Breakup of three particles within the adiabatic expansion method

General expressions for the breakup cross sections in the lab frame for $1+2$ reactions are given in terms of the hyperspherical adiabatic basis. The three-body wave function is expanded in this basis and the corresponding hyperradial functions are obtained by solving a set of second order differential equations. The ${\cal S}$-matrix is computed by using two recently derived integral relations. Even though the method is shown to be well suited to describe $1+2$ processes, there are nevertheless particular configurations in the breakup channel (for example those in which two particles move away close to each other in a relative zero-energy state) that need a huge number of basis states. This pathology manifests itself in the extremely slow convergence of the breakup amplitude in terms of the hyperspherical harmonic basis used to construct the adiabatic channels. To overcome this difficulty the breakup amplitude is extracted from an integral relation as well. For the sake of illustration, we consider neutron-deuteron scattering. The results are compared to the available benchmark calculations

Momentum distributions and reaction mechanisms for breakup of two--neutron halos

A theoretical model able to describe fragmentation reactions of three--body halo nuclei on different targets, from light to heavy, is used to compute neutron and core momentum distributions. Both Coulomb and nuclear interactions are simultaneously included. We specify the different reaction mechanisms related to various processes. The method is applied to fragmentation of $^6$He and $^{11}$Li on C and Pb. We find good agreement with the available experimental results.Comment: 10 pages, 3 figures, Phys.Lett.B in pres

Three-body structure of the low-lying 17^{17}Ne-states

The Borromean nucleus $^{17}$Ne ($^{15}$O$+ p + p$) is investigated by using the hyperspheric adiabatic expansion for a a three-body system. The measured size of $^{15}$O and the low-lying resonances of $^{16}$F ($^{15}$O$+ p$) are first used as constraints to determine both central and spin-dependent two-body interactions. Then, the ground state structure of $^{17}$Ne is found to be an almost equal mixture of $s^2$ and $d^2$ proton-$^{15}$O relative states, the two lowest excited states have about 80% of $sd$-mixed components, and for the next two excited three-body states the proton-$^{15}$O relative s-states do not contribute. The spatial extension is as in ordinary nuclei. The widths of the resonances are estimated by the WKB transmission through the adiabatic potentials and found in agreement with the established experimental limits. We compare with experimental information and previous works.Comment: 29 pages, 7 postscript figures, to be published in Nuclear Physics

Three-body bremsstrahlung and the rotational character of the 12C-spectrum

The electric quadrupole transitions between $0^+$, $2^+$, and $4^+$ states in $^{12}$C are investigated in a $3\alpha$ model. The three-body wave functions are obtained by means of the hyperspherical adiabatic expansion method, and the continuum is discretized by imposing a box boundary condition. Corresponding expressions for the continuum three-body ($3\alpha$) bremsstrahlung and photon dissociation cross sections are derived and computed for two different $\alpha-\alpha$ potentials. The available experimental energy dependence is reproduced and a series of other cross sections are predicted. The transition strengths are defined and derived from the cross sections, and compared to schematic rotational model predictions. The computed properties of the $^{12}$C resonances suggest that the two lowest bands are made, respectively, by the states $\{0^+_1, 2^+_1, 4^+_2\}$ and $\{0^+_2, 2^+_2, 4^+_1\}$. The transitions between the states in the first band are consistent with the rotational pattern corresponding to three alphas in an equal sided triangular structure. For the second band, the transitions are also consistent with a rotational pattern, but with the three alphas in an aligned distribution.Comment: To be published in Phys. Rev.

Inclusive quasielastic electron scattering on 6^6He: a probe of the halo structure

We investigate inclusive electron scattering reactions on two-neutron halo nuclei in the quasielastic region. Expressions for the cross section and structure functions are given assuming that the halo nucleus can be described as a three-body system (${core}+n+n$). The method is applied to $^6$He. We compute cross sections and structure functions, and investigate the kinematic conditions for which the observables are determined either by $\alpha$-knockout or by halo neutron-knockout. The optimal kinematical domain to disantangle the momentum distributions of the various components of the three--body system ($q \lesssim 200$ MeV/c and $\omega < q^2/2M_N + 20$ MeV) are explored.Comment: 10 pages, 3 figures. Physics Letters B, in pres

Spin-dependent effective interactions for halo nuclei

We discuss the spin-dependence of the effective two-body interactions appropriate for three-body computations. The only reasonable choice seems to be the fine and hyperfine interactions known for atomic electrons interacting with the nucleus. One exception is the nucleon-nucleon interaction imposing a different type of symmetry. We use the two-neutron halo nucleus 11Li as illustration. We demonstrate that models with the wrong spin-dependence are basically without predictive power. The Pauli forbidden core and valence states must be consistently treated.Comment: TeX file, 6 pages, 3 postscript figure

Dipole excited states in 11^{11}Li with complex scaling

The 1$^-$ excitations of the three--body halo nucleus $^{11}$Li are investigated. We use adiabatic hyperspherical expansion and solve the Faddeev equations in coordinate space. The method of complex scaling is used to compute the resonance states. The Pauli forbidden states occupied by core neutrons are excluded by constructing corresponding complex scaled phase equivalent two-body potentials. We use a recently derived neutron--core interaction consistent with known structure and reaction properties of $^{10}$Li and $^{11}$Li. The computed dipole excited states with $J^\pi=1/2^+$, $J^\pi=3/2^+$, and $J^\pi=5/2^+$ have energies ranging from 0.6 MeV to 1.0 MeV and widths between 0.15 MeV and 0.65 MeV. We investigate the dependence of the complex energies of these states on the $^{10}$Li spectrum. The finite spin 3/2 of the core and the resulting core-neutron spin-spin interaction are important. The connection with Coulomb dissociation experiments is discussed and a need for better measurements is pointed out.Comment: 28 pages, 6 figures, Nuclear Physics A, in pres

Efimov effect in nuclear three-body resonance decays

We investigate the effects of the nearly fulfilled Efimov conditions on the properties of three-body resonances. Using the hyper-spheric adiabatic expansion method we compute energy distributions of fragments in a three-body decay of a nuclear resonance. As a realistic example we investigate the 1- state in the halo nucleus 11Li within a three-body 9Li+n+n model. Characteristic features appear as sharp peaks in the energy distributions. Their origin, as in the Efimov effect, is in the large two-body s-wave scattering lengths between the pairs of fragments