Topics in many-body theory of nuclear effective interactions

Kuo, T.T.S.

doi:10.1007/3-540-10851-3_3

Cited by 12 publications

(37 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This problem is very hard to solve and approximations are needed. In approximate schemes that nonlinear equation is often reformulated into a linear form on a two-body level using the exactly known interacting two-body states (some references are [18] [13]). This is also a feasible way to proceed in our context as was displayed at the end of section 2.…”

Section: Effective Potential Scattering and Bound Statesmentioning

confidence: 99%

Effective theory for the two-nucleon system

et al. 1999

View full text Add to dashboard Cite

We apply the method of unitary transformations to a model two-nucleon potential and construct from it an effective potential in a subspace of momenta below a given cut-off Λ. The S-matrices in the full space and in the subspace are shown to be identical. We solve numerically the Schrödinger equation in the small momentum space and recover exactly the bound and scattering states of the full theory. We then expand the heavy repulsive meson exchange of the effective potential in a series of local contact terms and discuss the question of naturalness of the corresponding coupling constants. Using our exact effective theory we address further issues related to the chiral perturbation theory approach of the two-nucleon system. The coordinate space representation of the effective potential is also considered.

show abstract

Section: Effective Potential Scattering and Bound Statesmentioning

confidence: 99%

Effective theory for the two-nucleon system

et al. 1999

View full text Add to dashboard Cite

show abstract

“…The resulting starting-energy-independent two-body effective interaction is not Hermitian but its non-Hermiticity is found to be extremely small. We obtain the Hermitian effective interaction v (2) eff to be used in SM calculation by taking the average of the non-Hermitian effective interaction and its conjugate. It is pointed out in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…The calculation of the two-body effective interaction for the valence nucleons can be conveniently divided into three steps: (1) Calculate the Brueckner reaction matrix G [1] from a realistic NN potential; (2) Calculate the two-body Q-box [2] from the G-matrix; and (3) Calculate the folded diagrams [3] from the Q-box. The second step provides major difficulties, because one is unable to evaluate the core-polarization diagrams to all orders and there is no sign of convergence within the lowest few orders [4].…”

Section: Introductionmentioning

confidence: 99%

Simple approximation for the starting-energy-independent two-body effective interaction with applications toLi6

et al. 1994

View full text Add to dashboard Cite

We apply the Lee-Suzuki iteration method to calculate the linkedfolded diagram series for a new Nijmegen local NN potential. We obtain an exact starting-energy-independent effective two-body interaction for a multi-shell, no-core, harmonic-oscillator model space. It is found that the resulting effective-interaction matrix elements can be well approximated by the Brueckner G-matrix elements evaluated at starting energies selected in a simple way. These starting energies are closely related to the energies of the initial two-particle states in the ladder diagrams. The "exact" and approximate effective interactions are used to calculate the energy spectrum of 6 Li in order to test the utility of the approximate form.

show abstract

“…where the unitary operator Z := exp(G) ∈ SU(n) is the rotation (12). Equation (20) should be compared with Eqn.…”

Section: B Geometry Of the Model Spacementioning

confidence: 99%

“…The published mathematical theory of the effective Hamiltonian is complicated and usually focuses on perturbation theoretical aspects, diagram expansions, etc. [4,5,6,7,8,9,10,11,12,13]. In this article, we recast and reinterpret the basic elements of the theory geometrically.…”

Section: Introductionmentioning

confidence: 99%

Geometry of effective Hamiltonians

Kvaal

2008

Phys. Rev. C

View full text Add to dashboard Cite

We give a complete geometrical description of the effective Hamiltonians common in nuclear shell model calculations. By recasting the theory in a manifestly geometric form, we reinterpret and clarify several points. Some of these results are hitherto unknown or unpublished. In particular, commuting observables and symmetries are discussed in detail. Simple and explicit proofs are given, and numerical algorithms are proposed, that improve and stabilize common methods used today.

show abstract

Topics in many-body theory of nuclear effective interactions

Cited by 12 publications

References 55 publications

Effective theory for the two-nucleon system

Effective theory for the two-nucleon system

Simple approximation for the starting-energy-independent two-body effective interaction with applications toLi6

Geometry of effective Hamiltonians

Contact Info

Product

Resources

About