The many-nucleon theory of nuclear collective structure and its macroscopic limits: an algebraic perspective

Rowe, D.J.; McCoy, Anna E.; Caprio, M. A.

doi:10.1088/0031-8949/91/3/033003

Cited by 20 publications

(22 citation statements)

References 151 publications

(357 reference statements)

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“…As argued in sections 2.3.3 and 2.3.6, bases built on particlehole type expansions are not ideally suited to the description of collective correlations. The SA-NCSM [139] instead uses irreducible representations of SU (3) or Sp (3, ), the dynamical symmetry groups of collective models [263], to achieve a much more efficient description of collective behavior in nuclei. This is illustrated for the case of 20 Ne in Figure 14.…”

Section: Emergence Of Empirical Nuclear Structure Models From Ab Initmentioning

confidence: 99%

A Guided Tour of ab initio Nuclear Many-Body Theory

2020

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Over the last decade, new developments in Similarity Renormalization Group techniques and nuclear many-body methods have dramatically increased the capabilities of ab initio nuclear structure and reaction theory. Ground and excited-state properties can be computed up to the tin region, and from the proton to the presumptive neutron drip lines, providing unprecedented opportunities to confront two-plus three-nucleon interactions from chiral Effective Field Theory with experimental data. In this contribution, I will give a broad survey of the current status of nuclear many-body approaches, and I will use selected results to discuss both achievements and open issues that need to be addressed in the coming decade.

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Section: Emergence Of Empirical Nuclear Structure Models From Ab Initmentioning

confidence: 99%

A Guided Tour of ab initio Nuclear Many-Body Theory

2020

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“…The dynamical symmetry relationship between the bands is suggestive of an emerging physical structure. In the contraction limit, obtained for large values of the quantum numbers, the microscopic symplectic picture gives way to a collective interpretation of the dynamics in terms of effective coupled rotational and vibrational (giant resonance) degrees of freedom [40,41,81,82].…”

Section: Dynamical Symmetry Structurementioning

confidence: 99%

Probing ab initio emergence of nuclear rotation

et al. 2020

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Structural phenomena in nuclei, from shell structure and clustering to superfluidity and collective rotations and vibrations, reflect emergent degrees of freedom. Ab initio theory describes nuclei directly from a fully microscopic formulation. We can therefore look to ab initio theory as a means of exploring the emergence of effective degrees of freedom in nuclei. For the illustrative case of emergent rotational bands in the Be isotopes, we establish an understanding of the underlying oscillator space and angular momentum (orbital and spin) structure. We consider no-core configuration interaction (NCCI) calculations for 7,9,11 Be with the Dae-jeon16 internucleon interaction. Although shell model or rotational degrees of freedom are not assumed in the ab initio theory, the NCCI results are suggestive of the emergence of effective shell model degrees of freedom (0 ω and 2 ω excitations) and LS-scheme rotational degrees of freedom, consistent with an Elliott-Wilsdon SU(3) description. These results provide some basic insight into the connection between emergent effective collective rotational and shell model degrees of freedom in these light nuclei and the underlying ab initio microscopic description. arXiv:1912.00083v1 [nucl-th]

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“…Partially-coherent state representations, related to VCS representations, were also introduced for this purpose by Deenen and Quesne [23]. A recent review of the applications of VCS theory in nuclear physics can be found in [24]. Classes of vector coherent states, for which there is a resolution of the identity, have been considered more recently by Ali and others [25][26][27] but not, as far as we are aware, for the construction of Lie group or Lie algebra representations.…”

Section: Introductionmentioning

confidence: 99%

Dual Pairs of Holomorphic Representations of Lie Groups from a Vector-Coherent-State Perspective

Rowe

Repka

2016

Symmetry

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It is shown that, for both compact and non-compact Lie groups, vector-coherent-state methods provide straightforward derivations of holomorphic representations on symmetric spaces. Complementary vector-coherent-state methods are introduced to derive pairs of holomorphic representations which are bi-orthogonal duals of each other with respect to a simple Bargmann inner product. It is then shown that the dual of a standard holomorphic representation has an integral expression for its inner product, with a Bargmann measure and a simply-defined kernel, which is not restricted to discrete-series representations. Dual pairs of holomorphic representations also provide practical ways to construct orthonormal bases for unitary irreps which bypass the need for evaluating the integral expressions for their inner products. This leads to practical algorithms for the application of holomorphic representations to model problems with dynamical symmetries in physics.

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The many-nucleon theory of nuclear collective structure and its macroscopic limits: an algebraic perspective

Cited by 20 publications

References 151 publications

A Guided Tour of ab initio Nuclear Many-Body Theory

A Guided Tour of ab initio Nuclear Many-Body Theory

Probing ab initio emergence of nuclear rotation

Dual Pairs of Holomorphic Representations of Lie Groups from a Vector-Coherent-State Perspective

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