Microscopic derivation of a collective bosonic Hamiltonian with the generalized density matrix method

Jia, Lu; Zelevinsky, V. G.

doi:10.1103/physrevc.84.064311

Cited by 8 publications

(23 citation statements)

References 16 publications

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confidence: 99%

“…In compact form, there are only two equations, (14) and (23) in Ref. [1]. Results from the lowest orders give the well-known Hatree-Fock (HF) equations and random phase approximation (RPA).…”

mentioning

confidence: 99%

“…The GDM formulation with angular-momentum vector coupling has been considered in Ref [9]. The single particle (s.p.)…”

mentioning

confidence: 99%

“…Recently we proposed [1] a procedure based on the generalized density matrix (GDM) that was originally formulated in Refs. [5][6][7][8].…”

mentioning

confidence: 99%

“…[1], the GDM method fixes H b completely. In each even order (quadratic, quartic ...) in H b , the GDM method gives one constraint on Λ (mn) 's.…”

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confidence: 99%

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Validity of the generalized density matrix method for the microscopic calculation of a collective/bosonic Hamiltonian

Jia

Zelevinsky

2012

Phys. Rev. C

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Recently a procedure by generalized density matrix (GDM) is proposed [1] for calculating a collective/bosonic Hamiltonian microscopically from the shell-model Hamiltonian. In this work we examine the validity of the method by comparing the GDM results with that of the exact shellmodel diagonalization in a number of models. It is shown that the GDM method reproduces the low-lying collective states quite well, both for energies and transition rates, across the whole region going from vibrational to γ-unstable and deformed nuclei. It is a long-standing problem in nuclear physics to understand how macroscopic collective motion arises from microscopic single-particle motion. The shell-model (configuration interaction) successfully reproduces various collective behaviors by diagonalizing the nucleon Hamiltonian in a huge Slater-determinant basis. However, the dimension of the basis makes it impractical except for the cases with only a few valence nucleons. On the other hand, phenomenological bosonic approaches are often successful in fitting the experimental data (first of all the geometric Bohr Hamiltonian [2,3] and the interacting boson model [4]). This shows that, out of the huge Slater-determinant space, there exists a few degrees of freedom with a bosonic nature, which are usually enough in describing the collective states. Serious efforts were devoted to deriving those parameters of the bosonic Hamiltonian from the underlying shell-model Hamiltonian. However, the complete theory is still missing.Recently we proposed [1] a procedure based on the generalized density matrix (GDM) that was originally formulated in Refs. [5][6][7][8]. This procedure is rather simple, clean, and consistent. In compact form, there are only two equations, (14) and (23) in Ref. [1]. Results from the lowest orders give the well-known Hatree-Fock (HF) equations and random phase approximation (RPA). Higher orders fix the anharmonic terms in the collective/bosonic Hamiltonian. The aim of this work is to demonstrate the validity of the GDM method, by comparing its results with that of the exact shell-model diagonalization.In this work for simplicity we restrict ourselves to systems without rotational symmetry. The GDM formulation with angular-momentum vector coupling has been considered in Ref [9]. The single particle (s.p.) space in this work is drawn schematically in Fig. 1. There are two degenerate s.p. levels with energies e = ±1/2. The Fermi surface is in between, thus the lower levels are completely * Electronic address: jial@nscl.msu.edu filled and upper levels are empty. Each s.p. level has a quantum number m that is a half integer. Degenerate time-reversal pair has m with different sign, m1 = −m 1 . For fermions, |1 = −|1 , and we choose the phases such thatWe assume a two-body Hamiltonian,where f 12 = δ 12 e 1 , e 1 are the HF s.p. energies shown in Fig. 1. The density matrix ρ 12 = δ 12 n 1 , where the occupation number n 1 = 1(0) for the lower(upper) s.p. levels. N [a † 1 a † 2 a 3 a 4 ] is the normal-ordering form of operators. T...

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“…

…”

mentioning

confidence: 99%

mentioning

confidence: 99%

“…The GDM formulation with angular-momentum vector coupling has been considered in Ref [9]. The single particle (s.p.)…”

mentioning

confidence: 99%

“…Recently we proposed [1] a procedure based on the generalized density matrix (GDM) that was originally formulated in Refs. [5][6][7][8].…”

mentioning

confidence: 99%

“…[1], the GDM method fixes H b completely. In each even order (quadratic, quartic ...) in H b , the GDM method gives one constraint on Λ (mn) 's.…”

mentioning

confidence: 99%

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Validity of the generalized density matrix method for the microscopic calculation of a collective/bosonic Hamiltonian

Jia

Zelevinsky

2012

Phys. Rev. C

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Collective Modes

2017

Physics of Atomic Nuclei

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Examining a reduced jet-medium coupling in Pb+Pb collisions at the Large Hadron Collider

Betz

Gyulassy

2012

Phys. Rev. C

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Recent data on the nuclear modification factor RAA of jet fragments in 2.76 ATeV Pb+Pb collisions at the Large Hadron Collider (LHC) indicate that the jet-medium coupling in a Quark-Gluon Plasma (QGP) is reduced at LHC energies and not compatible with the coupling deduced from data at the Relativistic Hadron Collider (RHIC). We estimate the reduction factor from a combined fit to the available data on RAA( √ s, pT , b) and the elliptic flow v2( √ s, pT , b) at √ s = 0.2, 2.76 ATeV over a transverse momentum range pT ∼ 10 − 100 GeV and a broad impact parameter, b, range. We use a simple analytic "polytrop" model (dE/dx = −κE a x z T c ) to investigate the dynamical jet-energy loss model dependence. Varying a = 0 − 1 interpolates between weakly-coupled and strongly-coupled models of jet-energy dependence while z = 0 − 2 covers a wide range of possible jet-path dependencies from elastic and radiative to holographic string mechanisms. Our fit to LHC data indicates an approximate 60% reduction of the coupling κ from RHIC to LHC and excludes energy-loss models characterized by a jet-energy exponent with a > 1/3. In particular, the rapid rise of RAA with pT ≥ 10 GeV combined with the slow variation of the asymptotic v2(pT ) at the LHC rules out popular exponential geometric optics models (a = 1). The LHC data are compatible with 0 ≤ a ≤ 1/3 pQCD-like energy-loss models where the jet-medium coupling is reduced by approximately 10% between RHIC and LHC.

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Microscopic derivation of a collective bosonic Hamiltonian with the generalized density matrix method

Cited by 8 publications

References 16 publications

Validity of the generalized density matrix method for the microscopic calculation of a collective/bosonic Hamiltonian

Validity of the generalized density matrix method for the microscopic calculation of a collective/bosonic Hamiltonian

Collective Modes

Examining a reduced jet-medium coupling in Pb+Pb collisions at the Large Hadron Collider

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