Threebody Faddeev equations in twoparticle AltGrassbergerSandhas form with DistortedWaveBornapproximation amplitudes as effective potentials
Abstract
A(d, p)B reactions on heavier nuclei are peripheral at subCoulomb energies and can be peripheral even at energies above the Coulomb barrier due to the presence of the distorted waves in the initial and final channels. Usually, to analyze such reactions the distortedwaveBornapproximation (DWBA) is used. The DWBA amplitude for peripheral reactions is parametrized in terms of the asymptotic normalization coefficient (ANC) of the bound state B = (n A). However, in the DWBA, the coupling of the different channels is not taken into account explicitly. The threebody Faddeev equations written as the twoparticle AltGrassbergerSandhas (AGS) equations are very suitable for the analysis of the A(d, p)B reactions because they take into account explicitly the coupling of the different channels. It is well known that the overall normalization of the DWBA amplitude or even of the more advanced continuumdiscretized coupled channels (CDCC) amplitude for peripheral reactions (both subCoulomb and above the Coulomb barrier) is determined by the ANC. However, it is not apparent that it is the case for the AGS solution due to the coupling of the (d, p) channel to other channels. In this paper, it is proved that the subCoulomb A(d, p)B reaction amplitude, which is amore »
 Authors:

 Texas A & M Univ., College Station, TX (United States)
 Publication Date:
 Research Org.:
 Texas A & M Univ., College Station, TX (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1471708
 Alternate Identifier(s):
 OSTI ID: 1479852
 Grant/Contract Number:
 NA0003841; FG0293ER40773
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review C
 Additional Journal Information:
 Journal Volume: 98; Journal Issue: 4; Journal ID: ISSN 24699985
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Citation Formats
Mukhamedzhanov, Akram M. Threebody Faddeev equations in twoparticle AltGrassbergerSandhas form with DistortedWaveBornapproximation amplitudes as effective potentials. United States: N. p., 2018.
Web. doi:10.1103/PhysRevC.98.044626.
Mukhamedzhanov, Akram M. Threebody Faddeev equations in twoparticle AltGrassbergerSandhas form with DistortedWaveBornapproximation amplitudes as effective potentials. United States. doi:https://doi.org/10.1103/PhysRevC.98.044626
Mukhamedzhanov, Akram M. Tue .
"Threebody Faddeev equations in twoparticle AltGrassbergerSandhas form with DistortedWaveBornapproximation amplitudes as effective potentials". United States. doi:https://doi.org/10.1103/PhysRevC.98.044626. https://www.osti.gov/servlets/purl/1471708.
@article{osti_1471708,
title = {Threebody Faddeev equations in twoparticle AltGrassbergerSandhas form with DistortedWaveBornapproximation amplitudes as effective potentials},
author = {Mukhamedzhanov, Akram M.},
abstractNote = {A(d, p)B reactions on heavier nuclei are peripheral at subCoulomb energies and can be peripheral even at energies above the Coulomb barrier due to the presence of the distorted waves in the initial and final channels. Usually, to analyze such reactions the distortedwaveBornapproximation (DWBA) is used. The DWBA amplitude for peripheral reactions is parametrized in terms of the asymptotic normalization coefficient (ANC) of the bound state B = (n A). However, in the DWBA, the coupling of the different channels is not taken into account explicitly. The threebody Faddeev equations written as the twoparticle AltGrassbergerSandhas (AGS) equations are very suitable for the analysis of the A(d, p)B reactions because they take into account explicitly the coupling of the different channels. It is well known that the overall normalization of the DWBA amplitude or even of the more advanced continuumdiscretized coupled channels (CDCC) amplitude for peripheral reactions (both subCoulomb and above the Coulomb barrier) is determined by the ANC. However, it is not apparent that it is the case for the AGS solution due to the coupling of the (d, p) channel to other channels. In this paper, it is proved that the subCoulomb A(d, p)B reaction amplitude, which is a solution of the twobody AGS equations, is peripheral and is parametrized in terms of the ANC of the bound state B = (nA) if the corresponding DWBA amplitude is peripheral. Both nonlocal separable and local nuclear interaction potentials between the constituent particles are considered. To prove the peripheral character of the AGS amplitude for the subCoulomb A(d, p)B reactions the effective potentials are expressed in terms of the corresponding subCoulomb DWBA amplitudes of the different channels. The analysis of the A(d, p)B reactions above the Coulomb barrier requires the inclusion of the optical potentials. Hence, to analyze such reactions, the AGS equations are generalized by including the optical nuclear potentials in the same manner as it is done in the DWBA. The obtained AGS equations contain the DWBA effective potentials with distorted waves generated by the sum of the nuclear optical and the channel Coulomb potentials. It is shown that if the DWBA amplitude is peripheral than it is also the case for the AGS amplitude, which is also parametrized in terms of the ANC of the bound state B = (nA). Furthermore, the inclusion of the coupling of the different channels in the AGS formalism allows one to improve the treatment of the peripheral subCoulomb and above the Coulomb (d, p) reactions compared to the DWBA and CDCC method.},
doi = {10.1103/PhysRevC.98.044626},
journal = {Physical Review C},
number = 4,
volume = 98,
place = {United States},
year = {2018},
month = {10}
}
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