Three-body continuum energy correlations in Borromean halo nuclei. II

Abstract

The general properties of intrinsic energy correlations in the three-body continuum of Borromean halo nuclei are considered. A model that describes the system as a three-body α + n + n cluster structure and reproduces the experimentally known properties of 6 He and 6 Li is used to study low-lying resonances and soft modes. The intrinsic correlated structure of the 6 He continuum reveals a unique structure for three-body 2 + 1 , 2 + 2 , and 1 + 1 resonances and a lack of resonant structure in soft dipole and monopole modes.

Three-body continuum energy correlations in Borromean halo nuclei. III. Short-range external fields

“…One can expect four main physical sources for amplification of transitions, partly in correspondence with the possible amplification of cross sections for 3 → 3 scattering [3]: (i) True three-body resonances, which are due to interaction of all three particles in the interior domain; (ii) A long lived binary resonance in one of the constituent pairs; (iii) The response of an extended system to long-range transition operators used to excite the continuum; (iv) Resonances due to strong coupling between channels (CC resonance in a few channels) or a parametric resonance in quantum diffusion with complex coefficients [20,21].…”

“…[2] and [3] we summarized the Jacobi spatial x, y and relative momentum k x , k y coordinates necessary to describe the bound and scattering states of three-body systems consisting of a spinless core and two halo nucleons. We henceforth use the same notations for our three-body wave functions and all variables.…”

“…The earliest articles [1] examined simple transition responses, summed over all final states. More recently we have studied general features of the spatial two-dimensional densities [2] and intrinsic energy correlations in 3 → 3 scattering [3], again exemplified by the continuum of 6 He. Three-body core+n + n dynamics and the Schrödinger threebody equation, solved within the method of hyperspherical harmonics (HH) (see Refs.…”

“…Three-body core+n + n dynamics and the Schrödinger threebody equation, solved within the method of hyperspherical harmonics (HH) (see Refs. [1][2][3][4][5]), were used consistently for both bound and continuum states. For 6 He a 'realistic' αn interaction [1,4] with purely repulsive s-wave component and the GPT nn interaction [6] were used.…”

“…acts as a filter. Also, in contrast to transitions from compact bound states, the range of impact parameters acceptable in 3 → 3 scattering is limited by a maximal hypermoment K < 2mE/h 2 ρ where E is the continuum energy, m the nucleon mass and ρ 2 = (A c +2)R is the rms hyperradius of the bound state expressed via rms radii of the core (R A c ) and of the halo nucleus (R A c +2 ) [14], and is also the three-body impact parameter in the 3 → 3 scattering case [3]. The difference between the intrinsic structure of the continuum and responses is most dramatically seen if the binary interactions are set to zero for the continuum wave functions: this is the no-final-state-interaction (NoFSI) case often used for estimates.…”