FINAL SCIENTIFIC RAPORT
Project title:
DESCRIPTION OF FUNDAMENTAL FEATURES FOR
SOME ATOMIC AND NUCLEAR PROCESSES
acronym DFFSANP
The main research directions associated to this project were:
A) New properties of electron and atomic systems
B) Analytical properties for orthogonal polynomials, numerical algorithm for calculating
the roots.
C) Double beta decay for deformed nuclei on collective excited states.
D) Statistical aspects od nuclear multifragmentation
Below we enumerate the essential objectives whithin each major research direction:
A)New properties of electron and atomic systems
a) Obtain analitical formulae for the angular distribution for elastic scattered photons by 2s
bound electrons and the total cross section for the electron-pozitron pair production with the
electron created in the bound 2s state taking into account multipole, retardation and relativistic
kinematics effects.
b) We have obtained some mathematical results and a software which lead to a deterministic
algorithm for generating quasiperiodic packings of multi-shell clusters. Our method works for any
finite group G and any multi-shell G-cluster, and our software allows us to generate in a few
minutes hundreds of points of the model for rather complicated clusters. We intended to improve
our algoritm and our software and to analyse existing experimental data. We shall obtain
specialized versions for the models important from a physical point of view. Our model can be
used in order to analyse periodic approximants by using rational approximants for certain
irrational parameters.We intend to elaborate a method for determination of self-similarities of our
models and to analyse the restrictions imposed by these self-similarities to physical properties.
c) The RPA equations for a system of electrons moving in a deformed mean fielad and interacting
among themselves through a direct dipole-dipole term as an exchange force. The resulting wave
functions were used to calculated the excitation probability.
B) Analytical properties for orthogonal polynomials, numerical algorithm to calculate the
roots
The project investigated the following topics which now belong to the core analytic theory of
polynomials: i) Lower and upper bounds for the absolute values of the roots of complex and real
polynomials ii)Asymptotic properties of the roots iii)Localization of the roots iv)New properties on
the separation and asymptotic distributions of roots of orthogonal polynomials v)Factorization and
irreducibility of some classes of orthogonal polynomials
C) Double beta decay in deformed nuclei, on collective excited states.
The decay rates for the situation when the mother nucleus is in ground state while the daughter is
in a collective excited state. Both involved nuclei are deformed. The formalism employed is that of
boson expansion.
D) Statistical aspects of nuclear multifragmentation.
i). Searching for the Nuclear Phase Diagram
ii). Nuclear thermodynamics: impact of various parameters on the phase diagram
iii). Is there any distinctive stage identifiable as freeze-out in the process of collision between
two heavy ions?
Stage I : Improving the Katz-Duneau-Elser model by including icosahedral quasicristals
Stage II : Total cross section for a positron-electron production with the created
electron in the subshell 2s.
Stage III: Collective dipole excitations in deformed atomic clusters
Stage IV. Results for some orthogonal polynomials roots. Statistical aspects for nuclear
multifragmentation.
Stage V: Quasicristals selfsimilarities versus their physicsl properties
Stage VI..Relativistic elastic scattering of photons on a bound electron from the subshell
2s.Approximative estimation of the roots of some orthogonal polynomials.
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) N. Cotfas
Discrete quasiperiodic sets with predefined covering cluster
Phil. Mag. 86 895-900 (2006)
11) Costescu A, Spanulescu S
Retardation, multipole, and relativistic kinematics effects for x- and gamma-ray Compton scattering from Kshell electrons
Phys. Rev. A 73 022702 (2006)
12) N. Cotfas
On the linear epresentations of the symmetry groups of single-wall carbon nanotubes
J. Phys. A 9755 –9765 (2006)
13) N. Cotfas
An alternate mathematical model for single-wall carbon nanotubes
J. Geom. Phys. 55 123 –134 (2005)
14) Raduta Ah, Colonna M, Baran V, M.Di Toro
Statistical analysis of a dynamical multifragmentation path
Phys. Rev. C 74 034604 (2006)
15) D. Stefanescu
Inequalities on upper bounds for real polynomial Roots
Casc 4194 284-294 (2006)
16) Skwira-Chalot I, Siwek-Wilczynska K, ..... Amorini, A, ...,V. Baran, .. et a
Dynamics of binary Au+Au collisions as a test of energy dissipation mechanism
Acta Physica Polonica B 38 1509-1514 (2007)
17)Skwira-Chalot I, Siwek-Wilczynska K, ..... Amorini, A, ...,V. Baran, .. et al.,
Ternary reactions in Au+Au collisions revised
International Journal of Modern Physics E, 16 (2007) 511-515.
18) M. Papa, F. Amorini, ..V. Baran,et al.,
Dynamical multi-breakup in Sn+Ni system at 35MeV/n
Phys. Rev. C 75 54616 (2007)
19) N. Cotfas
Aperiodic packings of clusters obtained by projection
Philosophical Magazine 87 2823- 2830 (2007)
20) Costescu A, Spanulescu S, Stoica C
The second-order S-matrix element for the elastic scattering of photons by K-shell bound electrons: the
nonrelativistic limit
JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS
40 2995- 3014 (2007)
21) 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
Phys. Lett. B 647 265-270 (2007)
22) A. A. Raduta and F.D. Aaron
A simple description of the states 0+ and 2+ in 168Er
Jour. Phys. G. 34 2053-2061 (2007)
23) C. M. Raduta, A. A. Raduta
Unified descriptionof the double beta decay to the first quadrupole phonon state in spherical and deformed
nuclei
Phys. Rev. C 76 44306 (2007)
24) D. Stefanescu
Computation of dominant real roots of polynomials
Journal Programming and Computer Software vol 34 (2) pages 69-74 (2008)
25) Martin B, Pierroutsakou D, Agodi C,…. V. Baran et al.
Prompt dipole radiation in fusion reaction
PHYSICS LETTERS B Volume: 664 Issue: 1-2 Pages: 47-51 ( 2008)
26) Di Toro M, Colonna M, Rizzo C and V. Baran
The
dynamical
dipole
radiation
in
dissipative
collisions
with
exotic
beams
INTERNATIONAL JOURNAL OF MODERN PHYSICS E-NUCLEAR PHYSICS Vol. 17 (1) Pages: 110119 (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.