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We consider a specific form of explicitly correlated Gaussians -- with tensor pre-factors -- which appear naturally when dealing with certain few-body systems in nuclear and particle physics. We derive analytic matrix elements with these Gaussians -- overlap, kinetic energy, and Coulomb potential -- to be used in variational calculations of those systems. We also perform a quick test of the derived formulae by applying them to p- and d-waves of the hydrogen atom.

We show that the N(1440) Roper resonance naturally appears in the nuclear model with explicit mesons as a structure in the continuum spectrum of the physical proton which in this calculation is made of a bare nucleon dressed with a pion cloud.

We apply the nuclear model with explicit mesons to photoproduction of neutral pions off protons at the threshold. In this model the nucleons do not interact with each other via a potential but rather emit and absorb mesons that are treated explicitly on equal footing with the nucleons. We calculate the total cross section of the reaction for energies close to threshold and compare the calculations with available experimental data. We show that the model is able to reproduce the experimental data and determine the range of the parameters where the model is compatible with the experiment.

Combining laser spectroscopy in a Versatile Arc Discharge and Laser Ion Source, with Penning-trap mass spectrometry at the CERN-ISOLDE facility, this work reports on mean-square charge radii of neutron-rich mercury isotopes across the $N = 126$ shell closure, the electromagnetic moments of $^{207}$Hg and more precise mass values of $^{206-208}$Hg. The odd-even staggering (OES) of the mean square charge radii and the kink at $N = 126$ are analyzed within the framework of covariant density functional theory (CDFT), with comparisons between different functionals to investigate the dependence of the results on the underlying single-particle structure. The observed features are defined predominantly in the particle-hole channel in CDFT, since both are present in the calculations without pairing. However, the magnitude of the kink is still affected by the occupation of the $1i_{11/2}$ and $2g_{9/2}$ orbitals with a dependence on the relative energies as well as pairing., Comment: 20 pages, 12 figures, Phys. Rev. C in press

The mean-square charge radii of $^{207,208}$Hg ($Z=80, N=127,128$) have been studied for the first time and those of $^{202,203,206}$Hg ($N=122,123,126$) remeasured by the application of in-source resonance-ionization laser spectroscopy at ISOLDE (CERN). The characteristic \textit{kink} in the charge radii at the $N=126$ neutron shell closure has been revealed, providing the first information on its behavior below the $Z=82$ proton shell closure. A theoretical analysis has been performed within relativistic Hartree-Bogoliubov and non-relativistic Hartree-Fock-Bogoliubov approaches, considering both the new mercury results and existing lead data. Contrary to previous interpretations, it is demonstrated that both the kink at $N=126$ and the odd-even staggering (OES) in its vicinity can be described predominately at the mean-field level, and that pairing does not need to play a crucial role in their origin. A new OES mechanism is suggested, related to the staggering in the occupation of the different neutron orbitals in odd- and even-$A$ nuclei, facilitated by particle-vibration coupling for odd-$A$ nuclei., Comment: 7 pages, 5 figures, Physical Review C, in press

A nuclear model is proposed where the nucleons interact by emitting and absorbing mesons, and where the mesons are treated explicitly. A nucleus in this model finds itself in a quantum superposition of states with different number of mesons. Transitions between these states hold the nucleus together. The model---in its simplest incarnation---is applied to the deuteron, where the latter becomes a superposition of a neutron-proton state and a neutron-proton-meson state. Coupling between these states leads to an effective attraction between the nucleons and results in a bound state with negative energy, the deuteron. The model is able to reproduce the accepted values for the binding energy and the charge radius of the deuteron. The model, should it work in practice, has several potential advantages over the existing non-relativistic few-body nuclear models: the reduced number of model parameters, natural inclusion of few-body forces, and natural inclusion of mesonic physics.

The mesoscopic nature of the atomic nucleus gives rise to a wide array of macroscopic and microscopic phenomena. The size of the nucleus is a window into this duality: while the charge radii globally scale as $A^{1/3}$, their evolution across isotopic chains reveals unanticipated structural phenomena [1-3]. The most ubiquitous of these is perhaps the Odd-Even Staggering (OES) [4]: isotopes with an odd number of neutrons are usually smaller in size than the trend of their even-neutron neighbours suggests. This OES effect varies with the number of protons and neutrons and poses a significant challenge for nuclear theory [5-7]. Here, we examine this problem with new measurements of the charge radii of short-lived copper isotopes up to the very exotic $^{78}$Cu $(Z=29, N=49)$, produced at only 20 ions/s, using the highly-sensitive Collinear Resonance Ionisation Spectroscopy (CRIS) method at ISOLDE-CERN. Due to the presence of a single proton outside of the closed Z=28 shell, these measurements provide crucial insights into the single-particle proton structure and how this affects the charge radii. We observe an unexpected reduction in the OES for isotopes approaching the $N=50$ shell gap. To describe the data, we applied models based on nuclear Density Functional Theory [2,8] (DFT) and ab-initio Valence-Space In-Medium Similarity Renormalization Group (VS-IMSRG) theory [9,10]. Through these comparisons, we demonstrate a relation between the global behavior of charge radii and the saturation density of nuclear matter, and show that the local charge radii variations, which reflect the many-body polarization effects due to the odd neutron, naturally emerge from the VS-IMSRG calculations.

Within the Correlated Gaussian Method the parameters of the Gaussian basis functions are often chosen stochastically using pseudo-random sequences. We show that alternative low-discrepancy sequences, also known as quasi-random sequences, provide bases of better quality.

Neutron-deficient $^{177-185}$Hg isotopes were studied using in-source laser resonance-ionization spectroscopy at the CERN-ISOLDE radioactive ion-beam facility, in an experiment combining different detection methods tailored to the studied isotopes. These include either alpha-decay tagging or Multi-reflection Time-of-Flight gating to identify the isotopes of interest. The endpoint of the odd-even nuclear shape staggering in mercury was observed directly by measuring for the first time the isotope shifts and hyperfine structures of $^{177-180}$Hg. Changes in the mean-square charge radii for all mentioned isotopes, magnetic dipole and electric quadrupole moments of the odd-A isotopes and arguments in favor of $I = 7/2$ spin assignment for $^{177,179}$Hg were deduced. Experimental results are compared with Density Functional Theory (DFT) and Monte-Carlo Shell Model (MCSM) calculations. DFT calculations with several Skyrme parameterizations predict a large jump in the charge radius around the neutron $N = 104$ mid shell, with an odd-even staggering pattern related to the coexistence of nearly-degenerate oblate and prolate minima. This near-degeneracy is highly sensitive to many aspects of the effective interaction, a fact that renders perfect agreement with experiment out of reach for current functionals. Despite this inherent diffculty, the SLy5s1 and a modified UNEDF1^{SO} parameterization predict a qualitatively correct staggering that is off by two neutron numbers. MCSM calculations of states with the experimental spins and parities show good agreement for both electromagnetic moments and the observed charge radii. A clear mechanism for the origin of shape staggering within this context is identified: a substantial change in occupancy of the proton $\pi h_{9/2}$ and neutron $\nu i_{13/2}$ orbitals., Comment: 19 pages, 18 figures

Background: Shell evolution can impact the structure of the nuclei and lead to effects such as shape coexistence. The nuclei around $^{68}$Ni represent an excellent study case, however, spectroscopic information of the neutron-rich, $Z<28$ nuclei is limited. Purpose: The goal is to measure $\gamma$-ray transitions in $^{66}$Fe, $^{66}$Co and $^{66}$Ni populated in the $\beta^-$ decay of $^{66}$Mn, to determine absolute $\beta$-feedings and relative $\gamma$-decay probabilities and to compare the results with Monte Carlo Shell Model calculations in order to study the influence of the relevant single neutron and proton orbitals occupancies around $Z=28$ and $N=40$. Method: The low-energy structures of $^{65,66}$Fe, $^{66}$Co and $^{66}$Ni were studied in the $\beta^-$ decay of $^{66}$Mn produced at ISOLDE, CERN. The beam was purified by means of laser resonance ionization and mass separation. The $\beta$ and $\gamma$ events detected by three plastic scintillators and two MiniBall cluster germanium detectors, respectively, were correlated in time to build the low-energy excitation schemes and to determine the $\beta$-decay half-lives of the nuclei. Results: The relative small $\beta$-decay ground state feeding of $^{66}$Fe obtained in this work is at variant to the earlier studies. Spin and parity $1^+$ was assigned to the $^{66}$Co ground state based on the strong ground state feeding in the decay of $^{66}$Fe as well as in the decay of $^{66}$Co. Experimental log(ft) values, $\gamma$-ray deexcitation patterns and energies of excited states were compared to Monte Carlo Shell Model calculations. Based on this comparison, spin and parity assignments for the selected number of low-lying states in the $^{66}$Mn to $^{66}$Ni chain were proposed. Conclusions: The $\beta$-decay chain starting $^{66}$Mn towards $^{66}$Ni, crossing $N=40$, evolves from deformed nuclei to sphericity..., Comment: accepted for publication in PRC

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.

We investigate the two-proton capture reaction of the prominent rapid proton capture waiting point nucleus, $^{68}$Se, that produces the borromean nucleus $^{70}$Kr ($^{68}$Se$+p+p$). We apply a recently formulated general model where the core nucleus, $^{68}$Se, is treated in the mean-field approximation and the three-body problem of the two valence protons and the core is solved exactly. The same Skyrme interaction is used to find core-nucleon and core valence-proton interactions. We calculate $E2$ electromagnetic two-proton dissociation and capture cross sections, and derive the temperature dependent capture rates. We vary the unknown $2^+$ resonance energy without changing any of the structures computed self-consistently for both core and valence particles. We find rates increasing quickly with temperature below $2-4$~GK after which we find rates varying by less than a factor of two independent of $2^+$ resonance energy. The capture mechanism is sequential through the $f_{5/2}$ proton-core resonance, but the continuum background contributes significantly., Comment: 7 pages, 4 figures

The quantum mechanical three-body problem is a source of continuing interest due to its complexity and not least due to the presence of fascinating solvable cases. The prime example is the Efimov effect where infinitely many bound states of identical bosons can arise at the threshold where the two-body problem has zero binding energy. An important aspect of the Efimov effect is the effect of spatial dimensionality; it has been observed in three dimensional systems, yet it is believed to be impossible in two dimensions. Using modern experimental techniques, it is possible to engineer trap geometry and thus address the intricate nature of quantum few-body physics as function of dimensionality. Here we present a framework for studying the three-body problem as one (continuously) changes the dimensionality of the system all the way from three, through two, and down to a single dimension. This is done by considering the Efimov favorable case of a mass-imbalanced system and with an external confinement provided by a typical experimental case with a (deformed) harmonic trap., Comment: 11 pages, 4 figures, comments are most welcome

We investigate emergence of halos and Efimov states in nuclei by use of a newly designed model which combines self-consistent mean-field and three-body descriptions. Recent interest in neutron heavy calcium isotopes makes $^{72}$Ca ($^{70}$Ca+n+n) an ideal realistic candidate on the neutron dripline, and we use it as a representative example that illustrates our broadly applicable conclusions. By smooth variation of the interactions we simulate the crossover from well-bound systems to structures beyond the threshold of binding, and find that halo-configurations emerge from the mean-field structure for three-body binding energy less than $\sim 100$keV. Strong evidence is provided that Efimov states cannot exist in nuclei. The structure that bears the most resemblance to an Efimov state is a giant halo extending beyond the neutron-core scattering length. We show that the observable large-distance decay properties of the wave function can differ substantially from the bulk part at short distances, and that this evolution can be traced with our combination of few- and many-body formalisms. This connection is vital for interpretation of measurements such as those where an initial state is populated in a reaction or by a beta-decay., Comment: 5 pages, 5 figures, under review

Nuclear cluster physics implicitly assumes a distinction between groups of degrees-of-freedom, that is the (frozen) intrinsic and (explicitly treated) relative cluster motion. We formulate a realistic and practical method to describe the coupled motion of these two sets of degrees-of-freedom. We derive a coupled set of differential equations for the system using the phenomenologically adjusted effective in-medium Skyrme type of nucleon-nucleon interaction. We select a two-nucleon plus core system where the mean-field approximation corresponding to the Skyrme interaction is used for the core. A hyperspherical adiabatic expansion of the Faddeev equations is used for the relative cluster motion. We shall specifically compare both the structure and the decay mechanism found from the traditional three-body calculations with the result using the new boundary condition provided by the full microscopic structure at small distance. The extended Hilbert space guaranties an improved wave function compared to both mean-field and three-body solutions. We shall investigate the structures and decay mechanism of $^{22}$C ($^{20}$C+n+n). In conclusion, we have developed a method combining nuclear few- and many-body techniques without losing the descriptive power of each approximation at medium-to-large distances and small distances respectively. The coupled set of equations are solved self-consistently, and both structure and dynamic evolution are studied., Comment: 4 pages, 3 figures, conference proceedings, published

We investigate the region of the nuclear chart around $A \simeq 70$ from a three-body perspective, where we compute reaction rates for the radiative capture of two protons. One key quantity is here the photon dissociation cross section for the inverse process where two protons are liberated from the borromean nucleus by photon bombardment. We find a number of peaks at low photon energy in this cross section where each peak is located at the energy corresponding to population of a three-body resonance. Thus, for these energies the decay or capture processes proceed through these resonances. However, the next step in the dissociation process still has the option of following several paths, that is either sequential decay by emission of one proton at a time with an intermediate two-body resonance as stepping stone, or direct decay into the continuum of both protons simultaneously. The astrophysical reaction rate is obtained by folding of the cross section as function of energy with the occupation probability for a Maxwell-Boltzmann temperature distribution. The reaction rate is then a function of temperature, and of course depending on the underlying three-body bound state and resonance structures. We show that a very simple formula at low temperature reproduces the elaborate numerically computed reaction rate., Comment: 4 pages, 3 figures, conference proceedings, published

Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics.

We combine few- and many-body degrees of freedom in a model applicable to both bound and continuum states and adaptable to different subfields of physics. We formulate a self-consistent three-body model for a core-nucleus surrounded by two valence nucleons. We treat the core in the mean-field approximation and use the same effective Skyrme interaction between both core and valence nucleons. We apply the model to $^{26}$O where we reproduce the known experimental data as well as phenomenological models with more parameters. The decay of the ground state is found to proceed directly into the continuum without effect of the virtual sequential decay through the well reproduced $d_{3/2}$-resonance of $^{25}$O., Comment: 5 pages, 5 figures, under review

We investigate even-even two-proton borromean systems at prominent intermediate heavy waiting points for the rapid proton capture process. The most likely single-particle levels are used to calculate three-body energy and structure as a function of proton-core resonance energy. We establish a linear dependence between two- and three-body energies with the same slope, but the absolute value slightly dependent on partial wave structure. Using these relations we predict low-lying excited states in the isotones following the critical waiting points. The capture rate for producing a borromean bound state is described both based on a full three-body calculation and on a very simple analytic rate expression for temperatures about $1-5$~GK. This rate is valid for both direct and sequential capture paths, and it only depends on the three-body resonance energy. As a result the relevant path of the radiative capture reactions can be determined. We present numerical results for $E1$ and $E2$ photon emission, and discuss occurrence preferences in general as well as relative sizes of these most likely processes. Finally, we present narrow estimated intervals for the proton capture rates relevant for the critical waiting points., Comment: 17 pages, 9 figures, published version

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. C

We consider three-body recombination into deep dimers in a mass-imbalanced two-component atomic gas. We use an optical model where a phenomenological imaginary potential is added to the lowest adiabatic hyper-spherical potential. The consequent imaginary part of the energy eigenvalue corresponds to the decay rate or recombination probability of the three-body system. The method is formulated in details and the relevant qualitative features are discussed as functions of scattering lengths and masses. We use zero-range model in analyses of recent recombination data. The dominating scattering length is usually related to the non-equal two-body systems. We account for temperature smearing which tends to wipe out the higher-lying Efimov peaks. The range and the strength of the imaginary potential determine positions and shapes of the Efimov peaks as well as the absolute value of the recombination rate. The Efimov scaling between recombination peaks is calculated and shown to depend on both scattering lengths. Recombination is predicted to be largest for heavy-heavy-light systems. Universal properties of the optical parameters are indicated. We compare to available experiments and find in general very satisfactory agreement., Comment: 16 pages, 12 figures, 3 tables, revised version

The accuracy of three different sets of Hartree-Fock-Bogoliubov calculations of nuclear binding energies is systematically evaluated. To emphasize minor fluctuations, a second order, four-point mass relation, which almost completely eliminates smooth aspects of the binding energy, is introduced. Applying this mass relation yields more scattered results for the calculated binding energies. By examining the Gaussian distributions of the non-smooth aspects which remain, structural differences can be detected between measured and calculated binding energies. Substructures in regions of rapidly changing deformation, specifically around $(N,Z)=(60,40)$ and $(90,60)$, are clearly seen for the measured values, but are missing from the calculations. A similar three-point mass relation is used to emphasize odd-even effects. A clear decrease with neutron excess is seen continuing outside the experimentally known region for the calculations., Comment: 13 pages, 9 figures, published version

Borromean nuclear cluster structures are expected at the corresponding driplines. We locate the regions in the nuclear chart with the most promising constituents, it being protons and alpha-particles and investigate in details the properties of the possible borromean two-alpha systems in medium heavy nuclei. We find in all cases that the alpha-particles are located at the surface of the core-nucleus as dictated by Coulomb and centrifugal barriers. The two lowest three-body bound states resemble a slightly contracted $^{8}\text{Be}$ nucleus outside the core. The next two excited states have more complex structures but with strong components of linear configurations with the core in the middle. Alpha-removal cross sections would be enhanced with specific signatures for these two different types of structures. The even-even borromean two-alpha nucleus, $^{142}$Ba, is specifically investigated and predicted to have $^{134}\text{Te}-\alpha-\alpha$ structure in its ground state and low-lying spectrum., Comment: 18 pages, 21 figures, published version

The spectrum and properties of quantum bound states is strongly dependent on the dimensionality of space. How this comes about and how one may theoretically and experimentally study the interpolation between different dimensions is a topic of great interest in different fields of physics. In this paper we study weakly bound states of non-relativistic two and three boson systems when passing continuously from a three (3D) to a two-dimensional (2D) regime within a 'squeezed dimension' model. We use periodic boundary conditions to derive a surprisingly simple form of the three-boson Schr{\"o}dinger equation in momentum space that we solve numerically. Our results show a distinct dimensional crossover as three-boson states will either disappear into the continuum or merge with a 2D counterpart, and also a series of sharp transitions in the ratios of three-body and two-body energies from being purely 2D to purely 3D., Comment: 5 pages, 2 figures, revised version

The study of quantum mechanical bound states is as old as quantum theory itself. Yet, it took many years to realize that three-body borromean systems that are bound when any two-body subsystem is unbound are abundant in nature. Here we demonstrate the existence of borromean systems of spin-polarized (spinless) identical fermions in two spatial dimensions. The ground state with zero orbital (planar) angular momentum exists in a borromean window between critical two- and three-body strengths. The doubly degenerate first excited states of angular momentum one appears only very close to the two-body threshold. They are the lowest in a possible sequence of so-called super-Efimov states. While the observation of the super-Efimov scaling could be very difficult, the borromean ground state should be observable in cold atomic gases and could be the basis for producing a quantum gas of three-body states in two dimensions., Comment: 9 pages, 3 figures, published version

Bremsstrahlung emission in collisions between charged nuclei is equivalent to nuclear gamma decay between continuum states. The way the continuum spectrum can be treated is not unique, and efficiency and accuracy of cross section calculations depend on the chosen method. In this work we describe, relate, and compare three different methods in practical calculations of inelastic cross sections, that is, by (i) treating the initial and final states as pure continuum states on the real energy axis, (ii) discretizing the continuum states on the real energy axis with a box boundary condition, and (iii) complex rotation of the hamiltonian(complex scaling method). The electric quadrupole transitions, $2^+ \rightarrow 0^+$ and $4^+ \rightarrow 2^+$, in $\alpha+\alpha$ scattering are taken as an illustration., Comment: To be published in Few-body Systems

We study the two dimensional three-body problem in the general case of three distinguishable particles interacting through zero-range potentials. The Faddeev decomposition is used to write the momentum-space wave function. We show that the large-momentum asymptotic spectator function has the same functional form as derived previously for three identical particles. We derive analytic relations between the three different Faddeev components for three distinguishable particles. We investigate the one-body momentum distributions both analytically and numerically and analyze the tail of the distributions to obtain two- and three-body contact parameters. We specialize from the general cases to examples of two identical, interacting or non-interacting, particles. We find that the two-body contact parameter is not a universal constant in the general case and show that the universality is recovered when a subsystem is composed of two identical non-interacting particles. We also show that the three-body contact parameter is negligible in the case of one non-interacting subsystem compared to the situation where all subsystem are bound. As example, we present results for mixtures of Lithium with two Cesium or two Potassium atoms, which are systems of current experimental interest., Comment: 24 pages, 7 figures, published version

We use the two-alpha cluster model to describe the properties of $^{8}$Be. The rotational energy sequence of the $(0^+,2^+,4^+)$ resonances are reproduced with the complex energy scaling technique for Ali-Bodmer and Buck-potentials. However, both static and transition probabilities are far from the rotational values. We trace this observation to the prominent continuum properties of the $2^+$ and $4^+$ resonances. They resemble free continuum solutions although still exhibiting strong collective rotational character. We compare with cluster models and discuss concepts of rotations in the continuum in connection with central quantities as transition probabilities, inelastic cross sections and resonance widths. We compute the $6^+$ and $8^+$ $S$-matrix poles and discuss properties of this possible continuation of the band beyond the known $4^+$ state. Regularization of diverging quantities are discussed in order to extract observable continuum properties. We formulate division of electromagnetic transition probabilities into interfering contributions from resonance-resonance, continuum-resonance, resonance-continuum, and continuum-continuum transitions., Comment: To be published in Physical Review C

We investigate three-boson recombination of equal mass systems as function of (negative) scattering length, mass, finite energy, and finite temperature. An optical model with an imaginary potential at short distance reproduces experimental recombination data and allows us to provide a simple parametrization of the recombination rate as function of scattering length and energy. Using the two-body van der Waals length as unit we find that the imaginary potential range and also the potential depth agree to within thirty percent for Lithium and Cesium atoms. As opposed to recent studies suggesting universality of the threshold for bound state formation, our results suggest that the recombination process itself could have universal features., Comment: 5 pages, 5 figures

We solve the three-body bound state problem in three dimensions for mass imbalanced systems of two identical bosons and a third particle in the universal limit where the interactions are assumed to be of zero-range. The system displays the Efimov effect and we use the momentum-space wave equation to derive formulas for the scaling factor of the Efimov spectrum for any mass ratio assuming either that two or three of the two-body subsystems have a bound state at zero energy. We consider the single-particle momentum distribution analytically and numerically and analyse the tail of the momentum distribution to obtain the three-body contact parameter. Our finding demonstrate that the functional form of the three-body contact term depends on the mass ratio and we obtain an analytic expression for this behavior. To exemplify our results, we consider mixtures of Lithium with either two Caesium or Rubium atoms which are systems of current experimental interest., Comment: 16 pages, 9 figures, 1 appendix, revised version

We use the two-alpha cluster model to describe the properties of $^{8}$Be. The $E2$-transitions in a two-body continuum can be described as bremsstrahlung in an inelastic scattering process. We compute cross sections as functions of initial energy for the possible $E2$-transitions from initial angular momenta $(0^+,2^+,4^+,6^+,8^+)$. The dependence on the exact shape of potentials is very small when the low-energy scattering phase-shifts are the same. We relate to practical observables where energies of the emerging alpha-particles are restricted in various ways. The unphysical infrared contribution is removed. We find pronounced peaking for photon energies matching resonance positions. Contributions from intra-band transitions are rather small although substantial (and even dominating) for initial energies between resonances. Structure information are derived but both ${\cal B}^{(E2)}$ values and electromagnetic transition rates are ambiguous in the continuum., Comment: To be published in Physical Review C

We investigate finite-range effects in systems with three identical bosons. We calculate recombination rates and bound state spectra using two different finite-range models that have been used recently to describe the physics of cold atomic gases near Feshbach resonances where the scattering length is large. The models are built on contact potentials which take into account finite range effects; one is a two-channel model and the other is an effective range expansion model implemented through the boundary condition on the three-body wave function when two of the particles are at the same point in space. We compare the results with the results of the ubiquitous single-parameter zero-range model where only the scattering length is taken into account. Both finite range models predict variations of the well-known geometric scaling factor 22.7 that arises in Efimov physics. The threshold value at negative scattering length for creation of a bound trimer moves to higher or lower values depending on the sign of the effective range compared to the location of the threshold for the single-parameter zero-range model. Large effective ranges, corresponding to narrow resonances, are needed for the reduction to have any noticeable effect., Comment: 16 pages, 7 figures, published version

We search for Borromean three-body systems of identical bosons in two dimensional geometry, i.e. we search for bound three-boson system without bound two-body subsystems. Unlike three spatial dimensions, in two-dimensional geometry the two- and three-body thresholds often coincide ruling out Borromean systems. We show that Borromean states can only appear for potentials with substantial attractive and repulsive parts. Borromean states are most easily found when a barrier is present outside an attractive pocket. Extensive numerical search did not reveal Borromean states for potentials without an outside barrier. We outline possible experimental setups to observe Borromean systems in two spatial dimensions., Comment: 9 pages, 5 figures, published version

We have studied the three-particle decay of 12C, 9Be and 6Be resonances. These nuclei have been described as three-body systems by means of the complex scaled hyperspherical adiabatic expansion method. The short-distance part of the wave-function is responsible for the energies whereas the information related to the observable decay properties is contained at large distances, which must be computed accurately. As an illustration we show the results for the angular distribution of 9Be and 6Be resonances., Comment: Proceedings of the Nordic Conference on Nuclear Physics held in Stockholm (June 2011)

We compute the three-body structure of the lowest resonances of $^{12}$Be considered as two neutrons around an inert $^{10}$Be core. This is an extension of the bound state calculations of $^{12}$Be into the continuum spectrum. We investigate the lowest resonances of angular momenta and parities, $0^{\pm}$, $1^{-}$ and $2^{+}$. Surprisingly enough, they all are naturally occurring in the three-body model. We calculate bulk structure dominated by small distance properties as well as decays determined by the asymptotic large-distance structure. Both $0^{+}$ and $2^{+}$ have two-body $^{10}$Be-neutron d-wave structure, while $1^{-}$ has an even mixture of $p$ and d-waves. The corresponding relative neutron-neutron partial waves are distributed among $s$, $p$, and d-waves. The branching ratios show different mixtures of one-neutron emission, three-body direct, and sequential decays. We argue for spin and parities, $0^{+}$, $1^{-}$ and $2^{+}$, to the resonances at 0.89, 2.03, 5.13, respectively. The computed structures are in agreement with existing reaction measurements., Comment: To be published in Physical Review C

The momentum distribution is a powerful probe of strongly-interacting systems that are expected to display universal behavior. This is contained in the contact parameters which relate few- and many-body properties. Here we consider a Bose gas in two dimensions and explicitly show that the two-body contact parameter is universal and then demonstrate that the momentum distribution at next-to-leading order has a logarithmic dependence on momentum which is vastly different from the three-dimensional case. Based on this, we propose a scheme for measuring the effective dimensionality of a quantum many-body system by exploiting the functional form of the momentum distribution., Comment: 8 pages, 5 figures, final version

We calculate shallow three-body bound states in the universal regime, defined by Efimov, with inclusion of both scattering length and effective range parameters. The universal spectrum is recovered for the least bound states, whereas for larger binding energies we find corrections to the universal scaling laws. We recover known results for broad Feshbach resonances with small effective range, whereas in the case of narrow resonances we find a distinct non-monotonic behavior of the threshold at which the lowest Efimov trimer merges with the three-body continuum. To address the issue of the physical origin of the three-body parameter we provide a physically clear model for the relation between three-body physics and typical two-body atom-atom interactions. Our results demonstrate that experimental information from narrow Feshbach resonances and/or mixed systems are of vital importance to pin down the relation of two- and three-body physics in atomic systems., Comment: 6 pages, 6 figures, 1 appendix, accepted version

The virial expansion method is applied within a harmonic approximation to an interacting N-body system of identical fermions. We compute the canonical partition functions for two and three particles to get the two lowest orders in the expansion. The energy spectrum is carefully interpolated to reproduce ground state properties at low temperature and the non-interacting large temperature limit of constant virial coefficients. This resembles the smearing of shell effects in finite systems with increasing temperature. Numerical results are discussed for the second and third virial coefficients as function of dimension, temperature, interaction, and the transition temperature between low and high energy limits., Comment: 11 pages, 7 figures, published version

We consider few-body bound state systems and provide precise definitions of Borromean and Brunnian systems. The initial concepts are more than a hundred years old and originated in mathematical knot-theory as purely geometric considerations. About thirty years ago they were generalized and applied to the binding of systems in nature. It now appears that recent generalization to higher order Brunnian structures may potentially be realized as laboratory made or naturally occurring systems. With the binding energy as measure, we discuss possibilities of physical realization in nuclei, cold atoms, and condensed matter systems. Appearance is not excluded. However, both the form and the strengths of the interactions must be rather special. The most promising subfields for present searches would be in cold atoms because of external control of effective interactions, or perhaps in condensed-matter systems with non-local interactions. In nuclei, it would only be by sheer luck due to a lack of tunability., Comment: 8 pages, 5 figures, revised version

We describe a method to compute thermodynamic quantities in the harmonic approximation for identical bosons and fermions in an external confining field. We use the canonical partition function where only energies and their degeneracies enter. The number of states of given energy and symmetry is found by separating the center of mass motion, and counting the remaining states of given symmetry and excitation energy of the relative motion. The oscillator frequencies that enter the harmonic Hamiltonian can be derived from realistic model parameters and the method corresponds to an effective interaction approach based on harmonic interactions. To demonstrate the method, we apply it to systems in two dimensions. Numerical calculations are compared to a brute force method that is considerably more computationally intensive., Comment: 12 pages, 8 figures

We consider bound states of asymmetric three-body systems confined to two dimensions. In the universal regime, two energy ratios and two mass ratios provide complete knowledge of the three-body energy measured in units of one two-body energy. The lowest number of stable bound states is produced when one mass is larger than two similar masses. We focus on selected asymmetric systems of interest in cold atom physics. The scaled three-body energy and the two scaled two-body energies are related through an equation for a supercircle whose radius increases almost linearly with three-body energy. The exponents exhibit an increasing behavior with three-body energy. The mass dependence is highly non-trivial. We give a simple relation that predicts the universal three-body energy., Comment: 5 pages, 4 figures, final version

We investigate the low-temperature reaction rates for radiative capture processes of three particles. We compare direct and sequential capture mechanisms and rates using realistic phenomenological parametrizations of the corresponding photodissociation cross sections.Energy conservation prohibits sequential capture for energies smaller than that of the intermediate two-body structure. A finite width or a finite temperature allows this capture mechanism. We study generic effects of positions and widths of two- and three-body resonances for very low temperatures. We focus on nuclear reactions relevant for astrophysics, and we illustrate with realistic estimates for the $\alpha$-$\alpha$-$\alpha$ and $\alpha$-$\alpha$-$n$ radiative capture processes. The direct capture mechanism leads to reaction rates which for temperatures smaller than 0.1 GK can be several orders of magnitude larger than those of the NACRE compilation., Comment: To be published in European Physical Journal A

The momentum space zero-range model is used to investigate universal properties of three interacting particles confined to two dimensions. The pertinent equations are first formulated for a system of two identical and one distinct particle and the two different two-body subsystems are characterized by two-body energies and masses. The three-body energy in units of one of the two-body energies is a universal function of the other two-body energy and the mass ratio. We derive convenient analytical formulae for calculations of the three-body energy as function of these two independent parameters and exhibit the results as universal curves. In particular, we show that the three-body system can have any number of stable bound states. When the mass ratio of the distinct to identical particles is greater than 0.22 we find that at most two stable bound states exist, while for two heavy and one light mass an increasing number of bound states is possible. The specific number of stable bound states depends on the ratio of two-body bound state energies and on the mass ratio and we map out an energy-mass phase-diagram of the number of stable bound states. Realizable systems of both fermions and bosons are discussed in this framework., Comment: 21 pages, 8 figures, 4 tables, final version

We consider the N-body problem in a layered geometry containing cold polar molecules with dipole moments that are polarized perpendicular to the layers. A harmonic approximation is used to simplify the hamiltonian and bound state properties of the two-body inter-layer dipolar potential are used to adjust this effective interaction. To model the intra-layer repulsion of the polar molecules, we introduce a repulsive inter-molecule potential that can be parametrically varied. Single chains containing one molecule in each layer, as well as multi-chain structures in many layers are discussed and their energies and radii determined. We extract the normal modes of the various systems as measures of their volatility and eventually of instability, and compare our findings to the excitations in crystals. We find modes that can be classified as either chains vibrating in phase or as layers vibrating against each other. The former correspond to acoustic and the latter to optical phonons. Instabilities can occur for large intra-layer repulsion and produce diverging amplitudes of molecules in the outer layers. Lastly, we consider experimentally relevant regimes to observe the structures., Comment: 17 pages, 20 figures, accepted version

We investigate to what extent 18Ne can be descibed as a three-body system made of an inert 16O-core and two protons. We compare to experimental data and occasionally to shell model results. We obtain three-body wave functions with the hyperspherical adiabatic expansion method. We study the spectrum of 18Ne, the structure of the different states and the predominant transition strengths. Two 0+, two 2+, and one 4+ bound states are found where they are all known experimentally. Also one 3+ close to threshold is found and several negative parity states, 1-, 3-, 0-, 2-, most of them bound with respect to the 16O excited 3- state. The structures are extracted as partial wave components, as spatial sizes of matter and charge, and as probability distributions. Electromagnetic decay rates are calculated for these states. The dominating decay mode for the bound states is E2 and occasionally also M1., Comment: 17 pages, 5 figures (version to appear in EPJA)

We consider an analytic way to make the interacting N-body problem tractable by using harmonic oscillators in place of the relevant two-body interactions. The two body terms of the N-body Hamiltonian are approximated by considering the energy spectrum and radius of the relevant two-body problem which gives frequency, center position, and zero point energy of the corresponding harmonic oscillator. Adding external harmonic one-body terms, we proceed to solve the full quantum mechanical N-body problem analytically for arbitrary masses. Energy eigenvalues, eigenmodes, and correlation functions like density matrices can then be computed analytically. As a first application of our formalism, we consider the N-boson problem in two- and three dimensions where we fit the two-body interactions to agree with the well-known zero-range model for two particles in a harmonic trap. Subsequently, condensate fractions, spectra, radii, and eigenmodes are discussed as function of dimension, boson number N, and scattering length obtained in the zero-range model. We find that energies, radii, and condensate fraction increase with scattering length as well as boson number, while radii decrease with increasing boson number. Our formalism is completely general and can also be applied to fermions, Bose-Fermi mixtures, and to more exotic geometries., Comment: 30 pages, 12 figures, updated references

The triple alpha rate is obtained from the three-body bound and continuum states computed in a large box. The results from this genuine full three-body calculation are compared with standard reference rates obtained by two sequential two-body processes. The fairly good agreement relies on two different assumptions about the lowest $2^+$ resonance energy. With the same $2^+$ energy the rates from the full three-body calculation are smaller than those of the standard reference. We discuss the rate dependence on the experimentally unknown $2^+$ energy. Substantial deviations from previous results appear for temperatures above 3 GK., Comment: To be published in Physics Letters B

In-source resonant ionization laser spectroscopy of the even-$A$ polonium isotopes $^{192-210,216,218}$Po has been performed using the $6p^37s$ $^5S_2$ to $6p^37p$ $^5P_2$ ($\lambda=843.38$ nm) transition in the polonium atom (Po-I) at the CERN ISOLDE facility. The comparison of the measured isotope shifts in $^{200-210}$Po with a previous data set allows to test for the first time recent large-scale atomic calculations that are essential to extract the changes in the mean-square charge radius of the atomic nucleus. When going to lighter masses, a surprisingly large and early departure from sphericity is observed, which is only partly reproduced by Beyond Mean Field calculations., Comment: As submitted to PRL

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 $\alpha$ decay in connection with $2^+$ resonances and density and temperature dependence rates of recombination into light nuclei from $\alpha$-particles and neutrons., Comment: 9 pages, 8 figures. Proceedings of the 21st European Few Body Conference held in Salamanca (Spain) in August-September 2010

The complex-rotated hyperspherical adiabatic method is used to study the decay of low-lying $^9$Be and $^9$B resonances into $\alpha$, $\alpha$ 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., Comment: 4 pages, 2 figures. Proceedings of the SOTANCP2 conference held in Brussels in May 2010