Two-proton radioactivity and three-body decay. III. Integral formulae for decay widths in a simplified semianalytical approach

Three-body decays of resonant states are studied using integral formulae for decay widths. Theoretical approach with a simplified Hamiltonian allows semianalytical treatment of the problem. The model is applied to decays of the first excited $3/2^{-}$ state of $^{17}$Ne and the $3/2^{-}$ ground state of $^{45}$Fe. The convergence of three-body hyperspherical model calculations to the exact result for widths and energy distributions are studied. The theoretical results for $^{17}$Ne and $^{45}$Fe decays are updated and uncertainties of the derived values are discussed in detail. Correlations for the decay of $^{17}$Ne $3/2^-$ state are also studied.Comment: 19 pages, 20 figure

Halo Excitation of 6^6He in Inelastic and Charge-Exchange Reactions

Four-body distorted wave theory appropriate for nucleon-nucleus reactions leading to 3-body continuum excitations of two-neutron Borromean halo nuclei is developed. The peculiarities of the halo bound state and 3-body continuum are fully taken into account by using the method of hyperspherical harmonics. The procedure is applied for A=6 test-bench nuclei; thus we report detailed studies of inclusive cross sections for inelastic $^6$He(p,p')$^6$He$^*$ and charge-exchange $^6$Li(n,p)$^6$He$^*$ reactions at nucleon energy 50 MeV. The theoretical low-energy spectra exhibit two resonance-like structures. The first (narrow) is the excitation of the well-known $2^+$ three-body resonance. The second (broad) bump is a composition of overlapping soft modes of multipolarities $1^-, 2^+, 1^+, 0^+$ whose relative weights depend on transferred momentum and reaction type. Inelastic scattering is the most selective tool for studying the soft dipole excitation mode.Comment: Submitted to Phys. Rev. C., 11 figures using eps

Algebraic Model for scattering of three-s-cluster systems. II. Resonances in the three-cluster continuum of 6He and 6Be

The resonance states embedded in the three-cluster continuum of 6He and 6Be are obtained in the Algebraic Version of the Resonating Group Method. The model accounts for a correct treatment of the Pauli principle. It also provides the correct three-cluster continuum boundary conditions by using a Hyperspherical Harmonics basis. The model reproduces the observed resonances well and achieves good agreement with other models. A better understanding for the process of formation and decay of the resonance states in six-nucleon systems is obtained.Comment: 8 pages, 10 postscript figures, submitted to Phys. Rev.

Excitations in the Halo Nucleus He-6 Following The Li-7(gamma,p)He-6 Reaction

A broad excited state was observed in 6-He with energy E_x = 5 +/- 1 MeV and width Gamma = 3 +/- 1 MeV, following the reaction Li-7(gamma,p)He-6. The state is consistent with a number of broad resonances predicted by recent cluster model calculations. The well-established reaction mechanism, combined with a simple and transparent analysis procedure confers considerable validity to this observation.Comment: 3 pages of LaTeX, 3 figures in PostScript, approved for publication in Phys. Rev. C, August, 200

Comment on ``Large-space shell-model calculations for light nuclei''

In a recent publication Zheng, Vary, and Barrett reproduced the negative quadrupole moment of Li-6 and the low-lying positive-parity states of He-5 by using a no-core shell model. In this Comment we question the meaning of these results by pointing out that the model used is inadequate for the reproduction of these properties.Comment: Latex with Revtex, 1 postscript figure in separate fil

Transition energy correlations in the three-body continuum of Borromean halo nuclei

Energy correlations in transitions from the bound state to the three-body continuum of Borromean halo nuclei are considered. A core+n+n three-body cluster model which reproduces experimentally known properties of {sup 6}He and {sup 11}Li has been used to study low-lying resonances and soft modes. The analysis of the correlated responses in {sup 6}He shows that in the case of the narrow three-body 2{sub 1}{sup +} resonance the transition energy correlations are the same as in the intrinsic correlated structure in 3 {yields} 3 scattering. They differ significantly for wide 2{sub 2}{sup +}, 1{sub 1}{sup +} resonances, and also for the soft dipole and monopole modes, where, due to the transition operators, the intertwining of the ground state and the three-body continuum plays a significant role

Peculiar properties of the cluster-cluster interaction induced by the Pauli exclusion principle

Role of the Pauli principle in the formation of both the discrete spectrum and multi-channel states of the binary nuclear systems composed of clusters is studied in the Algebraic Version of the resonating-group method. Solutions of the Hill-Wheeler equations in the discrete representation of a complete basis of the Pauli-allowed states are discussed for 4He+n, 3H+3H, and 4He+4He binary systems. An exact treatment of the antisymmetrization effects are shown to result in either an effective repulsion of the clusters, or their effective attraction. It also yields a change in the intensity of the centrifugal potential. Both factors significantly affect the scattering phase behavior. Special attention is paid to the multi-channel cluster structure 6He+6He as well as to the difficulties arising in the case when the two clustering configurations, 6He+6He and 4He+8He, are taken into account simultaneously. In the latter case the Pauli principle, even in the absence of a potential energy of the cluster-cluster interaction, leads to the inelastic processes and secures an existence of both the bound state and resonance in the 12Be compound nucleus.Comment: 17 pages, 14 figures, 1 table; submitted to Phys.Rev.C Keywords: light neutron-rich nuclei, cluster model