NOVEL APPLICATIONS OF GROUP THEORY IN NUCLEAR PHYSICS

J. P. Draayer $^a$, J. G. Hirsch $^b$, G. Popa $^c$, Feng
Pan $^{a,d$,

G. Stoitcheva $^a$, A. I. Georgieva $^e$, K. D. Sviratcheva $^a$

$^{a$Louisiana State University, Department of Physics and
Astronomy, 
Baton Rouge, Louisiana, USA

$^b$Instituto de Ciencias Nucleares, Universidad Nacional
Aut\'onoma de M\'exico, M\'exico

$^c$Department of Physics, Rochester Institute of Technology,

Rochester, New York, USA

$^d$Department of Physics, Liaoning Normal University, Dalian, China

$^e$Institute of Nuclear Research and Nuclear Energy,
Bulgarian Academy of Sciences, Sofia, Bulgaria


A general procedure, based on the Bethe ansatz, is proposed for finding algebraic solutions for low-lying $J-0$ states of $2k$ nucleons interacting with one another through a $T-1$ charge independent pairing interaction. Results provided by Richardson are shown to be valid for up to two pairs, $k\leq 2$; we gave expressions for up to three pairs, $k\leq 3$. The results shown that a set of highly nonlinear equations must be solved for $3k \geq 3$.