85 research outputs found
A nucleon-pair and boson coexistent description of nuclei
We study a mixture of s-bosons and like-nucleon pairs with the standard
pairing interaction outside a inert core. Competition between the nucleon-pairs
and s-bosons is investigated in this scenario. The robustness of the BCS-BEC
coexistence and crossover phenomena is examined through an analysis of pf-shell
nuclei with realistic single-particle energies in which two configurations with
Pauli blocking of nucleon-pair orbits due to the formation of the s-bosons is
taken into account. When the nucleon-pair orbits are considered to be
independent of the s-bosons, the BCS-BEC crossover becomes smooth with the
number of the s-bosons noticeably more than that of the nucleonpairs near the
half-shell point, a feature that is demonstrated in the pf-shell for several
values of the standard pairing interaction strength. As a further test of the
robustness of the BCS-BEC coexistence and crossover phenomena in nuclei,
results are given for B(E2; 0^{+}_{g}->2^{+}_1) values of even-even 102-130Sn
with 100Sn taken as a core and valence neutron pairs confined within the 1d5/2,
0g7/2, 1d3/2, 2s1/2, 1h11/2 orbits in the nucleon-pair orbit and the s-boson
independent approximation. The results indicate that the B(E2) values are well
reproduced.Comment: 5.1 pages, 3 figures, LaTe
What a wonderful world - Simplicity within complexity
In this lecture, Louis Armstrong\u27s transformational Jazz, as exemplified by his signature recital of What a Wonderful World, will take us to the ever evolving World of Nuclear Physics. In particular, I will focus on the discovery of simplicities, or symmetry patterns, in complex nuclear systems. And as Jazz is to music, so too Nuclear Physics is a restless endeavor-the dissonance of forlorn flattened notes tracking with the intrigue of symmetry and its breaking in nuclei. I will also discuss some recent approaches to nuclear structure at this dawn of the 21st century, linking the intrigue of quarks and gluons with the fundamental science of the strong and weak interactions to the emergence of simplicity within complexity unveiled in atomic nuclei. © Published under licence by IOP Publishing Ltd
Exact solution of the two-axis countertwisting Hamiltonian for the half-integer case
Bethe ansatz solutions of the two-axis countertwisting Hamiltonian for any
(integer and half-integer) are derived based on the Jordan-Schwinger
(differential) boson realization of the algebra after desired Euler
rotations, where is the total angular momentum quantum number of the
system. It is shown that solutions to the Bethe ansatz equations can be
obtained as zeros of the extended Heine-Stieltjes polynomials. Two sets of
solutions, with solution number being and respectively when is an
integer and each when is a half-integer, are obtained. Properties
of the zeros of the related extended Heine-Stieltjes polynomials for
half-integer cases are discussed. It is clearly shown that double
degenerate level energies for half-integer are symmetric with respect to
the axis. It is also shown that the excitation energies of the `yrast'
and other `yrare' bands can all be asymptotically given by quadratic functions
of , especially when is large.Comment: LaTex 12 pages, 3 figures. Major cosmetic type revision. arXiv admin
note: text overlap with arXiv:1609.0558
Exact solution of the two-axis countertwisting Hamiltonian
It is shown that the two-axis countertwisting Hamiltonian is exactly solvable
when the quantum number of the total angular momentum of the system is an
integer after the Jordan-Schwinger (differential) boson realization of the
SU(2) algebra. Algebraic Bethe ansatz is used to get the exact solution with
the help of the SU(1,1) algebraic structure, from which a set of Bethe ansatz
equations of the problem is derived. It is shown that solutions of the Bethe
ansatz equations can be obtained as zeros of the Heine-Stieltjes polynomials.
The total number of the four sets of the zeros equals exactly to for a
given integer angular momentum quantum number , which proves the
completeness of the solutions. It is also shown that double degeneracy in level
energies may also occur in the limit for integer case
except a unique non-degenerate level with zero excitation energy.Comment: LaTex 10 pages. Version to appear in Annals of Physic
Fake Run-Time Selection of Template Arguments in C++
C++ does not support run-time resolution of template type arguments. To
circumvent this restriction, we can instantiate a template for all possible
combinations of type arguments at compile time and then select the proper
instance at run time by evaluation of some provided conditions. However, for
templates with multiple type parameters such a solution may easily result in a
branching code bloat. We present a template metaprogramming algorithm called
for_id that allows the user to select the proper template instance at run time
with theoretical minimum sustained complexity of the branching code.Comment: Objects, Models, Components, Patterns (50th International Conference,
TOOLS 2012
Microscopic description of the scissors mode in odd-mass heavy deformed nuclei
Pseudo-SU(3) shell-model results are reported for M1 excitation strengths in
157-Gd, 163-Dy and 169-Tm in the energy range between 2 and 4 MeV. Non-zero
pseudo-spin couplings between the configurations play a very important role in
determining the M1 strength distribution, especially its rapidly changing
fragmentation pattern which differs significantly from what has been found in
neighboring even-even systems. The results suggest one should examine
contributions from intruder levels.Comment: 5 pages, 3 figure
The Heine-Stieltjes correspondence and a new angular momentum projection for many-particle systems
A new angular momentum projection for systems of particles with arbitrary
spins is formulated based on the Heine-Stieltjes correspondence, which can be
regarded as the solutions of the mean-field plus pairing model in the strong
pairing interaction G ->Infinity limit. Properties of the Stieltjes zeros of
the extended Heine-Stieltjes polynomials, of which the roots determine the
projected states, and the related Van Vleck zeros are discussed. The
electrostatic interpretation of these zeros is presented. As examples,
applications to n nonidentical particles of spin-1/2 and to identical bosons or
fermions are made to elucidate the procedure and properties of the Stieltjes
zeros and the related Van Vleck zeros. It is shown that the new angular
momentum projection for n identical bosons or fermions can be simplified with
the branching multiplicity formula of U(N) supset O(3) and the special choices
of the parameters used in the projection. Especially, it is shown that the
solutions for identical bosons can always be expressed in terms of zeros of
Jacobi polynomials. However, unlike non-identical particle systems, the
n-coupled states of identical particles are non-orthogonal with respect to the
multiplicity label after the projection.Comment: 14 pages LaTeX with no figur
Geometrical interpretation for the outer SU(3) outer multiplicity label
A geometrical interpretation for the outer multiplicity rho that occurs in a reduction of the product of two SU(3) representations, (lambda(sub pi), mu(sub pi)) x (lambda(sub nu), mu(sub nu)) approaches sigma(sub rho)(lambda, mu)(sub rho), is introduced. This coupling of proton (pi) and neutron (nu) representations arises, for example, in both boson and fermion descriptions of heavy deformed nuclei. Attributing a geometry to the coupling raises the possibility of introducing a simple interaction that provides a physically meaningful way for distinguishing multiple occurrences of (lambda, mu) values that can arise in such products
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