Publications (36)112.9 Total impact
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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:nuclth/0506050 (2005)] and me [K. Neerg\aa rd, Phys. Rev. C \textbf{90}, 014318 (2014)] are explained by symmetry under particlehole conjugation and the structure of the irreps of the symplectic group Sp(4). A generalization is discussed.  [Show abstract] [Hide abstract]
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 singlenucleon 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. 
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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 24dimensional valence space, the HartreeBogolyubov (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 nonzero 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 NilssonStrutinsky calculation of nuclear masses near N = Z for A = 24100, 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. 
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ABSTRACT: For two neutrons and two protons or two neutron holes and two proton holes in a single jshell, 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.  [Show abstract] [Hide abstract]
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 HartreeBogolyubov (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 BardeenCooperSchrieffer states. NambuGoldstone RPA solutions appear due to global gauge invariance and isobaric invariance. In an idealized case of infinitely many equidistant singlenucleon levels, the symmetry energy is composed of contributions from the singlenucleon and isospin interaction energies and the RPA correlation energy. The contribution of the latter is dominated by a neutronproton NambuGoldstone 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 WoodsSaxon singlenucleon levels give results similar to those of the idealized case, whereas a somewhat different behavior is found with spherical WoodsSaxon levels. The calculations with WoodsSaxon singlenucleon levels reproduce surprisingly well the empirical symmetry energy. Comment: Minor formal corrections. To be published in Physical Review C 
Article: Survey of Collective and SingleParticle Features in the Yrast Domain of the A ~ 150 Nuclei
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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 singleparticle potentials. The calculations are confronted with the available experimental data like lowlying octupole bands, rotational bands of transitional nuclei with N 90 and evidence for collectivity in highspin singleparticle 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. 
Article: Yrast Spectra in the 146Gd Region
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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.  [Show abstract] [Hide abstract]
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.  [Show abstract] [Hide abstract]
ABSTRACT: The nuclear symmetry energy calculated in the RPA from the pairing plus symmetry force Hamiltonian with equidistant singlenucleon 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 oddeven mass staggering is essential for this result. The RPA contribution to the symmetry energy cannot be simulated by adding to the HartreeFockBogolyubov 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 singlenucleon level spacing than used in a previous investigation of the model.  [Show abstract] [Hide abstract]
ABSTRACT: In a schematic model with equidistant fourfold degenerate singlenucleon 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).  [Show abstract] [Hide abstract]
ABSTRACT: Tiltedaxis cranking calculations have been performed for multiquasiparticle 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 
Article: Rotating nuclear matter
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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 singlenucleon 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 singlenucleon density corresponds to anisotropic spin distributions at the surfaces of local neutron and proton Fermi spheres. The anisotropy results from the noncentral terms in the effective twonucleon interaction. Contrary to the situation in a system of noninteracting nucleons, the spin asymmetry induced by rotation is a strongly nonlinear function of the Fermi momentum. In symmetric nuclear matter at normal density it equals roughly that of the noninteracting system due to mutually cancelling contributions from the spinorbit and central parts of the effective twonucleon interaction. The volume contributions to the moments of inertia and singlenucleon Routhian of finite nuclei are calculated, and estimates obtained of certain surface contributions to the moment of inertia.  [Show abstract] [Hide abstract]
ABSTRACT: The sidefeeding patterns and the spectra of unresolved gammalines 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 manyquasiparticle configurations in a deformed oblate potential. The gammacascade is simulated by a Monte Carlo calculation. With a common average entry angular momentum of 35h to the noncollective oblate states considered, the observed variation of intensity of the strongest gammaline 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 twostage picture of the gammadecay. 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 gammalines.  [Show abstract] [Hide abstract]
ABSTRACT: The HartreeFockBogoliubov 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 MangSamadiRing 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. 
Article: On the calculation of matrix elements of operators between symmetryprojected Bogoliubov states
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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.  [Show abstract] [Hide abstract]
ABSTRACT: Using the surface delta interaction as the generating twobody force, we investigate the interdependence between the composition of the multipole pair field and the multipole moments of the relevant singleparticle 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 oddeven mass difference the shift is strongly reduced. 
Article: "NonRotating" Yrast States
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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.  [Show abstract] [Hide abstract]
ABSTRACT: The structure of the pair field of rotating nuclei is investigated for various choices of the parameters of the surfacedelta interaction, which was adopted as the generating twobody 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.
Publication Stats
1k  Citations  
112.90  Total Impact Points  
Top Journals
 Nuclear Physics A (11)
 Physics Letters B (8)
 Physical Review C (8)
 Physica Scripta (2)
 Physical Review Letters (1)
Institutions

2013

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


19812006

JustusLiebigUniversität Gießen
 Institut für Theoretische Physik
Gieben, Hesse, Germany


19691977

IT University of Copenhagen
København, Capital Region, Denmark


19751976

Joint Institute for Nuclear Research
Dubno, MO, Russia
