Convergence patterns of hyperspherical harmonic expansion—1S states of the helium atom

1998 ◽  
Vol 43 (8) ◽  
pp. 701-702
Author(s):  
Yixuan Wang ◽  
Yunjie Mi ◽  
Conghao Deng ◽  
Xiuhui Lu
Keyword(s):  
Helium Atom ◽  
Hyperspherical Harmonic ◽  
Hyperspherical Harmonic Expansion

Correlated hyperspherical-harmonic expansion for three-nucleon systems

1990 ◽  
Vol 9 (1) ◽  
pp. 1-9 ◽  
Author(s):  
S. Rosati ◽  
M. Viviani ◽  
A. Kievsky
Keyword(s):  
Hyperspherical Harmonic ◽  
Hyperspherical Harmonic Expansion

Beyond the first order of the Hyperspherical Harmonic Expansion Method

1982 ◽  
Vol 138 (2) ◽  
pp. 275-318 ◽  
Author(s):  
M Fabre de la Ripelle ◽  
H Fiedeldey ◽  
G Wiechers
Keyword(s):  
Expansion Method ◽  
Hyperspherical Harmonic ◽  
Hyperspherical Harmonic Expansion ◽  
First Order ◽  
Hyperspherical Harmonic Expansion Method

Fast convergent hyperspherical harmonic expansion for three-body systems

1989 ◽  
Vol 189 (1) ◽  
pp. 29-52 ◽  
Author(s):  
M.I Haftel ◽  
V.B Mandelzweig
Keyword(s):  
Hyperspherical Harmonic ◽  
Hyperspherical Harmonic Expansion ◽  
Three Body

Convergence of the hyperspherical harmonic expansion for crystallographic texture

2013 ◽  
Vol 46 (6) ◽  
pp. 1722-1728
Author(s):  
Jeremy K. Mason ◽  
Oliver K. Johnson
Keyword(s):  
Truncation Error ◽  
Orientation Distribution ◽  
Hyperspherical Harmonic ◽  
Addition Theorem ◽  
Hyperspherical Harmonic Expansion ◽  
Spatially Resolved ◽  
Ringing Artifacts ◽  
Pole Figures ◽  
Material Texture ◽  
Spurious Oscillations

Advances in instrumentation allow a material texture to be measured as a collection of spatially resolved crystallite orientations rather than as a collection of pole figures. However, the hyperspherical harmonic expansion of a collection of spatially resolved crystallite orientations is subject to significant truncation error, resulting in ringing artifacts (spurious oscillations around sharp transitions) and false peaks in the orientation distribution function. This article finds that the ringing artifacts and the accompanying regions of negative probability density may be mitigated or removed entirely by modifying the coefficients of the hyperspherical harmonic expansion by a simple multiplicative factor. An addition theorem for the hyperspherical harmonics is derived as an intermediate result.

THREE-BODY FORCES FROM n-BODY INVERSION

1995 ◽  
Vol 04 (02) ◽  
pp. 431-441
Author(s):  
E.J.O. GAVIN ◽  
H. FIEDELDEY ◽  
S.A. SOFIANOS
Keyword(s):  
Body Force ◽  
Order Approximation ◽  
Expansion Method ◽  
Bound State ◽  
Hyperspherical Harmonic ◽  
Hyperspherical Harmonic Expansion ◽  
Body Forces ◽  
Quark System ◽  
Three Body ◽  
Hyperspherical Harmonic Expansion Method

Within the context of the lowest order approximation to the calculation of the n-body bound state in the Hyperspherical Harmonic Expansion Method, the hypercentral potential may be determined from n-body spectral data. Previously, we showed how the two-body force can be determined exactly from the hypercentral potential in the absence of three-body forces. In this paper, we investigate to what extent the three-body force can be determined if the two-body force is assumed to be known. For this purpose, a three-quark system is considered.

Convergence of the hyperspherical-harmonic expansion for two-electron atoms

1994 ◽  
Vol 50 (4) ◽  
pp. 3521-3524 ◽  
Author(s):  
Tapan Kumar Das ◽  
Rakhi Chattopadhyay ◽  
Prasanta Kumar Mukherjee
Keyword(s):  
Hyperspherical Harmonic ◽  
Hyperspherical Harmonic Expansion

The first order of the hyperspherical harmonic expansion method

1979 ◽  
Vol 123 (1) ◽  
pp. 185-232 ◽  
Author(s):  
M Fabre de la Ripelle ◽  
J Navarro
Keyword(s):  
Expansion Method ◽  
Hyperspherical Harmonic ◽  
Hyperspherical Harmonic Expansion ◽  
First Order ◽  
Hyperspherical Harmonic Expansion Method

Convergence of the hyperspherical harmonic expansion for four body scattering problems

2004 ◽  
Vol 737 ◽  
pp. 205-209
Author(s):  
M. Viviani ◽  
A. Kievsky ◽  
S. Rosati
Keyword(s):  
Hyperspherical Harmonic ◽  
Scattering Problems ◽  
Hyperspherical Harmonic Expansion
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