Boson expansions and broken symmetry

Marshalek, E.R.

doi:10.1016/0003-4916(82)90219-6

Cited by 18 publications

(19 citation statements)

References 17 publications

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“…It is rotationally invariant but breaks the particle-number conservations, and is given by 4 -11) where lisho describes the single-particle Hamiltonian based on the spherical harmonic oscillator,*) (4)(5)(6)(7)(8)(9)(10)(11)(12) with C Z and C k being the nucleon creation and annihilation operators of the singleparticle state k of the oscillator, respectively. For simplifying the problem, two major shells are used for the calculation, i.e., Nosc=4 and 5 for the proton and Nosc=5 and 6 for the neutron.…”

Section: Numerical Calculations For Er Isotopesmentioning

confidence: 99%

“…The classical image is directly obtained by means of the time-dependent Hartree-Fock (TDHF) theory in the canonical-variable representation. 3 ),15), 16) The basic equation of the TDHF theory is (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15) where the time-dependent Slater determinant I¢(t» is given by (2 °16) with I¢o) being the deformed Hartree-Fock stationary solution. Instead of the variables {f;;(t), !ai(t)}, we introduce a new set of variables {Cti, Cai} through a variable transformation (2 °17) The symplectic structure of the TDHF theory3) always enables us to choose the variables {Cti, CaJ to be of the canonical-variable representation, in which the TDHF equation (2 °15) can be expressed as the canonical equations of motion in classical mechanics,…”

Section: Classical Image Of Boson Representation By Time-dependent Hamentioning

confidence: 99%

“…In solving the basic equations of the see method derived from the two conditions, we (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12) is determined by the see method, as well as the collective rotational Hamiltonian (2 -14) Once the lowest rank relations (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) and the collective Hamiltonian …”

Section: (2·10)mentioning

confidence: 99%

“…The terms i-sand P in Eq. (4 -11) are the conventional one-body operators defined by (4)(5)(6)(7)(8)(9)(10)(11)(12)(13) where i and s are the single-particle orbital angular momentum and its spin, respectively, and < P>Nosc=Nosc(Nosc+3)/2 is the expectation value of P averaged over each major shell with a definite value of Nose. The quantities QM(M=O, ±1, ±2), j\(r=p, n) and Nr are the quadrupole operators, the conventional monopole pair-operators and the number operators for the proton (p) and the neutron (n), respectively.…”

Section: Numerical Calculations For Er Isotopesmentioning

confidence: 99%

“….9[coll(J) are determined by the see method, the higher rank relations of Eq (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13). and .9[[n J (/3t, /3, J) in Eq (2)(3)(4)(5)(6)(7)(8)(9).…”

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Microscopic Description of Nuclear Collective Rotation by Means of the Self-Consistent Collective Coordinate Method: Occurrence Mechanism of Collective Rotation

Terasaki

Marumori

Sakata

1991

Progress of Theoretical Physics

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1235On the basis of the concept of spontaneous breakdown of the rotation symmetry in the deformed Hartree-Fock-Bogoliubov minimum as the origin of the nuclear collective rotation, the self-consistent collective coordinate (See) method is applied to disclosing occurrence mechanism of the coHective rotation. Through the intermediary of the see method, a manifest relationship between Marshalek and Weneser's full quantum theory of rotational .motion and the conventional cranking model approach is given.In order to reveal how the so-called rotation-vibration coupling effects are coherently organized so as to construct a global optimum subspace of collective rotation, a set of basic equations of the see method is solved for the low-spin ground-state rotational bands of Er isotopes. Systematic features of microscopic structure of rotation-vibration couplings are investigated in detail. § 1. IntroductionIn accordance with rapidly expanding experimental observations on nuclear collective phenomena, in the past decades it has become an inevitable theoretical subject to develop a microscopic theory of nuclear collective dynamics which enables us to describe global aspects of collectivity, e. g., occurrence, persistency, transfiguration, dissipation and termination of collective modes of motion.Since the nucleus is an isolated finite many-body quantum system in which the self-consistent mean field is realized, the collective modes of motion (associated with time evolution of the mean field) are of large amplitude and highly involved with non-collective (intrinsic) modes of motion in a strong self-consistent way_ Thus, the first task toward the microscopic theory of nuclear collective dynamics is to define an optimum "global" collective subspace and "global" collective variables specifying the subspace. The self-consistent collective coordinate (See) method 1 ),2) has been proposed for this purpose_ When once the optimum collective subspace is properly determined by the see method, the intrinsic modes of motion can be precisely defined in a compatible way with the see method_ 3 ) Thus, the whole nuclear dynamics is optimally described in terms of the collective and intrinsic modes of motion. 4 ) The transfiguration and dissipation of the collective modes are then described as results due to couplings with the intrinsic modes_ 4 ),5)The abOve scenario for the nuclear collective dynamics has been so far formulated, step by step (as INS-TSUKUBA joint research project on a large-amplitude collective motion), by examining its applicability in each step with the employment of simple numerically-solvable models.This is the first one of a series of papers with the purpose of applying the new microscopic theory in describing various phenomena associated with the nuclear

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Section: Numerical Calculations For Er Isotopesmentioning

confidence: 99%

Section: Classical Image Of Boson Representation By Time-dependent Hamentioning

confidence: 99%

Section: (2·10)mentioning

confidence: 99%

Section: Numerical Calculations For Er Isotopesmentioning

confidence: 99%

“….9[coll(J) are determined by the see method, the higher rank relations of Eq (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13). and .9[[n J (/3t, /3, J) in Eq (2)(3)(4)(5)(6)(7)(8)(9).…”

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confidence: 99%

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