Projection onto physical boson states in a collective subspace

Dobaczewski, J.; Geyer, H.B.; Hahne, F.J.W.

doi:10.1103/physrevc.44.1030

Cited by 19 publications

(37 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As shown in Refs. [10,9], the R projection of a spurious state gives zero, namely, &~4 spur) (3.8) where [ @, p"r) is the state conjugate to a spurious bracalculations.…”

Section: The Monopole Pairing Interaction In the Neutron Configurmentioning

confidence: 99%

“…This method of identifying spurious states becomes impracticable when physical and spurious states lie close together, and especially so when one wants to do several calculations in order to move through parameter space in search for a fit to experimental data. We now implement two simpler methods which have been discussed recently [6,9].…”

Section: The Monopole Pairing Interaction In the Neutron Configurmentioning

confidence: 99%

“…[9), is referred to as R projection. It amounts to replacing each boson creation operator appearing in a particular eigenstate by the boson image in which that boson operator appears as the leading order term, e. g., BP: (SP+)zi --BP(A -Np -Ny) -B~B~B".…”

Section: The Monopole Pairing Interaction In the Neutron Configurmentioning

confidence: 99%

See 2 more Smart Citations

Boson analyses in the Ge isotopes

et al. 1994

Self Cite

View full text Add to dashboard Cite

The strong variation in energy of the first excited 0 state in the even-even Ge isotopes is investigated with pairing type interactions in various model spaces. Although it had been possible in previous work to describe this variation in a BCS ra-ndom ph-ase ap-proximation (RPA) calculation in the neutron configuration only, the corresponding exact diagonalization disagrees with the BCS-RPA results and experixnent. It is furthermore shown that the behavior of the Qrst excited 0+ state cannot be obtained by a reasonable variation of parameters in the exact neutron pair calculations. This suggests that the model space be enlarged to include proton, neutron, and proton-neutron pairing. The construction of the corresponding basis is then simplified by performing a boson mapping and employing the ideal collective boson basis. This, however, may lead to the occurrence of spurious states, even at fairly low energies, and three separate methods by means of which they can be identified are discussed. Although the enlarged model space gives a desired lowering of excitation energy of the first excited 0+ states in an exact diagonalization, the strong experimental variation could not be achieved with this simple interaction. Nevertheless, the analysis yields further and new insight into applications of boson mappings, specifically about how and when spurious states may be identified in calculations which are performed in a truncated space not invariant under a given collective algebra.PACS number(s): 21.60. -n, 27.50.+e

show abstract

“…As shown in Refs. [10,9], the R projection of a spurious state gives zero, namely, &~4 spur) (3.8) where [ @, p"r) is the state conjugate to a spurious bracalculations.…”

Section: The Monopole Pairing Interaction In the Neutron Configurmentioning

confidence: 99%

Section: The Monopole Pairing Interaction In the Neutron Configurmentioning

confidence: 99%

See 1 more Smart Citation

Boson analyses in the Ge isotopes

et al. 1994

Self Cite

View full text Add to dashboard Cite

show abstract

“…These compact forms are useful for formal manipulation. Furthermore they have the powerful property of exactly expressing the fermion matrix elements under any truncation, a fact not previously appreciated in the literature even for the norm operator [17]. By this we mean the following: suppose we truncate our fermion Fock space to states constructed from a restricted set of pairs {σ}.…”

Section: Boson Representations Of Fermion Matrix Elementsmentioning

confidence: 99%

“…The norm operator can be conveniently and compactly expressed [17,15,18] in terms of the kth order Casimir operators of the unitary group SU(2Ω),Ĉ k = 2 k tr (P)…”

Section: Boson Representations Of Fermion Matrix Elementsmentioning

confidence: 99%

Fermion to boson mappings revisited

Ginocchio

Johnson

1996

Physics Reports

View full text Add to dashboard Cite

We briefly review various mappings of fermion pairs to bosons, including those based on mapping operators, such as Belyaev-Zelevinskii, and those on mapping states, such as Marumori; in particular we consider the work of Otsuka-Arima-Iachello, aimed at deriving the Interacting Boson Model. We then give a rigorous and unified description of state-mapping procedures which allows one to systematically go beyond Otsuka-Arima-Iachello and related approaches, along with several exact results.

show abstract

SDG Fermion-Pair Algebraic SO(12) and Sp(10) Models and Their Boson Realizations

et al. 1995

Self Cite

View full text Add to dashboard Cite

It is shown how the boson mapping formalism may be applied as a useful manybody tool to solve a fermion problem. This is done in the context of generalized Ginocchio models for which we introduce S-, D-, and G-pairs of fermions and subsequently construct the sdg-boson realizations of the generalized Dyson type. The constructed SO(12) and Sp(10) fermion models are solved beyond the explicit symmetry limits. Phase transitions to rotational structures are obtained, also in situations where there is no underlying SU(3) symmetry. * On leave of absence from the Institute of Nuclear Physics, Czech Academy of Sciences,Řež near Prague, Czech Republic

show abstract

Projection onto physical boson states in a collective subspace

Cited by 19 publications

References 26 publications

Boson analyses in the Ge isotopes

Boson analyses in the Ge isotopes

Fermion to boson mappings revisited

SDG Fermion-Pair Algebraic SO(12) and Sp(10) Models and Their Boson Realizations

Contact Info

Product

Resources

About