434 research outputs found
Basic Concepts Underlying Singular Perturbation Techniques
In many singular perturbation problems multiple scales are used. For instance, one may use both the coordinate x and the coordinate x^* = ε^(-1)x. In a secular-type problem x and x^* are used simultaneously. This paper discusses layer-type problems in which x^* is used in a thin layer and x outside this layer. Assume one seeks approximations to a function f(x,ε), uniformly valid to some order in ε for x in a closed interval D. In layer-type problems one uses (at least) two expansions (called inner and outer) neither of which is uniformly valid but whose domains of validity together cover the interval D. To define "domain of validity" one needs to consider intervals whose endpoints depend on epsilon. In the construction of the inner and outer expansions, constants and functions of e occur which are determined by comparison of the two expansions "matching." The comparison is possible only in the domain of overlap of their regions of validity. Once overlap is established, matching is easily carried out. Heuristic ideas for determining domains of validity of approximations by a study of the corresponding equations are illustrated with the aid of model equations. It is shown that formally small terms in an equation may have large integrated effects. The study of this is of central importance for understanding layer-type problems. It is emphasized that considering the expansions as the result of applying limit processes can lead to serious errors and, in any case, hides the nature of the expansions
Evolution of the N=50 gap from Z=30 to Z=38 and extrapolation towards 78Ni
The evolution of the N=50 gap is analyzed as a function of the occupation of
the proton f5/2 and p3/2 orbits. It is based on experimental atomic masses,
using three different methods of one or two-neutron separation energies of
ground or isomeric states. We show that the effect of correlations, which is
maximized at Z=32 could be misleading with respect to the determination of the
size of the shell gap, especially when using the method with two-neutron
separation energies. From the methods that are the least perturbed by
correlations, we estimate the N=50 spherical shell gap in 78Ni. Whether 78Ni
would be a rigid spherical or deformed nucleus is discussed in comparison with
other nuclei in which similar nucleon-nucleon forces are at play.Comment: 7 pages, 8 figures, accepted for publication PRC (22 december 2011
Phase Transitions in Finite Nuclei and the Integer Nucleon Number Problem
The study of spherical-deformed ground--state phase transitions in finite
nuclei as a function of N and Z is hindered by the discrete values of the
nucleon number. A resolution of the integer nucleon number problem, and
evidence relating to phase transitions in finite nuclei, are discussed from the
experimental point of view and interpreted within the framework of the
interacting boson model.Comment: 8 pages Latex + 8 figs (postscript). In Phys Rev Lett, June 199
Unified description of 0+ states in a large class of nuclear collective models
A remarkably simple regularity in the energies of 0+ states in a broad class
of collective models is discussed. A single formula for all 0+ states in
flat-bottomed infinite potentials that depends only on the number of dimensions
and a simpler expression applicable to all three IBA symmetries in the large
boson number limit are presented. Finally, a connection between the energy
expression for 0+ states given by the X(5) model and the predictions of the IBA
near the critical point is explored.Comment: 4 pages, 3 postscript figures, uses revTe
Structure of the doublet bands in doubly odd nuclei: The case of
The structure of the doublet bands in is
investigated within the framework of the Interacting Vector Boson Fermion Model
(IVBFM). A new, purely collective interpretation of these bands is given on the
basis of the used boson-fermion dynamical symmetry of the model. The energy
levels of the doublet bands as well as the absolute and
transition probabilities between the states of both yrast and yrare bands are
described quite well. The observed odd-even staggering of both and
values is reproduced by the introduction of an appropriate interaction
term of quadrupole type, which produces such a staggering effect in the
transition strengths. The calculations show that the appearance of doublet
bands in certain odd-odd nuclei could be a consequence of the realization of a
larger dynamical symmetry based on the non-compact supersymmetry group
.Comment: 12 pages, 8 figure
E(5), X(5), and Prolate to Oblate Shape Phase Transitions in Relativistic Hartree Bogoliubov Theory
Relativistic mean field theory with the NL3 force is used for producing
potential energy surfaces (PES) for series of isotopes suggested as exhibiting
critical point symmetries. Relatively flat PES are obtained for nuclei showing
the E(5) symmetry, while in nuclei corresponding to the X(5) case, PES with a
bump are obtained. The PES corresponding to the Pt chain of isotopes suggest a
transition from prolate to oblate shapes at 186-Pt.Comment: 21 pages, LaTeX, including 14 .eps figure
Regularities and symmetries of subsets of collective 0+ states
The energies of subsets of excited 0+ states in geometric collective models
are investigated and found to exhibit intriguing regularities. In models with
an infinite square well potential, it is found that a single formula, dependent
on only the number of dimensions, describes a subset of 0+ states. The same
behavior of a subset of 0+ states is seen in the large boson number limit of
the Interacting Boson Approximation (IBA) model near the critical point of a
first order phase transition, in contrast to the fact that these 0+ state
energies exhibit a harmonic behavior in all three limiting symmetries of the
IBA. Finally, the observed regularities in 0+ energies are analyzed in terms of
the underlying group theoretical framework of the different models.Comment: 9 pages, 3 figures, added reference [38
Enhanced Production of Neutron-Rich Rare Isotopes in Peripheral Collisions at Fermi Energies
A large enhancement in the production of neutron-rich projectile residues is
observed in the reactions of a 25 MeV/nucleon 86Kr beam with the neutron rich
124Sn and 64Ni targets relative to the predictions of the EPAX parametrization
of high-energy fragmentation, as well as relative to the reaction with the less
neutron-rich 112Sn target. The data demonstrate the significant effect of the
target neutron-to-proton ratio (N/Z) in peripheral collisions at Fermi
energies. A hybrid model based on a deep-inelastic transfer code (DIT) followed
by a statistical de-excitation code appears to account for part of the observed
large cross sections. The DIT simulation indicates that the production of the
neutron-rich nuclides in these reactions is associated with peripheral nucleon
exchange. In such peripheral encounters, the neutron skins of the neutron-rich
124Sn and 64Ni target nuclei may play an important role. From a practical
viewpoint, such reactions between massive neutron-rich nuclei offer a novel and
attractive synthetic avenue to access extremely neutron-rich rare isotopes
towards the neutron-drip line.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let
Staggering behavior of the low lying excited states of even-even nuclei in a Sp(4,R) classification scheme
We implement a high order discrete derivative analysis of the low lying
collective energies of even-even nuclei with respect to the total number of
valence nucleon pairs N in the framework of F- spin multiplets appearing in a
symplectic sp(4,R) classification scheme. We find that for the nuclei of any
given F- multiplet the respective experimental energies exhibit a Delta N=2
staggering behavior and for the nuclei of two united neighboring F- multiplets
well pronounced Delta N=1 staggering patterns are observed. Those effects have
been reproduced successfully through a generalized sp(4,R) model energy
expression and explained in terms of the step-like changes in collective modes
within the F- multiplets and the alternation of the F-spin projection in the
united neighboring multiplets. On this basis we suggest that the observed Delta
N=2 and Delta N=1 staggering effects carry detailed information about the
respective systematic manifestation of both high order alpha - particle like
quartetting of nucleons and proton (neutron) pairing interaction in nuclei.PACS
number(s):21.10.Re, 21.60.FwComment: 22 pages and 6 figures changes in the figure caption
New features of the triaxial nuclei described with a coherent state model
Supplementing the Liquid Drop Model (LDM) Hamiltonian, written in the
intrinsic reference frame, with a sextic oscillator plus a centrifugal term in
the variable and a potential in with a minimum in
, the Sch\"{o}dinger equation is separated for the two variables
which results in having a new description for the triaxial nuclei, called
Sextic and Mathieu Approach (SMA). SMA is applied for two non-axial nuclei,
Hf and W and results are compared with those yielded by the
Coherent State Model (CSM). As the main result of this paper we derive
analytically the equations characterizing SMA from a semi-classical treatment
of the CSM Hamiltonian. In this manner the potentials in and
variables respectively, show up in a quite natural way which contrasts their
ad-hoc choice when SMA emerges from LDM.Comment: 13 figures, 13 page
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