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Niels R. Walet

Publications and source records attributed to Niels R. Walet.

At least 73 records · Page 4Linked to original sources
arXiv1999

A basis of cranking operators for the pairing-plus-quadrupole model

We investigate the RPA normal-mode coordinates in the pairing-plus-quadrupole model, with an eye on simplifying the application of large amplitude collective motion techniques. At the Hartree-Bogoliubov minimum, the RPA modes are exactly the cranking operators of the collective coordinate approach. We examine the possibility of representing the self-consistent cranking operator by linear combinations of a limited number of one-body operators. We study the Sm nuclei as an example, and find that such representations exist in terms of operators that are state-dependent in a characteristic manner.

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arXiv1998

Collective coordinates, shape transitions and shape coexistence: a microscopic approach

We investigate a description of shape-mixing and shape-transitions using collective coordinates. To that end we apply a theory of adiabatic large-amplitude motion to a simplified nuclear shell-model, where the approximate results can be contrasted with exact diagonalisations. We find excellent agreement for different regimes, and contrast the results with those from a more standard calculation using a quadrupole constraint. We show that the method employed in this work selects diabatic (crossing) potential energy curves where these are appropriate, and discuss the implications for a microscopic study of shape coexistence.

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arXiv1997

Diabatic and Adiabatic Collective Motion in a Model Pairing System

Large amplitude collective motion is investigated for a model pairing Hamiltonian containing an avoided level crossing. A classical theory of collective motion for the adiabatic limit is applied utilising either a time-dependent mean-field theory or a direct parametrisation of the time-dependent Schrödinger equation. A modified local harmonic equation is formulated to take account of the Nambu-Goldstone mode. It turns out that in some cases the system selects a diabatic path. Requantizing the collective Hamiltonian, a reasonable agreement with an exact calculation for the low-lying levels are obtained for both weak and strong pairing force. This improves on results of the conventional Born-Oppenheimer approximation.

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arXiv1997

Large Amplitude Collective Motion in Nuclei and Metallic Clusters: Applicability of adiabatic theory for a pairing model

A model Hamiltonian describing a two-level system with a crossing plus a pairing force is investigated using technique of large-amplitude collective motion. The collective path, which is determined by the decoupling conditions, is found to be almost identical to the one in the Born-Oppenheimer approximation for the case of a strong pairing force. For the weak pairing case, the obtained path describes a diabatic dynamics of the system.

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arXiv1996

Translationally invariant treatment of pair correlations in nuclei: I. Spin and isospin dependent correlations

We study the extension of our translationally invariant treatment of few-body nuclear systems to heavier nuclei. At the same time we also introduce state-dependent correlation operators. Our techniques are tailored to those nuclei that can be dealt with in $LS$ coupling, which includes all nuclei up to the shell closure at $A=40$. We study mainly $p$-shell nuclei in this paper. A detailed comparison with other microscopic many-body approaches is made, using a variety of schematic nuclear interactions. It is shown that our methodology produces very good energies, and presumably also wave functions, for medium mass nuclei.

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arXiv1996

Application of a semi-microscopic core-particle coupling method to the backbending in odd deformed nuclei

In two previous papers, the Kerman-Klein-Donau-Frauendorf (KKDF) model was used to study rotational bands of odd deformed nuclei. Here we describe backbending for odd nuclei using the same model. The backbending in the neighboring even nuclei is described by a phenomenological two band model, and this core is then coupled to a large single-particle space, as in our previous work. The results obtained for energies and M1 transition rates are compared with experimental data for 165Lu and for energies alone to the experimental data for 179W. For the case of 165Lu comparison is also made with previous theoretical work.

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arXiv1996

Quantising the B=2 and B=3 Skyrmion systems

We examine the quantisation of a collective Hamiltonian for the two-baryon system derived by us in a previous paper. We show that by increasing the sophistication of the approximations we can obtain a bound state - or a resonance - not too far removed from the threshold with the quantum numbers of the deuteron. The energy of this state is shown to depend very sensitively on the parameters of the model. Subsequently we construct part of a collective Hamiltonian for the three baryon system. Large-amplitude quantum fluctuations play an important rôle in the intrinsic wave function of the ground-state, changing its symmetry from octahedral to cubic. Apart from the tetrahedron describing the minimum of the potential, we identify a ``doughnut'' and a ``pretzel'' as the most important saddle points in the potential energy surface. We show that it is likely that inclusion of fluctuations through these saddle points lead to an energy close to the triton's value.

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arXiv1995

Further application of a semi-microscopic core-particle coupling method to the properties of Gd155,157, and Dy159

In a previous paper a semi-microscopic core-particle coupling method that includes the conventional strong coupling core-particle model as a limiting case, was applied to spectra and electromagnetic properties of several well-deformed odd nuclei. This work, coupled a large single-particle space to the ground state bands of the neighboring even cores. In this paper, we generalize the theory to include excited bands of the cores, such as beta and gamma bands, and thereby show that the resulting theory can account for the location and structure of all bands up to about 1.5 MeV.

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arXiv1995

The large-$N_c$ limit and the behavior of $g_A^{(0)}$ and $g_A$

We investigate the isoscalar and isovector components of the axial vector coupling constants, $g_A^{(0)}$ and $g_A$, using algebraic models that lead to the correct symmetries of large-$N_c$ QCD. Results obtained previously in various chiral models are interpreted from this algebraic point of view. The results of the Skyrme model and the valence quark model are explained by simple realizations of the algebra.

hep-ph↗
arXiv1994

The kinetic energy and and the geometric structure in the $B=2$ sector of the Skyrme model: A study using the Atiyah-Manton Ansatz

We study the construction of the collective-coordinate manifold in the baryon number two sector of the Skyrme model. To that end we use techniques of adiabatic large amplitude collective motion, which treat potential and kinetic energy on an equal footing. In this paper the starting point is the Ansatz proposed by Atiyah and Manton (Phys.~Lett.~{\bf 438B}, 222 (1989)), which allows a study of the dynamics using a finite and small number of variables. From these variables we choose a subset of collective ones. We then study the behavior of inertial parameters along parts of the collective manifold, and study the dynamical parts of the interaction.

hep-ph↗
arXiv1993

Classical mappings of the symplectic model and their application to the theory of large-amplitude collective motion

We study the algebra Sp(n,R) of the symplectic model, in particular for the cases n=1,2,3, in a new way. Starting from the Poisson-bracket realization we derive a set of partial differential equations for the generators as functions of classical canonical variables. We obtain a solution to these equations that represents the classical limit of a boson mapping of the algebra. The relationship to the collective dynamics is formulated as a theorem that associates the mapping with an exact solution of the time-dependent Hartree approximation. This solution determines a decoupled classical symplectic manifold, thus satisfying the criteria that define an exactly solvable model in the theory of large amplitude collective motion. The models thus obtained also provide a test of methods for constructing an approximately decoupled manifold in fully realistic cases. We show that an algorithm developed in one of our earlier works reproduces the main results of the theorem.

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arXiv1993

The Skyrme model description of the spin-orbit force

We examine the derivation of the spin-orbit force from the Skyrme model. We find substantial agreement with phenomenological potentials. We show that a systematic and simultaneous treatment of all components of the kinetic energy introduces a minus sign relative to previous calculations for the iso-spin independent part of the interaction. We also explain the smallness of the iso-spin dependent part of the spin-orbit potential.

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arXiv1993

Inertial parameters of the Skyrmion-Skyrmion system with the product ansatz

The kinetic energy of the Skyrmion-Skyrmion system is calculated in the product ansatz. The energy is expanded in a set of rotationally invariant quadratic functions of translational and iso-rotational velocities in the product ansatz and all inertial parameters are evaluated. Most of the iso-spin dependent parameters are small at separations larger than 1 fm. However, some parameters of the coupling between the iso-rotational velocities of the Skyrmions decay slowly, as $1/R$, when zero pion mass is used. Otherwise we find that the results are not sensitive to the addition of the pion mass term.

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arXiv1993

Calculation of the properties of the rotational bands of $^{155,157}$Gd

We reexamine the long-standing problem of the microscopic derivation of a particle-core coupling model. We base our research on the Klein-Kerman approach, as amended by Dönau and Frauendorf. We describe the formalism to calculate energy spectra and transition strengths in some detail. We apply our formalism to the rotational nuclei $^{155,157}$Gd, where recent experimental data requires an explanation. We find no clear evidence of a need for Coriolis attenuation.

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arXiv1993

From Skyrmions to NN phaseshifts

We study the $NN$ phaseshifts in a Hamiltonian obtained from quantization of the collective modes in the Skyrme model. We show that a combination of an adiabatic and diabatic approximation gives a good $NN$ force, with sufficient attraction to produce a bound deuteron. The description of the repulsive core appears to be the main cause for the remaining discrepancies between the Skyrme model force and phenomenology. Finally we discuss the possibility of finding non-strange dibaryon resonances in the $J^π=3^+$ channel.

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arXiv1993

Quantum theory of large amplitude collective motion and the Born-Oppenheimer method

We study the quantum foundations of a theory of large amplitude collective motion for a Hamiltonian expressed in terms of canonical variables. In previous work the separation into slow and fast (collective and non-collective) variables was carried out without the explicit intervention of the Born Oppenheimer approach. The addition of the Born Oppenheimer assumption not only provides support for the results found previously in leading approximation, but also facilitates an extension of the theory to include an approximate description of the fast variables and their interaction with the slow ones. Among other corrections, one encounters the Berry vector and scalar potential. The formalism is illustrated with the aid of some simple examples, where the potentials in question are actually evaluated and where the accuracy of the Born Oppenheimer approximation is tested. Variational formulations of both Hamiltonian and Lagrangian type are described for the equations of motion for the slow variables.

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arXiv1993

Extracting Nuclear Transparency from p-A Cross sections

We study nuclear structure effects on the transparency in high transverse momentum $(p,2p)$ and $(e,e'p)$ reactions. We show that in the DWIA-eikonal approximation, even when correlations are included, one can get a factorized expression for the transparency. This depends only on the average nucleon density $ρ(r)$ and a correlation function. We develop a technique to include correlations in a Monte-Carlo Glauber type calculation. We compare calculations of $T$ using the eikonal formalism and a continuous density, with a Monte Carlo method based on discrete nucleons.

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