arXiv subjects

A. S. Jensen

Publications and source records attributed to A. S. Jensen.

At least 127 records · Page 7Linked to original sources

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

Trapped Bose gases with large positive scattering length

We calculate the energy and the condensate fraction of a system of trapped bosons interacting via a short-range two-body potential with positive scattering length. The potential is attractive and has a two-body bound state. When the scattering length is small compared to the trap length the system is model independent: all potential models -- attractive, repulsive and zero-range -- provide similar results. When the scattering length is large the attractive model differs qualitatively from the repulsive and zero-range models. In this regime the system with attractive potential becomes independent of the scattering length, with both the energy and the condensate fraction converging towards finite constants.

quant-ph↗

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.

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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↗

arXiv2005

Origin of three-body resonances

We expose the relation between the properties of the three-body continuum states and their two-body subsystems. These properties refer to their bound and virtual states and resonances, all defined as poles of the $S$-matrix. For one infinitely heavy core and two non-interacting light particles, the complex energies of the three-body poles are the sum of the two two-body complex pole-energies. These generic relations are modified by center-of-mass effects which alone can produce a Borromean system. We show how the three-body states evolve in $^6$He, $^6$Li, and $^6$Be when the nucleon-nucleon interaction is continuously switched on. The schematic model is able to reproduce the main properties in their spectra. Realistic calculations for these nuclei are shown in detail for comparison. The implications of a core with non-zero spin are investigated and illustrated for $^{17}$Ne ($^{15}$O+p+p). Dimensionless units allow predictions for systems of different scales.

nucl-th↗

arXiv2005

Correlated Gaussian method for dilute bosonic systems

The weakly interacting trapped Bose gases have been customarily described using the mean-field approximation in the form of the Gross-Pitaevskii equation. The mean-field approximation, however, has certain limitations, in particular it can not describe correlations between particles. We introduce here an alternative variational approach, based on the correlated Gaussian method, which in its simplest form is as fast and simple as the mean-field approximation, but which allows successive improvements of the trial wave-function by including correlations between particles.

physics.atom-ph↗

arXiv2004

Anatomy of three-body decay I. Schematic models

Sequential three-body decay proceeds via spatially confined quasi-stationary two-body configurations. Direct three-body decay populates the three-body continuum without intermediate steps. The relative importance of these decay modes is discussed in a schematic model employing only Coulomb or centrifugal barrier potentials. Decisive dimensionless charge, mass and energy ratios are derived. Sequential decay is usually favored for charged particles. Small charge and small mass of high energy is preferably emitted first. Without Coulomb potential the sequential decay is favored except when both resonance energy and intermediate two-body energy are large.

nucl-th↗

arXiv2004

Anatomy of three-body decay II. Decay mechanism and resonance structure

We use the hyperspherical adiabatic expansion method to discuss the the two mechanisms of sequential and direct three-body decay. Both short-range and Coulomb interactions are included. Resonances are assumed initially populated by a process independent of the subsequent decay. The lowest adiabatic potentials describe the resonances rather accurately at distances smaller than the outer turning point of the confining barrier. We illustrate with realistic examples of nuclei from neutron ($^{6}$He) and proton ($^{17}$Ne) driplines as well as excited states of beta-stable nuclei ($^{12}$C).

nucl-th↗

arXiv2004

Semi-analytic Faddeev solution to the $N$-boson problem with zero-range interactions

We study two-body correlations for $N$ identical bosons by use of the hyperspherical adiabatic expansion method. We use the zero-range interaction and derive a transcendental equation determining the key ingredient of the hyperradial potential. The necessary renormalization is for both repulsive and attractive interactions achieved with an effective range expansion of the two-body phase-shifts. Our solutions including correlations provide the properties of Bose-Einstein condensates exemplified by stability conditions as established by mean-field Gross-Pitaevskii calculations. The many-body Efimov states are unavoidable for large scattering lengths.

cond-mat.other↗

arXiv2004

Origin of Borromean systems

The complex energies of the three-body resonances for one infinitely heavy particle and two non-interacting light particles are the sum of the two contributing two-body complex resonance energies. The bound state of a Borromean system originates from a resonance when the third interaction is introduced, a finite mass is allowed and proper angular momentum coupling is included. The relative importance of these contributions are investigated and the resulting structure of Borromean systems are traced back to the two-body continuum properties. The $0^+$ and $2^+$ states in $^{6}$He result from neutron-core p-states and the ground and first excited state of $^{11}$Li originate from neutron-core $s^2$ and $sp$-states.

nucl-th↗