FINAL SCIENTIFIC REPORT
Project title:
Nuclear structure, double beta decay, fusion, fision and
nuclear multifragmentation
acronym: NSDBDFFNF
The main research directions associated to this project were:
A) Nuclear Structure
B) Double beta decay for deformed nuclei with an excited final state
C) Transport phenomena and the dynamics of phase transitions in nuclear and hadronic
systems.
Below we enumerate the essential objectives whithin each major research direction:
A) Nuclear Structure
a) Using the coherent state model the phase transition from SU(5) to SU(3) symmetry was
studied. The asymptotic behaviour of some quadrupole and octupole boson Hamiltonians near
the critical points of various phase transitions were analyzed. The phase transition for a sixth
order quadrupole boson Hamiltonian was considered.
b) A phenomenological model was proposed as to describe simultaneously 8 rotational bands, 4
of positive and 4 of negative parity.
c) Dynamic nuclear systems described by anharmonic boson Hamiltonians of quadrupole and
octupole type will be considered. The potential energy surface topology, the regular and chaotic
regions in the control parameter space, order to chaos transition, critical structure of the phase
portrait in the regular regions are under consideration. Also the normal Bikhoff forms for
quadrupole and octupole boson Hamiltonians will keep our attention.
d) Investigation of the influence of charge density changes and, consequently, the N/Z
equilibrium value at every step of overlap for fusion and/or fission processes. This point will
provide a path towards (Z1, Z2) directions by minimizing the potential barrier especially in fusion
reactions. Calculation of deformation energy for necked-in shapes. As a result, we expect to
emphasize to which degree quasi-fission could compete with complete fusion. Both surfaces and
contour plots will be used to illustrate the strong shell effects corresponding to the usual fission
mechanism and to heavy ion radioactivity.
e) Using an isospin non-invariant Hamiltonian, the competition between a T=1 and T=0 protonneutron pair in the ground state was studied.
f) Fully renormalized pnQRPA equations obeying the gauge symmetry were written for dipole
dipole proton-neutron interaction of Gamow-Teller type.
g) ) A DMRG scheme which conserves the angular momentum was constructed. First the
formalism was tested for a soluble of a SU(3) hamiltonian. The truncation scheme was finally
applied to some exotic nuclei.
B) Double beta decay for deformed nuclei with the daughter in an excited collective state.

daughter in a collective excited state were calculated. Situations where the involved nuclei are
deformed are considered.
C) Transport phenomena and the dynamics of phase transitions in nuclear and hadronic
systems.
Studies on the dependence of the reaction mechanisms and of various observables, on the
equation of state of asymmetric nuclear matter and effective interactions were performed. We
focused on new signatures of the various phase transitions in some finite fermionic systems as,
for example, the liquid-gas phase transition in multifragmentation and that of nuclear surface
between different dynamical symmetries.
The objectives were realized by following the whole activities associated to the program indicated
below:
Stage I : Phase transition in medium and heavy nuclei. Dipole bands in octupole
deformed nuclei. Isospin dependence of fusion barriers. The pnQRPA equations
renormalization.
Stage II : Neck influence on binary configuration shell effects. Transport phenomena and
dynamics of phase transition in nuclear and hadronic systems.
Stage III: Double beta transitions on collective excited states.
Stage IV : Potential energy surfaces of cluster emitting nuclei. Transport phenomena and
dynamics of phase transition in nuclear and hadronic systems.
Stage V: Competition between the pn T=1 and T=0 pairs in the structure of the ground
state. Geometry of collective states
Stage VI. Nuclear structure with density matrix renormalisation group. Transport
phenomena and dynamics of phase transition in the multi-fragmentation processes
The results related to this project were published in a number of articles and presentations
at international conferences. The most relevant papers are listed below:
1) A.A. Raduta and A. Faessler
A coherent state description of the shape phase transition in even-even Gd isotopes
J.Phys. G:Nucl. Part. Phys. 31(2005) 873-901
2) C. M. Raduta And A. A. Raduta
New results for the fully renormalized pnQRPA formalism
Nucl. Phys. A 756 153-175 (2005)
3) A. A. Raduta, A. Gheorghe And A. Faessler
Remarks on the shape transition from spherical to deformed gamma unstable nuclei
J.Phys. G 31 337-353 (2005)
4) A. A. Raduta, C.M. Raduta And Amand Faessler
Positive and negative parity dipole bands in octupole deformed nuclei
Phys. Lett. B 635 80-84 (2006)
5) A. A. Raduta, C. M. Raduta
Double beta decay to the first 2^+ state within a boson expansion formalism with a projected spherical single
particle basis
Phus. Lett. B
6) A. A. Raduta, C. M. Raduta And A. Escuderos
New results for the two neutrino double beta decay in deformed nuclei with angular momentum projected
basis
Phys. Rev. C 71 034317 (2005)
7) L. Zamick, A. Escuderos, S.J. Lee, A. L. Mekjan, E. Moya De Guerra, A. A. Raduta, P. Sarriguren
Expression for the number of J=0 pairs in even-even Ti isotopes
Phys. Rev. C 71 024307 (2005)
8) A. A. Raduta, A. D. Aaron And I. I. Ursu
Semiclassical description of a sixth order quadrupole boson Hamiltonian
Nucl. Phys. A 772 20-54 (2006)
9) M. I. Krivoruchenko, A. Faessler, A. A. Raduta And C. Fuchs
Underlying gauge symmetries of systems with second class constraints
Int. J. Mod. Phys. A
10) Baran V, Margueron J
Instabilities in nuclear matter and finite nuclei
Eur. J. Phys. A 30 141-151 (2006)
11) A. A. Raduta And C. M. Raduta
Positive and negative parity bands in 226Ra
Nucl. Phys. A 768 170 (2006)
12) M. I. Krivoruchenko, A. A. Raduta And Amand Faessler
Quantum deformation of the Dirac bracket
Phys. Rev. D 73 025008 (2006)
13) A. A.Raduta, Al. H. Raduta And C. M. Raduta
Simultaneous description of four positive and four negative parity bands
Phys. Rev. C 74 044312 (2006)
14) De Filippo E, Amorini F, Anzalone A, … Baran V Et Al.
Isoscaling in neck fragmentation
Acta Physica Polonica B 37 199-205 (2006)
15) Baran V, Colonna M, Di Toro M, Zielinska-Pfabe M, H. Wolter
Isospin transport at Fermi energies
Phys. Rev. C 72 064620 (2005)
16) De Filippo E, Pagano A, Wilczynski J,… Baran V Et Al.
Time sequence and time scale of intermediate mass fragment emission
Phys. Rev. C 71 044602 (2005)
17) Skwira-Chalot I, Siwek-Wilczynska K, Wilczynski J, … Baran V Et Al.
Dynamical evolution of the Au-197+Au-197 system at 15 MeV/nucleon
Int. J. Mod. Phys. E 15 495-499 (2006)
18) Russotto P, Piasecki E, Amorini F, .. V. Baran Et Al.
Dynamical fission in the Sn plus Ni interaction at 35A MeV
Int. J. Mod. Phys. E 15 410-416 (2006)
19) N. Cotfas
Systems of orthogonal polynomials defined by hypergeometric type equations
ETNA 24 45-54 (2006)
20) N. Cotfas
Shape invariant hypergeometric type operators with application
to quantum mechanics
Cejp 4 318-330 (2006)
21) D. Stefanescu
New bounds for positive roots of
polynomials
J. Univ. Comp. Sci. 11 2132-2141 (2005)
22) M. Di Toro, V. Baran, M. Colonna, G. Ferini, T. Gaitanos, V. Greco, J. Rizzo and H.H. Wolter,
Isospin Dynamics in Heavy Ion Collisions: EoS-sensitive Observables,
Nuclear Physics A, Volume 787, Issues 1-4, 1 May 2007, Pages 585-594
23) D.N. Poenaru, R.A. Gherghescu, N. Carjan,
Alpha-decay lifetime semiempirical relationship including shell effects,
Europhysics Letters 77 (2007) 62001
24) D. Pierroutsakou, B. Martin, .. R. Alba, V. Baran et al.,
Prompt dipole gamma ray emission: a new cooling mechanism in fusion of heavy-ion reactions,
AIP Conf. Proc. 884 (2007) 201-206.
25) A. C. Gheorghe, A. A. Raduta and A. Faessler
Solvable models for the gamma deformation having X(5) as limiting symmetry. Removing some drawbacks
of the existent descriptions
Phys. Lett. B 648 170-175 (2007)
26) A.A.Raduta, R. Budaca, C.M.Raduta
Semiclassical description of a triaxial rigid rotor
Phys.Rev.C 76 64309 (2007)
27) M. I. Krivoruchenko, A. Faessler, A. A. Raduta and C. Fuchs
Underlying gauge symmetries of systems with second class constraints
International Journal of Modern Physics A 22 787- 833 (2007)
28) Rizzo J, Colonna M, Baran V, et al.
Isospin
dynamics
in
peripheral
heavy
ion
Nuclear Physics A Volume: 806 Pages: 79-104 (2008)
29 )Planeta R, Amorini F, Anzalone A, Baran V. et al.
Centrality dependence of isospin effect signatures
Physical Review C Volume: 77 014610 (2008)
in
collisions
Sn-124+Ni-64
at
Fermi
energies
andSn-112+Ni-58reactions
30) Wilczynski J, Skwira-Chalot I, Siwek-Wilczynska K,…Baran V. et al
Re-separation
modes
of
Au-197+Au-197
system
at
sub-Fermi
energies
International Journal of Modern Physics E-Nuclear Physics Vol: 17 Issue: 1 Pages: 41-52 (2008)
Concluding, all objectives of the project were fully realized and the scientific results
certainly contributed to the increase of the visibility of Romanian fundamental research in
international community.