Empirical strengths of spin operators in nuclei

Wildenthal, B. H.

doi:10.1016/0146-6410(84)90011-5

Cited by 644 publications

(161 citation statements)

References 18 publications

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“…IV D 5 to a description of 28 Si in the sd-shell, using Kuo's interaction [73], with single-particle energies as given in Table II. This interaction is not the best shell-model interaction available (it is known that Wildenthal's W interaction [73,74] gives a much better description of the sd-shell nuclei), but this interaction is as close as possible to the unpublished interaction used by Pelet and Letourneux. Note that we use ellipsoidal symmetry, which is a limitation for the present case, where the lowest RPA mode at the HF minimum is a |∆K| = 3 mode, so that it may not be totally correct to consider only even multipoles.…”

Section: Quantum Correctionsmentioning

confidence: 99%

“…It is well known [72] that such a symmetry requires that K, the projection of the angular momentum on the intrinsic z-axis is even and also relates wavefunction components with positive K to those with negative K. In the latter regard, it duplicates the function of time reversal invariance, which for static solutions of the Hartree-Fock problem for even nuclei already implies that any pair of time-reversed orbits is either occupied or unoccupied. The requirement of ellipsoidal symmetry is indeed a strong limitation in the implementation of our algorithm, since any reasonable interaction [73][74][75] gives that for 28 Si the lowest-energy RPA mode at the Hartree-Fock minimum is a ∆K = 3 state. We thus reject this solution as a possible choice of cranking operator, and choose the lowest even-∆K solution for this purpose.…”

Section: Symmetriesmentioning

confidence: 99%

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Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

2000

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The goal of the present account is to review our efforts to obtain and apply a "collective" Hamiltonian for a few, approximately decoupled, adiabatic degrees of freedom, starting from a Hamiltonian system with more or many more degrees of freedom. The approach is based on an analysis of the classical limit of quantum-mechanical problems. Initially, we study the classical problem within the framework of Hamiltonian dynamics and derive a fully self-consistent theory of large amplitude collective motion with small velocities. We derive a measure for the quality of decoupling of the collective degree of freedom. We show for several simple examples, where the classical limit is obvious, that when decoupling is good, a quantization of the collective Hamiltonian leads to accurate descriptions of the low energy properties of the systems studied. In nuclear physics problems we construct the classical Hamiltonian by means of time-dependent mean-field theory, and we transcribe our formalism to this case. We report studies of a model for monopole vibrations, of 28 Si with a realistic interaction, several qualitative models of heavier nuclei, and preliminary results for a more realistic approach to heavy nuclei. Other * Email: Giu.Dodang@th.u-psud.fr † Email: aklein@walet.physics.upenn.edu ‡ Email: Niels.Walet@umist.ac.uk 1 topics included are a nuclear Born-Oppenheimer approximation for an ab initio quantum theory and a theory of the transfer of energy between collective and non-collective degrees of freedom when the decoupling is not exact. The explicit account is based on the work of the authors, but a thorough survey of other work is included. PACS number(s): 21.60.-n, 21.60.Jz, 21.60.Ev

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Section: Quantum Correctionsmentioning

confidence: 99%

Section: Symmetriesmentioning

confidence: 99%

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

2000

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“…These were obtained in the framework of the 1s − 0d shell model using the realistic effective interaction of Wildenthal [41]. As we have already mentioned, this interaction has been tested over many years.…”

Section: The Shell Model Nuclear Wave Functionsmentioning

confidence: 99%

The exotic double-charge exchange μ−→e+ conversion in nuclei

et al. 2002

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The formalism for the neutrinoless (µ − , e + ) conversion is investigated in detail and the relevant nuclear matrix elements for light intermediate neutrinos in the case of 27 Al(µ − , e + ) 27 N a are calculated. The nucleus 27 Al is going to be used as a stopping target in the MECO experiment at Brookhaven, one of the most sensitive probes expected to reach a sensitivity in the branching ratio of the order 10 −16 within the next few years. The relevant transition operators are constructed utilizing a variety of mechanisms present in current gauge theories, with emphasis on the intermediate neutrinos, both light and heavy, and heavy SUSY particles. The nuclear wave functions, both for the initial state and all excited final states are obtained in the framework of 1s − 0d shell model employing the well-known and tested Wildenthal realistic interaction. In the case of the light intermediate neutrinos the transition rates to all excited final states up to 25 M eV in energy are calculated. We find that the imaginary part of the amplitude is dominant. The total rate is calculated by summing over all these partial transition strengths. We also find that the rate due to the real part of the amplitude is much smaller than the corresponding quantity found previously by the closure approximation.

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“…Shell structure influences the locations of the neutron and proton drip lines and the stability of matter. Examples of changes in shell structure are the appearance of new magic numbers N = 14 and N = 16 in the neutron-rich oxygen isotopes [1,2], and the emergence of an N = 34 sub-shell closure in 54 Ca [3][4][5][6].Phenomenological shell-model Hamiltonians such as the sd Hamiltonian of Brown and Wildenthal [7,8] (abbreviated USD) and the p-sd Hamiltonian of Warturburton and Brown [9] (abbreviated WBP), have successfully described properties of nuclei with proton number Z and neutron number N less than about 20. To understand the origin of shell structure, however, researchers are now trying to derive the shell model from realistic nucleonnucleon (NN) and three-nucleon forces (3NFs), without further phenomenology [3,10,11].…”

mentioning

confidence: 99%

“…Phenomenological shell-model Hamiltonians such as the sd Hamiltonian of Brown and Wildenthal [7,8] (abbreviated USD) and the p-sd Hamiltonian of Warturburton and Brown [9] (abbreviated WBP), have successfully described properties of nuclei with proton number Z and neutron number N less than about 20. To understand the origin of shell structure, however, researchers are now trying to derive the shell model from realistic nucleonnucleon (NN) and three-nucleon forces (3NFs), without further phenomenology [3,10,11].…”

mentioning

confidence: 99%

Ab InitioCoupled-Cluster Effective Interactions for the Shell Model: Application to Neutron-Rich Oxygen and Carbon Isotopes

et al. 2014

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We derive and compute effective valence-space shell-model interactions from ab-initio coupledcluster theory and apply them to open-shell and neutron-rich oxygen and carbon isotopes. Our shell-model interactions are based on nucleon-nucleon and three-nucleon forces from chiral effectivefield theory. We compute the energies of ground and low-lying states, and find good agreement with experiment. In particular our calculations are consistent with the N = 14, 16 shell closures in 22,24 O, while for 20 C the corresponding N = 14 closure is weaker. We find good agreement between our coupled-cluster effective-interaction results with those obtained from standard single-reference coupled-cluster calculations for up to eight valence neutrons. Introduction. -The nuclear shell model is the foundation on which our understanding of nuclei is built. One of the most important problems in nuclear structure today is to understand how shell structure changes with neutron-to-proton ratio throughout the nuclear chart. Shell structure influences the locations of the neutron and proton drip lines and the stability of matter. Examples of changes in shell structure are the appearance of new magic numbers N = 14 and N = 16 in the neutron-rich oxygen isotopes [1,2], and the emergence of an N = 34 sub-shell closure in 54 Ca [3][4][5][6].Phenomenological shell-model Hamiltonians such as the sd Hamiltonian of Brown and Wildenthal [7,8] (abbreviated USD) and the p-sd Hamiltonian of Warturburton and Brown [9] (abbreviated WBP), have successfully described properties of nuclei with proton number Z and neutron number N less than about 20. To understand the origin of shell structure, however, researchers are now trying to derive the shell model from realistic nucleonnucleon (NN) and three-nucleon forces (3NFs), without further phenomenology [3,10,11]. Within the last few years, for example, Otsuka et al. [11] showed that 3NFs play a pivotal role in placing the drip line (correctly) in the oxygen isotopes at 24 O, and Holt et al. [3] showed that the inclusion of 3NFs are necessary to explain the high 2 + state in 48 Ca .Until recently, all work to compute effective shellmodel interactions was perturbative.Lately, however, nonperturbative calculations have become possible. Some have been based on the ab-initio no-core shell model [12,13], via a valence-cluster expansion [14][15][16], and others on the in-medium similarity renormalization group [17]. In this Letter we use a third approach, the ab-initio coupled-cluster method [18][19][20][21][22][23], to construct effective shell-model interactions for use in open-shell and neutron-rich nuclei. Starting from NN interactions and 3NFs generated by chiral effective-field-theory, we compute the ground-and excited-state energies of neutronrich carbon and oxygen isotopes with up to eight neu-

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Empirical strengths of spin operators in nuclei

Cited by 644 publications

References 18 publications

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

The exotic double-charge exchange μ−→e+ conversion in nuclei

Ab InitioCoupled-Cluster Effective Interactions for the Shell Model: Application to Neutron-Rich Oxygen and Carbon Isotopes

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