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W. Glockle

Publications and source records attributed to W. Glockle.

At least 19 recordsLinked to original sources
arXiv2011

Three-nucleon force in relativistic three-nucleon Faddeev calculations

We extend our formulation of relativistic three-nucleon Faddeev equations to include both pairwise interactions and a three-nucleon force. Exact Poincare invariance is realized by adding interactions to the mass Casimir operator (rest Hamiltonian) of the non-interacting system without changing the spin Casimir operator. This is achieved by using interactions defined by rotationally invariant kernels that are functions of internal momentum variables and single-particle spins that undergo identical Wigner rotations. To solve the resulting equations one needs matrix elements of the three-nucleon force with these properties in a momentum-space partial-wave basis. We present two methods to calculate matrix elements of three-nucleon forces with these properties. For a number of examples we show that at higher energies, where effects of relativity and of three-nucleon forces are non-negligible, a consistent treatment of both is required to properly analyze the data.

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arXiv2011

The Tucson-Melbourne Three-Nucleon Force in the automatized Partial Wave Decomposition

A recently developed procedure for a partial wave decomposition of a three-nucleon force is applied to the pi-pi, pi-rho and rho-rho components of the Tucson-Melbourne three-nucleon potential. The resulting matrix elements for the pi-pi and pi-rho components are compared with the values obtained using the standard approach to the partial wave decomposition, in which the pi-rho expressions for the matrix elements are also derived and presented. Several numerical tests and results for the triton binding energy and the correlation function prove the reliability and efficiency of the new method.

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arXiv2010

The Two-Nucleon System in Three Dimensions

A recently developed formulation for treating two- and three-nucleon bound states in a three-dimensional formulation based on spin-momentum operators is extended to nucleon-nucleon scattering. Here the nucleon-nucleon t-matrix is represented by six spin-momentum operators accompanied by six scalar functions of momentum vectors. We present the formulation and provide numerical examples for the deuteron and nucleon-nucleon scattering observables. A comparison to results from a standard partial wave decomposition establishes the reliability of this new formulation.

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arXiv2009

A new way to perform partial wave decompositions of few-nucleon forces

We formulate a general and exact method of partial wave decomposition (PWD) of any nucleon-nucleon (NN) potential and any three-nucleon (3N) force. The approach allows one to efficiently use symbolic algebra software to generate the interaction dependent part of the program code calculating the interaction. We demonstrate the feasibility of this approach for the one-boson exchange BonnB potential, a recent nucleon-nucleon chiral force and the chiral two-pion-exchange three-nucleon force. In all cases very good agreement between the new and the traditional PWD is found. The automated PWD offered by the new approach is of the utmost importance in view of future applications of numerous chiral N3LO contributions to the 3N force in three nucleon calculations.

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arXiv2009

On the discrepancies in the low energy neutron-deuteron breakup

In view of recent neutron-deuteron (nd) breakup data for neutron-neutron (nn) and neutron-proton (np) quasi-free-scattering (QFS) arrangements and the large discrepancy found between theoretical predictions and measured nn QFS cross sections, we analyze the sensitivity of the QFS cross sections to different partial wave components of the nucleon-nucleon (NN) interaction. We found that the QFS cross section is strongly dominated by the 1S0 and 3S1-3D1 contributions. Because the standard three-nucleon force (3NF) only weakly influence the QFS region, we conjecture, that it must be the nn 1S0 force component which is responsible for the discrepancy in the nn QFS peak. A stronger 1S0 nn force is required to bring theory and data into agreement. Such an increased strength of the nn interaction will, however, not help to explain the nd breakup symmetric-space-star (SST) discrepancy. Further experimental cross-checkings are required.

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arXiv2009

Treatment of the proton-proton Coulomb force in proton-deuteron breakup Faddeev calculations

We extend our approach to incorporate the proton-proton (pp) Coulomb force into the three-nucleon (3N) Faddeev calculations from elastic proton-deuteron (pd) scattering to the breakup process. The main new ingredient is a 3-dimensional screened pp Coulomb t-matrix obtained by a numerical solution of the 3-dimensional Lippmann-Schwinger equation. We demonstrate numerically that the proton-deuteron breakup observables can be determined from the resulting on-shell 3N amplitudes increasing the screening radius. However, contrary to the pd elastic scattering, the screening limit exists only after renormalisation of the pp t-matrices.

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arXiv2009

A novel treatment of the proton-proton Coulomb force in elastic proton-deuteron Faddeev calculations

We propose a novel approach to incorporate the proton-proton (pp) Coulomb force into the three-nucleon (3N) Faddeev calculations. The main new ingredient is a 3-dimensional screened pp Coulomb t-matrix obtained by a numerical solution of the 3-dimensional Lippmann-Schwinger (LS) equation. We demonstrate numerically and provide analytical insight that the elastic proton-deuteron (pd) observables can be determined directly from the resulting on shell 3N amplitude increasing the screening radius. The screening limit exists without the need of renormalisation not only for observables but for the elastic pd amplitude itself.

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arXiv2009

A New Treatment of 2N and 3N Bound States in Three Dimensions

The direct treatment of the Faddeev equation for the three-boson system in 3 dimensions is generalized to nucleons. The one Faddeev equation for identical bosons is replaced by a strictly finite set of coupled equations for scalar functions which depend only on 3 variables. The spin-momentum dependence occurring as scalar products in 2N and 3N forces accompanied by scalar functions is supplemented by a corresponding expansion of the Faddeev amplitudes. After removing the spin degrees of freedom by suitable operations only scalar expressions depending on momenta remain. The corresponding steps are performed for the deuteron leading to two coupled equations.

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arXiv2009

The exact three-dimensional half-shell t-matrix for a sharply cut-off Coulomb potential in the screening limit

The three-dimensional half-shell t-matrix for a sharply cut-off Coulomb potential is analytically derived together with its asymptotic form without reference to partial wave expansion. The numerical solutions of the three-dimensional Lippmann-Schwinger equation for increasing cut-off radii provide half-shell t-matrices which are in quite a good agreement with the asymptotic values.

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arXiv2009

Proton-proton scattering without Coulomb force renormalization

We demonstrate numerically that proton-proton (pp) scattering observables can be determined directly by standard short range methods using a screened pp Coulomb force without renormalization. In examples the appropriate screening radii are given. We also numerically investigate solutions of the 3-dimensional Lippmann-Schwinger (LS) equation for a screened Coulomb potential alone in the limit of large screening radii and confirm analytically predicted properties for off-shell, half-shell and on-shell Coulomb t-matrices. These 3-dimensional solutions will form a basis for a novel approach to include the pp Coulomb interaction into the 3N Faddeev framework.

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arXiv2008

3He Spin-Dependent Cross Sections and Sum Rules

We present a measurement of the spin-dependent cross sections for the \vec{^3He}(\vec{e},e')X} reaction in the quasielastic and resonance regions at four-momentum transfer 0.1 < Q^2< 0.9 GeV^2. The spin-structure functions have been extracted and used to evaluate the nuclear Burkhardt--Cottingham and extended GDH sum rules for the first time. Impulse approximation and exact three-body Faddeev calculations are also compared to the data in the quasielastic region.

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arXiv2008

Relativity and the low energy nd Ay puzzle

We solve the Faddeev equation in an exactly Poincare invariant formulation of the three-nucleon problem. The dynamical input is a relativistic nucleon-nucleon interaction that is exactly on-shell equivalent to the high precision CDBonn NN interaction. S-matrix cluster properties dictate how the two-body dynamics is embedded in the three-nucleon mass operator. We find that for neutron laboratory energies above 20 MeV relativistic effects on Ay are negligible. For energies below 20 MeV dynamical effects lower the nucleon analyzing power maximum slightly by 2% and Wigner rotations lower it further up to 10 % increasing thus disagreement between data and theory. This indicates that three-nucleon forces must provide an even larger increase of the Ay maximum than expected up to now.

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arXiv2006

Testing nuclear forces by polarization transfer coefficients in d(\vec p, \vec p)d and d(\vec p,\vec d)p reactions at E^{lab}_p = 22.7 MeV

The proton to proton polarization transfer coefficients K_x^{x'}, K_y^{y'}, K_z^{x'} and the proton to deuteron polarization transfer coefficients K_x^{x'}, K_y^{y'}, K_z^{x'}, K_x^{y'z'}, K_y^{z'z'}, K_z^{y'z'}, K_y^{x'z'} and K_y^{x'x'-y'y'} have been measured in d(\vec p, \vec p)d and d(\vec p, \vec d)p reactions at E^{lab}_p = 22.7 MeV, respectively. The data have been compared to predictions of modern nuclear forces obtained by solving the three-nucleon Faddeev equations in momentum space. Realistic (semi) phenomenological nucleon-nucleon potentials combined with model three-nucleon forces and modern chiral nuclear forces have been used. The AV18, CD Bonn, Nijm I and II nucleon-nucleon interactions have been applied alone or combined with the Tucson-Melbourne 99 three-nucleon force, adjusted separately for each potential to reproduce the triton binding energy. For the AV18 potential also the Urbana IX three-nucleon force have been used. In addition chiral NN potentials in the next-to-leading-order and chiral two- and three-nucleon forces in the next-to-next-to-leading-order have been applied. Only when three-nucleon forces are included a satisfactory description of all data results. For the chiral approach the restriction to the forces in the next-to-leading order is insufficient. Only when going over to the next-to-next-to-leading order one gets a satisfactory description of the data, similar to the one obtained with the (semi) phenomenological forces.

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arXiv2005

Polarization observables in the semiexclusive photoinduced three-body breakup of 3He

The photon and 3He analyzing powers as well as spin correlation coefficients in the semiexclusive three-body photodisintegration of 3He are investigated for incoming photon laboratory energies E=12, 40 and 120 MeV. The nuclear states are obtained by solving three-body Faddeev equations with the AV18 nucleon-nucleon potential alone or supplemented with the UrbanaIX three-nucleon force. Explicit pi- and rho-meson exchange currents are taken into account, but we also compare to other models of the electromagnetic current. In some kinematical conditions we have found strong effects of the three-nucleon force for the 3He analyzing power and spin correlation coefficients, as well strong sensitivities to the choice of the currents. This set of predictions should be a useful guidance for the planning of measurements. In addition, we compare our results for two-body 3He breakup induced by polarized photons with a few existing data.

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arXiv2004

Different formulations of 3He and 3H photodisintegration

Different momentum space Faddeev-like equations and their solutions for the radiative pd-capture and the three-nucleon photodisintegration of 3He are presented. Applications are based on the AV18 nucleon-nucleon and the Urbana IX three nucleon forces. Meson exchange currents are included using the Siegert theorem. A very good agreement has been found in all cases indicating the reliability of the used numerical methods. Predictions for cross sections and polarization observables in the pd-capture and the complete three nucleon breakup of 3He at different incoming deuteron/photon energies are presented.

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arXiv2003

Threshold Electrodisintegration of ^3He

Cross sections were measured for the near-threshold electrodisintegration of ^3He at momentum transfer values of q=2.4, 4.4, and 4.7 fm^{-1}. From these and prior measurements the transverse and longitudinal response functions R_T and R_L were deduced. Comparisons are made against previously published and new non-relativistic A=3 calculations using the best available NN potentials. In general, for q<2 fm^{-1} these calculations accurately predict the threshold electrodisintegration of ^3He. Agreement at increasing q demands consideration of two-body terms, but discrepancies still appear at the highest momentum transfers probed, perhaps due to the neglect of relativistic dynamics, or to the underestimation of high-momentum wave-function components.

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arXiv2003

Modern nuclear force predictions for the neutron-deuteron scattering lengths

The nd doublet and quartet scattering lengths have been calculated based on the modern NN and 3N interactions. We also studied the effect of the electromagnetic interactions in the form introduced in AV18. Switching them off for the various nuclear force models leads to shifts of up to +0.04 fm for doublet scattering length, which is significant for present day standards. The electromagnetic effects have also a noticeable effect on quartet scattering length, which otherwise is extremely stable under the exchange of the nuclear forces. For the current nuclear force models there is a strong scatter of the 3H binding energy and the doublet scattering length values around an averaged straight line (Phillips line). This allows to use doublet scattering length and the 3H binding energy as independent low energy observables.

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