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Title: Structure and decays of nuclear three-body systems: The Gamow coupled-channel method in Jacobi coordinates

Authors:
; ; ;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1398161
Grant/Contract Number:
SC0013365; SC0008511; SC0009971
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review C
Additional Journal Information:
Journal Volume: 96; Journal Issue: 4; Related Information: CHORUS Timestamp: 2017-10-05 17:35:41; Journal ID: ISSN 2469-9985
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English

Citation Formats

Wang, S. M., Michel, N., Nazarewicz, W., and Xu, F. R. Structure and decays of nuclear three-body systems: The Gamow coupled-channel method in Jacobi coordinates. United States: N. p., 2017. Web. doi:10.1103/PhysRevC.96.044307.
Wang, S. M., Michel, N., Nazarewicz, W., & Xu, F. R. Structure and decays of nuclear three-body systems: The Gamow coupled-channel method in Jacobi coordinates. United States. doi:10.1103/PhysRevC.96.044307.
Wang, S. M., Michel, N., Nazarewicz, W., and Xu, F. R. Thu . "Structure and decays of nuclear three-body systems: The Gamow coupled-channel method in Jacobi coordinates". United States. doi:10.1103/PhysRevC.96.044307.
@article{osti_1398161,
title = {Structure and decays of nuclear three-body systems: The Gamow coupled-channel method in Jacobi coordinates},
author = {Wang, S. M. and Michel, N. and Nazarewicz, W. and Xu, F. R.},
abstractNote = {},
doi = {10.1103/PhysRevC.96.044307},
journal = {Physical Review C},
number = 4,
volume = 96,
place = {United States},
year = {Thu Oct 05 00:00:00 EDT 2017},
month = {Thu Oct 05 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on October 5, 2018
Publisher's Accepted Manuscript

Citation Metrics:
Cited by: 1work
Citation information provided by
Web of Science

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  • The jacobi coordinates is used to eliminate center of mass motion of three body systems. We write the results in hyperspherical coordinates and expand eigenfunction in a series of orthonormal complete set of Y{sub k{alpha}{sub i}} ({omega}{sub i}) in partition i of jacobi coordinates. The matrix elements of two body interaction potential in hyperspherical harmonic approach are determined exactly using computed analytical form of Raynal-Revai coefficients to change the base set of Y{sub k{alpha}{sub i}} ({omega}{sub i}) to other set such as Y{sub k{alpha}{sub i}} ({omega}{sub j}. The generalized Laguerre functions are used to change the second order coupled differentialmore » equations to set of non-differential matrix equation. This is solved to find energy eigenvalues and eigenfunctions of three body molecules. The obtained analytical results are in a very good agreement with used computational method.« less
  • We discuss the bound states of weakly bound van der Waals trimers within the framework of hyperspherical coordinates. The wave function is expanded in terms of hyperspherical harmonics, which form a complete basis set in the angular variables. The resulting set of coupled second-order differential equations in the hyperradius is solved exactly. Our method gives a value for the zero-point energy of H{sup +}{sub 3} which is in excellent agreement with previous calculations. For (H{sub 2}){sub 3} and Ne{sub 3}, however, our results show some discrepancy with earlier work.
  • The continuum discretized coupled channels (CDCC) method is compared with the exact solution of the three-body Faddeev equations in momentum space. We present results for (i) elastic and breakup observables of d+{sup 12}C at E{sub d}=56 MeV (ii) elastic scattering of d+{sup 58}Ni at E{sub d}=80 MeV, and (iii) elastic, breakup, and transfer observables for {sup 11}Be+p at E{sub {sup 11}Be}/A=38.4 MeV. Our comparative studies show that in the first two cases, the CDCC method is a good approximation of the full three-body Faddeev solution, but for the {sup 11}Be exotic nucleus, depending on the observable or the kinematic regime,more » it may miss some of the dynamic three-body effects that appear through the explicit coupling to the transfer channel.« less
  • Relationships between alternative sets of hyperspherical coordinate systems for the treatment of three-body systems are developed. Transformations of hyperspherical harmonics for S states under a change of intrinsic angles are derived, and applied to harmonic expansions of potential energy surfaces.
  • The adiabatic channel wave functions of Coulombic three-body systems are investigated in mass-weighted hyperspherical coordinates. We consider the {ital ABA} Coulombic systems, where two of the particles are identical, and examine the density distribution functions at fixed hyperradii {ital R} for different systems as the mass ratio {lambda}={ital m}{sub {ital A}}/{ital m}{sub {ital B}} varies from the atomic limit ({lambda}{r arrow}0, as in H{sup {minus}}) to the molecular limit ({lambda}{r arrow}{infinity}, as in H{sub 2}{sup +}). The bonding and antibonding as well as the rovibrational characters of the three-body systems are illustrated by these density plots.