Preface

Adhikari, Sadhan K.; Kowalski, K. L.

doi:10.1016/b978-0-12-044273-7.50004-x

Cited by 6 publications

(24 citation statements)

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“…As the separate basis sets for the hydrogen and positronium levels are increased in size, it is possible for the basis consisting of both sets of states to become overcomplete. Under these circumstances the set of Lippmann-Schwinger equations can become unstable if the basis becomes sufficiently large (Adhikari and Kowalski 1991;Bransden and Noble 1994). In numerical terms, the resulting linear equations become linearly dependent and this manifests itself in the solution vector losing numerical precision.…”

Section: Details Of the Calculationsmentioning

confidence: 99%

Large Basis Calculation of Positron?Hydrogen Scattering at Low Energies

Mitroy¹

1995

Aust. J. Phys.

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Calculations of low energy positron-hydrogen scattering using the close coupling approach are reported at low energies. The channel space includes nine physical hydrogen and positronium states and in addition twelve hydrogen and positronium pseudo-states. For energies below the positronium formation threshold, phase shifts are reported for J = 0 to 6 and are believed to have an absolute accuracy of 0·0015 radian or better. Elastic scattering and positronium formation cross sections in the Ore gap for the J = 0 and J = 1 partial waves are essentially identical with previous variational calculations. Total elastic and positronium formation cross sections are reported at incident energies below the ionisation threshold. Cross sections for the excitation of the H( n=2), H( n=3) and Ps( n=2) levels are also reported over a restricted energy range, and the total reaction cross section has been computed and compared with experiment.

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Section: Details Of the Calculationsmentioning

confidence: 99%

Large Basis Calculation of Positron?Hydrogen Scattering at Low Energies

Mitroy¹

1995

Aust. J. Phys.

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“…We have no reasons here for analyzing in detail the technical differences which characterize the variety of separable-expansion methods available in the Literature (for this we refer to Ref. [15]); as long as they correctly reproduce the polar structure of the subsystem t-matrices we generically denote all these methods as "quasiparticle" approaches, although the quasiparticle idea historically refers to the application in terms of Weinberg states [25].…”

Section: The Quasiparticle Formalismmentioning

confidence: 99%

“…Treatments of the like, based upon the idea of pole dominance of the three-body subsystem operators in the kernel of the standard four-body equations, have been suggested in various forms [28,15] (for a short review on recent applications, see also Ref. [29]).…”

Section: Rearrangement and Break-up Amplitudesmentioning

confidence: 99%

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Pion-three-nucleon problem with two-cluster connected-kernel equations

Canton

1998

Phys. Rev. C

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It is found that the coupled πNNN-NNN system breaks into fragments in a nontrivial way. Assuming the particles as distinguishable, there are indeed four modes of fragmentation into two clusters, while in the standard three-body problem there are three possible two-cluster partitions and conversely the four-body problem has seven different possibilities. It is shown how to formulate the pion-threenucleon collision problem through the integral-equation approach by taking into account the proper fragmentation of the system. The final result does not depend on the assumption of separability of the two-body t-matrices. Then, the quasiparticle methodà la Grassberger-Sandhas is applied and effective two-cluster connected-kernel equations are obtained. The corresponding bound-state problem is also formulated, and the resulting homogeneous equation provides a new approach which generalizes the commonly used techniques to describe the three-nucleon bound-state problem, where the meson degrees of freedom are usually suppressed.PACS numbers: 21.45.+v, 25.10+s, 25.80.Hp, 21.30.Fe

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“…In the recent past there has been many benchmark calculations involving realistic two-and three-nucleon potentials. [1][2][3] Though it has been possible to fit most of the low-energy three-nucleon observables using an appropriate ad hoc mixture of reasonable two-and three-nucleon potentials, not much physics was learnt from these calculations. No reasonable criteria for preferring one nonrelativistic meson-theoretic [4] potential model over another for this system has been obtained from these calculations.…”

Section: Introductionmentioning

confidence: 99%

Relativistic Three-Particle Dynamical Equations II. Application to the Trinucleon System

Adhikari

Tomio

1994

Annals of Physics

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We calculate the contribution of relativistic dynamics on the neutron-deuteron scattering length and triton binding energy employing five sets trinucleon potential models and four types of three-dimensional relativistic three-body equations suggested in the preceding paper. The relativistic correction to binding energy may vary a lot and even change sign depending on the relativistic formulation employed.The deviations of these observables from those obtained in nonrelativistic models follow the general universal trend of deviations introduced by off-and on-shell variations of two-and three-nucleon potentials in a nonrelativistic model calculation.Consequently, it will be difficult to separate unambiguously the effect of off-and on-shell variations of two-and three-nucleon potentials on low-energy three-nucleon observables from the effect of relativistic dynamics.

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Preface

Cited by 6 publications

References 0 publications

Large Basis Calculation of Positron?Hydrogen Scattering at Low Energies

Large Basis Calculation of Positron?Hydrogen Scattering at Low Energies

Pion-three-nucleon problem with two-cluster connected-kernel equations

Relativistic Three-Particle Dynamical Equations II. Application to the Trinucleon System

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