Download construction of antisymmetric basis states for six bo…

CONSTRUCTION OF ANTISYMMETRIC BASIS STATES FOR SIX BODY
SYSTEMS IN TRANSLATIONALLY INVARIANT BASIS
Augustinas Stepšys1 , Saulius Mickevičius2 , Darius Germanas3 , Ramutis Kazys Kalinauskas3
1 Department
of Theoretical Physics,Faculty of Physics of Vilnius University, Saulėtekio Avenue 9,build. 3, 10222,
Vilnius , Lithuania
2 Vytautas Magnus University, K. Donelaičio str. 58, LT-44248, Kaunas, Lithuania
3 Center for Physical Sciences and Technology, Savanoriu str. 231, LT-02300 Vilnius, Lithuania
[email protected]
Ab-initio approach allows solving nuclear physics problems using minimal approximations. Recent developments in
ab-initio methods and computing power allows exploration of more complex systems. It also enables us to find out more
about the role of nuclear forces[1][2] or structure of exotic nuclei[3][4].
For constructing wavefunction of the nuclear system, we must ensure antisymmetrization of a given system and the
center of mass (CM) elimination. CM problem can be solved by direct construction of the CM free wavefunction. For
this, the relative (Jakobi) coordinates of an identical fermion system are convenient. If the Jakobi coordinates are used,
then the antisymetrization procedure can be done in isospin formalism. Then use of Slater determinants is not necessary
and spurious state elimination from antisymmetrized wavefunction sample is avoided. This allows significant reduction
of matrix dimensions and certain simplification of whole antisymmetrization procedure.
Construction of antisymmetric wavefunction for a six body system in translationally invariant basis can be based
on eigenvalue calculation of two particle transposition operator P of a symmetry group S6 . In this method, six particle
system is partitioned into three particle sub-clusters (Fig.1). The separate subcluster nucleon basis states are already
antisymmetrized[5]. Then the six body system can be characterized by good quantum numbers: Oscillator quanta E, total
angular momentum J, parity π, isospin T and additional integer quantum number ∆ for unambiguous enumeration of the
basis states.
In presentation, the procedure of antisymmetric basis state construction using symmetry group transposition operators for six particle nuclear system with intrinsic clusterization will be given.
Fig. 1. Six body system in Jacobi coordinates with intrinsic bi-clusterization.
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S. Mickevičius, D. Germanas, R. K. Kalinauskas, Cent. Eur. J. Phys. 11 (2013), 568.