Few Body Systems
A1 Integral Equations (AGS)
A2 Integro-differential equations (Hyperspherical Harmonics)
A3 Time evolution methods
A4 Supersymmetric Quantum Mechanics (SUSY) and Few-Body systems
A5 Astrophysics
A6 Few--quark systems
A7 Eta-meson light nucleus scattering
A8 Resonances
A9 Molecular Systems
A10 Numerical and computational methods
Collaborators:
Prof. W. Sandhas and members of his group (Bonn),
Dr M. Fabre de la Ripelle (Orsay)
Prof. I. Lagaris and members of his group (Ioannina)
Prof. V.B. Belyaev and members of his group (Dubna),
Dr S.A. Rakityansky (Dubna)
Dr H. Leeb (Vienna)
Prof. E.O. Alt (Mainz),
Dr W. Schweizer (T\"ubingen)
Prof. S.Y. Larsen (Temple),
Mr I. Matamba (Venda).
Prof S Oryu (Tokyo)
[A.1] Integral Equations (AGS)
Purpose:
Study of few-body reactions, such as
n + 3He ---> n + 3He
p + 3H ---> d + d
n + 4He ---> n + 4He
in order to
obtain insight into the low-energy dynamics;
Test the Nucleon-Nucleon force;
study break up and clustering;
phenomena of light nuclei;
study inter-cluster interactions;
study photo- and electro-processes;
develop the necessary numerical methods to
handle reliably fusion and astrophysical reactions.
Published work (during the last 4 years):
----------------------------------------1. S. A Sofianos, H. Fiedeldey, and W. Sandhas, "Photo-disintegration of $^4He$ in the
Integro-differential Equation approach" Phys. Rev. C 48, 2285 (1993).
2. S. A Sofianos, H. Fiedeldey, and W. Sandhas, Photo-induced Reactions on 4He"
Few-Body Systems 7, 193 (1994).
3. S.A. Sofianos, H. Fiedeldey, and G. Ellerkmann, "Inclusion of Final--State-Interaction
Effects in the Photo-disintegration of the alpha-particle"
Few-Body Systems 18, 173(1995).
4. G. Ellerkmann, W. Sandhas, and S. A. Sofianos "Integral Equation Calculations for the
Photo-disintegration of 4He" Few-Body Systems Suppl. 8, 102(1995).
5. G. Ellerkmann, W. Sandhas, S. A. Sofianos, and H. Fiedeldey "Integral Equation
Calculations for the Photo-disintegration process 4He(gamma,n)3He" Phys. Rev C 53, 2638
(1996).
6. S.A. Sofianos, H. Fiedeldey, G. Ellerkmann, and W. Sandhas "Photo-induced Reactions
on 4He" Few-Body Systems
7, 193 (1994). 7. R.M. Adam, H. Fiedeldey, S. A. Sofianos, and H. Leeb, "Error propagation
from the nucleon--nucleon data to three- and four-nucleon binding energies" Nucl. Phys.,
A559, 157 (1993).
8. L. L. Howell, S. A. Sofianos, H. Fiedeldey, and G. Pantis, "Nucleon-alpha Potential by
Marchenko Inversion and Supersymmetry" Nucl. Phys., A556, 29 (1993)
[A.2] Integro-differential equations
(Hyperspherical Harmonics)
Purpose:
Easy construction of wave functions
Obtain Bound states
GO BEYOND A = 4
Published work:
1. M. Fabre de la Ripelle, M. Braun, and S. A. Sofianos, "Integro-differential Equation for a
Large Number of Particles" Submitted: Prog. Theor Phys.
[A.3] Time evolution methods
Purpose:
Study systems where the underlying Hamiltonian is time-dependent. Developing
computational methods for handling the evolution of quantum mechanical systems in time,
i.e., "photograph" the events of a certain process such as the electron-light nucleus
scattering.
Published work:
1. I. E. Lagaris, D. G. Papageorgiou, M. Braun, and S. A. Sofianos, "A Relaxation method
for Nonlocal and non-Hermitian Operators" J. of Comp. Phys. 125, 229 (1996)
[A.4] Supersymmetric Quantum Mechanics (SUSY) and Few-Body systems
Purpose:
To study:
Deep NN potential and their SUSY partners.
Effect of SUSY applied at two--body level on few--body systems. # Intercluster interactions.
Published work: --------------- (see SUSY)
[A.5]Astrophysics
Purpose:
To study Helium--like Atoms in Strong (Astrophysical) Magnetic fields
Besides the astrophysical aspects white dwarf stars are ``high magnetic field laboratories''
For example: The spectrum of the magnetic white dwarf GD229, discovered two decades
ago, is still a complete mystery. This is the same situation as for hydrogen rich white dwarfs
a few years ago. By calculating transitions of helium in strong magnetic fields it might be
possible to decipher these spectra (Step towards understanding white dwarfs)
Calculate bound/bound transitions for helium in strong magnetic fields relevant for white
dwarf stars.
Nucleosynthesis; Primordial abundances of the light elements and their impact on the
standard big--bang nucleosynthesis theory. As a staring point we studied: p + d + e- --->
3He+e- 3He + 4He + e- ----> 3He + 4He + e- at thermonuclear energies.
Published work:
1. S. A. Rakityansky, S. A. Sofianos, L. L. Howell, M. Braun, and V. B. Belyaev, "Nonradiative proton-deuteron fusion in stellar plasastrma" To appear: Nucl. Phys. A.
[A.6] Few--quark systems
Purpose:
Study the few quark system within the non-relativistic few--body theory
Published work:
1. E.J.O Gavin, H.Fiedeldey, H. Leeb, and S. A. Sofianos, "Supersymmetric quantum
mechanics applied to non-relativistic quark models" Int. J. Mod. Phys. A, 8, 1437 (1993).
2. E. J. O. Gavin, H. Fiedeldey, and S. A. Sofianos, "Three-body forces from n-body
inversion" Intern. Journal of Modern Phys. E 4, 431(1995)
3. E. J. O. Gavin, R. M. Adam, H. Fiedeldey, and S. A. Sofianos, "Relationship between the
proton charge form factor and the quark--quark interaction" Few-Body Systems 19,
59(1995)
[A.7] Eta-meson light nucleus scattering
Purpose:
To study the question of isotopic invariance breaking, the meson--nucleus scattering
mechanism and various other particle and nuclear physics questions. Published work: -------------1. S. Rakityansky, S. A. Sofianos and B. V. Belyaev, "Near Threshold eta-meson interaction
with light nuclei in "Effective Interactions in Quantal Systems" ed. S. A. Sofianos, Unisa,
Dec. 1994.
2. S. Rakityansky, S. A. Sofianos, V. B. Belyaev, and W. Sandhas in "On the possibility of
an eta-meson light nucleus bound state formation'' Few-Body Systems Suppl. 9, 227(1995).
3. S. Rakityansky, S. A. Sofianos, W. Sandhas, and V. B. Belyaev "Threshold scattering of
the eta-meson off light nuclei" Physics Letter B 359, 33(1995).
4. V. B. Belyaev, S. A. Rakityansky, S. A. Sofianos, M Braun, and W. Sandhas in "Low-energy interaction of eta-meson with light nuclei'' Chinese Journal of Physics 34,998
(1996).
5. S. A. Rakityansky, S. A. Sofianos, M Braun, V. B. Belyaev, and W. Sandhas in "Quasi-bound states of eta-nucleus systems" Phys. Rev. C 53, R2043 (1996).
[A.8] Resonances
Purpose:
Investigate via an exact method the presence of potential resonances (two-body) and their
manifestation and effects in few-body systems. Extremely important in molecular physics.
Published work:
1. S. Rakityansky, S. A. Sofianos, and K. Amos "A method of calculating the Jost function
for analytic potentials" Il Nuovo Cimento, 111 B, 353 (1996).
2. S. A. Sofianos and S. A. Rakityansky, "Exact method for locating potential resonances
and Regge trajectories" Accepted: J. of Phys. G
[A.9] Molecular systems
Purpose:
Investigate Molecular systems: bound states and ultra-low energy scattering.
The 4He trimer is of interest in various areas of Physics Chemistry, and Molecular physics
such as the condensed-matter, nuclear, and the rare-gas atoms behaviour under
First step towards understanding liquid 4He drops, superfluidity in 4He films.
Work using Variational and Monte-Carlo.
Exact microscopic calculations can, in principle, performed using Faddeev equations.
However, the underlying van der Waal forces are of a hard-core nature which make
investigations via these equations cumbersome and tedious.
Use of Boundary Condition Model.
Published work:
1. M. Braun, S. A. Sofianos, D. G. Papageorgiou, I. E. Lagaris, "Ground State Calculations
for 4He-molecules" Submitted: Nuovo Cimento
2. E. A. Kolganova, A. K. Motovilov, and S. A. Sofianos "Ultra-low energy scattering of a
He atom off a He dimer" Submitted: PRA (Rapid Comm.)
3. E. A. Kolganova, A. K. Motovilov, and S. A. Sofianos "Three--Body Configuration Space
Calculations with Hard Core Potentials" Submitted: PRA
[A.10] Numerical and computational methods
Purpose:
Study various numerical analysis questions!
Published work:
1. M. Braun, S. A. Sofianos, D. G. Papageorgiou, I. E. Lagaris, "An Efficient Chebyshev-Lanzcos Method for obtaining Eigensolutions of the Schr\"odinger Equation on a Grid" J.
Comput. Phys. 125, 215 (1996).