101 research outputs found
Transition from the Seniority to the Anharmonic Vibrator Regime in Nuclei
A recent analysis of experimental energy systematics suggests that all
collective nuclei fall into one of three classes -- seniority, anharmonic
vibrational, or rotational -- with sharp phase transitions between them. We
investigate the transition from the seniority to the anharmonic vibrator regime
within a shell model framework involving a single large j-orbit. The
calculations qualitatively reproduce the observed transitional behavior, both
for U(5) like and O(6) like nuclei. They also confirm the preeminent role
played by the neutron-proton interaction in producing the phase transition.Comment: 9 pages with 2 tables, submitted to Physical Review C, November 199
Scattering of weakly interacting massive particles from Ge 73
We use a “hybrid” method, mixing variationally-determined triaxial nuclear Slater determinants, to calculate the response of 73Ge to hypothetical darkmatter particles such as neutralinos. The method is a hybrid in that rotational invariance is approximately restored prior to variation and then fully restored before the mixing of intrinsic states. We discuss such features of 73Ge as shape coexistence and triaxiality, and their effects on spin-dependent neutralino cross sections. Our calculations yield a satisfactory quadrupole moment and an accurate magnetic moment in this very complicated nucleus, suggesting that the spin structure and thus the axial–vector response to dark matter particles is modeled well
Systematic study of deformed nuclei at the drip lines and beyond
An improved prescription for choosing a transformed harmonic oscillator (THO)
basis for use in configuration-space Hartree-Fock-Bogoliubov (HFB) calculations
is presented. The new HFB+THO framework that follows accurately reproduces the
results of coordinate-space HFB calculations for spherical nuclei, including
those that are weakly bound. Furthermore, it is fully automated, facilitating
its use in systematic investigations of large sets of nuclei throughout the
periodic table. As a first application, we have carried out calculations using
the Skyrme Force SLy4 and volume pairing, with exact particle number projection
following application of the Lipkin-Nogami prescription. Calculations were
performed for all even-even nuclei from the proton drip line to the neutron
drip line having proton numbers Z=2,4,...,108 and neutron numbers
N=2,4,...,188. We focus on nuclei near the neutron drip line and find that
there exist numerous particle-bound even-even nuclei (i.e., nuclei with
negative Fermi energies) that have at the same time negative two-neutron
separation energies. This phenomenon, which was earlier noted for light nuclei,
is attributed to bound shape isomers beyond the drip line.Comment: 12 ReVTeX4 pages, 6 EPS figures. See also
http://www.fuw.edu.pl/~dobaczew/thodri/thodri.htm
New Discrete Basis for Nuclear Structure Studies
A complete discrete set of spherical single-particle wave functions for
studies of weakly-bound many-body systems is proposed. The new basis is
obtained by means of a local-scale point transformation of the spherical
harmonic oscillator wave functions. Unlike the harmonic oscillator states, the
new wave functions decay exponentially at large distances. Using the new basis,
characteristics of weakly-bound orbitals are analyzed and the ground state
properties of some spherical doubly-magic nuclei are studied. The basis of the
transformed harmonic oscillator is a significant improvement over the harmonic
oscillator basis, especially in studies of exotic nuclei where the coupling to
the particle continuum is important.Comment: 13 pages, RevTex, 6 p.s. figures, submitted to Phys. Rev.
Dobinski-type relations and the Log-normal distribution
We consider sequences of generalized Bell numbers B(n), n=0,1,... for which
there exist Dobinski-type summation formulas; that is, where B(n) is
represented as an infinite sum over k of terms P(k)^n/D(k). These include the
standard Bell numbers and their generalizations appearing in the normal
ordering of powers of boson monomials, as well as variants of the "ordered"
Bell numbers. For any such B we demonstrate that every positive integral power
of B(m(n)), where m(n) is a quadratic function of n with positive integral
coefficients, is the n-th moment of a positive function on the positive real
axis, given by a weighted infinite sum of log-normal distributions.Comment: 7 pages, 2 Figure
Traveling Waves, Front Selection, and Exact Nontrivial Exponents in a Random Fragmentation Problem
We study a random bisection problem where an initial interval of length x is
cut into two random fragments at the first stage, then each of these two
fragments is cut further, etc. We compute the probability P_n(x) that at the
n-th stage, each of the 2^n fragments is shorter than 1. We show that P_n(x)
approaches a traveling wave form, and the front position x_n increases as
x_n\sim n^{\beta}{\rho}^n for large n. We compute exactly the exponents
\rho=1.261076... and \beta=0.453025.... as roots of transcendental equations.
We also solve the m-section problem where each interval is broken into m
fragments. In particular, the generalized exponents grow as \rho_m\approx
m/(\ln m) and \beta_m\approx 3/(2\ln m) in the large m limit. Our approach
establishes an intriguing connection between extreme value statistics and
traveling wave propagation in the context of the fragmentation problem.Comment: 4 pages Revte
Polynomial iterative algorithms for coloring and analyzing random graphs
We study the graph coloring problem over random graphs of finite average
connectivity . Given a number of available colors, we find that graphs
with low connectivity admit almost always a proper coloring whereas graphs with
high connectivity are uncolorable. Depending on , we find the precise value
of the critical average connectivity . Moreover, we show that below
there exist a clustering phase in which ground states
spontaneously divide into an exponential number of clusters. Furthermore, we
extended our considerations to the case of single instances showing consistent
results. This lead us to propose a new algorithm able to color in polynomial
time random graphs in the hard but colorable region, i.e when .Comment: 23 pages, 10 eps figure
The Density Matrix Renormalization Group for finite Fermi systems
The Density Matrix Renormalization Group (DMRG) was introduced by Steven
White in 1992 as a method for accurately describing the properties of
one-dimensional quantum lattices. The method, as originally introduced, was
based on the iterative inclusion of sites on a real-space lattice. Based on its
enormous success in that domain, it was subsequently proposed that the DMRG
could be modified for use on finite Fermi systems, through the replacement of
real-space lattice sites by an appropriately ordered set of single-particle
levels. Since then, there has been an enormous amount of work on the subject,
ranging from efforts to clarify the optimal means of implementing the algorithm
to extensive applications in a variety of fields. In this article, we review
these recent developments. Following a description of the real-space DMRG
method, we discuss the key steps that were undertaken to modify it for use on
finite Fermi systems and then describe its applications to Quantum Chemistry,
ultrasmall superconducting grains, finite nuclei and two-dimensional electron
systems. We also describe a recent development which permits symmetries to be
taken into account consistently throughout the DMRG algorithm. We close with an
outlook for future applications of the method.Comment: 48 pages, 17 figures Corrections made to equation 19 and table
Shortest paths and load scaling in scale-free trees
The average node-to-node distance of scale-free graphs depends
logarithmically on N, the number of nodes, while the probability distribution
function (pdf) of the distances may take various forms. Here we analyze these
by considering mean-field arguments and by mapping the m=1 case of the
Barabasi-Albert model into a tree with a depth-dependent branching ratio. This
shows the origins of the average distance scaling and allows a demonstration of
why the distribution approaches a Gaussian in the limit of N large. The load
(betweenness), the number of shortest distance paths passing through any node,
is discussed in the tree presentation.Comment: 8 pages, 8 figures; v2: load calculations extende
Quadrupole deformations of neutron-drip-line nuclei studied within the Skyrme Hartree-Fock-Bogolyubov approach
We introduce a local-scaling point transformation to allow for modifying the
asymptotic properties of the deformed three-dimensional Cartesian harmonic
oscillator wave functions. The resulting single-particle bases are very well
suited for solving the Hartree-Fock-Bogoliubov equations for deformed drip-line
nuclei. We then present results of self-consistent calculations performed for
the Mg isotopes and for light nuclei located near the two-neutron drip line.
The results suggest that for all even-even elements with =10--18 the most
weakly-bound nucleus has an oblate ground-state shape.Comment: 20 pages, 7 figure
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