Structure and dynamics of few-helium clusters using soft-core potentials

In this work we investigate the structure and dynamics of small clusters of Helium atoms. We consider bound states of clusters having A = 2, 3, 4, 5, 6 atoms and continuum states in the three-atom system. Motivated by the fact that the He-He system has a very large scattering length a compared to the range r ₀ of the He-He potential (r ₀/a < 1/10), we propose the use of a soft-core interparticle potential. We use an attractive gaussian potential that reproduces the values of the dimer binding energy and the atomatom scattering length obtained with one of the widely used He-He interactions, the LM2M2 potential. In addition, we include a repulsive three-body force to reproduce the trimer binding energy. With this model, consisting in the sum of a two- and a three-body potential, we show the spectrum of the four, five, and sixparticle systems and phase-shifts and inelasticities in the three-atom system. Comparisons to calculations using realistic He-He potentials are given. In addition some universal relations are explored.     

Trajectory of virtual, bound and resonant Efimov states

The pole trajectory of Efimov states for a three-body ααβ system with αα unbound and αβ bound is calculated using a zero-range Dirac-δ potential. It is shown that a three-body bound state turns into a virtual one by increasing the αβ binding energy. This result is consistent with previous results for three equal mass particles. The present approach considers the n-n-¹⁸C halo nucleus. However, the results have good perspective to be tested and applied in ultracold atomic systems, where one can realize such three-body configuration with tunable two-body interaction.     

Excited states of confined quarks. II

We continue an analysis of the low lying excitations of colored quarks and gluons in the bag theory. These states correspond to members of an SU(6) L = 1 [56] and [70]. A study of the small oscillations of the surface of bags reveals the presence of a translation mode, an L = 1 [56]. Physical states must be constructed which are orthogonal to it. The spectrum of these states is too low but in qualitative agreement with observation. The lowest excited states form a [70]. In addition, L = 1 [56]'s should also be present, elevated in energy with respect to the [70]. We discuss ways of improving our results and the relation of our model to other calculations of baryonic spectra and mixing angles.     

Efimov Physics in Small Bosonic Clusters

We study small clusters of bosons, A = 2, 3, 4, 5, 6, characterized by a resonant interaction. Firstly, we use a soft-gaussian interaction that reproduces the values of the dimer binding energy and the atom-atom scattering length obtained with LM2M2 potential, a widely used ⁴He-⁴He interaction. We change the intensity of the potential to explore the clusters’ spectra in different regions with large positive and large negative values of the two-body scattering length and we report the clusters’ energies on Efimov plot, which makes the scale invariance explicit. Secondly, we repeat our calculation adding a repulsive three-body force to reproduce the trimer binding energy. In all the region explored, we have found that these systems present two states, one deep and one shallow close to the A ? 1 threshold, and scale invariance has been investigated for these states. The calculations are performed by means of Hyperspherical Harmonics basis set.     

Six “beyond Collins and Sivers” transverse spin asymmetries at COMPASS

COMPASS is a fixed-target high energy physics experiment at the SPS at CERN [1]. One of the important objectives of the experiment is the exploration of the transverse spin structure of the nucleon via spin dependent azimuthal asymmetries in single-hadron production in deep inelastic scattering of polarized leptons off transversely polarized target. For this purpose a series of measurements were made in COMPASS, using 160 GeV/c longitudinally polarized muon beam and transversely polarized ⁶LiD (in 2002, 2003 and 2004) and NH₃ (in 2007 and 2010) targets. Till now main attention was focused on Collins and Sivers asymmetries and obtained results play an important role in the general understanding of the three-dimensional nature of the nucleon and mechanism of SIDIS processes in terms of Transverse Momentum Dependent (TMD) Parton Distribution Functions (PDFs) and Fragmentation Functions (FFs). In addition to these two measured leading-twist effects, the SIDIS cross-section counts six more target transverse spin dependent azimuthal effects, which have their own well defined leading or higher-twist interpretation in terms of QCD parton model. So far COMPASS presented preliminary results for these asymmetries from deuteron [2, 3] and “proton-2007” data [4]. In this contribution we review the results obtained with the last “proton-2010” data sample.     

Searching for a light Higgs boson

The Lindé-Weinberg bound [1] on the mass of the Higgs boson does not apply if one of the fermions of the standard model is very massive [2] or in non-standard models with multiple Higgs particles [1]. We consider both the standard model and a common extension thereof to two or more Higgs doublets. If the Higgs responsible for lepton masses is very light, one reliable method for indirectly detecting it would be a more careful measurement of g − 2 for the muon. More direct is the search for Higgs particles detected in association with τ pairs in existing or defunct e⁺e⁻ colliders operating well below the Z mass. We analyze both methods in detail, and find that data from several existing colliders could eliminate large portions of parameter space - or, perhaps, find the Higgs boson.     

Model three-body problem in the molecular mass limit

The bound states of a three-body molecule composed of two identical heavy nuclei and a light “electron” interacting through short-range s-wave potentials are studied. The spectrum of three-body bound states grows as the mass ratio m between the heavy and light particles increases, and presents a remarkable vibration rotation structure that can be fitted with the usual empirical energy formulas of molecular spectroscopy. The results of the exact three-body calculation for the binding energy and bound-state wavefunction are compared with the predictions of the Born-Oppenheimer method for the same system. We find that for m > 30, the Born-Oppenheimer approximation yields very good results for both the binding energies and wavefunctions. For smaller m (1 <m < 30) the Born-Oppenheimer results are still surprisingly good and this is shown to be related to the range of the two-body interactions.     

Fusion-fission of light nuclear systems

Considerable interest has been devoted to fusion reactions between light heavy ions specially between weakly bound ones, due to the anomalous decrease of the fusion cross sections when compared to the total reaction cross section in the energy region around the barrier [1–4]. While the exact nature of the process responsible for the fusion cross section limitation at barrier energies is still unclear, this study shows an inhibition of the yield as the system mass decreases, resulting from the progressive increase of the barrier height and decrease of the effective barrier radius [3]. Furthermore, extensive efforts have been made recently in the study of energy-damped binary yields from light heavy-ion collisions [2,4]. Based on the substantial amount of data accumulated so far, it is now generally accepted and supported by the transition state model [4], that the observed yields arise mostly from a fusion-fission process. Data on complete fusion, fusion-fission and ‘elastic fission’ for the ⁹Be, ^10,11B+^10,11B; ^16,17,18O + ^10,11B; ¹⁹F+¹²C; ^6,7Li+⁹Be, ¹²C reactions among others, are presented. For the loosely bound nuclei it was found that the severe fusion cross section limitation is due to a low survival probability of the weakly bound nuclei until the instant of the collision [1].     

Theoretical Study of Triatomic Systems Involving Helium Atoms

The triatomic ⁴He system and its isotopic species ${^4{\rm He}_2^3{\rm He}}$ are theoretically investigated. By adopting the best empirical helium interaction potentials, we calculate the bound state energy levels as well as the rates for the three-body recombination processes: ⁴He + ⁴He + ⁴He → ⁴ He₂ + ⁴He and ⁴He + ⁴He + ³He → ⁴He₂ + ³He. We consider not only zero total angular momentum J = 0 states, but also J > 0 states. We also extend our study to mixed helium-alkali triatomic systems, that is ⁴He₂ X with X = ⁷Li, ²³Na, ³⁹K, ⁸⁵ Rb, and ¹³³Cs. The energy levels of all the J ≥ 0 bound states for these species are calculated as well as the rates for three-body recombination processes such as ⁴He + ⁴He + ⁷Li → ⁴ He₂ + ⁷Li and ⁴He + ⁴He + ⁷Li → ⁴ He⁷Li + ⁴He. In our calculations, the adiabatic hyperspherical representation is employed but we also obtain preliminary results using the Gaussian expansion method.     

Does Σ–Σ–α Form Quasi-Bound States?

For the Σ–Σ–α system we theoretically look into the possible existence of a quasi-bound state in the framework of Faddeev calculations. We are particularly interested in the state of total iso-spin T=2, because there is no strong conversion between Ξ–N–α and ${\Lambda-\Lambda-\alpha}$ . An analytic continuation using the point method is applied to search the eigenvalue in the complex energy plane. In our results the Σ–Σ–α three-body system has two quasi-bound states (J ^π  = 0⁺) where, depending on the potential parameters in the Nijmegen NSC97 model potential, the energy ranges between ?1.4 and ?2.4 MeV and the level width is about 0.4 MeV for the ground state. In addition, we obtained the excited state at ?0.15 MeV (width 4 MeV).     

Effective Field Theory Analysis of Three-Boson Systems at Next-To-Next-To-Leading Order

We use an effective field theory for short-range forces (SREFT) to analyze systems of three identical bosons interacting via a two-body potential that generates a scattering length, a, which is large compared to the range of the interaction, ?. The amplitude for the scattering of one boson off a bound state of the other two is computed to next-to-next-to-leading order (N²LO) in the ?/a expansion. At this order, two pieces of three-body data are required as input in order to renormalize the amplitude (for fixed a). We apply our results to a model system of three Helium-4 atoms, which are assumed to interact via the TTY potential. We generate N²LO predictions for atom-dimer scattering below the dimer breakup threshold using the bound-state energy of the shallow Helium-4 trimer and the atom-dimer scattering length as our two pieces of three-body input. Based on the convergence pattern of the SREFT expansion, as well as differences in the predictions of two renormalization schemes, we conclude that our N²LO phase- shift predictions will receive higher-order corrections of < 0.2 %. In contrast, the prediction of SREFT for the binding energy of the “deep” trimer of Helium-4 atoms displays poor convergence.     

Experimental Search for μd 3He Fusion

The vast majority of muon catalyzed fusion research has been concerned with muonic molecules of hydrogen isotopes only, since the dynamics of higher-Z muonic atoms in general preclude the formation of molecular systems. In the specific case of hydrogen–helium mixtures, bound muonic molecular states can exist, and thus it is possible to search for the reaction μd ³He $$\xrightarrow{{\tilde \lambda f}}$$ μ+α(3.66 MeV)+p(14.64 MeV). Until recently, the theoretical predictions for the nuclear fusion rate in the μd ³He molecule, ${\tilde \lambda }$ _f , ranged over one order of magnitude, from 10⁵ to 10⁶ per second. An experimental upper limit has been measured for ${\tilde \lambda }$ _f in HD + ³He giving a value (<6×10⁴ s^?1 [1]). We report on the analysis of an experiment in D₂ + ³He which has shown a signal coming either from the muon catalyzed reaction, or from the fusion in flight of ³He's formed from dμd fusion.     

Trajectory of neutron–neutron–C excited three-body state

The trajectory of the first excited Efimov state is investigated by using a renormalized zero-range three-body model for a system with two bound and one virtual two-body subsystems. The approach is applied to n–n–¹⁸C, where the n–n$n\text{–}n$ virtual energy and the three-body ground state are kept fixed. It is shown that such three-body excited state goes from a bound to a virtual state when the n–¹⁸C binding energy is increased. Results obtained for the n–¹⁹C elastic cross-section at low energies also show dominance of an S-matrix pole corresponding to a bound or virtual Efimov state. It is also presented a brief discussion of these findings in the context of ultracold atom physics with tunable scattering lengths.     

Glueball masses and string tension Smeared loop-loop correlation functions

By using results obtained by the Ape Collaboration [1] we study the glueball spectrum and the string tension in lattice QCD by analyzing correlation functions between operators. We use and discuss the smearing method. We consider a 5³ × 16 lattice at β = 5.6 as a test case, and a 12³ × 32 lattice at β = 5.9 in order to compare with the old wall results of ref. [3]. We study the structure of the excited states.     

Approximate Treatment of 3-Body Coulomb Systems: Discrete Spectrum

We present a method for treatment of three charged particles. The proposed method has universal character and is applicable both for bound and continuum states. A finite-rank approximation is used for Coulomb potential in the Lippman?CSchwinger equation, that results in a system of one-dimensional coupled integral equations. Preliminary numerical results for three-body atomic and molecular systems like H ^?, He, pp?? and other are presented.     

Screening corrections in cold deuterium fusion rates

We have recalculated the fusion rates of the free deuterium molecule, ion and mesomolecule taking into account the shielding of the Coulomb barrier by the electrons and muon. Electron screening increases the rates by several orders of magnitude. The fusion of hydrogen nuclei is known to be the source of energy of stars occuring in their high-temperature, high-pressure interiors. In terrestrial conditions, one attempts currently to tap this source of nuclear fusion energy by alternative techniques, i.e. high-temperature plasmas or muon-catalyzed fusion. Very recently cold fusion in solids has achieved worldwide attention, since experimental evidence for increased hydrogenic fusion rates in palladium and titanium has been reported[1,2]. These reports have motivated us to reconsider the fusion probability of free hydrogen molecules, ions and mesomolecules, following closely the studies of Refs. [3,4,5]. Our aim however is to improve the previous estimates of the respective fusion rates by taking account of the screening effects of the electrons and muons on the nuclear Coulomb barrier which will turn out to be quite important. As in Ref. [5] we will restrict our numerical results to deuterium only.     

A three-body calculation of πd scattering

We present a theoretical treatment of the pion-deuteron system, meant specifically for the energy region below 100 MeV, and based on the Faddeev method for three-body scattering. This includes all orders of multiple scattering, two- and three-body unitarity (to a good approximation), nucleon recoil, deuteron d-state and a correct treatment of spin and isospin. For consistency with nuclear physics we treat the nucleons non-relativistically. However, relativistic kinematics are used for the pion. In order to obtain one-dimensional integral equations in the three-body system, we have constructed a set of separable πN t-matrices (with analytic form factors), which fit selected data up to 300 MeV. A comparison is made with existing π⁺d data at 48 MeV. This data tends to favour the Faddeev type of energy dependence for the πN t-matrix in the πd system. This could also be important in low-energy pion-nucleus scattering.     

The transverse electron scattering response function of 3He

Results on the transverse response function R _T (q,ω) of ³He obtained within the Lorentz integral transform [LIT] [1] method are presented. The response is calculated using the BonnRA nucleon-nucleon potential [2], the Tucson-Melbourne [3] three-body force, and the Coulomb potential for various momentum transfers. The results are compared with available data.     

Free Energy of a Dilute Bose Gas: Lower Bound

A lower bound is derived on the free energy (per unit volume) of a homogeneous Bose gas at density \(\varrho\) and temperature T. In the dilute regime, i.e., when \(a^3\varrho \ll 1\) , where a denotes the scattering length of the pair-interaction potential, our bound differs to leading order from the expression for non-interacting particles by the term \(4{\pi}a ( 2{\varrho^2}-[\varrho-\varrho_c]_+^2 )\) . Here, \(\varrho_c(T)\) denotes the critical density for Bose-Einstein condensation (for the non-interacting gas), and \([\, \cdot \, ]_+ = \max\{ \, \cdot\, , 0\}\) denotes the positive part. Our bound is uniform in the temperature up to temperatures of the order of the critical temperature, i.e., T ~ \(\varrho\) ^2/3 or smaller. One of the key ingredients in the proof is the use of coherent states to extend the method introduced in [17] for estimating correlations to temperatures below the critical one.