
Volume 47, Number 12, 2002


Professor Aurel Săndulescu ordinary member of the Romanian Academy at his 70^{th} anniversary 

Page 
Title & Author(s) 
3 
Foreword
W. Greiner, W. Scheid, R. J. Liotta


7 
A Cruise in the Arhipelagos of Superheavy Elements, HeavyCluster Emitters and Nuclear Molecules
Walter Greiner
I review some of the most important achievements in the theoretical investigations that we carried in the last three decades at Frankfurt on the extension of the periodic system and heavyion emission. After discussing the problem of cold fusion and formation of Superheavy Elements (SHE) I will consider the reverse process, i.e. the spontaneous cold fragmentation of heavy nuclei into different channels like cluster radioactivity and cold fission. I will also speculate on the properties of the putative quasimolecules arising in the recent discovery of the tripple fission of $^{252}$Cf.


23 
Flat Potentials in Nuclei
R. F. Casten
The recent twin developments of critical point symmetries for transitional nuclei and of evidence for multiphonon vibrational levels in spherical nuclei focuses attention on the role of potentials in nuclei that are significantly flatter in the deformation degree of freedom than has heretofore been widely appreciated.


33 
Contributions of Aurel Sandulescu to the Theory of Alpha Decay
Serban Mişicu
We review the most important contributions brought by Prof. Aurel Săndulescu, member of the Romanian Academy, to the theory of $\alpha$decay on occasion of his 70$^{\mathrm{th}}$ birthday. The covered period spans two decades from the beginning of seventees up to the end of seventees and focus on subjects like favored $\alpha$ transitions, $\alpha$nucleus potential in $\alpha$decay, Feschbach theory of $\alpha$decay, superfluid model of $\alpha$decay and fine structure effects.


43 
He and Be Ternary Spontaneous Fission of $^{252}$Cf
I. K. Hwang, C. J. Beyer, A. V. Ramayya, J. H. Hamilton, GANDS Collaboration
Ternary and binary fission studies of $^{252}$Cf have been carried out by using the Gammasphere detector array with a light charged particle (LCD) detectors. The relative $^4$He and $^5$He ternary fission yields were determined. The kinetic energies of the $^5$He and $^4$He ternary particles were found to be approximately 11 and 16 MeV, respectively. The $^5$He particles contribute 1020% to the total observed alpha ternary yield. The data indicate that in nuclei with octupole deformations the population for the negative parity bands might be enhanced in the $\alpha$ ternary fission. From LCP$\gamma$ double gated spectra, neutron multiplicity distributions for a ternary fission pairs were measured. The average neutron multiplicity decrease about 0.7 AMU in going from the binary to $\alpha$ ternary fission in the approximately same mass aplittings (104146). From the analysis of the $\gamma  \gamma$ matrix gated on the $^{10}$Be particles, the two fragment pairs of $^{138}$Xe$^{104}$Zr and $^{106}$Mo$^{136}$Te with no neutrons emitted are among the most strongly populated pairs. The first LCP$\gamma$ data indicate that the cold (neutronless) process could be more dominant in ternary SF with the third particle being $^{10}$Be with the high kinetic energy. The most favored cases of cold $^{10}$Be ternary SF processes are the deformed and spherical fragment pairs.


57 
Ternary Fission and Cluster Radioactivities
D. N. Poenaru, Y. Nagame, W. Greiner, R. A. Gherghescu, J. H. Hamilton, A. V. Ramayya
Ternary fission yield for different kinds of light particle accompanied fission processes is compared to the Qvalues for the corresponding cold phenomena, showing a striking correlation. The experimental evidence for the existence of a quasimolecular state in $^{10}$Be accompanied fission of $^{252}$Cf may be explained using a threecenter phenomenological model which generates a third minimum in the deformation energy at a separation distance very close to the touching point. This model is a natural extension of the unified approach of three groups of binary decay modes (cold fission, cluster radioactivities and $\alpha$ decay), illustrated by $^{234}$U decay modes, and the $\alpha$ valley on the potential energy surface of $^{106}$Te. New measurements of cluster decay modes, confirming earlier predictions within analytical superasymmetric fission model, are included in a comprehensive halflife systematics.


71 
Fragment Angular Momenta and Descent Dynamics in $^{252}$Cf Spontaneous Fission
G. S. Popeko, G. M. TerAkopian, J. H. Hamilton, J. Kormicki, A. V. Daniel, Yu. Ts. Oganessian, A. V. Ramayya, J. K. Hwang, W. Greiner, A. Săndulescu, A. Florescu, J. Kliman, M. Morhac, J. O. Rasmussen, M. A. Stoyer, J. D. Cole, GANDS95 Collaboration
Average angular momentum values of primary fission fragments as a function of neutron multiplicity and neutrontoproton ratio were extracted for the first time for the MoBa and ZrCe charge splits of $^{252}$Cf. The results are discussed in terms of the energy balance occurring at the scission point.


81 
Uncertainty Relations, Quantum and Thermal Fluctuations in Lindblad Theory of Open Quantum Systems
A. Isar, W. Scheid
In the framework of the Lindblad theory for open quantum systems we derive closed analytical expressions of the uncertainty relation for a particle moving in a harmonic oscillator potential. The particle is in an arbitrarily squeezed initial state and interacts with an environment at finite temperature. We examine how the quantum and thermal fluctuations of the environment contribute to the uncertainty in the canonical variables of the system and study their relative importance in the evolution of the system towards equilibrium with the aim of clarifying the meaning of quantum, classical and thermal dissipation of energy. We show that upon contact with the bath the system evolves from a quantumdominated state to a thermaldominated state in a time which is of the same order as the decoherence time calculated before in similar models in the context of a transition from quantum mechanics to classical mechanics.


97 
Towards a Microscopic Description of an $\alpha$Condensate in Nuclei
D. S. Delion, G. G. Dussel, R. J. Liotta
A theory to describe $\alpha$condensates in nuclei is presented. The corresponding quasiparticles consist of fermions as well as bosons. The fermions are a combination of oneparticle and threehole states, while the bosons are combinations of pairparticles and pairholes. A relation between the fermionic and bosonic gap parameters is predicted and confirmed by experimental data.


107 
Hyperspherical Coordinate Approach to Weakly Bound Nuclei
R. A. Ionescu, C. Haţegan
The weakly bound, spatially extended states in a three body system in the limit of one infinetely large mass is studied. The description is given in the Schrödinger picture and the interactions are taken into account only by their scattering properties in the zero energy limit.


123 
Nonlinear Approach to Inelastic Scattering
K. A. Gridnev, V. G. Kartavenko, E. Hefter, W. Greiner, V. Riech, G. Lindström, E. Fretwurst
Solitonlike solutions of the KortewegdeVries equation are shown to describe collective excitations of nuclei observed in inelastic $\alpha$particle and proton scattering. Respective deformation lengths for different projectiletarget systems are predicted. The results are compared with experimental data. We explain the difference in the data obtained with the inelastic scattering of $\alpha$particles and protons, also the behavior of the deformation parameters for different nuclei and their isotopes.


133 
Theoretical Estimates of AlphaHalfLives for the Superheavy Elements with Z = 102120
I. Silişteanu, W. Scheid, A. O. Silişteanu
The $\alpha$halflives for superheavy nuclei are estimated within an approach based on a unified picture for the heavyion and $\alpha$ resonances. $\alpha$decay data of somewhat limited accuracy, are used to extend, with support from theoretical investigations, the spinparity and level energy informations from the daughter to parent. This extension allows to identify the initial parent and its descendants by their characteristic $\alpha$decay and the observed $\alpha$(parent)$\alpha$(daughter) correlations. A new systematics of the $Q_{\alpha}$values and $\alpha$halflives versus the valence nucleon number is used to extract the information on nuclear clustering and $\alpha$like resonances. Some of the latest results in the field and also some future perspectives are reviewed.


149 
Nonlinear Approach to Ternary Scission
V. G. Kartavenko, A. Săndulescu, W. Greiner
Description of threecenter configuration within meanfield approaches meets uncertainties to select a peculiar set of constraints. We suggest to use the inverse mean field method to solve singleparticle Schrödinger equation, instead of constrained selfconsistent HartreeFock equations. It is shown, that it is possible to simulate onedimensional threecenter system in the approximation of reflectless singleparticle potentials.


159 
Carbon Preformation Probabilities in the Cold Ternary Fragmentation of $^{252}$Cf
A. Florescu
The preformation probabilities for $^{12}$C and $^{14}$C clusters in the cold ternary fission of $^{252}$Cf are estimated within a microscopic model starting from single particle spherical WoodsSaxon wave functions and with a large space BCStype configuration mixing. One obtains that the maximum of cluster preformation probability is situated in the region between the two heavier fragments near the scission point and it approaches the fission axis as the distance between the final fragments increases.


167 
Shell Effects in the Superasymmetric Fission
M. Mirea
A new formalism based on the LandauZener promotion mechanism intends to explain the fine structure of alpha and cluster decay. The analysis of this phenomenon is accomplished by following the modality in which the shells are reorganised during the disintegration process beginning with the initial ground state of the parent towards to the final configuration of two separated nuclei. A realistic level scheme is obtained in the framework of the superasymmetric twocentre shell model.


177 
Microscopic Structure of Four Body Resonances
D. S. Delion, J. Suhonen
A microscopic approach of four body states, seen as decaying states or scattering resonances, is given. The equations of motion describing clusterlike states are derived within the multistep shellmodel approach. The lowest collective twoparticle eigenmodes are used as building blocks for the $\alpha$like states. A good agreement with the lowlying states in $^{212}$Po is obtained. The spectroscopic factor of the $\alpha$decay between ground states is reproduced. It is shown that only by including the continuum part of the single particle spectrum the decay width for $\alpha$ and clusterdecay processes is reproduced. The $\alpha$like structure of the lowest states in $^{212}$Po is analyzed and strong highlying resonances are predicted. A good agreement with experimantal quasimolecular states in $^{40}$Ca is obtained.


189 
On Lieb's Conjecture
Horia Scutaru
The reformulation of Lieb's conjecture, in the frame of the harmonic analysis on the $SO(3)$ group, makes it evident that the exact value of the classical entropy of a pure quantum state, which belongs to the Hilbert space $\mathcal{H}_J$ of a $(2J + 1 )$dimensional, unitary, irreducible representation $\mathcal{U}_J$ of the $SO(3)$ group, depends only on the parameters which characterize the orbits of $\mathcal{U}_J$ in $\mathcal{H}_J$. In the case $J = 1$ we give the exact analytic dependence of the classical entropy of a quantum state on the parameters which characterize the orbits and as a consequence we obtain a verification of Lieb's entropy conjecture. We verify this conjecture also for any value of $J$ for the states of the canonical basis of $\mathcal{H}_J$. A natural generalization of Lieb's entropy conjecture, which is a new "phenomenon" in the harmonic analysis on $SO(3)$, is discussed in the case $J = 1$.


199 
The Decay of a Fermi System through ParticleParticle Dissipation
Eliade Ştefănescu
Fermi systems are essential for describing very important phenomena as nuclear resonances, fissionfusion reactions, semiconductor nanostructures and the high temperature superconductivity. In such systems, the dissipative coupling is very important. We study the decay of a system of fermions interacting with a dissipative environment of particles through a twobody potential. The master equation in the secondorder approximation describes singleparticle transitions that, for a resonant dissipation, conserves the number of particles and describes the entropy increase of the system. Every transition $ j > \to  i >$ is described by diffusion and friction terms of the wellknown form previously obtained by Săndulescu and Scutaru for the harmonic oscillator. The higherorder terms of the master equation describe manyparticle transitions. As applications, we consider the nuclear cold fission and giant resonances.


221 
Towards Numerically Solving the TwoDimensional TimeDependent Schrödinger Equation for LongLived Decaying States
Nicolae Carjan, Dan Stroitman, Margarit Rizea
The numerical challenge associated with the timedependent approach to the general problem of bidimensional quantumtunneling is discussed and methods towards its application to concrete problems are developed.


243 
Nuclear Aspects of the Double Beta Decay
S. Stoica, V. Păun
Calculations of the neutrinoless doublebeta decay (0νββ) matrix elements are performed with the second quasi random phase approximation (SQRPA) method ([14], [16]) for several nuclei. The results display a weak dependence on the single particle basis used and the Ikeda sum rule is fulfilled with good accuracy. Comparing our calculations with similar ones performed with other QRPAbased methods we estimate the accuracy of these methods in the prediction of the 0νββ decay matrix elements and neutrino mass parameter, which is settled to about 50% from their calculated values. Taking the most recent experimental limits for the neutrinoless halflives, we also deduced new limits for the neutrino mass parameter.


255 
Strong Evidences for Nuclear Mesonic ČherenkovLike Radiation from High Energy Hadronic Collisions
D. B. Ion
In this paper essential characteristic features of the nuclear pionic Čherenkovlike radiation (NPICR) are discussed and compared with the recent experimental results obtained at IUCNDubna.


267 
Optical Spatiotemporal Solitons: Recent Studies
D. Mihalache
A brief overview of the recent advances in the theoretical and experimental study of optical spatiotemporal solitons is given.


273 
Enhancing Reliability of Interpolatory Quadrature Rules
Gh. Adam, S. Adam
The paper investigates ways of enhancing the reliability of interpolatory quadrature rules which derive their local error estimates from specific pairs $\{Q_n, Q_{2n+1}\}$ of quadrature sums involving $n$ and $2n+1$ knots, respectively. Towards this end, a validating scheme of the computed local error estimates is derived from the study of parametric elementary integrals. According to this scheme, a local error estimate is unconditionally rejected as unreliable if its magnitude exceeds a given fraction of $Q_{2n+1}$. Moreover, it is only conditionally accepted iff: (i) the average value $\bar{f}$ of the integrand does not belong to one or more of the ranges of variation of the integrand $f$ over its monotonicity subranges defined over the $2n+1$knot sampling of $Q_{2n+1}$ and/or (ii) the isolated fixed points of the quadrature mesh, defined as the common extremal points of $f$ over the corresponding $n$ and $2n+1$knot samplings such that they are not consecutive extrema inside the $n$knot sampling, result in smaller stability regions around the $2n+1$knot extrema as compared to those arising from the $n$knot extrema.
The procedure is illustrated on the archetypal GaussKronrod 1021 quadrature rule.


289 
On the Critical Temperature of the Ising Ferromagnets
M. Apostol
The critical temperature of the twodimensional Ising ferromagnet is computed by a simple method, which can be extended to various others lattice models, including the Ising ferromagnet in three dimensions.


293 
Effective Spinodal Curve of a ThreeComponent Molecular System
Florin D. Buzatu, Daniela Buzatu
We consider a lattice model for threecomponent systems in which the lattice bonds are covered by molecules of type $AA$, $BB$, and $AB$, and the only interactions are between the molecular ends of a common lattice site. The model is equivalent to the standard Ising model, and the coexistence curves for different lattices and/or some specific form of the interactions have been previously investigated. We derive the spinodal curve of the model on the threecoordinated Bethelattice and, at zero temperature, we find that some metastable states still exist. This inconsistency can be solved by introducing, within meanfieldlike theories of firstorder phase transitions, the concept of effective nonequilibrium states: to each nonequilibrium state we associate a certain equilibrium state of another system, with a renormalized coupling constant. In comparison with the standard spinodal, the effective spinodal curve is always closer to the coexistence curve and, at zero temperature, they coincide.


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