arXiv subjects

V. G. Gueorguiev

Publications and source records attributed to V. G. Gueorguiev.

34 records · Page 2Linked to original sources

arXiv2005

Aspects of Diffeomorphism Invariant Theory of Extended Objects I: The Relativistic Particle and its d-brane Cousins

General structure of classical reparametrization-invariant matter systems, mainly the relativistic particle and its $d$-brane generalization, are studied. The exposition is in close analogy with the relativistic particle in an electromagnetic field as reparametrization-invariant system. The structure of a diffeomorphism invariant Lagrangian action for an extended object ($d$-brane) embedded in a bulk space M is discussed. Our construction uses first order homogeneous Lagrangians to achieve general covariance in contrast to the constructions that use scalar Lagrangians along with metric dependent integration measure. The framework contains intrinsically the relativistic point particle, string theory, and Dirac-Nambu-Goto Lagrangians. In a natural way, the matter Lagrangian contains background interaction fields, such as a 1-form field, analogous to the electromagnetic vector potential, and a metric tensor. The framework naturally suggests new classical interaction fields beyond electromagnetism and gravity. Construction of aninteraction field Lagrangian that is background free and consistent with the gauge symmetries presented in the equations of motion for the matter is outlined. Keywords: diffeomorphism invariant systems, reparametrization-invariant matter systems, matter Lagrangian, homogeneous singular Lagrangians, relativistic particle, string theory, extended objects, d-branes, interaction fields, classical forces beyond electromagnetism and gravity, generally covariant theory, gauge symmetries, background free theories.

math-ph↗

arXiv2005

Confined One Dimensional Harmonic Oscillator as a Two-Mode System

The one-dimensional harmonic oscillator in a box problem is possibly the simplest example of a two-mode system. This system has two exactly solvable limits, the harmonic oscillator and a particle in a (one-dimensional) box. Each of the two limits has a characteristic spectral structure describing the two different excitation modes of the system. Near each of these limits, one can use perturbation theory to achieve an accurate description of the eigenstates. Away from the exact limits, however, one has to carry out a matrix diagonalization because the basis-state mixing that occurs is typically too large to be reproduced in any other way. An alternative to casting the problem in terms of one or the other basis set consists of using an "oblique" basis that uses both sets. Through a study of this alternative in this one-dimensional problem, we are able to illustrate practical solutions and infer the applicability of the concept for more complex systems, such as in the study of complex nuclei where oblique-basis calculations have been successful. Keywords: one-dimensional harmonic oscillator, particle in a box, exactly solvable models, two-mode system, oblique basis states, perturbation theory, coherent states, adiabatic mixing.

math-ph↗

arXiv2004

Generalized Richardson-Gaudin Nuclear Models

The exact solvability of several nuclear models with non-degenerate single-particle energies is outlined and leads to a generalization of integrable Richardson-Gaudin models, like the $su(2)$-based fermion pairing, to any simple Lie algebra. As an example, the $so(5)\sim sp(4)$ model of T=1 pairing is discussed and illustrated for the case of $^{64}$Ge with non-degenerate single-particle energies.

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arXiv2004

Extended Pairing Model for Heavy Nuclei

We study binding energies in three isotopic chains ($^{100-130}$Sn, $^{152-181}$Yb, and $^{181-202}$Pb) using the extended pairing model with Nilsson single-particle energies. The exactly solvable nature of the model means that the pairing strength G(A) required to reproduce the experimental binding energies can be determined uniquely. The valence space consists of the neutron single-particle levels between two closed shells corresponding to the magic numbers 50-82 and 82-126. In all three isotopic chains, log(G(A)) has a smooth quadratic behavior for even as well as odd nucleon numbers A; log(G(A)) for even and odd A are very similar. Remarkably, G(A) for all the Pb isotopes can be also described by a two parameter expression that is inversely proportional to the dimensionality of the model space.

nucl-th↗

arXiv2003

Mixed Symmetry Nuclear Shell Model

A mixed-symmetry nuclear shell-model scheme for carrying out calculations in regimes where there is a competition between two or more modes is proposed. A one-dimensional toy model is used to demonstrate the concept. The theory is then applied to $^{24}Mg$ and $^{44}Ti$. For lower pf-shell nuclei such as $^{44-48}Ti$ and $^{48}Cr$ there is strong SU(3) symmetry breaking due to the spin-orbit interaction. However, the quadrupole collectivity as measured by B(E2) transition strengths in the yrast band remain high even though SU(3) appears to be broken. Some results for the so-called X(5) symmetry that falls along the U(5) $\leftrightarrow$ SU(3) leg of the Interacting Boson Model are also considered. The results show that the mixed-symmetry concept is effective, even when strong symmetry breaking occurs.

nucl-th↗

arXiv2003

Algebraic Solutions of an Extended Pairing Model for Well-Deformed Nuclei

A Nilsson mean-field plus extended pairing interaction Hamiltonian with many-pair interaction terms is proposed. Eigenvalues of the extended pairing model are easy to obtain. Our investigation shows that one- and two-body interactions continue to dominate the dynamics for relatively small values of the pairing strength. As the strength of the pairing interaction grows, however, the three- and higher many-body interaction terms grow in importance. A numerical study of even-odd mass differences in the $^{154-171}$Yb isotopes shows that the extended pairing model is applicable to well-deformed nuclei.

nucl-th↗

arXiv2003

Aspects of Diffeomorphism Invariant Theory of Extended Objects

The structure of a diffeomorphism invariant Lagrangians for an extended object W embedded in a bulk space M is discussed by following a close analogy with the relativistic particle in electromagnetic field as a system that is reparametrization-invariant. The current construction naturally contains, relativistic point particle, string theory, and Dirac--Nambu--Goto Lagrangians with Wess--Zumino terms. For Lorentzian metric field, the non-relativistic theory of an integrally submerged W-brane is well defined provided that the brane does not alter the background interaction fields. A natural time gauge is fixed by the integral submergence (sub-manifold structure) within a Lorentzian signature structure. A generally covariant relativistic theory for the discussed brane Lagrangians is also discussed. The mass-shell constraint and the Klein--Gordon equation are shown to be universal when gravity-like interaction is present. A construction of the Dirac equation for the W-brane that circumvents some of the problems associated with diffeomorphism invariance of such Lagrangians by promoting the velocity coordinates into a non-commuting gamma variables is presented.

math-ph↗

arXiv2003

Study of $^{44}$Ti in a Mixed--Symmetry Basis

The structure of $^{44}$Ti is studied in an oblique-basis that includes spherical and SU(3) shell-model basis states. The results show that the oblique-basis concept is applicable, even though the strong spin-orbit interaction, which breaks the SU(3) symmetry, generates significant splitting of the single-particle levels. Specifically, a model space that includes a few SU(3) irreducible representations (irreps), namely, the leading (12,0) and next to the leading (10,1) irreps -- including spin S=0 and 1 configurations of the latter, plus spherical shell-model configurations (SSMC) that have at least two valence nucleons confined to the $f_{7/2}$ orbit -- the SM(2) case, yield results that are comparable to SSMC with at least one valence nucleon confined to the $f_{7/2}$ orbit -- the SM(3) case.

nucl-th↗

arXiv2003

Oblique-Basis Calculations for $^{44}$Ti

The spectrum and wave functions of $^{44}$Ti are studied in oblique-basis calculations using spherical and SU(3) shell-model states. Although the results for $^{44}$Ti are not as good as those previously reported for $^{24}$Mg, due primarily to the strong spin-orbit interaction that generates significant splitting of the single-particle energies that breaks the SU(3) symmetry, a more careful quantitative analysis shows that the oblique-basis concept is still effective. In particular, a model space that includes a few SU(3) irreducible representations, namely, the leading irrep (12,0) and next to the leading irrep (10,1) including its spin S=0 and 1 states, plus spherical shell-model configurations (SSMC) that have at least two valence nucleons confined to the $f_{7/2}$ orbit -- the SM(2) states, provide results that are compatible with SSMC with at least one valence nucleon confined to the $f_{7/2}$ orbit -- the SM(3) states.

nucl-th↗

arXiv2002

Mixed-Symmetry Shell-Model Calculations

The one-dimensional harmonic oscillator in a box problem is used to introduce the concept of an oblique-basis shell-model theory. The method is applied to nuclei by combining traditional spherical shell-model states with SU(3) collective configurations. An application to $^{24}$Mg, using the realistic two-body interaction of Wildenthal, is used to explore the validity of this oblique-basis, mixed-symmetry shell-model concept. The applicability of the theory to the lower pf-shell nuclei $^{44-48}$Ti and $^{48}$Cr using the Kuo-Brown-3 interaction is also discussed. While these nuclei show strong SU(3) symmetry breaking due mainly to the single-particle spin-orbit splitting, they continue to yield enhanced B(E2) values not unlike those expected if the symmetry were not broken. Other alternative basis sets are considered for future oblique-basis shell-model calculations. The results suggest that an oblique-basis, mixed-symmetry shell-model theory may prove to be useful in situations where competing degrees of freedom dominate the dynamics.

nucl-th↗

arXiv2002

Mixed-Mode Calculations in Nuclear Physics

The one-dimensional harmonic oscillator in a box problem is used to introduce the concept of a mixed-mode shell-model scheme. The method combines low-lying ``pure mode'' states of a system to achieve a better description in situations where complete calculations cannot be done and the dynamics is driven by a combination of modes. The scheme is tested for real nuclei by combining traditional spherical states, which yield a diagonal representation of the single-particle interaction, with collective SU(3) configurations that track deformation. An application to the ds-shell $^{24}$Mg nucleus, using the realistic two-body interaction of Wildenthal, is explored to test the validity of the concept. The results shown that the mixed-mode scheme reproduces the correct binding energy of $^{24}$Mg (within 2% of the exact result) as well as low-energy configurations that have greater than 90% overlap with exact solutions in a space that spans less than 10% of the full space. In the pf-shell, the Kuo-Brown-3 interaction is used to illustrate coherent structures of the low-lying states of $^{48}$Cr. Alternative basis sets are suggested for future mixed-mode shell-model studies.

nucl-th↗

arXiv2002

q-Analogue of $A_{m-1}\oplus A_{n-1}\subset A_{mn-1}$

A natural embedding $A_{m-1}\oplus A_{n-1}\subset A_{mn-1}$ for the corresponding quantum algebras is constructed through the appropriate comultiplication on the generators of each of the $A_{m-1}$ and $A_{n-1}$ algebras. The above embedding is proved in their $q$-boson realization by means of the isomorphism between the $\mathcal{A}_q^{-}$ (mn)$\sim {\otimes} ^n \mathcal{A}_q^{-}$(m)$\sim {\otimes}^m\mathcal{A}_q^{-}$(n) algebras.

math.QA↗

arXiv2002

Mixed-Mode Shell-Model Calculations

A one-dimensional harmonic oscillator in a box is used to introduce the oblique-basis concept. The method is extended to the nuclear shell model by combining traditional spherical states, which yield a diagonal representation of the usual single-particle interaction, with collective configurations that track deformation. An application to 24Mg, using the realistic two-body interaction of Wildenthal, is used to explore the validity of this mixed-mode shell-model scheme. Specifically, the correct binding energy (within 2% of the full-space result) as well as low-energy configurations that have greater than 90% overlap with full-space results are obtained in a space that spans less than 10% of the full-space. The theory is also applied to lower pf-shell nuclei, 44Ti-48Ti and 48Cr, using the Kuo-Brown-3 interaction. These nuclei show strong SU(3) symmetry breaking due mainly to the single-particle spin-orbit splitting. Nevertheless, the results also show that yrast band B(E2) values are insensitive to fragmentation of the SU(3) symmetry. Specifically, the quadrupole collectivity as measured by B(E2) strengths remains high even though the SU(3) symmetry is rather badly broken. The IBM and broken-pair models are considered as alternative basis sets for future oblique-basis shell-model calculations.

nucl-th↗

arXiv2001

A mixed-mode shell-model theory for nuclear structure studies

We introduce a shell-model theory that combines traditional spherical states, which yield a diagonal representation of the usual single-particle interaction, with collective configurations that track deformations, and test the validity of this mixed-mode, oblique basis shell-model scheme on $^{24}$Mg. The correct binding energy (within 2% of the full-space result) as well as low-energy configurations that have greater than 90% overlap with full-space results are obtained in a space that spans less than 10% of the full space. The results suggest that a mixed-mode shell-model theory may be useful in situations where competing degrees of freedom dominate the dynamics and full-space calculations are not feasible.

nucl-th↗

arXiv2001

Deformations of the fermion realization of the sp(4) algebra and its subalgebras

With a view towards future applications in nuclear physics, the fermion realization of the compact symplectic sp(4) algebra and its q-deformed versions are investigated. Three important reduction chains of the sp(4) algebra are explored in both the classical and deformed cases. The deformed realizations are based on distinct deformations of the fermion creation and annihilation operators. For the primary reduction, the su(2) sub-structure can be interpreted as either the spin, isospin or angular momentum algebra, whereas for the other two reductions su(2) can be associated with pairing between fermions of the same type or pairing between two distinct fermion types. Each reduction provides for a complete classification of the basis states. The deformed induced u(2) representations are reducible in the action spaces of sp(4) and are decomposed into irreducible representations.

nucl-th↗

arXiv2001

SU(3) symmetry breaking in lower fp-shell nuclei

Results of shell-model calculations for lower fp-shell nuclei show that SU(3) symmetry breaking in this region is driven by the single-particle spin-orbit splitting. However, even though states of the yrast band exhibit SU(3) symmetry breaking, the results also show that the yrast band B(E2) values are insensitive to this fragmentation of the SU(3) symmetry; specifically, the quadrupole collectivity as measured by B(E2) transition strengths between low lying members of the yrast band remain high even though SU(3) appears to be broken. Results for $^{44,46,48}Ti$ and $^{48}Cr$ using the Kuo-Brown-3 two-body interaction are given to illustrate these observations.

nucl-th↗