We study possible bound states of the ⌬⌬ and ⌬⌬⌬ systems by using a two-body interaction derived from the chiral quark cluster model. The systems of two and three deltas, which will appear in nature as dibaryon and tribaryon resonances with zero strangeness, have large similarities with the corresponding two-and threenucleon systems. The two deepest bound ⌬⌬ states are those with angular momentum and isospin ( j,i)ϭ(1,0) and ( j,i)ϭ(0,1) which have the same quantum numbers as the 3 S 1 -3 D 1 ͑deuteron͒ and 1 S 0 ͑virtual͒ NN states. Similarly, the more strongly bound ⌬⌬⌬ state is that with angular momentum and isospin (J,I)ϭ( 1 2 , 1 2 ) which has precisely the same quantum numbers as the triton.
We construct the Perelomov number coherent states for any three su(1, 1) Lie algebra generators and study some of their properties. We introduce three operators which act on Perelomov number coherent states and close the su(1, 1) Lie algebra. We show that the most general SU (1, 1) coherence-preserving Hamiltonian has the Perelomov number coherent states as eigenfunctions, and we obtain their time evolution. We apply our results to obtain the non-degenerate parametric amplifier eigenfunctions, which are shown to be the Perelomov number coherent states of the two-dimensional harmonic oscillator.
We calculate the two- and three-body spectra of deltas using a chiral
quark cluster model and a meson-exchange model for the ΔΔ
interaction. The ordering of the states is pretty much model independent.
Both models predict the existence of four ΔΔ bound states
that couple to the NN system. Three of these states can be identified
with known NN states. The fourth state corresponds to a new NN
resonance with isospin 0, spin 3 and positive parity. A possible signal of
this resonance appears in recent analyses of NN data.
We show in a systematic and clear way how factorization methods can be used to construct the generators for hidden and dynamical symmetries. This is shown by studying the 2D problems of hydrogen atom, the isotropic harmonic oscillator and the radial potential Aρ 2ζ−2 − Bρ ζ−2 . We show that in these cases the non-compact (compact) algebra corresponds to so(2, 1) (su (2)).
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