Construction of<i>SU</i>(3) irreps in canonical<i>SO</i>(3)-coupled bases

Rowe, D.J.; Thiamová, G.

doi:10.1088/1751-8113/41/6/065206

Cited by 4 publications

(9 citation statements)

References 18 publications

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“…Rosensteel, Leschber and colleagues [123,127] suggested that the SU(3) states of the corresponding pairs should be eigenstates of some linear combination of the SO(3)-invariant operators [ L ⊗ Q2 ⊗ L] 0 and [ L⊗[ Q⊗ Q] 2 ⊗ L] 0 . This proved to be correct [128] and, as this section shows, gives useful canonical SO(3)coupled bases for irreducible SU(3) representations with extraordinarily good K quantum numbers.…”

Section: B the K Quantum Numbermentioning

confidence: 73%

“…(A similar comparison of such matrix elements for (32 5) and (10 4) representations was given in Ref. [128].) that is diagonal in a U(3)-coupled basis for the representation, z∇ is a tensor with components (z∇…”

Section: Representations Of Sp(3 R) In a U(3) Basismentioning

confidence: 77%

“…It has been shown [128] that rotor model states with good K quantum numbers and for which the intrinsic quadrupole moments take the constant K-independent values…”

Section: B the K Quantum Numbermentioning

confidence: 99%

“…Λ is a U(3) scalar operator 5) and (10 4) representations was given in Ref. [128].) that is diagonal in a U(3)-coupled basis for the representation, z∇ is a tensor with components (z∇) ij = k z ik ∇ kj and z · ∇ = i (z∇) ii .…”

Section: Representations Of Sp(3 R) In a U(3) Basismentioning

confidence: 99%

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

2016

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The nuclear collective models introduced by Bohr, Mottelson and Rainwater, together with the Mayer-Jensen shell model, have provided the central framework for the development of nuclear physics. This paper reviews the microscopic evolution of the collective models and their underlying foundations. In particular, it is shown that the Bohr-Mottelson models have expressions as macroscopic limits of microscopic models that have precisely-defined expressions in many-nucleon quantum mechanics. Understanding collective models in this way is especially useful because it enables the analysis of nuclear properties in terms of them to be revisited and reassessed in the light of their microscopic foundations.

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Section: B the K Quantum Numbermentioning

confidence: 73%

Section: Representations Of Sp(3 R) In a U(3) Basismentioning

confidence: 77%

“…It has been shown [128] that rotor model states with good K quantum numbers and for which the intrinsic quadrupole moments take the constant K-independent values…”

Section: B the K Quantum Numbermentioning

confidence: 99%

Section: Representations Of Sp(3 R) In a U(3) Basismentioning

confidence: 99%

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

2016

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“…The adjustment of the inner product to that of a finite-dimensional SU(3) irrep is straightforward [235,236], but has the result that K is no longer a precise integer-valued quantum number. Nevertheless, it transpires that an orthonormal SO(3) basis for an SU(3) irrep can be defined [237] as eigenstates of a linear combination of SO(3)-invariant operators that have expectation values of K that take integer values to an extraordinarily high degree of accuracy.…”

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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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Permutation-symmetric three-particle hyper-spherical harmonics based on the S 3 ⊗ SO (3) rot ⊂ O (2)⊗ SO (3) rot ⊂ U (3)⋊ S 2 ⊂ O (6) subgroup chain

Salom

Dmitrašinović

2017

Nuclear Physics B

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Construction ofSU(3) irreps in canonicalSO(3)-coupled bases

Cited by 4 publications

References 18 publications

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

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

The evolving many-nucleon theory of nuclear rotations

Permutation-symmetric three-particle hyper-spherical harmonics based on the S 3 ⊗ SO (3) rot ⊂ O (2)⊗ SO (3) rot ⊂ U (3)⋊ S 2 ⊂ O (6) subgroup chain

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