Symmetric orthogonalized-plane-wave Born approximation for charge exchange

Lo, Chung‐Mau; Girardeau,

doi:10.1103/physreva.41.158

Cited by 13 publications

(6 citation statements)

References 19 publications

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“…Lo and Girardeau [7] applied this iso-orthogonalized matrix element to reaction (3) with superb agreement with the variational result of Brown and Humberston [8], reproduced in Fig. 5.…”

Section: Iso-orthoconalizationsupporting

confidence: 71%

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Formation of positronium ine++H−collisions

Straton

Drachman²

1991

Phys. Rev. A

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Cross sections for positronium formation by capture from the negative hydrogen ion are given. Orthogonalization corrections to the Coulomb (first-order) Born approximation (CBA) difFerential and total cross sections are calculated using approximate H wave functions of both Lowdin [Phys. Rev. 90, 123 (1953)] and Chandrasekhar [Astrophys. J. 100, 176 (1944)]. The present calculation of the CBA cross sections using the post interaction for Lowdin's wave function (LCBAPS) disagrees with the calculation of Choudhury, Mukherjee, and Sural (CMS) [Phys. Rev. A 38, 2358], whereas our results using the prior interaction agree. Thus, where CMS found an order of magnitude post-prior discrepancy in the differential cross sections except at forward angles, and a markedly different shape to the minima. , the present post, and prior results differ by 1 -10'K at 100 eV, and the minima have the same shape and occur within one degree of each other. Chandrasekhar's "open-shell" wave function, which is superior to Lowdin's in bound-state problems since it gives a negative binding energy, gives post and prior cross sections that are almost indistinguishable at this energy and are 2 to 3 as large as the LCBA. Various methods of orthogonalizing the unbound projectile to the possible bound states are considered. It is found that treating the atomic nuclei as if they were isotopic spin projections [Straton and Girardeau, Phys. Rev. A 40, 2991 (1989)] of a single type of "nucleon" gives cross sections that are an improvement over the CBA. PACS number(s): 34.70.+e, 34.10+x,36.10.Dr

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“…Lo and Girardeau [7] applied this iso-orthogonalized matrix element to reaction (3) with superb agreement with the variational result of Brown and Humberston [8], reproduced in Fig. 5.…”

Section: Iso-orthoconalizationsupporting

confidence: 71%

“…Also included is the further presumption [6] of treating the proton and positron as isospinlike projections (of different mass) of a single species of "nucleon, " that produced remarkable agreement between the orthogonalized first-order calculation [7] of charge transfer from hydrogen and the (presumably exact) variational result [8].…”

mentioning

confidence: 99%

Formation of positronium ine++H−collisions

Straton

Drachman²

1991

Phys. Rev. A

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“…Here, a more systematic and elegant, although equivalent procedure of Lo and Girardeau [26] is followed. The generator of the transformation F is generalized to…”

Section: A Transformation Of the Quark Operatorsmentioning

confidence: 99%

“…[17,24], and incorporates the improvements and new aspects developed in Refs. [25,26]. In subsection II B we introduce a model microscopic quark Hamiltonian, implement its Fock-Tani transformation, and discuss the physical interpretation of the different terms of the transformed Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

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Mapping of Composite Hadrons into Elementary Hadrons and Effective Hadronic Hamiltonians

et al. 1998

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A mapping technique is used to derive in the context of constituent quark models effective Hamiltonians that involve explicit hadron degrees of freedom. The technique is based on the ideas of mapping between physical and ideal Fock spaces and shares similarities with the quasiparticle method of Weinberg. Starting with the Fock-space representation of singlehadron states, a change of representation is implemented by a unitary transformation such that composites are redescribed by elementary Bose and Fermi field operators in an extended Fock space. When the unitary transformation is applied to the microscopic quark Hamiltonian, effective, hermitian Hamiltonians with a clear physical interpretation are obtained. Applications and comparisons with other composite-particle formalisms of the recent literature are made using the nonrelativistic quark model. Academic Press

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