Use of supersymmetric
isospectral formalism
to realistic quantum many-body problems
BARNALI CHAKRABARTI
Department of Physics,
Kolkata 700 017,
E-mail: chakb@rediffmail.com
Abstract. We
propose a novel mathematical approach for the
calculation of resonances in weakly
bound systems. For any
potential, families of strictly isospectral potentials (with very
different shape) having desirable
and adjustable features can be
generated. For systems having no
bound ground state, an isospectral
potential with a bound state in the
continuum is possible. The
quasi-bound state in the original
shallow potential will be
effectively trapped in the deep
well of the isospectral family,
facilitating more accurate
calculation of resonance energy.
Application to $^{6}$He, $^{6}$Li
and $^{6}$Be yield excellent
results. Another application is the
calculation of Efimov states in
weakly bound three-body system. We
present the result of $^{4}$He
trimer,
where the first excited state is claimed to be an Efimov
state.
Keywords. Halo nuclei;
resonance; isospectral potential; Efimov.
PACS Nos 21.45.+v; 21.10.Dr; 27.10.+h