arXiv subjects

A. S. Jensen

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

At least 109 records · Page 6Linked to original sources

arXiv2010

Few-body decay and recombination in nuclear astrophysics

Three-body continuum problems are investigated for light nuclei of astrophysical relevance. We focus on three-body decays of resonances or recombination via resonances or the continuum background. The concepts of widths, decay mechanisms and dynamic evolution are discussed. We also discuss results for the triple $α$ decay in connection with $2^+$ resonances and density and temperature dependence rates of recombination into light nuclei from $α$-particles and neutrons.

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arXiv2010

Momentum distributions from three-body decaying 9Be and 9B resonances

The complex-rotated hyperspherical adiabatic method is used to study the decay of low-lying $^9$Be and $^9$B resonances into $α$, $α$ and $n$ or $p$. We consider six low-lying resonances of $^9$Be ($1/2^\pm$, $3/2^\pm$ and $5/2^\pm$) and one resonance of $^9$B ($5/2^-$) to compare with. The properties of the resonances at large distances are decisive for the momentum distributions of the three decaying fragments. Systematic detailed energy correlations of Dalitz plots are presented.

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arXiv2010

Structure and three-body decay of $^9$Be resonances

The complex-rotated hyperspherical adiabatic method is used to study the decay of low-lying $^9$Be resonances into one neutron and two $α$-particles. We investigate the six resonances above the break-up threshold and below 6 MeV: $1/2^\pm$, $3/2^\pm$ and $5/2^\pm$. The short-distance properties of each resonance are studied, and the different angular momentum and parity configurations of the $^8$Be and $^5$He two-body substructures are determined. We compute the branching ratio for sequential decay via the $^8$Be ground state which qualitatively is consistent with measurements. We extract the momentum distributions after decay directly into the three-body continuum from the large-distance asymptotic structures. The kinematically complete results are presented as Dalitz plots as well as projections on given neutron and $α$-energy. The distributions are discussed and in most cases found to agree with available experimental data.

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arXiv2010

Relative production rates of $^{6}$He, $^{9}$Be, $^{12}$C in astrophysical environments

We assume an environment of neutrons and $α$-particles of given density and temperature where nuclear syntheses into $^{6}$He, $^{9}$Be and $^{12}$C are possible. We investigate the resulting relative abundance as a function of density and temperature. When the relative abundance of $α$-particles $Y_α$ is between 0.2 and 0.9, or larger than 0.9, the largest production is $^{9}$Be or $^{12}$C, respectively. When $Y_α<0.2$ $^{6}$He is mostly frequently produced for temperatures above about 2 GK whereas the $^{9}$Be production dominates at smaller temperatures.

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arXiv2010

Bound States and Universality in Layers of Cold Polar Molecules

The recent experimental realization of cold polar molecules in the rotational and vibrational ground state opens the door to the study of a wealth of phenomena involving long-range interactions. By applying an optical lattice to a gas of cold polar molecules one can create a layered system of planar traps. Due to the long-range dipole-dipole interaction one expects a rich structure of bound complexes in this geometry. We study the bilayer case and determine the two-body bound state properties as a function of the interaction strength. The results clearly show that a least one bound state will always be present in the system. In addition, bound states at zero energy show universal behavior and extend to very large radii. These results suggest that non-trivial bound complexes of more than two particles are likely in the bilayer and in more complicated chain structures in multi-layer systems.

cond-mat.quant-gas↗

arXiv2010

Universality of Brunnian ($N$-body Borromean) four and five-body systems

We compute binding energies and root mean square radii for weakly bound systems of $N=4$ and $5$ identical bosons. Ground and first excited states of an $N$-body system appear below the threshold for binding the system with $N-1$ particles. Their root mean square radii approach constants in the limit of weak binding. Their probability distributions are on average located in non-classical regions of space which result in universal structures. Radii decrease with increasing particle number. The ground states for more than five particles are probably non-universal whereas excited states may be universal.

cond-mat.quant-gas↗

arXiv2010

Above threshold s-wave resonances illustrated by the 1/2$^+$ states in $^9$Be and $^9$B

We solve the persistent problem of the structure of the lowest $1/2^+$ resonance in $^9$Be which is important to bridge the A=8 gap in nucleosynthesis in stars. We show that the state is a genuine three-body resonance even though it decays entirely into neutron-$^8$Be relative s-waves. The necessary barrier is created by "dynamical" evolution of the wave function as the short-distance $α$-$^5$He structure is changed into the large-distance n-$^8$Be structure. This decay mechanism leads to a width about two times smaller than table values. The previous interpretations as a virtual state or a two-body resonance are incorrect. The isobaric analog 1/2$^+$ state in $^9$B is found to have energy and width in the vicinity of 2.0 MeV and 1.5 MeV, respectively. We also predict another 1/2$^+$ resonance in $^9$B with similar energy and width.

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arXiv2009

Thomas-Fermi Approximation for a Condensate with Higher-order Interactions

We consider the ground state of a harmonically trapped Bose-Einstein condensate within the Gross-Pitaevskii theory including the effective-range corrections for a two-body zero-range potential. The resulting non-linear Schrödinger equation is solved analytically in the Thomas-Fermi approximation neglecting the kinetic energy term. We present results for the chemical potential and the condensate profiles, discuss boundary conditions, and compare to the usual Thomas-Fermi approach. We discuss several ways to increase the influence of effective-range corrections in experiment with magnetically tunable interactions. The level of tuning required could be inside experimental reach in the near future.

cond-mat.quant-gas↗

arXiv2009

Conditions for Efimov Physics for Finite Range Potentials

We consider a system of three identical bosons near a Feshbach resonance in the universal regime with large scattering length usually described by model independent zero-range potentials. We employ the adiabatic hyperspherical approximation and derive the rigorous large-distance equation for the adiabatic potential for finite-range interactions. The effective range correction to the zero-range approximation must be supplemented by a new term of the same order. The non-adiabatic term can be decisive. Efimov physics is always confined to the range between effective range and scattering length. The analytical results agree with numerical calculations for realistic potentials.

quant-ph↗

arXiv2009

Calculating few-body resonances using an oscillator trap

We investigate the possibility of calculating the parameters of few-body resonances using the oscillator trap boundary conditions. We place the few-body system in an oscillator trap and calculate the energy spectrum and the strength function of a suitably chosen transition. Broader resonances are identified as Lorentzian peaks in the strength function. Narrower resonances are identified through the pattern of avoided crossings in the spectrum of the system as function of the trap size. As an example we calculate 0+ resonances in 12C within the 3-alpha model.

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.

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arXiv2008

Nuclear alpha-particle condensates: Definitions, occurrence conditions, and consequences

There has been a recent flurry of interest in the possibility of condensates of $α$-particles in nuclei. In this letter we discuss occurrence conditions for such states. Using the quantality condition of Mottelson we show that condensates are only marginally expected in $α$-particle states. We proceed to demonstrate that few-body nuclear condensates are ill-defined, and emphasize the conflict between $α$-localization and $α$-condensate formation. We also explore the connection between Ikeda diagrams, linear chains, and Tonks-Girardeau gases. Our findings show that no new information is contained in the approximations of nuclear states as $α$-cluster condensates. Furthermore, condensates of more than three $α$-particles are very unlikely to exist due to couplings to other degrees of freedom.

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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.

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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

N-body Efimov states of trapped bosons

We demonstrate the possibility of existence of meta-stable N-body Efimov states in trapped Bose systems with large scattering length. We calculate spectra of trapped systems of N=3,4,5,6, and 7 bosons using a stochastic variational method with a restricted correlated Gaussian basis. For each system the calculations reveal a series of Efimov states where the energy and the r.m.s. radius exhibit the characteristic exponential dependence upon the state number. We also estimate the contribution of these states to the recombination rate of Bose-Einstein condensates.

physics.atom-ph↗

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.

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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.

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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.

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