arXiv subjects

A. S. Jensen

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

At least 19 recordsLinked to original sources

arXiv2025

Dineutron clusters in $^7$He and $^8$He structure

The hyper-radial barrier strongly hinders formation of more than three clusters. We investigate how well the dominating cluster components in $^7$He and $^8$He, respectively can be described as $α$+$n$+$^2n$ and $α$+$^2n$+$^2n$, where $^2n$ is the dineutron. Effective interactions compatible with $^5$He and $^6$He are used. We vary the lesser known $n$-$^2n$ and $^2n$-$^2n$ interactions, where very small strengths are required. We provide energies, radii, and partial wave decomposition of all computed, predicted or measured, ground and resonance states. We predict substructures within each of the three-body quantum states. We also calculate the neutron-structure sensitive invariant mass spectrum of the four-nucleon system, after fast removal of the $α$-particle from $^8$He. We show that all available experimental information are fairly well reproduced. Very little room is left for variation of the effective interaction parameters. Thus, the dominating features of the subsequently derived reaction and structure properties are well supported.

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arXiv2025

Three-body structures of low-lying nuclear states of $^8$Li

The four nucleons in $^8$Li outside the $α$-particle ($α=^4$He) can be divided into pairs of one neutron ($n$) and 3 nucleons in the triton ($t=^3$H), or 2 in the deuteron ($d=^2$H) and two neutrons in a dineutron ($^2n$). The corresponding three-body structures, $α$+$t$+$n$ or $α$+$d$+$^2n$, are suggested to describe the bulk part of the low-energy ($<10$~MeV) states of $^8$Li. Several breakup thresholds influence the structures and possible decays. We calculate the three-body structures of the various $J^π$ states, where different clustering appear, e.g. $^7$Li*+$n$, $^6$Li*$+^2n$, $^6$He*$+d$. The experimental $^8$Li spectrum can be reproduced with fine tuning by a three-body potential parameter. Three unobserved $0^+$ and an excited 2$^+$ states are found. All states appear as bound states or resonances. The lowest or highest energies have cluster structures, $α$+$t$+$n$ or $α$+$d$+$^2n$, respectively. We give calculated energy and width (if possible), geometry, and partial wave decomposition for all states.

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arXiv2025

Beta-delayed particle emission and collective rotations

Beta-delayed proton emission in the lower half of the sd-shell will involve deformed nuclei. We derive the normalized matrix element connecting emission of one particle from an initial rotational nuclear state to another final rotating state, and we extract selection rules involving the $K$ quantum number. The initial state is approximated as having a core identical to the final nuclear state. The formalism is then directly applicable to $β^+$-delayed proton decays of even-$Z$, odd-$N$ nuclei or $β^-$-delayed neutron decays of odd-$Z$, even $N$ nuclei. These beta-decay results are compared to the outcomes of possible transfer reactions. As an example the beta-delayed proton emission of $^{21}$Mg is considered, where new quantum numbers can be assigned to several states in $^{21}$Na.

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arXiv2024

Confinement of $N$-body systems and non-integer dimensions

The squeezing process of a three-dimensional quantum system by use of an external deformed one-body oscillator potential can also be described by the $d$-method, without external field and where the dimension can take non-integer values. In this work we first generalize both methods to $N$ particles and any transition between dimensions below $3$. Once this is done, the use of harmonic oscillator interactions between the particles allows complete analytic solutions of both methods, and a direct comparison between them is possible. Assuming that both methods describe the same process, leading to the same ground state energy and wave function, an analytic equivalence between the methods arises. The equivalence between both methods and the validity of the derived analytic relation between them is first tested for two identical bosons and for squeezing transitions from 3 to 2 and 1 dimensions, as well as from 2 to 1 dimension. We also investigate the symmetric squeezing from 3 to 1 dimensions of a system made of three identical bosons. We have in all the cases found that the derived analytic relations between the two methods work very well. This fact permits to relate both methods also for large squeezing scenarios, where the brute force numerical calculation with the external field is too much demanding from the numerical point of view, especially for systems with more than two particles.

quant-ph↗

arXiv2023

Tuning of Efimov states in non-integer dimensions

The purpose of this paper is to show that, by combining Feshbach resonances with external confining potentials, the energy scale factor of neighboring Efimov states can be tremendously reduced. The Efimov conditions can be reached for systems made of three different particles. For the case of two identical light particles and a heavy particle the energy factor can be reduced by many orders of magnitude, and the Efimov states are in this way more easily reachable experimentally. The equivalence between external potentials and the formulation in terms of non-integer dimensions, $d$, is exploited. The technically simpler $d$-method is used to derive analytic expressions for two-component relative wave functions describing two short-range square-well interacting particles. The two components express one open and one closed channel. The scattering length is obtained after phase shift expansion, providing an analytic form for the Efimov condition. We illustrate the results by means of systems made of $^7$Li, $^{39}$K, and $^{87}$Rb, with realistic parameters. The related pairs of dimension and magnetic field are shown and discussed. The results are universal as they only rely on large-distance properties.

physics.atom-ph↗

arXiv2023

Three-body calculations of beta decay applied to $^{11}$Li

A novel practical few-body method is formulated to include isospin symmetry for nuclear halo structures. The method is designed to describe beta decay, where the basic concept of isospin symmetry facilitates a proper understanding. Both isobaric analogue and anti-analogue states are treated. We derive general and explicit formulas for three-body systems using hyperspherical coordinates. The example of the beta decaying $^{11}$Li ($^{9}$Li+$n$+$n$) is chosen as a challenging application for numerical calculations of practical interest. The detailed results are compared to existing experimental data and good agreement is found at high excitation energies, where the isobaric analogue and anti-analogue states are situated in the daughter nucleus. An interpretation of the decay pattern at lower excitation energies is suggested. Decays of the $^{9}$Li-core and the two halo-neutrons are individually treated and combined to the daughter system with almost unique isospin, which we predict to be broken by about $0.4\%$ probability. Properties of decay products are predicted as possible future tests of this model.

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arXiv2022

Three-body continuum states and Efimov physics in non-integer geometry

Continuum structures of three short-range interacting particles in a deformed external one-body field are investigated. We use the equivalent $d$-method employing non-integer dimension, $d$, in a spherical calculation with a dimension-dependent angular momentum barrier. We focus on dimensions close to the critical dimension, $d=d_E$, between two and three, defined by zero two-body energies, where the Efimov effect can occur. We design for this dimension region a schematic, long-distance realistic, square-well based, three-body spherical model, which is used to derive analytic expressions for the wave functions, scattering lengths, phase shifts, and elastic scattering cross sections. The procedure and the results are universal, valid for all short-range potentials, and for large scattering lengths. We discuss the properties and validity of the derived expressions by means of the simplest system of three identical bosons. The derived expressions are particularly useful for very small energies, where full numerical calculations are often not feasible. For energies where the numerical calculations can be performed, a good agreement with the analytic results is found. These model results may be tested by scattering experiments for three particles in an equivalent external deformed oscillator potential. The cross sections all vanish in the zero-energy limit for $d<3$ with definite $d$-dependent power of energy.

physics.atom-ph↗

arXiv2021

Efimov effect evaporation after confinement

The continuous confinement of quantum systems can be described by means of the $d$-method, where the dimension $d$ is taken as a continuous parameter. In this work we describe in detail how this method can be used to obtain the root mean square radii for a squeezed three-body system. These observables are used to investigate the disappearance of the Efimov states around the two-body threshold during a progressive confinement of the system from three to two dimensions. We illustrate how the disappearance takes place through the loss of one of the particles, whereas the other two remain bound.

quant-ph↗

arXiv2021

Direct and sequential four-body recombination rates at low temperatures

We investigate four-body nuclear reactions in stellar environments contributing to creation of light nuclei, exemplified by $^9$Be and $^{12}$C. The originally assumed process is radiative capture, where nuclear clusters combine into the excited final nucleus and photon emission populates the stable nuclear ground states. Instead, we consider nuclear four-body recombination reactions where a spectator nuclear particle replaces the photon. We first develop the elaborate formalism for both, direct and sequential capture processes, where the decaying three-body resonance is formed without and with population of an intermediate two-body resonance, respectively. To facilitate both calculations and practical applications we parameterize the involved cross sections as done successfully in previous computations of reaction rates. We consider the lowest-lying nuclear states with their dominant contributions at low stellar temperatures. We calculate and compare reaction and production rates for different processes. The direct reaction mechanism dominates by many orders of magnitude at low temperature, where the sequential stepping stones are energetically too expensive to use. At somewhat higher temperatures these two different nuclear four-body mechanisms become comparable. Comparison to radiative three-body capture reveals already formally, but also numerically, that four-body nuclear recombination must dominate for sufficiently high nuclear densities. Numerical values are given for all these rates as function of temperature and density. The relative importance is exhibited.

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arXiv2020

Efimov effect in non-integer dimensions induced by an external field

The Efimov effect can be induced by means of an external deformed one-body field that effectively reduces the allowed spatial dimensions to less than three. To understand this new mechanism, conceptually and practically, we employ a formulation using non-integer dimension, which is equivalent to the strength of an external oscillator field. The effect most clearly appears when the crucial two-body systems are unbound in three, but bound in two, dimensions. We discuss energy variation, conditions for occurrence, and number of Efimov states, as functions of the dimension. We use practical examples from cold atom physics of $^{133}$Cs-$^{133}$Cs-$^{133}$Cs, $^{87}$Rb-$^{87}$Rb-$^{87}$Rb, $^{133}$Cs-$^{133}$Cs-$^{6}$Li, and $^{87}$Rb-$^{87}$Rb-$^{39}$K. Laboratory tests of the effect can be performed with two independent parameters, i.e. the external one-body field and the Feshbach two-body tuning. The scaling and (dis)appearance of these Efimov states occur precisely as already found in three dimensions.

physics.atm-clus↗

arXiv2020

Three identical bosons: Properties in non-integer dimensions and in external fields

Three-body systems that are continuously squeezed from a three-dimensional (3D) space into a two-dimensional (2D) space are investigated. Such a squeezing can be obtained by means of an external confining potential acting along a single axis. However, this procedure can be numerically demanding, or even undoable, especially for large squeezed scenarios. An alternative is provided by use of the dimension $d$ as a parameter that changes continuously within the range $2\leq d \leq 3$. The simplicity of the $d$-calculations is exploited to investigate the evolution of three-body states after progressive confinement. The case of three identical spinless bosons with relative $s$-waves in 3D, and a harmonic oscillator squeezing potential is considered. We compare results from the two methods and provide a translation between them, relating dimension, squeezing length, and wave functions from both methods. All calculations are then possible entirely within the simpler $d$-method, but simultaneously providing the equivalent geometry with the external potential.

cond-mat.quant-gas↗

arXiv2020

Few-body structures in the mirror nuclei, $^{11}$O and $^{11}$Li

We investigate the dripline mirror nuclei, $^{11}$Li and $^{11}$O, located on the neutron and proton dripline, respectively. We calculate the lowest four states, $3/2^-$, $1/2^+$, $3/2^+$ and $5/2^+$, built on double occupancy in the nuclear $s_{1/2}$ and $p_{1/2}$ valence single-particle states. We use the hyperspherical adiabatic expansion method to solve the three-body problem for a frozen nuclear core surrounded by two identical nucleons. The four analogue states in $^{11}$O are obtained with precisely the same interactions as used for the four states in $^{11}$Li, except for addition of the Coulomb interaction from the charge of the substituted valence protons. Surprisingly the four energies deviate from each other only by less than a few hundred keV. Any of them could then turn out to be the ground state, due to the uncertainty related to the angular momentum and parity dependence of the three-body potential. Still, our calculations marginally favor the $1/2^+$ state. The structures of these four states in $^{11}$O deviate substantially from the analogue states in the mirror, $^{11}$Li.

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arXiv2019

Quasi-One-Dimensional Few-Body Systems with Correlated Gaussians

The theoretical study of ultracold few-body systems is often done using an idealized 1D model with zero range interactions. Here we study these systems using a more realistic 3D model with finite range interactions. We place three-particles, two identical and one impurity, in an axial symmetric harmonic trap and solve the corresponding stationary Schrödinger equation using the correlated Gaussian method for different particle types, aspect ratios and interactions strength. We show that the idealized model is accurate for small and intermediate strength interactions at aspect ratios larger than four, independently of the particle types. In the strongly interacting limit, the idealized model is acceptable for bosonic systems, but not for fermionic systems even at large aspect ratios.

cond-mat.quant-gas↗

arXiv2019

Confinement of two-body systems and calculations in $d$ dimensions

A continuous transition for a system moving in a three-dimensional (3D) space to moving in a lower-dimensional space, 2D or 1D, can be made by means of an external squeezing potential. A squeeze along one direction gives rise to a 3D to 2D transition, whereas a simultaneous squeeze along two directions produces a 3D to 1D transition, without going through an intermediate 2D configuration. In the same way, for a system moving in a 2D space, a squeezing potential along one direction produces a 2D to 1D transition. In this work we investigate the equivalence between this kind of confinement procedure and calculations without an external field, but where the dimension $d$ is taken as a parameter that changes continuously from $d=3$ to $d=1$. The practical case of an external harmonic oscillator squeezing potential acting on a two-body system is investigated in details. For the three transitions considered, 3D~$\rightarrow$~2D, 2D~$\rightarrow$~1D, and 3D~$\rightarrow$~1D, a universal connection between the harmonic oscillator parameter and the dimension $d$ is found. This relation is well established for infinitely large 3D scattering lengths of the two-body potential for 3D~$\rightarrow$~2D and 3D~$\rightarrow$~1D transitions, and for infinitely large 2D scattering length for the 2D~$\rightarrow$~1D case. For finite scattering lengths size corrections must be applied. The traditional wave functions for external squeezing potentials are shown to be uniquely related with the wave functions for specific non-integer dimension parameters, $d$.

physics.atm-clus↗

arXiv2019

$^{42}$Ca and $^{50}$Ca with the (Many- and Few-body) Unified Method

A new method unifying many and few-body aspects of nuclear structure has recently been introduced \cite{hov18}. This method combines the many-body description of a core and the few-body structure of this core surrounded by two valence nucleons. For this reason this method is expected to work specially well when applied to nuclei close to the driplines, where the few-body halo structure with one or more nucleons outside the core is established. In this work we apply the new method to nuclei close to the valley of stability, with $^{42}$Ca and $^{50}$Ca as illustrations. We compare the results from uncorrelated mean-field calculations with the ones obtained with the unified method allowing arbitrary correlations in the valence space. We find that the unified method provides results rather similar, although distinguishable, to the Hartree-Fock calculations. The correlations are much less pronounced than at the driplines, which initially were targets for the unified method. The halo structure is not artificially maintained, but the correlations are here demonstrated to be applicable to well-bound nuclei. Excited states built on valence degrees of freedom are calculated for the same nuclei.

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arXiv2019

Few-body quantum method in a $d$-dimensional space

In this work we investigate the continuous confinement of quantum systems from three to two dimensions. Two different methods will be used and related. In the first one the confinement is achieved by putting the system under the effect of an external field. This method is conceptually simple, although, due to the presence of the external field, its numerical implementation can become rather cumbersome, especially when the system is highly confined. In the second method the external field is not used, and it simply considers the spatial dimension $d$ as a parameter that changes continuously between the ordinary integer values. In this way the numerical effort is absorbed in a modified strength of the centrifugal barrier. Then the technique required to obtain the wave function of the confined system is precisely the same as needed in ordinary three dimensional calculations without any confinement potential. The case of a two-body system squeezed from three to two dimensions is considered, and used to provide a translation between all the quantities in the two methods. Finally we point out perspectives for applications on more particles, different spatial dimensions, and other confinement potentials.

physics.atom-ph↗

arXiv2018

Efimov states of three unequal bosons in non-integer dimensions

The Efimov effect for three bosons in three dimensions requires two infinitely large $s$-wave scattering lengths. We assume two identical particles with very large scattering lengths interacting with a third particle. We use a novel mathematical technique where the centrifugal barrier contains an effective dimension parameter, which allows efficient calculations precisely as in ordinary three spatial dimensions. We investigate properties and occurrence conditions of Efimov states for such systems as functions of the third scattering length, the non-integer dimension parameter, mass ratio between unequal particles, and total angular momentum. We focus on the practical interest of the existence, number of Efimov states and their scaling properties. Decreasing the dimension parameter from $3$ towards $2$ the Efimov effect and states disappear for critical values of mass ratio, angular momentum and scattering length parameter. We investigate the relations between the four variables and extract details of where and how the states disappear. Finally, we supply a qualitative relation between the dimension parameter and an external field used to squeeze a genuine three dimensional system.

physics.atm-clus↗

arXiv2018

Combined few-body and mean-field model for nuclei

The challenging nuclear many-body problem is discussed along with classifications and qualitative descriptions of existing methods and models. We present detailed derivations of a new method where cluster correlations co-exist with an underlying mean-field described core-structure. The variation of an antisymmetrized product of cluster and core wave functions and a given nuclear interaction, provide sets of self-consistent equations of motion. After the applications on dripline nuclei we discuss perspectives with improvements and applications. In the conclusion we summarize while emphasizing the merits of consistently treating both short- and large-distance properties, few- and many-body correlations, ordinary nuclear structure, and concepts of halos and Efimov states.

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