dorsal/arxiv
View SchemaLong-range behavior of the optical potential for the elastic scattering of charged composite particles
| Authors | E. O. Alt, A. M. Mukhamedzhanov |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9503018 |
| URL | https://arxiv.org/abs/nucl-th/9503018 |
| DOI | 10.1103/PhysRevA.51.3852 |
| Journal | Phys.Rev. A51 (1995) 3852-3867 |
Abstract
The asymptotic behavior of the optical potential, describing elastic scattering of a charged particle $\alpha$ off a bound state of two charged, or one charged and one neutral, particles at small momentum transfer $\Delta_{\alpha}$ or equivalently at large intercluster distance $\rho_{\alpha}$, is investigated within the framework of the exact three-body theory. For the three-charged-particle Green function that occurs in the exact expression for the optical potential, a recently derived expression, which is appropriate for the asymptotic region under consideration, is used. We find that for arbitrary values of the energy parameter the non-static part of the optical potential behaves for $\Delta_{\alpha} \rightarrow 0$ as $C_{1}\Delta_{\alpha} + o\,(\Delta_{\alpha})$. From this we derive for the Fourier transform of its on-shell restriction for $\rho_{\alpha} \rightarrow \infty$ the behavior $-a/2\rho_{\alpha}^4 + o\,(1/\rho_{\alpha}^4)$, i.e., dipole or quadrupole terms do not occur in the coordinate-space asymptotics. This result corroborates the standard one, which is obtained by perturbative methods. The general, energy-dependent expression for the dynamic polarisability $C_{1}$ is derived; on the energy shell it reduces to the conventional polarisability $a$ which is independent of the energy. We emphasize that the present derivation is {\em non-perturbative}, i.e., it does not make use of adiabatic or similar approximations, and is valid for energies {\em below as well as above the three-body dissociation threshold}.
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"abstract": "The asymptotic behavior of the optical potential, describing elastic\nscattering of a charged particle $\\alpha$ off a bound state of two charged, or\none charged and one neutral, particles at small momentum transfer\n$\\Delta_{\\alpha}$ or equivalently at large intercluster distance\n$\\rho_{\\alpha}$, is investigated within the framework of the exact three-body\ntheory. For the three-charged-particle Green function that occurs in the exact\nexpression for the optical potential, a recently derived expression, which is\nappropriate for the asymptotic region under consideration, is used. We find\nthat for arbitrary values of the energy parameter the non-static part of the\noptical potential behaves for $\\Delta_{\\alpha} \\rightarrow 0$ as\n$C_{1}\\Delta_{\\alpha} + o\\,(\\Delta_{\\alpha})$. From this we derive for the\nFourier transform of its on-shell restriction for $\\rho_{\\alpha} \\rightarrow\n\\infty$ the behavior $-a/2\\rho_{\\alpha}^4 + o\\,(1/\\rho_{\\alpha}^4)$, i.e.,\ndipole or quadrupole terms do not occur in the coordinate-space asymptotics.\nThis result corroborates the standard one, which is obtained by perturbative\nmethods. The general, energy-dependent expression for the dynamic\npolarisability $C_{1}$ is derived; on the energy shell it reduces to the\nconventional polarisability $a$ which is independent of the energy. We\nemphasize that the present derivation is {\\em non-perturbative}, i.e., it does\nnot make use of adiabatic or similar approximations, and is valid for energies\n{\\em below as well as above the three-body dissociation threshold}.",
"arxiv_id": "nucl-th/9503018",
"authors": [
"E. O. Alt",
"A. M. Mukhamedzhanov"
],
"categories": [
"nucl-th"
],
"doi": "10.1103/PhysRevA.51.3852",
"journal_ref": "Phys.Rev. A51 (1995) 3852-3867",
"title": "Long-range behavior of the optical potential for the elastic scattering of charged composite particles",
"url": "https://arxiv.org/abs/nucl-th/9503018"
},
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