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We determine cross sections and astrophysical S-factors of the reactions generated in collisions between $^{6}$Li and $^{3}$H, and $^{6}$Li and $^{3}$He. A microscopic three-cluster model is employed to study the dynamics of reactions occurring in the mirror nuclei $^{9}$Be and $^{9}$B. In a previous study [Phys. Rev. C {\bf 109}, 045803 (2024)], this model was successfully applied to investigate the resonance structure of $^{9}$Be and $^{9}$B, as well as reactions induced by the interaction of deuterons with $^7$Li and $^7$Be. A fairly good agreement between theoretical results and available experimental data was achieved. To the best of our knowledge, appropriate experimental data for the astrophysical S-factors of the reactions generated by the interaction of $^6$Li with $^3$H and with $^3$He are currently unavailable. Thus, our results can serve as a guideline for future experimental efforts., Comment: 26 pages, 12 figures, 2 tables

Purpose: In this paper we investigated emission of bremsstrahlung photons in the scattering of protons off deuterons within the microscopic cluster models in a wide region of the beam energy from low energies up to 1.5 GeV. Methods: Three-cluster model of bremsstrahlung is constructed for such a reaction. Formalism of the model includes form factor of deuteron which characterizes dependence of bremsstrahlung cross sections on structure of deuteron. This gives possibility to investigate the structure of nuclei from analysis of bremsstrahlung cross sections. Results: We studied dependence of the bremsstrahlung cross section on the structure of deuteron. We use three different shapes of the deuteron wave functions. Besides, we also calculate the cross section by neglecting internal structure of deuteron. Analysis of dependence of the cross section on such a parameter shows the following. (1) At beam energies 145 and 195 MeV used in experiments bremsstrahlung cross section is not sensitive visibly on variations of the shape of the deuteron wave functions. (2) Stable difference between cross sections calculated with and without internal structure of deuteron is observed at higher energy of beam (larger 500 MeV). (3) The spectrum is increased as we pass from structureless deuteron (the oscillator length $b=0$) to the deuteron discribed by the shell-model wave function (the realistic oscillator length) inside the full energy region of the emitted photons. Conclusion: Our cluster model is a suitable tool to study the structure of deuteron with high enough precision from bremsstrahlung analysis. We propose new experiments for such an investigation., Comment: 33 pages, 18 captured figures

Systematic analysis of parameters and properties of the Pauli resonance states are performed for light nuclei $^{6}$Li, $^{7}$Li, $^{8}$Be, $^{9}$Be and $^{10}$B, which are treated as two-cluster systems. The Pauli resonance states are redundant solutions of the resonating group method appearing when one try use more advanced description of the internal structure of interacting clusters. Our calculations are performed in a standard and advanced versions of the resonating group method. The standard version employs wave functions of many-particle shell model to describe internal motion of nucleons within each cluster. The advanced version is based on three-cluster resonating group method. As in the standard version, the internal wave functions of three clusters are approximated by wave functions of many-particle shell model model. However, in advanced version one of pair of clusters forms a bound state, and third cluster is considered to interact with such state. It is found that the Pauli resonance states in nuclei under consideration have energy between 11 and 46 MeV, and their widths vary from 8 keV to 6.7 MeV. Analysis of wave functions of Pauli resonance states and matrix elements of norm kernel allowed us to formulate an effective method for eliminating Pauli resonance states. It is demonstrated that this method effectively eliminate all determined the Pauli resonance states., Comment: 54 pages, 28 figures, typos are corrected and few paragraph are added with more detailed explanations, submitted to Phys. Rev. C

We present a many-channel microscopic model that extends the three-cluster model previously formulated in \cite{2009NPA...V37}. This extended model incorporates multiple three-cluster configurations, which are subsequently reduced to a comprehensive set of binary channels. These channels dictate the dynamics of various nuclear processes and the resonance structure of a compound nucleus across a broad energy spectrum. The application of this model focuses on investigating the nature of high-energy resonance states in $^{9}$Be and $^{9}$B, as well as the astrophysical $S$-factors for the reactions $^{7}$Li$(d,n)\alpha\alpha$ and $^{7}$Be$(d,p)\alpha\alpha$, particularly pertinent to the cosmological lithium problem. Parameterization of resonance states is performed across a wide range of total angular momenta and includes states of both positive and negative parity. Dominant decay channels are identified for each resonance state. Detailed analysis of astrophysical $S$ factors resulting from deuteron interactions with $^{7}$Li and $^{7}$Be is conducted within an energy range from zero to 2 MeV. Four exit channels in $^{9}$Be ($^{8}$Be($0^{+}$)$+n$, $^{8}$Be($2^{+}$)$+n$, $^{5}$He($3/2^{-}$)$+\alpha$, $^{5}$He($1/2^{-}$)$+\alpha$) and four in $^{9}$B ($^{8}$Be($0^{+}$)$+p$, $^{8}$Be($2^{+}$)$+p$, $^{5}$Li($3/2^{-}$)$+\alpha$, $^{5}$Li($1/2^{-}$)$+\alpha$) are considered. A clear hierarchy of reactions is established for the energy range 0$\leq E<$1.0 MeV. Notably, reactions $^{7}$Li$+d=^{8}$Be($0^{+}$)$+n$ and $^{7}$Be$+d=^{8}$Be($0^{+}$)$+p$ substantially dominate over all other reactions within this energy range. The model satisfactory describes the experimental astrophysical $S$ factors for these reactions., Comment: 36 pages, 23 figures, to be submitted to Phys. Rev. C

Translational research requires data at multiple scales of biological organization. Advancements in sequencing and multi-omics technologies have increased the availability of these data, but researchers face significant integration challenges. Knowledge graphs (KGs) are used to model complex phenomena, and methods exist to construct them automatically. However, tackling complex biomedical integration problems requires flexibility in the way knowledge is modeled. Moreover, existing KG construction methods provide robust tooling at the cost of fixed or limited choices among knowledge representation models. PheKnowLator (Phenotype Knowledge Translator) is a semantic ecosystem for automating the FAIR (Findable, Accessible, Interoperable, and Reusable) construction of ontologically grounded KGs with fully customizable knowledge representation. The ecosystem includes KG construction resources (e.g., data preparation APIs), analysis tools (e.g., SPARQL endpoints and abstraction algorithms), and benchmarks (e.g., prebuilt KGs and embeddings). We evaluated the ecosystem by systematically comparing it to existing open-source KG construction methods and by analyzing its computational performance when used to construct 12 large-scale KGs. With flexible knowledge representation, PheKnowLator enables fully customizable KGs without compromising performance or usability.

A new model of bremsstrahlung emission in the scattering of light nuclei is constructed with main focus on strict cluster formulation of nuclear processes. Analysis is performed in frameworks of the folding approximation of the formalism with participation of $s$-nuclei. Reactions $p$ +$^4$He, $^2$D + $^4$He, $^3$H + $^4$He, $^3$He + $^4$He are included to analysis. Systematic analysis of properties of emission of bremsstrahlung photons in the wide region of kinetic energy of relative motion of two nuclei from 7 to 1000~MeV is performed. Influence of the oscillator length on the calculated spectra of bremsstrahlung emission is analyzed. On the example of $^3$H + $^4$He, dependence of the bremsstrahlung spectra on parameters of nuclear component of interacting potential is established (at first time for the light nuclei). Experimental bremsstrahlung data for the proton-deuteron scattering and proton-$\alpha$-particle scattering are analyzed on the basis of this model., Comment: 27 pages, 8 captured figures

We study the ground and the first excited $0^{+}$ states of two mirror nuclei $^{14}$C and $^{14}$O within a five-cluster model (three alpha-particles and two extra nucleons) with the use of high accuracy variational approach with Gaussian bases. The first excited $0^{+}$ state of these nuclei is shown to be connected with a change of the structure of the two-nucleon subsystem moving in the field of the $^{12}$C cluster. The density distributions, electric form factors (both the elastic and transition ones), pair correlation functions, and the momentum distributions of the constituent particles are found. The most probable shapes of five-cluster systems are revealed., Comment: 25 pages, 8 figures

Background: Common data models solve many challenges of standardizing electronic health record (EHR) data, but are unable to semantically integrate all the resources needed for deep phenotyping. Open Biological and Biomedical Ontology (OBO) Foundry ontologies provide computable representations of biological knowledge and enable the integration of heterogeneous data. However, mapping EHR data to OBO ontologies requires significant manual curation and domain expertise. Objective: We introduce OMOP2OBO, an algorithm for mapping Observational Medical Outcomes Partnership (OMOP) vocabularies to OBO ontologies. Results: Using OMOP2OBO, we produced mappings for 92,367 conditions, 8611 drug ingredients, and 10,673 measurement results, which covered 68-99% of concepts used in clinical practice when examined across 24 hospitals. When used to phenotype rare disease patients, the mappings helped systematically identify undiagnosed patients who might benefit from genetic testing. Conclusions: By aligning OMOP vocabularies to OBO ontologies our algorithm presents new opportunities to advance EHR-based deep phenotyping., Comment: Supplementary Material is included at the end of the manuscript

Similar to managing software packages, managing the ontology life cycle involves multiple complex workflows such as preparing releases, continuous quality control checking, and dependency management. To manage these processes, a diverse set of tools is required, from command line utilities to powerful ontology engineering environments such as ROBOT. Particularly in the biomedical domain, which has developed a set of highly diverse yet inter-dependent ontologies, standardising release practices and metadata, and establishing shared quality standards, are crucial to enable interoperability. The Ontology Development Kit (ODK) provides a set of standardised, customisable, and automatically executable workflows, and packages all required tooling in a single Docker image. In this paper, we provide an overview of how the ODK works, show how it is used in practice, and describe how we envision it driving standardisation efforts in our community., Comment: 19 pages, 2 supplementary tables, 1 supplementary figure

Despite progress in the development of standards for describing and exchanging scientific information, the lack of easy-to-use standards for mapping between different representations of the same or similar objects in different databases poses a major impediment to data integration and interoperability. Mappings often lack the metadata needed to be correctly interpreted and applied. For example, are two terms equivalent or merely related? Are they narrow or broad matches? Are they associated in some other way? Such relationships between the mapped terms are often not documented, leading to incorrect assumptions and making them hard to use in scenarios that require a high degree of precision (such as diagnostics or risk prediction). Also, the lack of descriptions of how mappings were done makes it hard to combine and reconcile mappings, particularly curated and automated ones. The Simple Standard for Sharing Ontological Mappings (SSSOM) addresses these problems by: 1. Introducing a machine-readable and extensible vocabulary to describe metadata that makes imprecision, inaccuracy and incompleteness in mappings explicit. 2. Defining an easy to use table-based format that can be integrated into existing data science pipelines without the need to parse or query ontologies, and that integrates seamlessly with Linked Data standards. 3. Implementing open and community-driven collaborative workflows designed to evolve the standard continuously to address changing requirements and mapping practices. 4. Providing reference tools and software libraries for working with the standard. In this paper, we present the SSSOM standard, describe several use cases, and survey some existing work on standardizing the exchange of mappings, with the goal of making mappings Findable, Accessible, Interoperable, and Reusable (FAIR). The SSSOM specification is at http://w3id.org/sssom/spec., Comment: Corresponding author: Christopher J. Mungall

We investigate properties of bound and resonance states in the $_{\Lambda}^{9}$Be nucleus. To reveal the nature of these states, we use a three-cluster $2\alpha+\Lambda$ microscopic model. The model incorporates Gaussian and oscillator basis functions and reduces a three-cluster Schr\"{o}dinger equation to a two-body like many-channel problem with the two-cluster subsystems ($_{\Lambda}^{5}$He and $^8$Be) being in a bound or a pseudo-bound state. Influence of the cluster polarization on the energy and widths of resonance states in $_{\Lambda}^{9}$Be and on elastic and inelastic $_{\Lambda}^{5}$He+$\alpha$ scattering is analyzed., Comment: 42 pages, 5 figures, extended version of the paper, submitted to Nucl. Phys. A

A two-cluster microscopic model is applied to study elastic alpha-alpha scattering and resonance structure of $^{8}$Be. The model is an algebraic version of the Resonating Group Method, which makes use complete set of oscillator functions to expand wave function of two-cluster system. Interaction between clusters is determined by well-known semi-realistic nucleon-nucleon potentials of Hasegawa-Nagata, Minnesota and Volkov. Detail analysis of resonance wave functions is carried out in oscillator, coordinate and momentum spaces. Effects of the Pauli principle on wave functions of the $^{8}$Be continuous spectrum states are thoroughly studied., Comment: 35 pages, 14 figures

Single-cell RNA-Sequencing (scRNA-Seq) has undergone major technological advances in recent years, enabling the conception of various organism-level cell atlassing projects. With increasing numbers of datasets being deposited in public archives, there is a need to address the challenges of enabling the reproducibility of such data sets. Here, we describe guidelines for a minimum set of metadata to sufficiently describe scRNA-Seq experiments, ensuring reproducibility of data analyses.

We study effects of the Pauli principle on the potential energy of two-cluster systems. The object of the investigation is the lightest nuclei of p-shell with a dominant $\alpha$-cluster channel. For this aim we construct matrix elements of two-cluster potential energy between cluster oscillator functions with and without full antisymmetrization. Eigenvalues and eigenfunctions of the potential energy matrix are studied in detail. Eigenfunctions of the potential energy operator are presented in oscillator, coordinate and momentum spaces. We demonstrate that the Pauli principle affects more strongly the eigenfunctions than the eigenvalues of the matrix and leads to the formation of resonance and trapped states., Comment: 10 pages, 8 figures, contribution to Proceedings of the 24th European Few Body Conference, Surrey, UK, 2-4 September 2019

We study effects of the antisymmetrization on the potential energy of two-cluster systems. The object of the investigation is the lightest nuclei of p-shell with a dominant alpha-cluster channel. For this aim we construct matrix elements of two-cluster potential energy between cluster oscillator functions with and without full antisymmetrization. Eigenvalues and eigenfunctions of the potential energy matrix are studied in detail. Eigenfunctions of the potential energy operator are presented in oscillator, coordinate and momentum spaces. We demonstrate that the Pauli principle affects more strongly the eigenfunctions than the eigenvalues of the matrix and leads to the formation of resonance and trapped states., Comment: 45 pages, 23 figures, submitted to Ann. Phys

We investigate how the Coulomb interaction affects the energy $E$ and width $\Gamma$ of resonance states in mirror nuclei. We employ a three-cluster microscopic model to determine position of resonance states in two- and three-body continua. Two parameters are introduced to quantify effects of the Coulomb interactions. As the energy and width of the corresponding resonance states of mirror nuclei are displayed on an $E$-$\Gamma$ plane, these parameters determine a rotation and a dilatation. With the help of these parameters we found resonance states with strong, small and medium effects of the Coulomb interaction. We also found two different scenarios of the motion of resonance states due to the Coulomb interaction. The first standard (major) scenario represent resonance states with the larger energy and larger width than their counterparts have. The second rear scenario includes resonance states with the larger energy but smaller width., Comment: 55 pages, 22 figures, two new paragraphs are added and typos are corrected, submitted to Nucl. Phys . A

Matrix elements of potential energy are examined in detail. We consider a model problem - a particle in a central potential. The most popular forms of central potential are taken up, namely, square-well potential, Gaussian, Yukawa and exponential potentials. We study eigenvalues and eigenfunctions of the potential energy matrix constructed with oscillator functions. It is demonstrated that eigenvalues coincide with the potential energy in coordinate space at some specific discrete points. We establish approximate values for these points. It is also shown that the eigenfunctions of the potential energy matrix are the expansion coefficients of the spherical Bessel functions in a harmonic oscillator basis. We also demonstrate a close relation between the separable approximation and $L^{2}$ basis (J-matrix) method for the quantum theory of scattering., Comment: 47 pages, 19 figures, matches the published version

We investigate resonance states in three-cluster continuum of some light nuclei $^{9}$Be, $^{9}$B, $^{10}$B, $^{11}$B and $^{11}$C. These nuclei are considered to have a three-cluster configuration consisting of two alpha-particles and neutron, proton, deuteron, triton and nucleus $^{3}$He. In this study, we make use two different microscopic three-cluster models. The first model employs the Hyperspherical Harmonics basis to numerate channels and describe three-cluster continuum. The second model is the well-known complex scaling method. The nucleon-nucleon interaction is modeled by the semi-realistic Minnesota and Hasegawa-Nagata potentials. Our main aim is to find the Hoyle-analog states in these nuclei or, in other words, whether it is possible to synthesize these nuclei in a triple collision of clusters. We formulate the criteria for selecting such states and apply them to resonance states, emerged from our calculations. We found that there are resonance states obeying the formulated criteria which make possible syntheses of these nuclei in a stellar environment., Comment: 15 pages, 15 figures, submitted to Phys. Rev. C

We study nature of the low-lying resonance states in mirror nuclei $^{9}$Be and $^{9}$B. Investigations are performed within a three-cluster model. The model makes use of the hyperspherical harmonics, which provides convenient description of three-cluster continuum. The dominant three-cluster configurations $\alpha+\alpha+n$ and $\alpha+\alpha+p$ in $^{9}$Be and $^{9}$B, respectively, are taken into account. Dominant decay channels for all resonance states in $^{9}$Be and $^{9}$B are explored. Much attention is paid to the controversial $1/2^{+}$ resonance states in both nuclei. We study effects of the Coulomb interaction on energy and width of three-cluster resonances in the mirror nuclei $^{9}$Be and $^{9}$B. We also search for the Hoyle-analogue state which is a key step for alternative way of $^{9}$Be and $^{9}$B syntheses in a triple collision of clusters in a stellar environment., Comment: 17 pages, 16 figures, submitted to Phys. Rev. C

We consider a set of three-cluster systems ($^{4}$He, $^{7}$Li, $^{7}$Be, $^{8}$Be, $^{10}$Be) within a microscopic model which involves the hyperspherical harmonics to represent intercluster motion. We selected such three-cluster systems which have at least one binary channel. Our aim is to study whether the hyperspherical harmonics are able and under what conditions to describe two-body channel(s) (nondemocratic motion) or they are suitable for describing three-cluster continuum only (democratic motion). It is demonstrated that a rather restricted number of the hyperspherical harmonics allows us to describe bound states and scattering states in two-body continuum for a three-cluster system., Comment: 18 pages, 19 figures, extended version of the paper, new figures and references added, submitted to Phys. Rev. C

We investigate T-matrix for bound and continuous-spectrum states in the discrete oscillator representation. The investigation is carried out for a model problem - the particle in the field of a central potential. A system of linear equations is derived to determine the coefficients of the T-matrix expansion in the oscillator functions. We selected four potentials (Gaussian, exponential, Yukawa, and square-well ones) to demonstrate peculiarities of the T-matrix and its dependence on the potential shape. We also study how the T-matrix expansion coefficients depend on the parameters of the oscillator basis such as the oscillator length and the number of basis functions involved in calculations., Comment: 12 pages, 12 figures, UJP style file provided

We present a phase-space representation of quantum state vectors for two-cluster systems. Density distributions in the Fock--Bargmann space are constructed for bound and resonance states of $^{6,7}$Li and $^{7,8}$Be, provided that all these nuclei are treated within a microscopic two-cluster model. The density distribution in the phase space is compared with those in the coordinate and momentum representations. Bound states realize themselves in a compact area of the phase space, as also do narrow resonance states. We establish the quantitative boundaries of this region in the phase space for the nuclei under consideration. Quantum trajectories are demonstrated to approach their classical limit with increasing energy., Comment: 35 pages, 15 figures, submitted to Nucl. Phys. A

We explore the structure of resonance states in $^{6}$He by experimental and theoretical methods. We present the results of experimental investigations of the three-body continuous spectrum of $^{6}$He. For this aim, we use the reaction $^{3}$H$( \alpha,p\alpha)nn$, which is induced by the interaction of alpha-particles with a triton at the beam energy $E_{\alpha} =$~67.2 MeV. The theoretical analysis of the resonance structure in $^{6}$He is carried out within the framework of a three-cluster microscopic model. The model exploits the hyperspherical harmonics to describe the intercluster dynamics. The set of new resonance states is discovered by the experimental and theoretical methods. The energy, width, and dominant decay channels of resonances are determined.The obtained results are compared in detail with the results of different theoretical models and experiments as well., Comment: 16 pp, 17 figures, UJP style file provided

We investigate both bound and resonance states in 12C embedded in a three-\alpha-cluster continuum using two distinct three-cluster microscopic models. The first one relies on the Hyperspherical Harmonics basis to enumerate the channels describing the three-cluster continuum. The second model incorporates both Gaussian and Oscillator basis functions, and reduces the three-cluster problem to a two-cluster one, in which a two-cluster subsystem is described by a set of pseudo-bound state states. It is shown that the results agree well with comparable calculations from the literature., Comment: 31 pages, 12 figures, 9 tables

Homogeneous isotropic models with two torsion functions built in the framework of the Poincare gauge theory of gravity based on general expression of gravitational Lagrangian by certain restrictions on indefinite parameters are analyzed numerically. Special points of cosmological solutions at asymptotics and conditions of their stability in dependence of indefinite parameters are found. Procedure of numerical integration of the system of gravitational equations at asymptotics is considered. Numerical solution for accelerating Universe without dark energy and dark matter is obtained. It is shown that by certain restrictions on indefinite parameters obtained cosmological solutions are in agreement with SNe Ia observational data and Big Bang Nucleosynthesis predictions. Statefinder diagnostics is discussed in order to compare considered cosmological model with other models., Comment: 19 pages, 6 figures, jcappub style file

The paper proposes a hybrid method for calculating scattering processes that combines the $J$-matrix method with exterior complex scaling as an absorbing boundary condition. It represents the wave function as a finite sum of oscillator eigenstates in the inner region and on grid in the outer region. The method is validated for one and two dimensional model partial wave equation equations. Finally, the method calculates nuclear $p$-shell scattering.

A microscopic model for three-cluster configurations in light nuclei is presented. It uses an expansion in terms of Faddeev components for which the dynamic eqations are derived. The model is designed to investigate binary channel processes in a compound system. Gaussian and oscillator bases are used to expand the wave function and to represent appropriate boundary conditions. We study the effect of cluster polarization on ground and resonance states of 7Be, and on the astrophysical S-factor of the reaction 6Li(p,3He)4He., Comment: 20 pages, 8 Postscript figures, uses elsart1p.sty, submitted to Nucl. Phys. A

We investigate the effect of monopole and quadrupole modes on the elastic alpha-alpha resonance structure of $^{8}$Be. To this end we make a fully microscopic coupled channels calculation with three coupled channels, using the Algebraic Model. The continuum spectrum and wave functions are analyzed in terms of the individual channels to understand the nature of the resonances. It is shown that both monopole and quadrupole modes have a non-negligible effect on the resonances in the alpha-alpha continuum., Comment: 20 pages, 4 figures. submitted to Phys.Rev.C

We investigate the effects of the regularization procedure used in the J-Matrix method. We show that it influences the convergence, and propose an alternative regularization approach. We explicitly perform some model calculations to demonstrate the improvement., Comment: 17 pages, 7 figures. 'J-matrix method and its applications', (A.Alhaidari), ed., N.Y.: Nova Science Publishers, 2004. [in press]

We present a fully microscopic three-cluster nuclear model for light nuclei on the basis of a J-Matrix approach. We apply the Modified J-Matrix method on $^{6}He$ and $^{6}Be$ for both scattering and reaction problems, analyse the Modified J-Matrix calculation, and compare the results to experimental data., Comment: 43 pages 21 figures, submitted to "J-matrix method and its applications", A. Alhaidari et al, editors., N.Y.: Nova Science Publishers, Inc

The resonance states of $^{4}H$, $^{4}He$ and $^{4}Li$, embedded in the three-cluster $d+N+N$ continuum, are investigated within a three-cluster model. The model treats the Pauli principle exactly and incorporates the Faddeev components for proper description of the boundary conditions for the two- and three-body continua. The hyperspherical harmonics are used to distinguish and numerate channels of the three-cluster continuum. It is shown that the effective barrier, created by three-cluster configuration $d+N+N$, is strong enough to accommodate two resonance states., Comment: 20 page, 4 figures

The structure of $^8$He is investigated within a three-cluster microscopic model. The three-cluster configuration $\alpha+^2n+^2n$ was used to describe the properties of the ground state of the nucleus. The obtained results evidently indicate the existence of a neutron halo in $^8$He., Comment: 14 pages, 6 postscript figures, submitted to Phys. Atom. Nucl

The convergence problem for scattering states is studied in detail within the framework of the Algebraic Model, a representation of the Schrodinger equation in an L^2 basis. The dynamical equations of this model are reformulated featuring new "Dynamical Coefficients", which explicitly reveal the potential effects. A general analysis of the Dynamical Coefficients leads to an optimal basis yielding well converging, precise and stable results. A set of strategies for solving the equations for non-optimal bases is formulated based on the asymptotic behaviour of the Dynamical Coefficients. These strategies are shown to provide a dramatically improved convergence of the solutions., Comment: 31 pages, 41 postscript figures

A framework to calculate two-particle matrix elements for fully antisymmetrized three-cluster configurations is presented. The theory is developed for a scattering situation described in terms of the Algebraic Model. This means that the nuclear many-particle state and its asymptotic behaviour are expanded in terms of oscillator states of the intra-cluster coordinates. The Generating Function technique is used to optimize the calculation of matrix elements. In order to derive the dynamical equations, a multichannel version of the Algebraic Model is presented., Comment: 20 pages, 1 postscript figure, submitted to Phys. Rev. C

The resonance states embedded in the three-cluster continuum of 6He and 6Be are obtained in the Algebraic Version of the Resonating Group Method. The model accounts for a correct treatment of the Pauli principle. It also provides the correct three-cluster continuum boundary conditions by using a Hyperspherical Harmonics basis. The model reproduces the observed resonances well and achieves good agreement with other models. A better understanding for the process of formation and decay of the resonance states in six-nucleon systems is obtained., Comment: 8 pages, 10 postscript figures, submitted to Phys. Rev. C