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W. Glöckle

Publications and source records attributed to W. Glöckle.

26 records · Page 2Linked to original sources
arXiv1998

Effective theory for the two-nucleon system

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.

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arXiv1998

Scaling properties of the longitudinal and transversal asymmetries of the $\vec{n}\vec{d}$ total cross section

The longitudinal and transversal asymmetries of the total $\vec{n}\vec{d}$ cross section are calculated. Four modern nucleon-nucleon interactions: AV18, CD Bonn, NijmI and NijmII, give different predictions for these observables. When the three-nucleon Hamiltonian is supplemented by the $2π$-exchange Tucson-Melbourne three-nucleon force (3NF), individually adjusted with each particular NN potential to reproduce the experimental triton binding energy, all predictions practically coincide. We propose to check this scaling behavior experimentally in order to get a clear signal for 3NF effects in the low energy three-nucleon continuum. Connected to that is the proposal to measure the energy at which the longitudinal asymmetry goes through zero. This energy is shifted by about 400 keV when 3NF's are acting.

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arXiv1998

Low-momentum effective theory for nucleons

Starting from a precise two-nucleon potential, we use the method of unitary transformations to construct an effective potential that involves only momenta less than a given maximal value. We describe this method for an S-wave potential of the Malfliet-Tjon type. It is demonstrated that the bound and scattering state spectrum calculated within the effective theory agrees exactly with the one based on the original potential. This might open an avenue for the construction of effective chiral few-nucleon forces and for a systematic treatment of relativistic effects in few-body systems.

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arXiv1998

Nuclear forces from chiral Lagrangians using the method of unitary transformation I: Formalism

We construct the two- and three-nucleon potential based on the most general chiral effective pion-nucleon Lagrangian using the method of unitary transformations. For that, we develop a power counting scheme consistent with this projection formalism. In contrast to previous results obtained in old-fashioned time-ordered perturbation theory, the method employed leads to energy-independent potentials. We discuss in detail the similarities and differences to the existing chiral nucleon-nucleon potentials. We also show that to leading order in the power counting, the three-nucleon forces vanish lending credit to the result obtained by Weinberg using old-fashioned time-ordered perturbation theory.

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arXiv1996

The nonmesonic weak decay of the hypertriton

The nonmesonic decay of the hypertriton is calculated based on a hypertriton wavefunction and 3N scattering states, which are rigorous solutions of 3-body Faddeev equations using realistic NN and hyperon-nucleon interactions. The pion-exchange together with heavier meson exchanges for the $ΛN \to N N $ transition is considered. The total nonmesonic decay rate is found to be 0.5% of the free $Λ$ decay rate. Integrated as well as differential decay rates are given. The p- and n- induced decays are discussed thoroughly and it is shown that the corresponding total rates cannot be measured individually.

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arXiv1996

Pion Absorption Cross Section for ^2H and ^3He in the Delta-Isobar Region: A Phenomenological Connection

The absorption of π^+ on ^3He in the $Δ$-region is evaluated with exact inclusion of the final state interaction among the three emerging protons. The absorption is described by a $πN \to Δ$ vertex and a $NΔ- NN$ transition t-matrix which are calculated from a phenomenological model for NN and πd reactions. In a calculation where the initial pion scattering effects are neglected, the predicted peaks of the pion absorption cross sections for ^2H and ^3He lie too high in energy in relation to the data. The effect of the final state three-nucleon interaction turns out to be too small for changing the magnitude and shifting the peak position of the total absorption cross section for ^3He. We demonstrate that the adjustment of the peak position for the deuteron cross section by small modifications of the $Δ$-parameters, automatically leads to the correct peak position in ^3He.

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arXiv1996

A New Look into the Partial Wave Decomposition of Three-Nucleon Forces

We demonstrate that the partial wave decomposition of three-nucleon forces used up to now in momentum space has to be necessarily unstable at high partial waves. This does not affect the applications performed up to now, which were restricted to low partial waves. We present a new way to perform the partial wave decomposition which is free of that defect. This is exemplified for the most often used $2π$-exchange Tuscon-Melbourne three-nucleon force. For the lower partial waves the results of the old method are reproduced.

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