentrance in a finite nucleus?
D. Chakrabarty & V. Datar
B.K. Agrawal & T. Agrawal
(BARC Mumbai)
(SINP Kolkata)
Nuclear level density
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.
is predicted to change shape from prolate at J ≤ 30ħ to oblate at
higher J.

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