An approximate projection technique for the calculation of electromagnetic properties of deformed nuclei

Islam, Shareeful; Mang, H.J.; Ring, P.

doi:10.1016/0375-9474(79)90373-7

Cited by 40 publications

(30 citation statements)

References 13 publications

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“…Using (3.23) an integration over , gives the first-order periodic approximation for the overlap: 26) where I 0 is the modified Bessel function of first kind and zero order. To obtain this formula we have also assumed that the second cumulant is larger than half the absolute value of the third.…”

Section: M=1-periodic Approximationmentioning

confidence: 99%

“…However, the classical nature of the description of rotational properties inherent to this description is sometimes a weak point in angular momentum regions where quantum fluctuations play an important role [24,25]. In axially symmetric deformed systems, this problem can be overcome by the VAP method which defines the wave-function of the quantum states as a superposition of the energetically degenerate states with different orientation and extracts from the intrinsic wave-packet sates with a given angular momentum [26]. For a triaxial deformed system, the VAP must be extended to account for the non Abelian structure of the SU2 group.…”

Section: Introductionmentioning

confidence: 99%

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On the Restoration of Symmetry in Paired Fermion Systems

Flocard

Onishi

1997

Annals of Physics

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Section: M=1-periodic Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Restoration of Symmetry in Paired Fermion Systems

Flocard

Onishi

1997

Annals of Physics

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“…Since cranking states are not eigenstates of angular momentum, it is not straightforward to determine transition rates in nuclei which are not very well deformed. To overcome this difficulty, approximations [6][7][8] have been developed for transitions within a band. However, they are only valid when the structure of the nuclear states are not affected by rotation, i.e.…”

Section: Introductionmentioning

confidence: 99%

Configuration mixing of mean-field wave functions projected on angular momentum and particle number: Application to Mg

Valor¹,

Heenen²,

Bonche³

2000

Nuclear Physics A

113

148

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We present in this paper the general framework of a method which permits to restore the rotational and particle number symmetries of wave functions obtained in Skyrme HF+BCS calculations. This restoration is nothing but a projection of mean-field intrinsic wave functions onto good particle number and good angular momentum. The method allows also to mix projected wave functions. Such a configuration mixing is discussed for sets of HF+BCS intrinsic states generated in constrained calculations with suitable collective variables. This procedure gives collective states which are eigenstates of the particle number and the angular momentum operators and between which transition probabilities are calculated. An application to 24 Mg is presented, with mean-field wave functions generated by axial quadrupole constraints. Theoretical spectra and transition probabilities are compared to the experiment.

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“…The naive GOA takes F (θ) = θ 2 , which was proposed in early papers on the subject [22,23]. Another form suggested in ref.…”

Section: Angular Projectionmentioning

confidence: 99%

“…In our case here, the wave functions are invariant under time reversal and have additional rotational symmetries as well. With quadrupolar amplitudes to be rotated, a form having the correct limit for small deformations is [23] …”

Section: Angular Projectionmentioning

confidence: 99%

Correlation energies by the generator coordinate method: Computational aspects for quadrupolar deformations

2004

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We investigate truncation schemes to reduce the computational cost of calculating correlations by the generator coordinate method based on mean-field wave functions. As our test nuclei, we take examples for which accurate calculations are available. These include a strongly deformed nucleus, 156 Sm, a nucleus with strong pairing, 120 Sn, the krypton isotope chain which contains examples of soft deformations, and the lead isotope chain which includes the doubly magic 208 Pb. We find that the Gaussian overlap approximation for angular momentum projection is effective and reduces the computational cost by an order of magnitude. Cost savings in the deformation degrees of freedom are harder to realize. A straightforward Gaussian overlap approximation can be applied rather reliably to angular-momentum projected states based on configuration sets having the same sign deformation (prolate or oblate), but matrix elements between prolate and oblate deformations must be treated with more care. We propose a two-dimensional GOA using a triangulation procedure to treat the general case with both kinds of deformation. With the computational gains from these approximations, it should be feasible to carry out a systematic calculation of correlation energies for the nuclear mass table.

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An approximate projection technique for the calculation of electromagnetic properties of deformed nuclei

Cited by 40 publications

References 13 publications

On the Restoration of Symmetry in Paired Fermion Systems

On the Restoration of Symmetry in Paired Fermion Systems

Configuration mixing of mean-field wave functions projected on angular momentum and particle number: Application to Mg

Correlation energies by the generator coordinate method: Computational aspects for quadrupolar deformations

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