K. Neergård

University of Notre Dame, South Bend, Indiana, United States

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Publications (36)112.9 Total impact

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    K. Neergård
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    ABSTRACT: Conservation laws in the $1f_{7/2}$ shell model of $^{48}$Cr found in numeric studies by Escuderos, Zamick and Bayman [A. Escuderos, L. Zamick, and B. F. Bayman, arXiv:nucl-th/0506050 (2005)] and me [K. Neerg\aa rd, Phys. Rev. C \textbf{90}, 014318 (2014)] are explained by symmetry under particle-hole conjugation and the structure of the irreps of the symplectic group Sp(4). A generalization is discussed.
    Preview · Article · Feb 2015 · Physical Review C
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    K. Neergård
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    ABSTRACT: The ground states of 48Cr, 88Ru, and 92Pd are studied in the 1f7/2 or 1g9/2 shell model with effective interactions from the literature. They are found to be composed, quite independently of the shell and the interaction, roughly of 75% of (s,t)=(0,0) and 25% of (s,t)=(4,0), where s is the seniority and t the reduced isospin. Other irreps of the symplectic group Sp(2j+1), where j is the single-nucleon angular momentum, make only very small contributions. The state chi obtained by antisymmetrizing and normalizing the ground state in the stretch scheme of Danos and Gillet has a very different structure where the Sp(2j+1) irreps other than (s,t)=(0,0) and (4,0) contribute 20% and 41% for j=7/2 and 9/2, respectively. The contributions of chi and the s=0 state to the calculated ground states state are about equal for 48Cr. For 88Ru and 92Pd the s=0 state is unambiguously a better approximation to the calculated states than chi.
    Preview · Article · Apr 2014
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    I. Bentley · K. Neergârd · S. Frauendorf

    Full-text · Article · Mar 2014 · Physical Review C
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    I. Bentley · K. Neergård · S. Frauendorf
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    ABSTRACT: A model with nucleons in a charge independent potential well interacting by an isovector pairing force is considered. For a 24-dimensional valence space, the Hartree-Bogolyubov (HB) plus Random Phase (RPA) approximation to the lowest eigenvalue of the Hamiltonian is shown to be accurate except near values of the pairing force coupling constant G where the HB solution shifts from a zero to a non-zero pair gap. In the limit G->infinity the HB + RPA is asymptotically exact. The inaccuracy of the HB + RPA in the critical regions of G can be remedied by interpolation. The resulting algoritm is used to calculate pairing corrections in the framework of a Nilsson-Strutinsky calculation of nuclear masses near N = Z for A = 24-100, where N and Z are the numbers of neutrons and protons, and A = N + Z. The dimension of the valence space is 2A in these calculations. Adjusting five liquid drop parameters and a power law expression for the constant G as a function of A allows us to reproduce the measured binding energies of 112 doubly even nuclei in this range with a root mean square deviation of 0.95 MeV. Several combinations of the masses for different N, Z, and isospin T are considered and the calculations found to be in good agreement with the data. It is demonstrated by examples how fluctuations as a function of A of the constant X in an expansion of the symmetry energy of the form T(T+X)/(2 theta) can be understood from the shell structure.
    Full-text · Article · Nov 2013 · Physical Review C
  • K. Neergård

    No preview · Article · Oct 2013 · Physical Review C
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    K. Neergård
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    ABSTRACT: For two neutrons and two protons or two neutron holes and two proton holes in a single j-shell, the state |phi> with isospin and seniority zero and the lowest angular momentum zero state |chi> produced by an attractive interaction of quasinucleon pairs with angular momentum 2j have a large overlap for all relevant j and large contents of quasinucleon pairs with angular momenta 2j and 0, respectively. In the 1f7/2 and 1g9/2 shells, the large negative matrix elements of the effective interaction in these two channels relative to most of the rest therefore_cooperate_ to produce a ground state which is essentially a linear combination of |phi> and |chi> with comparable coefficients. Interaction matrix elements in other channels influence significantly the_ratio_ of these coefficients. The state |phi> makes up about 80 % of the calculated ground states. The overlaps of the latter with |chi> are_less_ in the 1g9/2 shell than in the 1f7/2 shell.
    Preview · Article · May 2013 · Physical Review C
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    K. Neergård
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    ABSTRACT: As a model which displays a picture of the symmetry energy as an energy of rotation in isospace of a Cooper pair condensate, a Hamiltonian with a pairing force and an interaction of isospins is analyzed in the Hartree-Bogolyubov (HB) plus Random Phase (RPA) approximation. The HB energy minus Lagrangian multiplier terms is shown to be locally minimized by a product of neutron and proton Bardeen-Cooper-Schrieffer states. Nambu-Goldstone RPA solutions appear due to global gauge invariance and isobaric invariance. In an idealized case of infinitely many equidistant single-nucleon levels, the symmetry energy is composed of contributions from the single-nucleon and isospin interaction energies and the RPA correlation energy. The contribution of the latter is dominated by a neutron-proton Nambu-Goldstone solution, which makes the total symmetry energy nearly proportional to T(T+1). Observations reported from Skyrme force calculations are discussed in the light of these results. Calculations with deformed Woods-Saxon single-nucleon levels give results similar to those of the idealized case, whereas a somewhat different behavior is found with spherical Woods-Saxon levels. The calculations with Woods-Saxon single-nucleon levels reproduce surprisingly well the empirical symmetry energy. Comment: Minor formal corrections. To be published in Physical Review C
    Preview · Article · May 2009 · Physical Review C
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    ABSTRACT: Collective properties at low and high spin for nuclei with Z 64 and N 82 are calculated on the basis of deformed single-particle potentials. The calculations are confronted with the available experimental data like low-lying octupole bands, rotational bands of transitional nuclei with N 90 and evidence for collectivity in high-spin single-particle spectra. In the latter collective triaxiality and collective rotation perpendicular to the aligned spin are investigated by cranking and RPA. Predicted regimes of different shapes and shape transitions at high spins are presented. In a gamma cascade calculation, it is shown how the calculated regimes for 152Dy are consistent with the measured inclusive spectrum.
    Full-text · Article · Dec 2006 · Physica Scripta
  • T Døssing · K Neergård · H Sagawa
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    ABSTRACT: Selected topics related to the yrast spectroscopy in the 146Gd region are discussed from the point of view of the deformed independent particle model with empirically based spherical single particle energies, a pairing force treated in the BCS approximation with variation of the gap parameters after particle number projection, and Strutinsky renormalization.
    No preview · Article · Dec 2006 · Physica Scripta
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    S. Frauendorf · K. Neergård
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    ABSTRACT: The paper does not take into account previous work where the effect the authors discuss is explored in detail. It is known from this previous work that the approach is incomplete.
    Full-text · Article · Mar 2004 · Physical Review C
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    Kai Neergård
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    ABSTRACT: The nuclear symmetry energy calculated in the RPA from the pairing plus symmetry force Hamiltonian with equidistant single-nucleon levels is for mass number A=48 approximately proportional to T(T+1.025), where T is the isospin quantum number. An isovector character of the pair field assumed to produce the observed odd-even mass staggering is essential for this result. The RPA contribution to the symmetry energy cannot be simulated by adding to the Hartree-Fock-Bogolyubov energy a term proportional to the isospin variance in the Bogolyubov quasiparticle vacuum, and there are significant corrections to the approximation which consist in adding half the isocranking angular velocity. The present calculation employs a smaller single-nucleon level spacing than used in a previous investigation of the model.
    Preview · Article · May 2003 · Physics Letters B
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    Kai Neergård
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    ABSTRACT: In a schematic model with equidistant fourfold degenerate single-nucleon levels, a conventional isovector pairing force and a symmetry force, the RPA correlation energy rises almost linearly with the isospin T, thus producing a Wigner term in accordance with the empirical proportionality of the symmetry energy to T(T+1).
    Preview · Article · Jan 2002 · Physics Letters B
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    S. Frauendorf · K. Neergård · JA Sheikh · P. M. Walker
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    ABSTRACT: Tilted-axis cranking calculations have been performed for multi-quasiparticle states in well deformed A$\approx$180 nuclei. In the limit of zero pairing, not only are the calculated moments of inertia substantially smaller than for rigid rotation, but also they are close to the experimental values. The moments of inertia are found to be insensitive to dynamic pair correlations. Comment: 8 pages 6 figures, figure 6 replaced
    Full-text · Article · Feb 2000 · Physical Review C
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    S. Frauendorf · K. Neergård
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    ABSTRACT: Rotating nuclear matter is defined as the system of infinitely many nucleons in a rotating frame neglecting the electrostatic interaction and centrifugal single-nucleon potential. We study the ground state of this system as a function of the densities of neutrons and protons. In the limit where the angular velocity is much smaller than the Fermi energy, the structure of the single-nucleon density corresponds to anisotropic spin distributions at the surfaces of local neutron and proton Fermi spheres. The anisotropy results from the non-central terms in the effective two-nucleon interaction. Contrary to the situation in a system of non-interacting nucleons, the spin asymmetry induced by rotation is a strongly non-linear function of the Fermi momentum. In symmetric nuclear matter at normal density it equals roughly that of the non-interacting system due to mutually cancelling contributions from the spin-orbit and central parts of the effective two-nucleon interaction. The volume contributions to the moments of inertia and single-nucleon Routhian of finite nuclei are calculated, and estimates obtained of certain surface contributions to the moment of inertia.
    Full-text · Article · Nov 1996 · Zeitschrift für Physik A Hadrons and Nuclei
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    Sven Åberg · Thomas Døssing · Kai Neergård
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    ABSTRACT: The side-feeding patterns and the spectra of unresolved gamma-lines are calculated for Gd, Dy and Er nuclei with neutron numbers from 82 to 86. Energies and configurations for states from the yrast line and approximately 2 MeV higher in energy are calculated as many-quasiparticle configurations in a deformed oblate potential. The gamma-cascade is simulated by a Monte Carlo calculation. With a common average entry angular momentum of 35h to the non-collective oblate states considered, the observed variation of intensity of the strongest gamma-line with spin is well reproduced. The stretched dipole part of the continuum spectra is also well reproduced, whereas the stretched quadrupole part cannot be accounted for. These findings are in accordance with a two-stage picture of the gamma-decay. First comes a cascade of stretched quadrupole transitions, probably of collective nature. This cascade feeds into numerous weakly oblate states around spin ~ 35h, and the decay proceeds first by weak transitions, mainly dipoles, and later by strong gamma-lines.
    Full-text · Article · Sep 1985 · Nuclear Physics A
  • K. Mühlhans · K. Neergård · U. Mosel
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    ABSTRACT: The Hartree-Fock-Bogoliubov equations are solved with a new method using the canonical representation in each step of the iteration. This is achieved by a modification of the Mang-Samadi-Ring gradient method. The canonical representation is the ideal basis for various projection techniques. Expressions are developed for the unprojected case and for the case with particle number projection before the variation. As a first test, an HFBC calculation for 158Dy is performed. The resulting yrast lines, multipole pair fields and gyromagnetic factors with and without number projection are presented and compared.
    No preview · Article · May 1984 · Nuclear Physics A
  • K NEERGARD · E. Wüst
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    ABSTRACT: We show how one can determine the sign of the matrix element of a symmetry operator between Bogoliubov states and discuss the numerical effect.
    No preview · Article · Jun 1983 · Nuclear Physics A
  • K. Mühlhans · M. Diebel · K. Neergård · U. Mosel
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    ABSTRACT: Using the surface delta interaction as the generating two-body force, we investigate the interdependence between the composition of the multipole pair field and the multipole moments of the relevant single-particle states. A decrease of the quadrupole pair field is found in going from light to heavy rare earth nuclei. The inclusion of higher multipole moments shifts an existing backbend to higher frequency but when the force parameters are readjusted to reproduce the experimental odd-even mass difference the shift is strongly reduced.
    No preview · Article · Jan 1983 · Physics Letters B
  • Kai Neergård
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    ABSTRACT: Calculations for nuclei in the vicinity of 146Gd based on a version of the deformed independent particle model are discussed. Particular attention is paid to systematic trends in the calculated deformations, deformation energies and pairing energies.
    No preview · Article · Jan 1983
  • E.M. Müller · K. Mühlhans · K. Neergård · U. Mosel
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    ABSTRACT: The structure of the pair field of rotating nuclei is investigated for various choices of the parameters of the surface-delta interaction, which was adopted as the generating two-body force. The response of a T = 0 or T = 1 pair field to increasing angular momentum is analysed in the case of 24Mg. With realistic force parameters, yielding a pure T = 0 pairing, the empirical yrast line up to I = 8 is well reproduced by the calculations. By enforcing a T = 1 multipole pair field in 24Mg the situation in heavy nuclei is simulated. A T = 1 and T = 0 pair field is found to be mutually exclusive.
    No preview · Article · Jul 1982 · Nuclear Physics A

Publication Stats

1k Citations
112.90 Total Impact Points

Institutions

  • 2013
    • University of Notre Dame
      • Department of Physics
      South Bend, Indiana, United States
  • 1981-2006
    • Justus-Liebig-Universität Gießen
      • Institut für Theoretische Physik
      Gieben, Hesse, Germany
  • 1969-1977
    • IT University of Copenhagen
      København, Capital Region, Denmark
  • 1975-1976
    • Joint Institute for Nuclear Research
      Dubno, MO, Russia