Asymptotic wave function for three charged particles in the continuum

Mukhamedzhanov, A. M.; Lieber, Michael D.

doi:10.1103/physreva.54.3078

Cited by 36 publications

(42 citation statements)

References 7 publications

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“…Below the three-body threshold when only two-cluster channels are open, this presents no difficulty. However, above that threshold the complete boundary condition to be imposed in the region where all three particles eventually become asymptotically free [8][9][10][11] has, to our knowledge, not yet been implemented satisfactorily in any solution scheme.…”

Section: Introductionmentioning

confidence: 99%

Proton-deuteron elastic scattering from 2.5 to 22.7 MeV

et al. 2002

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We present the results of a calculation of differential cross sections and polarization observables for proton-deuteron elastic scattering, for proton laboratory energies from 2.5 to 22.5 MeV. The Paris potential parametrisation of the nuclear force is used. As solution method for the charged-composite particle equations the 'screening and renormalisation approach' is adopted which allows to correctly take into account the Coulomb repulsion between the two protons. Comparison is made with the precise experimental data of Sagara et al. [Phys. Rev. C 50, 576 (1994)] and of Sperison et al. [Nucl. Phys. A422, 81 (1984)].

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Section: Introductionmentioning

confidence: 99%

Proton-deuteron elastic scattering from 2.5 to 22.7 MeV

et al. 2002

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“…In that investigation, we used the asymptotic three-charged-particle wave function proposed in Ref. [16]. Since, however, this wave function is, by construction, an exact solution of the Schrödinger equation only asymptotically (i.e., in leading and in next-to-leading order) it can only be expected to provide a first estimation of the PDA effect within genuine three-body Coulomb dynamics.…”

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confidence: 99%

Three-body Coulomb interaction effects in the final state of thePb208(B8,
Alt
¹
,
Irgaziev
²
,
Mukhamedzhanov
³

2005
Phys. Rev. C
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32
3
43
0
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The photodissociation reaction 8 B + γ → 7 Be + p is used to provide information on the astrophysical S 17 factor of the inverse radiative capture reaction, knowledge of which is crucial for an estimation of the high-energy neutrino flux from the sun. Since, at present, the Coulomb field of a fully stripped nucleus serves as the source of the photons, an adequate analysis requires a genuine three-body treatment of this reaction. Among the uncertainties still affecting present analyses, the possible modification of the dissociation cross section by the post-decay acceleration of the fragments 7 Be and p in the target field plays a major role. Working with the prior form of the dissociation amplitude, we first discuss why the standard approximation for the final-state wave function is not appropriate for a proper investigation of this problem; instead, use of a genuine three-particle wave function for the final state proves to be mandatory. Such is provided by a recently proposed wave function for three charged particles in the continuum [A. M. Mukhamedzhanov and M. Lieber, Phys. Rev. A 54, 3078 (1996)] which possesses all the essential features required. It is an exact solution of the three-body Schrödinger equation, but only asymptotically, i.e., for large distances. Therefore, only qualitative predictions can be made currently, such as predicting the kinematic configurations in which post-decay acceleration effects play a negligible role. Explicit calculations are presented for the single and the double differential cross sections for the 208 Pb( 8 B, 7 Be p) 208 Pb Coulomb breakup reaction. We also investigate the influence of the E2 multipole and find its contribution to be small for small scattering angles, but comparable to the one from the E1 dipole for large scattering angles.

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“…It is remarkable that when we use Eq. (62) in deriving the amplitudes in the post form only the term given by Eq. (197) contributes.…”

Section: Discussionmentioning

confidence: 99%

Surface-integral formulation of scattering theory

et al. 2009

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a b s t r a c tWe formulate scattering theory in the framework of a surface-integral approach utilizing analytically known asymptotic forms of the two-body and three-body scattering wavefunctions. This formulation is valid for both short-range and long-range Coulombic interactions. New general definitions for the potential scattering amplitude are presented. For the Coulombic potentials, the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure. New post and prior forms for the Coulomb three-body breakup amplitude are derived. This resolves the problem of the inability of the conventional scattering theory to define the post form of the breakup amplitude for charged particles. The new definitions can be written as surfaceintegrals convenient for practical calculations. The surface-integral representations are extended to amplitudes of direct and rearrangement scattering processes taking place in an arbitrary three-body system. General definitions for the wave operators are given that unify the currently used channel-dependent definitions.

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Asymptotic wave function for three charged particles in the continuum

Cited by 36 publications

References 7 publications

Proton-deuteron elastic scattering from 2.5 to 22.7 MeV

Proton-deuteron elastic scattering from 2.5 to 22.7 MeV

Three-body Coulomb interaction effects in the final state of thePb208(B8,
Alt
¹
,
Irgaziev
²
,
Mukhamedzhanov
³

2005
Phys. Rev. C
Self Cite
32
3
43
0
View full text Add to dashboard Cite

Surface-integral formulation of scattering theory

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Asymptotic wave function for three charged particles in the continuum

Cited by 36 publications

References 7 publications

Proton-deuteron elastic scattering from 2.5 to 22.7 MeV

Proton-deuteron elastic scattering from 2.5 to 22.7 MeV

Three-body Coulomb interaction effects in the final state of thePb208(B8,Alt1, Irgaziev2, Mukhamedzhanov3 2005Phys. Rev. CSelf Cite323430View full textAdd to dashboardCite

Surface-integral formulation of scattering theory

Contact Info

Product

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Three-body Coulomb interaction effects in the final state of thePb208(B8,
Alt
¹
,
Irgaziev
²
,
Mukhamedzhanov
³

2005
Phys. Rev. C
Self Cite
32
3
43
0
View full text Add to dashboard Cite