Three-dimensional angular momentum projection in relativistic mean-field theory

Yao, J. M.; Meng, J.; Ring, P.; Arteaga, Daniel

doi:10.1103/physrevc.79.044312

Cited by 109 publications

(130 citation statements)

References 110 publications

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“…This triaxiality in VAP-JTA, in comparison with VAP-TA, is likely caused by the spin projection. Nuclear triaxiality caused by the spin projection has been previously discussed by several authors [16][17][18][23][24][25]. To determine if this phenomenon is more general, we performed systematic VAP calculations for a larger number of even-even sd-shell nuclei.…”

Section: The Vap Methodsmentioning

confidence: 99%

Variation after projection with a triaxially deformed nuclear mean field

2015

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We implemented a variation after projection (VAP) algorithm based on a triaxially deformed Hartree-Fock-Bogoliubov vacuum state. This is the first projected mean field study that includes all the quantum numbers (except parity), i.e., spin (J), isospin (T ) and mass number (A). Systematic VAP calculations with JT A-projection have been performed for the even-even sd-shell nuclei with the USDB Hamiltonian. All the VAP ground state energies are within 500 keV above the exact shell model values. Our VAP calculations show that the spin projection has two important effects: (1) the spin projection is crucial in achieving good approximation of the full shell model calculation.(2) the intrinsic shapes of the VAP wavefunctions with spin projection are always triaxial, while the Hartree-Fock-Bogoliubov methods likely provide axial intrinsic shapes. Finally, our analysis suggests that one may not be possible to associate an intrinsic shape to an exact shell model wave function.

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Section: The Vap Methodsmentioning

confidence: 99%

Variation after projection with a triaxially deformed nuclear mean field

2015

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“…To disentangle those contributions and reduce, in this way, the computational cost of the evaluation of the norm it is convenient to consider the limit of fully empty levels. This limit was considered by other authors [11][12][13][14] in the past but in the more traditional formulation of the overlap not including the phase. In the limit of fully empty levels the evaluation of the overlap can be recast in terms of matrices with dimensionality equal to the number of orbitals with nonzero occupancy.…”

Section: B Limit Of Fully Empty Levelsmentioning

confidence: 99%

“…The relevance of the present formulation is a direct consequence of the increasing popularity of the so-called "beyond mean-field methods" in nuclear physics [12,[19][20][21][22][23] that demand the evaluation of both the modulus and phase of the overlaps between arbitrary HFB wave functions. A reliable determination of the sign of the norm can also be useful in to order to pin down the location of the zeros of the HFB overlaps [24].…”

Section: Introductionmentioning

confidence: 99%

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Technical aspects of the evaluation of the overlap of Hartree-Fock-Bogoliubov wave functions

Robledo

2011

Phys. Rev. C

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Several technical aspects concerning the evaluation of the overlap between two mean-field wave functions of the Hartree-Fock-Bogoliubov type are discussed. The limit when several orbitals become fully occupied is derived as well as the formula to reduce the dimensionality of the problem when exactly empty orbitals are present. The formalism is also extended to deal with different bases for each of the wave functions. Several practical results concerning the evaluation of pfaffians, as well as the canonical decomposition of norm overlaps, are also discussed in the Appendices.

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“…One of them is the restoration of rotational symmetry broken by the time-odd fields at mean-field level. A significant progress has been made in the implementation of angular momentum projection based on the RMF approaches [62][63][64][65][66] in the past decade. Due to the numerical complexity, these implementations are currently restricted to even-even nuclei.…”

Section: Nuclear Magnetic Moments From Covariant Density Functional Tmentioning

confidence: 99%

Recent progress in theoretical studies of nuclear magnetic moments

Zhao

2012

Chin. Sci. Bull.

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Nuclear magnetic moment is highly sensitive to the underlying structure of atomic nuclei and therefore serves as a stringent test of nuclear models. The advanced nuclear structure models have been successful in analyzing many nuclear structure properties, but they still cannot provide a satisfactory description of nuclear magnetic moments. Recently attempts to summarize the present understanding on nuclear magnetic moments in both relativistic and non-relativistic theoretical models have been made. The detailed contents are covered in the issue entitled "Nuclear magnetic moments and related topics" (in Sci China Phys Mech Astron, Vol. 54, No. 2, 2011). In this paper some of the related achievements will be highlighted. nuclear magnetic moments, status and progress, relativistic and non-relativistic many-body models Citation: Zhao E G. Recent progress in theoretical studies of nuclear magnetic moments. Chin Sci Bull, 2012Bull, , 57: 4394-4399, doi: 10.1007 Nuclear magnetic moment is an important physical observable that reflects the interplay between collective and singleparticle degrees of freedom in atomic nuclei. It therefore provides a stringent test of various nuclear structure models. A concise but interesting history and present understanding of nuclear magnetic moments have been provided in [1].Since the successes of the nuclear shell model established in 1949 by Mayer and Jensen for the explanation of the magic numbers (Z or N = 2, 8, 20, 28, 50, 82, . . . ), the understanding of the magnetic moment of an odd-A nucleus has been done in the extreme single-particle picture which leads to the well known Schmidt values [2]. It was observed in the early 1950s [3], however, that almost all nuclear magnetic moments are sandwiched between the two Schmidt lines.The pion, predicted by Yukawa in 1935, and discovered experimentally by Powell in 1947, was pointed out to be very important for understanding nuclear magnetic moments by Miyazawa in 1951 [4] and by Villars in 1952 [5] via the one-pion exchange currents, which can be understood as a medium correction in comparison with the free nuclear magnetic moments. Besides the pion effect, the first-order configuration mixing was pointed out to be also important in the email: egzhao@mail.itp.ac.cn odd-A nuclei with a j j-closed core by Arima and Horie in 1954 [6,7]. This effect is also called the first-order core polarization or Arima-Horie effect. However, for the nuclei with a LS -closed core ± 1 nucleon, the first-order configuration mixing does not contribute to nuclear magnetic moments. In order to understand the difference between Schmidt values and experiment data in this type of nuclei, it was realized that one has to take into account the second-order configuration mixing, which is also called the tensor correlation. The isoscalar magnetic moments provide us the best evidence of the tensor correlations. There were also lots of discussion on whether the Δ-hole mixing can explain the magnetic moments [8][9][10].In the past decades, covariant density functio...

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Three-dimensional angular momentum projection in relativistic mean-field theory

Cited by 109 publications

References 110 publications

Variation after projection with a triaxially deformed nuclear mean field

Variation after projection with a triaxially deformed nuclear mean field

Technical aspects of the evaluation of the overlap of Hartree-Fock-Bogoliubov wave functions

Recent progress in theoretical studies of nuclear magnetic moments

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