Quadrupole-collective states in a large single-<i>j</i>shell

Burzyński, K.; Dobaczewski, J.

doi:10.1103/physrevc.51.1825

Cited by 23 publications

(31 citation statements)

References 44 publications

(73 reference statements)

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“…The key ingredient will be to find a (quasi-particle) basis that allows the computation of the energy kernel Φ 0 |H|Φ 1 / Φ 0 |Φ 1 in terms of the SWT instead of the commonly used GWT. The question if and how this is possible has been addressed already from various perspectives in the past [36,58,78,79].…”

Section: A Notation and Preliminary Discussionmentioning

confidence: 99%

“…First, E Note finally that the three-body terms should also be corrected for spurious self-interaction and self-pairing problems. Expressions equivalent to (58) and (59) can be derived without difficulty for three-body vertices (not shown here).…”

Section: B Correcting Higher-order Functionalsmentioning

confidence: 99%

“…omitting the density-dependent part of the Gogny interaction and keeping exactly all exchange terms in the computation of MR kernels. In fact, MR calculations employing Hamiltonian operators are rather performed within a limited valence space, in the spirit of the interacting shell model, either of projected-GCM type [58,59,60,61] or using more elaborate schemes to select the set of reference states like in the MONSTER and VAMPIR approaches [62,63,64].…”

Section: Strict Projected-gcm Approachmentioning

confidence: 99%

“…Refs. [58,78,79] also dedicated to finding a canonical representation appropriate to non-diagonal overlaps. However, they focus on the more difficult task of finding a basis where both vacua are simultaneously put into a canonical form.…”

Section: Standard Bcs Techniques Allow Us To Express |φmentioning

confidence: 99%

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Configuration mixing within the energy density functional formalism: Removing spurious contributions from nondiagonal energy kernels

2009

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Multi-reference calculations along the lines of the Generator Coordinate Method or the restoration of broken symmetries within the nuclear Energy Density Functional (EDF) framework are becoming a standard tool in nuclear structure physics. These calculations rely on the extension of a singlereference energy functional, of the Gogny or the Skyrme types, to non-diagonal energy kernels. There is no rigorous constructive framework for this extension so far. The commonly accepted way proceeds by formal analogy with the expressions obtained when applying the generalized Wick theorem to the non-diagonal matrix element of a Hamilton operator between two product states. It is pointed out that this procedure is ill-defined when extended to EDF calculations as the generalized Wick theorem is taken outside of its range of applicability. In particular, such a procedure is responsible for the appearance of spurious divergences and steps in multi-reference EDF energies, as was recently observed in calculations restoring particle number or angular momentum. In the present work, we give a formal analysis of the origin of this problem for calculations with and without pairing, i.e. constructing the density matrices from either Slater determinants or quasi-particle vacua. We propose a method to regularize non-diagonal energy kernels such that divergences and steps are removed from multi-reference EDF energies. Such a removal is a priori quasi-particle-basis dependent. A special feature of the method we use to proceed to the actual regularization is that it singles out one basis among all possible ones. The regularization method is applicable to calculations based on any symmetry restoration or generator coordinate but is limited to EDFs depending only on integer powers of the normal and anomalous density matrices. Eventually, the method is formally illustrated for particle number restoration and is specified to configuration mixing calculations based on Slater determinants.

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Section: A Notation and Preliminary Discussionmentioning

confidence: 99%

Section: B Correcting Higher-order Functionalsmentioning

confidence: 99%

Section: Strict Projected-gcm Approachmentioning

confidence: 99%

Section: Standard Bcs Techniques Allow Us To Express |φmentioning

confidence: 99%

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Configuration mixing within the energy density functional formalism: Removing spurious contributions from nondiagonal energy kernels

2009

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“…The PPQ model is well known and has been used many times to test collective properties of fermion systems; here we use the version defined in detail in Ref. [30]. Calculations were performed in the j=19/2 shell (Ω=10).…”

Section: E Pairing-plus-quadrupole Modelmentioning

confidence: 99%

Odd-even staggering of binding energies as a consequence of pairing and mean-field effects

et al. 2001

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Odd-even staggering of binding energies is studied in finite fermion systems with pairing correlations. We discuss contributions of the pairing and mean-field to the staggering, and we construct the binding-energy filters which measure the magnitude of pairing correlations and the effective singleparticle spacings in a given system The analysis is based on studying several exactly-solvable manybody Hamiltonians as well as on the analytical formulas that can be applied in the weak and strong pairing limits. PACS number(s): 21.10. Dr, 21.10.Pc, 21.60.Jz, 71.15.Mb

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Capability of the generator coordinate method combined with angular momentum projection

2001

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The generator coordinate method (GCM) with triaxiai angular monetum projection is applied to a single j-shell model with a microscopic quadrupole-quadrupole interaction. It is confirmed that the GCM reproduces exactly the shell model level schemes of the excited states for the 4-hole (and also 4-particle) systems in the single j-shell model. It is shown that the triaxial angular momentum projection plays an essential role in taking account of large contributions from triaxially deformed configurations to the physical states.

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Quadrupole-collective states in a large single-jshell

Cited by 23 publications

References 44 publications

Configuration mixing within the energy density functional formalism: Removing spurious contributions from nondiagonal energy kernels

Configuration mixing within the energy density functional formalism: Removing spurious contributions from nondiagonal energy kernels

Odd-even staggering of binding energies as a consequence of pairing and mean-field effects

Capability of the generator coordinate method combined with angular momentum projection

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