An SU(3) approach to nuclear multi-cluster problems

Abstract

By combining SU(3) recoupling techniques with the use of the Bergmann-Segal integral transform closed expressions are derived for the interaction kernels of the nuclear cluster model. In a cluster model basis in which the relative motion and internal oscillator wave functions (with arbitrary and different oscillator frequencies) are expanded in SU(3) coupled form, SU(3) reduced matrix elements are evaluated by integral transform methods. Matrix elements in a basis of good angular momentum can be constructed for multi-cluster systems by combining these SU(3) reduced matrix elements with readily available SU(3) Wigner coefficients .

Spectroscopic amplitudes for complex cluster systems

“…This point can be illustrated by the "C + "C cluster decomposition of the A = 24 system. With "C internal functions of SU(3) symmetry (n,~,) = (04), (J,_,P~__,) = (04), the possible channel internal SU(3) quantum numbers are (&) = (OS), (16), (24), (32) and (40). For such a system of two identical fragments, however, the symmetrically coupled internal functions with &+P~ = even, (&) = (08), (24), (40), can couple only with relative motion functions of even Q, (and hence even L), and have positive parity; whereas the antisymmetrically coupled internal functions with &+P~ = odd, (&cr,) = (16), (32) couple only with relative motion functions of odd Q and have negative parity.…”

“…The potential of this technique has been illustrated with a few examples in ref. 24). Details of the technique have also been demonstrated with the calculation of the norms for cluster systems made up of a heavy fragment and an a-particle 25*26) for states of arbitrarily high oscillator excitation in the relative motion degree of freedom.…”

“…In their treatment the complex generator coordinate R corresponds to the Bargmannspace K variable of refs. [23][24][25][26].…”

“…(A detailed discussion of the interaction kernel problem for simple 3-and 4cluster systems can be found in ref. 24)).…”

“…5), analytic expressions are given for the norms of binary-fragment cluster systems in which a light fragment of mass number ft f s 4, has OS internal excitation only. This light fragment is combined with a heavy fragment of mass number A -f, with A-J =< 24, where for simplicity it is assumed that the heavy fragment is in the state of highest possible space symmetry and highest possible W(3) (oscillator quanta) symmetry. This is a useful example since the 5 cases, 4 s A-f s 8,8 5 A-f 5 12, 12 $ A-f 5…”