Theoretical approaches to many-body perturbation theory and the challenges

Barrett, B. R.

doi:10.1088/0954-3899/31/8/013

Cited by 2 publications

(3 citation statements)

References 53 publications

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“…Distribution of the non-analogue Fermi strength, as experimentally measured recently in 62 Ga [105], can shed light on the mixing matrix elements to cross-check the theory.…”

Section: Isospin-forbidden β-Decaymentioning

confidence: 81%

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Isospin-Symmetry Breaking within the Nuclear Shell Model: Present Status and Developments

Smirnova

2023

Physics

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The paper reviews the recent progress in the description of isospin-symmetry breaking within the nuclear shell model and applications to actual problems related to the structure and decay of exotic neutron-deficient nuclei and nuclei along the N=Z line, where N is the neutron number and Z the atomic number. The review recalls the fundamentals of the isospin formalism for two-nucleon and many-nucleon systems, including quantum numbers, the spectrum’s structure and selection rules for weak and electromagnetic transitions; and at the end, summarizes experimental signatures of isospin-symmetry breaking effects, which motivated efforts towards the creation of a relevant theoretical framework to describe those phenomena. The main approaches to construct accurate isospin-nonconserving Hamiltonians within the shell model are briefly described and recent advances in the description of the structure and (isospin-forbidden) decay modes of neutron-deficient nuclei are highlighted. The paper reviews major implications of the developed theoretical tools to (i) the fundamental interaction studies on nuclear decays and (ii) the estimation of the rates of nuclear reactions that are important for nuclear astrophysics. The shell model is shown to be one of the most suitable approaches to describing isospin-symmetry breaking in nuclear states at low energies. Further efforts in extending and refining the description to larger model spaces, and in developing first-principle theories to deal with isospin-symmetry breaking in many-nucleon systems, seem to be indispensable steps towards our better understanding of nuclear properties in the precision era.

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“…Distribution of the non-analogue Fermi strength, as experimentally measured recently in 62 Ga [105], can shed light on the mixing matrix elements to cross-check the theory.…”

Section: Isospin-forbidden β-Decaymentioning

confidence: 81%

“…This feature was ascribed to missing 3N forces. In addition, a number of theoretical issues in application of many-body perturbation theory to nuclear effective interaction problem have been raised regarding convergence of the expansion [62], which have not convincingly been answered yet.…”

Section: Formalismmentioning

confidence: 99%

Isospin-Symmetry Breaking within the Nuclear Shell Model: Present Status and Developments

Smirnova

2023

Physics

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“…The following will show that the relationships between AMF theory and the representation of a Lie algebra with a lowest-(and/or highest-) weight state makes it possible to take advantage of the complementary contributions of two major approaches to nuclear structure theory: mean-field theory and algebraic modelling. Mean-field theory [205] is well known to be of fundamental importance in establishing the foundations of many-body theory and the nuclear shell model [206]. The power of algebraic methods in exposing the dynamical content of a system is likewise recognised; e.g., in Elliott's SU(3) model [10], Kerman's quasi-spin model [207], the Lipkin model [208], the Interacting Boson Models [209], the algebraic version of the Bohr Model [152], and the other models discussed in Section VI.…”

Section: Algebraic Mean-field (Amf) Theorymentioning

confidence: 99%

The evolving many-nucleon theory of nuclear rotations

Rowe

2017

Preprint

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The many approaches that have been pursued in seeking an understanding of nuclear rotational dynamics are reviewed and reassessed with a view to their development in the light of recent progress and the research tools that are now available. A motivation for this review is the widespread observation of nuclear shape coexistence and sequences of rotational states in all regions of the nuclear periodic table combined with the recognition that the study of the rotational dynamics of quantum fluids has led to significant advances in the quantum theory of many-boson systems. Recent experimental investigations of the rotational dynamics of a low-temperature 6 Li gas indicate that its slow rotational flows are likewise the irrotational flows of a superfluid. In this context, the dynamics of rotating nuclei are of fundamental interest because the nucleus is a unique zero-temperature finite many-fermion quantum system. A promising approach is provided by algebraic mean-field theory which, as its name suggests, is a combination of algebraic and mean-field methods. Static meanfield theories play a central role in many-body theory by defining optimal independent-particle and independent quasi-particle basis states for the quantum mechanics of many-fermion systems. Their time-dependent extensions also lead, in the small-amplitude random-phase approximation, to the quantisation of the classical normal-mode vibrations of many-fermion systems about their static equilibrium states. This review shows that mean-field methods become significantly more powerful when combined with algebraic methods and an appropriate coupling scheme for the nuclear shell model.

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Theoretical approaches to many-body perturbation theory and the challenges

Cited by 2 publications

References 53 publications

Isospin-Symmetry Breaking within the Nuclear Shell Model: Present Status and Developments

Isospin-Symmetry Breaking within the Nuclear Shell Model: Present Status and Developments

The evolving many-nucleon theory of nuclear rotations

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