arXiv subjects

E. Garrido

Publications and source records attributed to E. Garrido.

At least 73 records · Page 4Linked to original sources

arXiv2009

Integral relations for three-body continuum states with the adiabatic expansion

Application of the Hyperspherical Adiabatic expansion to describe three-body scattering states suffers the problem of a very slow convergence. Contrary to what happens for bound states, a huge number of hyperradial equations has to be solved, and even if done, the extraction of the scattering amplitude is problematic. In this paper we show how to obtain accurate scattering phase shifts using the Hyperspherical Adiabatic expansion. To this aim two integral relations, derived from the Kohn Variational Principle, are used. The convergence of this procedure is as fast as for bound states.

nucl-th↗

arXiv2008

Three-body decays: structure, decay mechanism and fragment properties

We discuss the three-body decay mechanisms of many-body resonances. R-matrix sequential description is compared with full Faddeev computation. The role of the angular momentum and boson symmetries is also studied. As an illustration we show the computed $α$-particle energy distribution after the decay of 12C(1^+) resonance at 12.7 MeV.

nucl-th↗

arXiv2008

Necessary conditions for accurate computations of three-body partial decay widths

The partial width for decay of a resonance into three fragments is largely determined at distances where the energy is smaller than the effective potential producing the corresponding wave function. At short distances the many-body properties are accounted for by preformation or spectroscopic factors. We use the adiabatic expansion method combined with the WKB approximation to obtain the indispensable cluster model wave functions at intermediate and larger distances. We test the concept by deriving conditions for the minimal basis expressed in terms of partial waves and radial nodes. We compare results for different effective interactions and methods. Agreement is found with experimental values for a sufficiently large basis. We illustrate the ideas with realistic examples from $α$-emission of $^{12}$C and two-proton emission of $^{17}$Ne. Basis requirements for accurate momentum distributions are briefly discussed.

nucl-th↗

arXiv2008

alpha particle momentum distributions from 12C decaying resonances

The computed $α$ particle momentum distributions from the decay of low-lying $^{12}$C resonances are shown. The wave function of the decaying fragments is computed by means of the complex scaled hyperspherical adiabatic expansion method. The large-distance part of the wave functions is crucial and has to be accurately calculated. We discuss energy distributions, angular distributions and Dalitz plots for the $4^+$, $1^+$ and $4^-$ states of $^{12}$C.

nucl-th↗

arXiv2008

Momentum distributions of $α$-particles from decaying low-lying $^{12}$C-resonances

The complex scaled hyperspherical adiabatic expansion method is used to compute momentum and energy distributions of the three $α$-particles emerging from the decay of low-lying $^{12}$C-resonances. The large distance continuum properties of the wave functions are crucial and must be accurately calculated. We discuss separately decays of natural parity states: two $0^+$, one $1^{-}$, three $2^+$, one $3^-$, two $4^+$, one $6^+$, and one of each of unnatural parity, $1^{+}$, $2^-$, $3^+$, $4^-$. The lowest natural parity state of each $J^π$ decays predominantly sequentially via the $^{8}$Be ground state whereas other states including unnatural parity states predominantly decay directly to the continuum. We present Dalitz plots and systematic detailed momentum correlations of the emerging $α$-particles.

nucl-th↗

arXiv2008

Distinction between sequential and direct three-body decays

We discuss the three-body decay mechanisms of many-body resonances. Sequential decays proceed via two-body configurations after emission of the third particle. In direct decay all three particles leave simultaneously their interaction regions. The intermediate paths within the interaction regions are not observables and only accessible through models. The momentum distributions carry, apart from polarization, all possible information about decay modes and resonance structure. In this context we discuss detailed results for the decay of the $^{9}$Be($5/2^-$) resonance.

nucl-th↗

arXiv2008

Three-body structure of low-lying 12Be states

We investigate to what extent a description of 12Be as a three-body system made of an inert 10Be-core and two neutrons is able to reproduce the experimental 12Be data. Three-body wave functions are obtained with the hyperspherical adiabatic expansion method. We study the discrete spectrum of 12Be, the structure of the different states, the predominant transition strengths, and the continuum energy spectrum after high energy fragmentation on a light target. Two 0+, one 2+, one 1- and one 0- bound states are found where the first four are known experimentally whereas the 0- is predicted as an isomeric state. An effective neutron charge, reproducing the measured B(E1) transition and the charge rms radius in 11Be, leads to a computed B(E1) transition strength for 12Be in agreement with the experimental value. For the E0 and E2 transitions the contributions from core excitations could be more significant. The experimental 10Be-neutron continuum energy spectrum is also well reproduced except in the energy region corresponding to the 3/2- resonance in 11Be where core excitations contribute.

nucl-th↗

arXiv2008

Cluster sum rules for three-body systems with angular-momentum dependent interactions

We derive general expressions for non-energy weighted and energy-weighted cluster sum rules for systems of three charged particles. The interferences between pairs of particles are found to play a substantial role. The energy-weighted sum rule is usually determined by the kinetic energy operator, but we demonstrate that it has similar additional contributions from the angular momentum and parity dependence of two- and three-body potentials frequently used in three-body calculations. The importance of the different contributions is illustrated with the dipole excitations in $^6$He. The results are compared with the available experimental data.

nucl-th↗

arXiv2007

Isomeric 0- halo-states in 12Be and 11Li

We predict the existence of an isomeric 0$^-$-state in $^{12}$Be at an excitation energy of about 2.5 MeV, and a 0$^-$-resonance in $^{11}$Li with both energy and width of about 1 MeV corresponding to two-neutron emission. The structure of these halo-like states are like the 1$^-$-states which means essentially a core surrounded by two neutrons in single-particle $s$ and p-states. The life-time of the $^{12}$Be state is determined by $M1$ or $M2$-emission, $τ(M1) \approx 10^{-11}$ s or $τ(M2) \approx 10^{-8}$ s estimated for photon energies of 0.1 MeV and 0.6 MeV, respectively.

nucl-th↗

arXiv2007

Decay of low-lying 12C resonances within a 3alpha cluster model

We compute energy distributions of three $α$-particles emerging from the decay of $^{12}$C resonances by means of the hyperspherical adiabatic expansion method combined with complex scaling. The large distance continuum properties of the wave functions are crucial and must be accurately calculated. The substantial changes from small to large distances determine the decay mechanisms. We illustrate by computing the energy distributions from decays of the $1^{+}$ and $3^-$-resonances in $^{12}$C. These states are dominated by direct and sequential decays into the three-body continuum respectively.

nucl-th↗

arXiv2007

Triple charged-particle decays of resonances illustrated by 12C-states

The hyperspherical adiabatic expansion is combined with complex scaling and used to calculate the energy distributions of the particles arising from three-body decaying low-lying $^{12}$C resonances. The large distance continuum properties of the wavefunctions are crucial and must be accurately calculated. The substantial changes from small to large distances determine the decay mechanisms. We illustrate by computing the energy distributions from decays of the $1^{-}$, $2^-$ and $4^{-}$-resonances in $^{12}$C. These states are dominated by sequential ($1^-$), through the $^{8}$Be ground state, and direct ($2^-$, $4^-$) decays.

nucl-th↗

arXiv2007

Energy distributions from three-body decaying many-body resonances

We compute energy distributions of three particles emerging from decaying many-body resonances. We reproduce the measured energy distributions from decays of two archetypal states chosen as the lowest $0^{+}$ and $1^{+}$-resonances in $^{12}$C populated in $β$-decays. These states are dominated by sequential, through the $^{8}$Be ground state, and direct decays, respectively. These decay mechanisms are reflected in the ``dynamic'' evolution from small, cluster or shell-model states, to large distances, where the coordinate or momentum space continuum wavefunctions are accurately computed.

nucl-th↗

arXiv2007

Isospin mixing and energy distributions in three-body decay

The structure of the second 2$^+$ resonance in $^{6}$Li is investigated with special emphasis on its isospin 0 components. The wave functions are computed in a three-body model ($α$+$n$+$p$) using the hyperspherical adiabatic expansion method combined with complex scaling. In the decay into three free particles the symmetry conserving short-range interaction dominates at short distance whereas the symmetry breaking Coulomb interaction dominates at intermediate and large distances resulting in substantial isospin mixing. We predict the mixing and the energy distributions of the fragments after decay. Computations are consistent with available experiments. We conjecture that nuclear three-body decays frequently produce such large isospin mixing at large distance where the energy distributions. are determined.

nucl-th↗

arXiv2007

Structure of low-lying 12C-resonances

The hyperspherical adiabatic expansion is combined with complex scaling and used to calculate low-lying nuclear resonances of $^{12}$C in the $3α$-model. We use Ali-Bodmer potentials and compare results for other potentials $α-α$ with similar $^{8}$Be-properties. A three-body potential is used to adjust the $^{12}$C-resonance positions to desired values extending the applicability of the method to many-body systems decaying into three $α$-particles. For natural choices of three-body potentials we find 14 resonances below the proton separation threshold, i.e. two $0^{+}$, three $2^{+}$, two $4^{+}$, one of each of $1^{\pm}$, $2^{-}$, $3^{\pm}$, $4^{-}$, and $6^{+}$. The partial wave decomposition of each resonance is calculated as function of hyperradius. Strong variation is found from small to large distance. Connection to previous experimental and theoretical results are discussed and agreements as well as disagreements are emphasized.

nucl-th↗

arXiv2007

Neutron-$^3$H potentials and the $^5$H-properties

The continuum resonance spectrum of $^5$H ($^3$H+$n$+$n$) is investigated by use of the complex scaled hyperspherical adiabatic expansion method. The crucial $^3$H-neutron potential is obtained by switching off the Coulomb part from successful fits to $^3$He-proton experimental data. These two-body potentials must be expressed exclusively by operators conserving the nucleon-core mean field angular momentum quantum numbers. The energies $E_R$ and widths $Γ_R$ of the $1/2^+$ ground-state resonance and the lowest two excited $5/2^+$ and $3/2^+$-resonances are found to be $(1.6,1.5)$ MeV, $(2.8,2.5)$ MeV and $(3.2,3.9)$ MeV, respectively. These results agree with most of the experimental data. The energy distributions of the fragments after decay of the resonances are predicted.

nucl-th↗

arXiv2007

Resonances in three-body systems with short and long-range interactions

The complex scaling method permits calculations of few-body resonances with the correct asymptotic behaviour using a simple box boundary condition at a sufficiently large distance. This is also valid for systems involving more than one charged particle. We first apply the method on two-body systems. Three-body systems are then investigated by use of the (complex scaled) hyperspheric adiabatic expansion method. The case of the 2$^+$ resonance in $^6$Be and $^6$Li is considered. Radial wave functions are obtained showing the correct asymptotic behaviour at intermediate values of the hyperradii, where wave functions can be computed fully numerically.

nucl-th↗

arXiv2006

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.

nucl-th↗

arXiv2005

Anatomy of three-body decay III. Energy distributions

We address the problem of calculating momentum distributions of particles emerging from the three-body decay of a many-body resonance. We show that these distributions are determined by the asymptotics of the coordinate-space complex-energy wave-function of the resonance. We use the hyperspherical adiabatic expansion method where all lengths are proportional to the hyperradius. The structures of the resonances are related to different decay mechanisms. For direct decay all inter-particle distances increase proportional to the hyperradius at intermediate and large distances. Sequential three-body decay proceeds via spatially confined quasi-stationary two-body configurations. Then two particles remain close while the third moves away. The wave function may contain mixtures which produce coherence effects at small distances, but the energy distributions can still be added incoherently. Two-neutron halos are discussed in details and illustrated by the $2^+$ resonance in $^{6}$He. The dynamic evolution of the decay process is discussed.

nucl-th↗