arXiv subjects

W. Gloeckle

Publications and source records attributed to W. Gloeckle.

106 records · Page 6Linked to original sources

arXiv1999

A Momentum Transformation Connecting a NN Potential in the Nonrelativistic and the Relativistic Two-Nucleon Schroedinger Equation

An analytical relation between center of mass momenta in a nonrelativistic and a relativistic two-nucleon Schrödinger equation is proposed which allows to analytically rewrite the two Schrödinger equations into each other. As a consequence a NN potential occurring in the relativistic Schrödinger equation can be gained from a nonrelativistic one by an analytical procedure. The S-matrices in the two equations are exactly identical and therefore the two-nucleon phase shifts.

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arXiv1999

On the Impossibility to Measure the Total Neutron- and Proton Induced Nonmesonic Decays for Hypertriton

Based on realistic calculations for the nonmesonic decay rate of Hypertriton we demonstrate, that in principle it is not possible to measure the total n- and p- induced decay rates and as a consequence $Γ_n /Γ_p$ for that lightest hypernucleus.For the nonmesonic decay process the calculations are performed with modern YN forces based on various meson exchanges and taking the final state interaction among the three nucleons fully into account. Our findings have consequences also for the interpretation of experimental $Γ_n/Γ_p$ ratios for heavier hypernuclei where severe discrepancies exist to theoretical $Γ_n/Γ_p$ ratios.

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arXiv1999

Resonances in the three-neutron system

A study of 3-body resonances has been performed in the framework of configuration space Faddeev equations. The importance of keeping a sufficient number of terms in the asymptotic expansion of the resonance wave function is pointed out. We investigated three neutrons interacting in selected force components taken from realistic nn forces.

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arXiv1999

Modern NN Force Predictions for the Total ND Cross Section up to 300 MeV

For several modern nucleon-nucleon potentials state-of-the-art Faddeev calculations are carried out for the $nd$ total cross section between 10 and 300 MeV projectile energy and compared to new high precision measurements. The agreement between theory and data is rather good, with exception at the higher energies where a 10% discrepancy builds up. In addition the convergence of the multiple scattering series incorporated in the Faddeev scheme is studied numerically with the result, that rescattering corrections remain important. Based on this multiple scattering series the high energy limit of the total $nd$ cross section is also investigated analytically. In contrast to the naive expectation that the total $nd$ cross section is the sum of the $np$ and $nn$ total cross sections we find additional effects resulting from the rescattering processes, which have different signs and different behavior as function of the energy. A shadowing effect in the high energy limit only occurs for energies higher than 300 MeV. The expressions in the high energy limit have qualitatively a similar behavior as the exactly calculated expressions, but can be expected to be valid quantitatively only at much higher energies.

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arXiv1998

Spurious states in the Faddeev formalism for few-body systems

We discuss the appearance of spurious solutions of few-body equations for Faddeev amplitudes. The identification of spurious states, i.e., states that lack the symmetry required for solutions of the Schroedinger equation, as well as the symmetrization of the Faddeev equations is investigated. As an example, systems of three and four electrons, bound in a harmonic-oscillator potential and interacting by the Coulomb potential, are presented.

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arXiv1998

Shadowing and Antishadowing Effects in a Model for the n+d Total Cross Section

Based on the multiple scattering series incorporated in the Faddeev scheme the high energy limit of the total n+d cross section is evaluated in a nonrelativistic model system where spins are neglected. In contrast to the naive expectation that the total n+d scattering cross section is the sum of two NN cross sections we find two additional effects resulting from rescattering processes. These additional terms have different signs (shadowing and antishadowing) and a different behavior as function of the energy. Our derivation of these results which are already known from Glauber theory is based on the analytical evaluation of elastic transition amplitudes in the high energy limit. It does not depend on the diffraction type assumptions connected with Glauber theory. In this model of spinless Yukawa type forces (with no absorption) the total n+d cross section does not approach twice the NN total cross section in the high energy limit but rather approaches the total NN cross section multiplied by a number larger than two. Therefore, the enhancement effect resulting from rescattering is larger than the shadowing effect, which decreases faster with energy.

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arXiv1998

Weak capture of protons by protons

The cross section for the proton weak capture reaction $^1H(p,e^+ν_e)^2H$ is calculated with wave functions obtained from a number of modern, realistic high-precision interactions. To minimize the uncertainty in the axial two-body current operator, its matrix element has been adjusted to reproduce the measured Gamow-Teller matrix element of tritium $β$ decay in model calculations using trinucleon wave functions from these interactions. A thorough analysis of the ambiguities that this procedure introduces in evaluating the two-body current contribution to the pp capture is given. Its inherent model dependence is in fact found to be very weak. The overlap integral $Λ^2(E=0)$ for the pp capture is predicted to be in the range 7.05--7.06, including the axial two-body current contribution, for all interactions considered.

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arXiv1998

Benchmark calculations for polarization observables in 3N scattering

High precision benchmark calculations for phase-shifts and mixing parameters as well as observables in elastic neutron-deuteron scattering below the deuteron breakup threshold are presented using a realistic nucleon-nucleon potential. Two totally different methods, one using a variational principle in configuration space and the other solving the Faddeev equations in momentum space are used and compared to each other. The agreement achieved in phase-shifts and mixing parameters as well as in the polarization observables is excellent. The extreme sensitivity of the vector analyzing power Ay to small changes of the phase shifts and mixing parameters is pointed out.

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arXiv1998

Electromagnetic Processes in Three-Nucleon Systems

Results gained for electron scattering on $^3$He in a nonrelativistic framework are reviewed. The electromagnetic current is truncated to a single nucleon operator, but the interaction among the three nucleons is treated exactly. Thus initial and final 3N states are evaluated consistently as solutions of Faddeev equations based on realistic NN forces. The correct inclusion of the final state interaction turned out to be important. The agreement to data is reasonably good, but the neglection of MEC's can be seen. That inconsistency should be removed. For pd capture processes we included some MEC's via the Siegert theorem, which dramatically improves the description of the pd capture data.

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arXiv1998

Three Body Bound State Calculations without Angular Momentum Decomposition

The Faddeev equations for the three body bound state are solved directly as three dimensional integral equation without employing partial wave decomposition. The numerical stability of the algorithm is demonstrated. The three body binding energy is calculated for Malfliet-Tjon type potentials and compared with results obtained from calculations based on partial wave decomposition. The full three body wave function is calculated as function of the vector Jacobi momenta. It is shown that it satisfies the Schrödinger equation with high accuracy. The properties of the full wave function are displayed and compared to the ones of the corresponding wave functions obtained as finite sum of partial wave components. The agreement between the two approaches is essentially perfect in all respects.

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arXiv1998

The cross section minima in elastic Nd scattering: a ``smoking gun'' for three nucleon force effects

Neutron-deuteron elastic scattering cross sections are calculated at different energies using modern nucleon-nucleon interactions and the Tucson-Melbourne three-nucleon force adjusted to the triton binding energy. Predictions based on NN forces only underestimate nucleon-deuteron data in the minima at higher energies starting around 60 MeV. Adding the three-nucleon forces fills up those minima and reduces the discrepancies significantly.

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arXiv1997

N-Nucleon Effective Generators of the Poincare Group Derived from a Field Theory

It is shown that the ten generators of the Poincare group acting in the Fock space of nucleons and mesons and based on standard Lagrangians can be blockdiagonalized by one and the same unitary transformation such that the space of a fixed number of nucleons is separated from the rest of the Fock space. The existence proof is carried through in a formal power series expansion in the coupling constant to all orders. In this manner one arrives at effective generators of the Poincare group which act in the two subspaces separately.

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arXiv1997

Pi-mesonic decay of the hypertriton

The pi-mesonic 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 total pi-mesonic decay rate is found to be 92% of the free Lambda decay rate, which is close to the experimental data. Together with the nonmesonic decay the total life time of 3Lambda H is predicted to be 2.78 x 10^-10 sec which is 6 % larger than for the free Lambda particle. The differential decay rate is evaluated as a function of the pion momentum. The decay into the N+d+pi channel is stronger than in the 3N+pi channel in contrast to the situation for the nonmesonic decay. The ratio for the decay rate into 3He + pi^- to the decay rate into all channels including pi^- is found to be 0.40, which is close to the experimental value. We visualise the decay into the dominant channel p+d+pi^- in a Dalitz plot. Finally we compare the polarisation of the outgoing proton in free unpolarised Lambda-decay to the polarisation of 3He in unpolarised 3_Lambda H-decay and we compare the closely related asymmetry of pi^- emitted parallel and antiparallel with respect to the spin-direction for a polarised Lambda to the corresponding asymmetry for a polarised 3_Lambda H.

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arXiv1997

Two-Body T-Matrices without Angular Momentum Decomposition: Energy and Momentum Dependencies

The two-body t-matrix is calculated directly as function of two vector momenta for different Malfliet-Tjon type potentials. At a few hundred MeV projectile energy the total amplitude is quite a smooth function showing only a strong peak in forward direction. In contrast the corresponding partial wave contributions, whose number increases with increasing energy, become more and more oscillatory with increasing energy. The angular and momentum dependence of the full amplitude is studied and displayed on as well as off the energy shell as function of positive and negative energies. The behavior of the t-matrix in the vicinity of bound state poles and resonance poles in the second energy sheet is studied. It is found that the angular dependence of T exhibits a very characteristic behavior in the vicinity of those poles, which is given by the Legendre function corresponding to the quantum number either of the bound state or the resonance (or virtual) state. This behavior is illustrated with numerical examples.

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arXiv1997

Benchmark Calculations for the Triton Binding Energy for Modern NN Forces and the pi-pi Exchange Three-Nucleon Force

We present high precision benchmark calculations for the triton binding energy using the most recent, phase equivalent realistic nucleon-nucleon (NN) potentials and the Tuscon-Melbourne pi-pi three-nucleon force (3NF). That 3NF is included with partial waves up to a total two-body angular momentum of j_max=6. It is shown that the inclusion of the 3NF slows down the convergence in the partial waves and j_max=5 is needed in order to achieve converged results within a few keV. We adjust the cut-off parameter Lambda in the form factors of the Tuscon-Melbourne 3NF separately for the different NN potentials to the triton binding energy. This provides a set of phenomenological three-nucleon Hamiltonians which can be tested in three-nucleon scattering and systems with A>3. A connection between the probability to find two nucleons at short distances in the triton and the effect of that 3NF on the triton binding energy is pointed out.

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arXiv1996

Nucleon Scattering from Very Light Nuclei: Intermediate Energy Expansions for Transition Potentials and Breakup Processes

Optical potentials for elastic p-d scattering and the coupled processes p+$^3$He $\rightarrow$ p+$^3$He and p+$^3$He $\rightarrow$ d+d are derived in the Faddeev-Yakubovsky framework with special emphasis on leading order terms, which are expected to be valid at intermediate energies. In addition, equations for the fragmentations $^3$He(p,ppp)n and $^3$He(p,pp)d are derived within the same framework. Again leading order terms for intermediate energies are considered.

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