<i>Nuclear Collective Motion: Models and Theory</i>

Rowe, David J.; Goldhammer, Paul

doi:10.1063/1.3070684

Cited by 143 publications

(347 citation statements)

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“…We address the question to which extent are the UCOM-HF single-nucleon basis and the residual interaction based on the correlated realistic NN interaction sufficient for a description of highly collective excitation phenomena, such as giant resonances. Since details about the derivation of RPA equations are available in textbooks [27,50], we review the basic principles only briefly.…”

Section: Outline Of the Ucom Random-phase Approximationmentioning

confidence: 99%

“…6, the isoscalar monopole and quadrupole responses in 16 O are displayed for the two cases: (i) with the bare multipole operators (27), (28) (Fig. 6).…”

Section: The Role Of Correlated Multipole Transition Operatorsmentioning

confidence: 99%

“…One of the standard approaches to derive RPA is the equation of motion method using the quasiboson approximation [27], with the RPA vacuum ap- and the RPA eigenvalues ω ν is given by,…”

Section: Outline Of the Ucom Random-phase Approximationmentioning

confidence: 99%

“…[ 27,28,29,30,31,32,33,34,35,36]), but also in studies of exotic nuclear structure of collective excitations in nuclei away from the valley of β-stability [37,38,39,40,41,42,43,44,45]. In the present study, correlated realistic NN interactions are employed for the first time to investigate collective excitations in both light and heavy closed-shell nuclear systems.…”

Section: Introductionmentioning

confidence: 99%

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Collective multipole excitations based on correlated realistic nucleon-nucleon interactions

et al. 2006

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We investigate collective multipole excitations for closed shell nuclei from 16 O to 208 Pb using correlated realistic nucleon-nucleon interactions in the framework of the random phase approximation (RPA). The dominant short-range central and tensor correlations are treated explicitly within the Unitary Correlation Operator Method (UCOM), which provides a phase-shift equivalent correlated interaction V UCOM adapted to simple uncorrelated Hilbert spaces. The same unitary transformation that defines the correlated interaction is used to derive correlated transition operators. Using V UCOM we solve the Hartree-Fock problem and employ the single-particle states as starting point for the RPA. By construction, the UCOM-RPA is fully self-consistent, i.e. the same correlated nucleon-nucleon interaction is used in calculations of the HF ground state and in the residual RPA interaction. Consequently, the spurious state associated with the center-ofmass motion is properly removed and the sum-rules are exhausted within ±3%. The UCOM-RPA scheme results in a collective character of giant monopole, dipole, and quadrupole resonances in closed-shell nuclei across the nuclear chart. For the isoscalar giant monopole resonance, the resonance energies are in agreement with experiment hinting at a reasonable compressibility. However, in the 1 − and 2 + channels the resonance energies are overestimated due to missing long-range correlations and three-body contributions.

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Section: Outline Of the Ucom Random-phase Approximationmentioning

confidence: 99%

“…6, the isoscalar monopole and quadrupole responses in 16 O are displayed for the two cases: (i) with the bare multipole operators (27), (28) (Fig. 6).…”

Section: The Role Of Correlated Multipole Transition Operatorsmentioning

confidence: 99%

“…One of the standard approaches to derive RPA is the equation of motion method using the quasiboson approximation [27], with the RPA vacuum ap- and the RPA eigenvalues ω ν is given by,…”

Section: Outline Of the Ucom Random-phase Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Collective multipole excitations based on correlated realistic nucleon-nucleon interactions

et al. 2006

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“…This paper presents a computationally tractable version of the standard Bohr-Mottelson (BM) collective model [1,2,3]. The need for such a version of the model arises because the expansion of rotational wave functions in a spherical vibrational basis is so slowly convergent that the diagonalization of a general coupled-rotor-vibrator collective model Hamiltonian in this basis is virtually impossible.…”

Section: Introductionmentioning

confidence: 99%

A computationally tractable version of the collective model

2004

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A computationally tractable version of the Bohr-Mottelson collective model is presented which makes it possible to diagonalize realistic collective models and obtain convergent results in relatively small appropriately chosen subspaces of the collective model Hilbert space. Special features of the proposed model is that it makes use of the beta wave functions given analytically by the softened-beta version of the Wilets-Jean model, proposed by Elliott et al., and a simple algorithm for computing SO(5) ⊃ SO(3) spherical harmonics. The latter has much in common with the methods of Chacon, Moshinsky, and Sharp but is conceptually and computationally simpler. Results are presented for collective models ranging from the sherical vibrator to the Wilets-Jean and axially symmetric rotor-vibrator models.

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Valence States of BeO Feynman's Way

Sorensen¹,

England²

2000

Int. J. Quant. Chem.

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Energy curves are computed by adding a second‐order Feynman diagram to a zero of energy. Third order confirms the goodness of second order. The zero of energy includes charge transfer and polarization. It is an average of a limited configuration‐mixing model. Evaluation of diagrams requires one set of model orbitals for all valence states, one set of probability amplitudes for all valence states, and two parameters for each valence state. Parameters are evaluated with the zero of energy. Spectroscopic constants and excitation and dissociation energies approach limits of the chosen basis set. Average (maximum) errors between second order and experiment for X, a, A, and B are 0.9 (2.1) pm for Re; 17 (31) kJ/mol for De; 2 (6) kJ/mol for Te; 35 (45) cm−1 for ωe; and 9 (21) kJ/mol for T∞. Frequencies and bond distances for C do not match any calculated for a single state. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 259–279, 2000

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Nuclear Collective Motion: Models and Theory

Cited by 143 publications

References 0 publications

Collective multipole excitations based on correlated realistic nucleon-nucleon interactions

Collective multipole excitations based on correlated realistic nucleon-nucleon interactions

A computationally tractable version of the collective model

Valence States of BeO Feynman's Way

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