Search

We study the ^99Be ground-state energy with non-local \alpha nαn and \alpha \alphaαα potentials derived from Cluster Effective Field Theory. The short-distance dependence of the interaction is regulated with a momentum cutoff. The potential parameters are fitted to reproduce the scattering length and effective range. We implement such potential models in a Non-Symmetrized Hyperspherical Harmonics (NSHH) code in momentum space. In addition we calculate ground-state energies of various alpha nuclei. Work is in progress on a calculation of the photodisintegration of ^99Be with the Lorentz Integral Transform (LIT) method.

It is aimed to describe the nucleus of \(^9\)Be in an \(\alpha \)-\(\alpha \)-neutron cluster model, where the \(\alpha \)-\(\alpha \) and \(\alpha \)-neutron interactions are determined via an effective field theory (EFT) for halo nuclei (halo-EFT). Here, only the \(\alpha \)-\(\alpha \) case is discussed more detailed and hence results are given for \(\alpha \)-\(\alpha \) phase shifts and for the ground-state energy of \(^{12}\)C as a three \(\alpha \) cluster. The calculation of the \(^{12}\)C wave function is made via an expansion on nonsymmetrized hyperspherical harmonics (NSHH) in momentum space.

In view of the growing interest in neutrino scattering with nuclei we show that it is possible to extend to relatively high energies and momentum transfers the accurate ab initio results obtained by the integral transform (IT) approach for quasi-elastic (q.e) kinematics. This is made possible by performing the calculation in a specific frame and by employing a q.e. kinematical model that helps in reducing the frame dependence. The results are validated comparing theoretical and experimental (e, e\(^\prime \)) cross sections.

We introduce a few extensions to the Hyperspherical Harmonics (HH) approach in order to include intrinsic excitations degrees of freedom. To this end we adapt the HH expansion method, usually built up starting from a fixed mass-weighted set of Jacobi coordinates, to the more general case where an arbitrary weighted set of coordinates is adopted. We provide a few results for 3- and 4-body bound state calculations.

The electromagnetic responses obtained from Green's function Monte Carlo (GFMC) calculations are based on realistic treatments of nuclear interactions and currents. The main limitations of this method comes from its nonrelativistic nature and its computational cost, the latter hampering the direct evaluation of the inclusive cross sections as measured by experiments. We extend the applicability of GFMC in the quasielastic region to intermediate momentum transfers by performing the calculations in a reference frame that minimizes nucleon momenta. Additional relativistic effects in the kinematics are accounted for employing the two-fragment model. In addition, we developed a novel algorithm, based on the concept of first-kind scaling, to compute the inclusive electromagnetic cross section of $^4$He through an accurate and reliable interpolation of the response functions. A very good agreement is obtained between theoretical and experimental cross sections for a variety of kinematical setups. This offers a promising prospect for the data analysis of neutrino-oscillation experiments that requires an accurate description of nuclear dynamics in which relativistic effects are fully accounted for., 10 pages, 7 figures

Some general remarks about integral transform approaches to response functions are made. Their advantage for calculating cross sections at energies in the continuum is stressed. In particular we discuss the class of kernels that allow calculations of the transform by matrix diagonalization. A particular set of such kernels, namely the wavelets, is tested in a model study., Comment: 7 pages, 2 figures. Contribution to the 23rd European Conference on Few-Body Problems in Physics Aarhus, Denmark, 8-12 August 2016

These lecture notes intend to give a brief overview of some ab initio approaches currently used to study nuclear structure properties and reactions. In the first part particular attention is devoted to two methods useful to account for bound state properties. They are both based on the diagonalization of the full many-body Hamiltonian matrix, but share in addition the use of similarity transformations. Transforming the bare potential into an effective one, the latter help in speeding up the convergence of the results. In the second part ab initio methods for reaction cross sections involving the continuum part of the nuclear spectrum is described, with emphasis on perturbation induced reactions. They are based on integral transforms which make it possible to reduce the many-body scattering problem to a bound state problem, allowing to take advantage of any of the methods described in the first part.

The Schrodinger equation is solved for an A-nucleon system using an expansion of the wave function in nonsymmetrized hyperspherical harmonics. Our approach is based on the formalism developed by Gattobigio et al. (Phys Rev A 79:032513, 2009; Few-Body Syst 45:127, 2009; Phys Rev C 83:024001, 2011), where it was applied to four- and six-body systems using central and central spin dependent potentials. In addition we include isospin dependence and noncentral forces in order to be able to make calculations also with more realistic NN potential models. Furthermore, a more efficient procedure to determine the fermionic spectrum is used. The approach is applied to four- and six-body nuclei (4He,6Li) with various NN potential models including for 4He the realistic AV18 potential. It is shown that the results for ground-state energy and radius agree well with those from the literature.

The electric dipole polarizability quantifies the low-energy behaviour of the dipole strength and is related to critical observables such as the radii of the proton and neutron distributions. Its computation is challenging because most of the dipole strength lies in the scattering continuum. In this paper we combine integral transforms with the coupled-cluster method and compute the dipole polarizability using bound-state techniques. Employing different interactions from chiral effective field theory, we confirm the strong correlation between the dipole polarizability and the charge radius, and study its dependence on three-nucleon forces. We find good agreement with data for the 4He, 40Ca, and 16O nuclei, and predict the dipole polarizability for the rare nucleus 22O., 12 pages, 11 figures

We review the Lorentz integral transform coupled-cluster method for the calculation of the electric dipole polarizability. We benchmark our results with exact hyperspherical harmonics calculations for 4He and then we move to a heavier nucleus studying 16O. We observe that the implemented chiral nucleon-nucleon interaction at next-to-next-to-next-to-leading order underestimates the electric dipole polarizability., 4 pages, 2 figures, proceedings of the 21st International Conference on Few-Body Problems in Physics (FB21), May 2015, Chicago

What is the size of the atomic nucleus? This deceivably simple question is difficult to answer. Although the electric charge distributions in atomic nuclei were measured accurately already half a century ago, our knowledge of the distribution of neutrons is still deficient. In addition to constraining the size of atomic nuclei, the neutron distribution also impacts the number of nuclei that can exist and the size of neutron stars. We present an ab initio calculation of the neutron distribution of the neutron-rich nucleus Ca-48. We show that the neutron skin (difference between the radii of the neutron and proton distributions) is significantly smaller than previously thought. We also make predictions for the electric dipole polarizability and the weak form factor; both quantities that are at present targeted by precision measurements. Based on ab initio results for Ca-48, we provide a constraint on the size of a neutron star.

This poster presentation is intended to show preliminary results from calculations of the inclusive (e,e′) transverse response functions of 4He. Up to now we have only included the E1 and M1 multipoles and therefore no comparison with experiment is shown. That will be done once all relevant multipoles have been calculated. Details of the calculation are summarized in the text below.

Theoretical longitudinal and transverse electron scattering response functions are discussed in the quasi-elastic region for momentum transfers q ≥ 500 MeV/c. The response functions are calculated nonrelativistically, however, relativistic corrections to the nucleon one-body charge and current operators are taken into account. The frame dependence of the results is illustrated and it is shown that the so-called active nucleon Breit frame is the most suitable reference frame. In addition we review the results of a two-fragment model, which takes into account the correct relativistic energy of the final hadronic state assuming that a nucleon is knocked out quasi-elastically. New results for the transverse response function are presented at 700 MeV/c ≤ q ≤ 1 GeV/c.

The isoscalar monopole excitation of $^{4}\mathrm{He}$ is studied within a few-body ab initio approach. We consider the transition density to the low-lying and narrow ${0}^{+}$ resonance, as well as various sum rules and the strength energy distribution itself at different momentum transfers $q$. Realistic nuclear forces of chiral and phenomenological nature are employed. Various indications for a collective breathing mode are found: (i) the specific shape of the transition density, (ii) the high degree of exhaustion of the non-energy-weighted sum rule at low $q,$ and (iii) the complete dominance of the resonance peak in the excitation spectrum. For the incompressibility $K$ of the $\ensuremath{\alpha}$ particle, two different definitions give two rather small values (22 and 36 MeV).

We combine the coupled-cluster method and the Lorentz integral transform for the computation of inelastic reactions into the continuum. We show that the bound-state-like equation characterizing the Lorentz integral transform method can be reformulated based on extensions of the coupled-cluster equation-of-motion method, and we discuss strategies for viable numerical solutions. Starting from a chiral nucleon-nucleon interaction at next-to-next-to-next-to-leading order, we compute the giant dipole resonances of $^{4}\mathrm{He}$, ${}^{16,22}\mathrm{O}$, and $^{40}\mathrm{Ca}$, truncating the coupled-cluster equation-of-motion method at the two-particle--two-hole excitation level. Within this scheme, we find a low-lying $E1$ strength in the neutron-rich $^{22}\mathrm{O}$ nucleus, which compares fairly well with data from Leistenschneider et al. [Phys. Rev. Lett. 86, 5442 (2001)]. We also compute the electric dipole polarizability in $^{40}\mathrm{Ca}$. Deficiencies of the employed Hamiltonian lead to overbinding, too-small charge radii, and a too-small electric dipole polarizability in $^{40}\mathrm{Ca}$.

The Lorentz Integral Transform (LIT) method is reformulated via the Lanczos algorithm both for inclusive and exclusive reactions. The new technique is tested for the total photoabsorption cross section of 3H and 4He. Due to the rapid convergence of the algorithm one has a decrease in cpu time by two orders of magnitude, but at the same time an excellent agreement with the results of a conventional LIT calculation. The present work opens up the possibility of ab initio calculations for inclusive and exclusive processes for A greater equal 6 with inclusion of complete final state interactions.

This contribution deals with the problem of implementing the Pauli principle in a variational calculation of the binding energy of a fermionic system on the hyperspherical harmonics (HH) basis. We summarize the main points of a method that avoids the antysimmetrization of the basis functions. In fact this gets increasingly cumbersome as the number of particles increases. The method is tested on the binding energies of two nuclei ( 4 He and 6 Li), using various nuclear potential models, including a realistic one.

Techniques for using Gaussian QCD sum-rules to predict hadronic resonance properties are developed for single-resonance and two-resonance phenomenological models, and criteria are developed for determining which of these models is required for analyzing a particular hadronic channel. The vector current sum-rule coupled to the $\rho$ meson is shown to be consistent with a single resonance model, and the Gaussian sum-rule analysis results in an accurate $\rho$ mass prediction which exhibits excellent agreement between the theoretical prediction of the Gaussian sum-rule and the phenomenological model. A two-resonance model is shown to be necessary for the Gaussian sum-rule for the non-strange quark scalar ($\bar n n$) currents. The two-resonance Gaussian sum-rule analysis of the isoscalar and isovector ($I=0,1$) $\bar n n$ scalar mesons exhibits excellent agreement between the theoretical prediction and phenomenological model. The prediction of the resonance properties of the $I=0,1$ $\bar n n$ scalar mesons in this two-resonance model provides valuable information for the interpretation of the scalar mesons, including the X(1775)., Comment: latex2e, 29 pages, 10 eps figures embedded in latex2e. Revised version includes additions to reference [28] and correction to equation (56)

Total photonuclear absorption cross sections of $^3$H and $^3$He are studied using realistic NN and NNN forces. Final state interactions are fully included. Two NN potential models, the AV14 and the r-space Bonn-A potentials, are considered. For the NNN forces the Urbana-VIII and Tucson-Melbourne models are employed. We find the cross section to be sensitive to nuclear dynamics. Of particular interest in this work is the effect which NNN forces have on the cross section. The addition of NNN forces not only lowers the peak height but increases the cross section beyond 70 MeV by roughly 15%. Cross sections are computed using the Lorentz integral transform method., Results for Bonn potential with model Bonn rA instead of model rB. The Bonn rB results contained a small inexactness. After the correction it turned out that Bonn rA is more suited for our purpose because it leads to a binding energy of 8.15 MeV (about 0.25 MeV more than Bonn rB). In addition the results for the other realistic potentials models are improved at low energies (HH expansion was not completely convergent for the low-energy results). LaTeX, 8 pages, 4 ps figures

The inclusive reactions \(\) and \(\) are studied with the Lorentz integral transform method. The method allows the inclusion of the full final-state interaction without explicit knowledge of the continuum states. Features of the inversion procedure are discussed in this work. The technique for the calculation of the matrix elements of the Hamiltonian is described. The total photoabsorption cross section of 3H is calculated with a realistic super-soft-core NN force. In the threshold region the cross section is rather similar to that obtained with central forces only, while in the peak the realistic NN interaction leads to more strength. For the longitudinal (e, e′) response we extend our calculation with a semirealistic force to \(\) MeV/c. Rather good agreement with experimental data is found. The accuracy of the quasielastic response approximation is discussed.

A non-conventional approach to calculating reactions in quantum mechanics is presented. Reaction observables are obtained with bound state calculation techniques. The accuracy of the method to calculate few-nucleon response functions is discussed., 6 pages, Latex (REVTEX), 2 Postscript figures, XV Int. Conf. on Few-Body Problems in Physics, Groningen 1997, to appear in Nucl. Phys. A. Figure captions missed in the previous version are added

Here we summarize how the LIT and CC methods can be coupled, in order to allow for ab initio calculations of reactions in medium mass nuclei. Results on 16O are reviewed and preliminary calculations on 40Ca are presented., Comment: Contribution presented at the 22nd European Conference on Few Body Problems in Physics, Krakow, Poland, 9 - 13 September 2013

The Schroedinger equation is solved for an A-nucleon system using an expansion of the wave function in nonsymmetrized hyperspherical harmonics. Our approach is both an extension and a modification of the formalism developed by Gattobigio et al.. The extension consists in the inclusion of spin and isospin degrees of freedom such that a calculation with more realistic NN potential models becomes possible, whereas the modification allows a much simpler determination of the fermionic ground state. The approach is applied to four- and six-body nuclei (4He, 6Li) with various NN potential models. It is shown that the results for ground-state energy and radius agree well with those from the literature., 15 pages

The utility of ([ital e],[ital e][prime][ital d]) reactions in providing information about dynamical correlations in nuclei is discussed. The breakup of [sup 4]He into two deuterons is taken as a model case. We show how two-nucleon dynamics of both short range and tensor nature affects the ([ital e],[ital e][prime][ital d]) cross section in different kinematical regions. The role of final state interactions is also discussed. Within our model, kinematical conditions can be chosen to emphasize the sensitivity to a particular aspect of the ground state dynamics thereby suggesting promoting avenues for experiment.

The transverse electron scattering response function of $^{3}\mathrm{He}$ was recently studied by us in the quasielastic peak region for momentum transfers $q$ between 500 and 700 MeV/$c$. Those results, obtained using the active nucleon Breit (ANB) frame, are here supplemented by calculations in the laboratory, Breit, and ANB frames using the two-fragment model discussed in our earlier work on the frame dependence of the longitudinal response function ${R}_{L}(q,\ensuremath{\omega})$. We find relatively frame-independent results and good agreement with experiment especially for the lower momentum transfers. This agreement occurs when we neglect an $\ensuremath{\omega}$-dependent piece of the one-body current relativistic correction. Inclusion of this term leads, however, to a rather pronounced frame dependence at $q=700$ MeV/$c$. A discussion of this term is given here. This report also includes a correction to our previous ANB results for ${R}_{T}(q,\ensuremath{\omega})$.

A detailed study of the $^{4}\mathrm{He}$ longitudinal response function ${R}_{L}(\ensuremath{\omega},q)$ is performed at different kinematics, with particular emphasis on the role of three-nucleon forces. The effects reported are the results of an $\mathrm{ab} \mathrm{initio}$ calculation where the full four-body continuum dynamics is considered via the Lorentz integral transform method. The contributions of the various multipoles to the longitudinal response function are analyzed, and integral properties of the response are discussed as well. The Argonne V18 nucleon-nucleon interaction and two three-nucleon force models (Urbana IX and Tucson-Melbourne\ensuremath{'}) are used. At lower momentum transfers ($q\ensuremath{\leqslant}200 \mathrm{MeV}/c$) three-nucleon forces play an important role. One even finds a dependence of ${R}_{L}$ on the three-nucleon force model itself, with differences of up to 10%. Thus a Rosenbluth separation of the inclusive electron scattering cross section of $^{4}\mathrm{He}$ at low momentum transfers would be of great value for differentiating among force models.

In this series of lectures it is illustrated how one can study the strong dynamics of nuclei by means of the electroweak probe. In particular, the most important steps to derive the cross sections in first order perturbation theory are reviewed. In the derivation the focus is put on the main ingredients entering the hadronic part (response functions), i.e. the initial and final states of the system and the operators relevant for the reaction. Emphasis is put on the electromagnetic interaction with few-nucleon systems. The Lorentz integral transform method to calculate the response functions ab initio is described. A few examples of the comparison between theoretical and experimental results are shown. The dependence of the response functions on the nuclear interaction and in particular on three-body forces is emphasized., Comment: Lectures given at the International Scientific Meeting on Nuclear Physics, La Rabida, Huelva (Spain), July 4-10, 2009

The threshold transverse response functions R_T(q,omega) for 3He and 3H are calculated using the AV18 nucleon-nucleon potential, the UrbanaIX three-body force, and the Coulomb potential. Final states are completely taken into account via the Lorentz integral transform technique. Consistent two-body pi- and rho-meson exchange currents as deduced using the Arenh\"ovel-Schwamb technique are included. The convergence of the method is shown and a comparison of the corresponding MEC contribution is made to that of a consistent MEC for the meson theoretical r-space BonnA potential. The response R_T is calculated in the threshold region at q=174, 324, and 487 MeV/c and compared with available data. The strong MEC contributions in the threshold region are nicely confirmed by the data at q=324 and 487 MeV/c although some differences between theoretical and experimental results remain. A comparison is also made with other calculations, where the same theoretical input is used. The agreement is generally rather good, but leaves also some space for further improvement., Comment: 16 pages, 5 figures

The Coulomb sum rule is evaluated for a large class of nuclei up to the heavy ones. Beyond mean-field effects, short-range correlations are taken into account. The latter decrease the sum rule in the whole considered momentum range. The size of the reduction increases with the average proton density reaching its maximum for medium heavy nuclei.

We present an ab initio calculation of the longitudinal electron scattering response function off $^{4}\mathrm{He}$ with two- and three-nucleon forces and compare to experimental data. The full four-body continuum dynamics is considered via the Lorentz integral transform method. The importance of the final-state interaction is shown at various energies and momentum transfers $q$. The three-nucleon force reduces the quasielastic peak by 10% for $q$ between 300 and $500\text{ }\text{ }\mathrm{MeV}/c$. Its effect increases significantly at lower $q$, up to about 40% at $q=100\text{ }\text{ }\mathrm{MeV}/c$. At very low $q$, however, data are missing.

The transverse response function ${R}_{T}(q,\ensuremath{\omega})$ for $^{3}\mathrm{He}$ is calculated using the configuration space BonnA nucleon-nucleon potential, the Tucson-Melbourne three-body force, and the Coulomb potential. Final states are completely taken into account via the Lorentz integral transform technique. Nonrelativistic one-body currents plus two-body \ensuremath{\pi} and \ensuremath{\rho} meson exchange currents (MECs) as well as the Siegert operator are included. The response ${R}_{T}$ is calculated for $q=174$, 250, 400, and 500 MeV/$c$ and in the threshold region at $q=174$, 324, and 487 MeV/$c$. Strong MEC effects are found in low- and high-energy tails, but due to MECs there are also moderate enhancements of the quasielastic peak (6--10%). The calculation is performed both directly and via transformation of electric multipoles to a form that involves the charge operator. The contribution of the latter operator is suppressed in and below the quasielastic peak, while at higher energies the charge operator represents almost the whole MEC contribution at the lowest $q$ value. The effect of the Coulomb force in the final state interaction is investigated for the threshold region at $q=174$ MeV/$c$. Its neglect enhances ${R}_{T}$ by more than 10% in the range up to 2 MeV above threshold. In a comparison with experimental data, one finds relatively good agreement at $q=250$ and 400 MeV/$c$, while at $q=500$ MeV/$c$, presumably due to relativistic effects, the theoretical quasielastic peak position is shifted to somewhat higher energies. The strong MEC contributions in the threshold region are nicely confirmed by data at $q=324$ and 487 MeV/$c$.

The sum rules (SR) are introduced showing their connection with the linear response of a nucleus to an external electromegnetic field. Their relation to some macroscopic “collective” aspects of the nucleus are briefly outlined. Energy weighted sum rules (EWSR) for electron scattering at constant momentum transfer are studied for light and medium weight nuclei. The q-dependence of the different contributions to these SR permits to discuss the role of the nuclear potential and of correlations in the electroexcitation process.

The role played by np tensor correlations in the longitudinal and transverse response functions is investigated in the quasi-free region. A model is proposed where the response in plane-wave impulse approximation is modified by introducing responses of strongly correlated deuteron-like pairs. Various pair correlations are studied. The introduction of the pair responses does not lead to a violation of the Coulomb- and the f -sum rules. The results show that tensor correlations shift the strength from the quasi-elastic peak towards higher energy. The additional contributions of meson exchange and isobar currents in the transverse channel can compensate the quenching due to correlations.

Inclusive electron scattering off 4 He is investigated for low and medium energy and momentum transfers. The final state interaction, given by the simple semirealistic Malfliet-Tjon potential, is treated rigorously applying the Lorentz integral transform (LIT) method. In addition to the nonrelativistic one-body current a consistent meson exchange current is constructed and implemented. Results are presented for both longitudinal and transverse response functions at various momentum transfers. Good agreement with experimental data is found for the longitudinal response function, whereas some strength is missing in the transverse response function on the low energy side of the quasi-elastic peak.

The J-matrix inverse scattering nucleon-nucleon potentials (JISP), describing both two-nucleon data and bound and resonant states of light nuclei to high accuracy, are tested on the total photoabsorption cross sections of Deuteron, Triton, 3He and 4He. The calculations in the three- and four-body systems are carried out via the Lorentz integral transform method and the hyperspherical harmonics (HH) technique. To this end the HH formalism has been adapted to accommodate non-local potentials. The cross sections calculated with the JISP are compared to those obtained with more traditional realistic interactions, which include two- and three-nucleon forces. While the results of the two kinds of potential models do not differ significantly at lower energies, beyond the resonance peak they show fairly large discrepancies, which increase with the nuclear mass. We argue that these discrepancies may be due to a probably incorrect long range behavior of the JISP, since the one pion exchange is not manifestly implemented there., 18 pages, 4 figures, 1 table

Both the no-core shell model and the effective interaction hyperspherical harmonic approaches are applied to the calculation of different response functions to external electromagnetic probes, using the Lorentz integral transform method. The test is performed on the four-body nuclear system, within a simple potential model. The quality of the agreement in the various cases is discussed, together with the perspectives for rigorous ab initio calculations of cross sections of heavier nuclei., Comment: 9 pages, to be submitted for publication

Using the Lorentz Integral Transform (LIT) method we compare the results for the triton total photodisintegration cross section obtained using the Correlated Hyperspherical Harmonics (CHH) and the Effective Interaction Hyperspherical Harmonics (EIHH) techniques. We show that these two approaches, while rather different both conceptually and computationally, lead to results which coincide within high accuracy. The calculations which include two- and three-body forces are of the same high quality in both cases. We also discuss the comparison of the two approaches in terms of computational efficiency. These results are of major importance in view of applications to the much debated case of the four-nucleon photoabsorption., 12 pages, 3 figures

Last October Achim Richter ended his term as Director of ECT*. A farewell ceremony took place in Trento at the Aula Grande of the “Fondazione Bruno Kessler” (FBK), the Trentino institution that hosts, and concurs in funding, ECT*. Many colleagues and friends attended the event, livened up by a concert played by the “guest of honor” as violist and two colleagues of the Edmund Mach Foundation on the clarinet and piano. The Kegelstatt Trio by Mozart and two pieces for Clarinetto, Viola and Piano by Max Bruch gave Achim Richter the opportunity to show publicly one of his many talents. His main talent as an outstanding experimental physicist has become well known to the physics community during his long and successful career, and his ability as a competent and capable manager and Director of a theory center was celebrated on October 19 by the speeches of Wolfram Weise, the next Director of ECT*, Angela Bracco, Chair of NuPECC, and Sandro Stringari of the Physics Department.

The total photoabsorption cross sections of the six-body nuclei are calculated including a complete final state interaction via the Lorentz integral transform method. The effect of nucleon-nucleon central P-wave forces is investigated. Comparing to results with central potentials containing S-wave forces only, one finds considerable more strength in the low-energy cross sections and a rather strong improvement in comparison with experimental data, in particular for $^{6}\mathrm{Li}$.

It is shown how a bare three-nucleon force is incorporated into the formalism of the effective interaction approach for hyperspherical harmonics. As a practical example we calculate the ground state properties of 3H and 3He using the Argonne V18 nucleon-nucleon potential and the Urbana IX three-nucleon force. A very good convergence of binding energies and matter radii is obtained. We also find a very good agreement of our results compared to other high precision calculations., 17 pages, 3 figures

Gaussian sum-rules, which are related to a two-parameter Gaussian-weighted integral of a hadronic spectral function, are able to examine the possibility that more than one resonance makes a significant contribution to the spectral function. The Gaussian sum-rules, including instanton effects, for scalar gluonic and non-strange scalar quark currents clearly indicate a distribution of the resonance strength in their respective spectral functions. Furthermore, analysis of a two narrow resonance model leads to excellent agreement between theory and phenomenology in both channels. The scalar quark and gluonic sum-rules are remarkably consistent in their prediction of masses of approximately 1.0 GeV and 1.4 GeV within this model. Such a similarity would be expected from hadronic states which are mixtures of gluonium and quark mesons., latex2e using amsmath, 11 pages, 4 eps figures embedded in latex file. Write-up of presentation for the 2003 SUNY IT (Utica) workshop on scalar mesons

We present an improvement of the recently developed effective interaction method for the hyperspherical formalism (EIHH). The method is extended to include contributions of three-body effective forces and the non adiabatic kinetic energy term. It is shown that the rate of convergence is improved considerably, opening up the way for application of the method to realistic 6-body calculations.

The total cross section of the process 4 He(γ, n)3 He is calculated. The four-nucleon problem is solved, and Final State Interaction (FSI) is taken rigorously into account both below and beyond the three-body breakup threshold. This is accomplished with the help of the Lorentz Integral Transform (LIT) method [1, 2]. The semi-realistic MTI-III potential [3] is taken as NN interaction. The excitation energy range up to 30 MeV is considered which includes the giant resonance peak, in particular. Like for the case of the total 4 He photoabsorbtion cross section in [4, 5] it is sufficient to take into account transitions induced by the unretarded dipole operator D [6]. The cross section is $$\begin{array}{*{20}{c}} {{{\sigma }_{{(\gamma ,n) = }}}({{e}^{2}}/\hbar c){{\omega }_{\gamma }}k\mu {{\pi }^{{ - 1}}}\int {d{{\Omega }_{k}}|\langle {{\Psi }^{ - }}({{E}_{f}})} |D|{{\Psi }_{\alpha }}\rangle {{|}^{2}},} & {{{E}_{f}} = {{\omega }_{\gamma }} + {{E}_{\alpha }}.} \\ \end{array}$$ .

Six-body inelastic reactions are calculated microscopically including the full six-nucleon final state interaction. The total cross sections of $\ensuremath{\gamma}+\text{ }{\text{ }}^{6}\mathrm{H}\mathrm{e}\text{ }(\text{ }{\text{ }}^{6}\mathrm{L}\mathrm{i})\ensuremath{\rightarrow}X$ are considered as examples. The Lorentz integral transform method and the effective interaction approach for the hyperspherical formalism are employed. While $\text{ }{\text{ }}^{6}\mathrm{L}\mathrm{i}$ has a single broad giant resonance peak, there are two well separated peaks for $\text{ }{\text{ }}^{6}\mathrm{H}\mathrm{e}$ corresponding to the breakup of the neutron halo and the $\ensuremath{\alpha}$ core, respectively. The comparison with the few available experimental data is discussed.

Two conceptually different hyperspherical harmonics expansions are used for the calculation of the total 4He photoabsorption cross section. Besides the well known method of CHH the recently introduced effective interaction approach for the hyperspherical formalism is applied. Semi-realistic NN potentials are employed and final state interaction is fully taken into account via the Lorentz integral transform method. The results show that the effective interaction leads to a very good convergence, while the correlation method exhibits a less rapid convergence in the giant dipole resonance region. The rather strong discrepancy with the experimental photodisintegration cross sections is confirmed by the present calculations.

The recently developed effective interaction method for the hyperspherical harmonic formalism is extended to noncentral forces. Binding energies and radii of three- and four-body nuclei are calculated with AV6 and AV14 NN potentials. Excellent results for the convergence of the expansion are found, particularly for the three-nucleon system. Due to the higher density the convergence rate is a bit slower for the alpha particle. In comparison to central potential models there is only a very slight deterioration of the convergence due the tensor force, while other potential terms have no visible effect on the convergence. The obtained values for binding energy and radii also agree well with the results in the literature obtained with other few-body techniques., LaTeX, 12 pages, 6 ps figures, Figures in correct order in this replacement

In the past, several efficient methods have been developed to solve the Schroedinger equation for four-nucleon bound states accurately. These are the Faddeev-Yakubovsky, the coupled-rearrangement-channel Gaussian-basis variational, the stochastic variational, the hyperspherical variational, the Green's function Monte Carlo, the no-core shell model and the effective interaction hyperspherical harmonic methods. In this article we compare the energy eigenvalue results and some wave function properties using the realistic AV8' NN interaction. The results of all schemes agree very well showing the high accuracy of our present ability to calculate the four-nucleon bound state., Comment: 17 pages, 1 figures

The method of effective interaction, traditionally used in the framework of an harmonic oscillator basis, is applied to the hyperspherical formalism of few-body nuclei (A=3-6). The separation of the hyperradial part leads to a state dependent effective potential. Undesirable features of the harmonic oscillator approach associated with the introduction of a spurious confining potential are avoided. It is shown that with the present method one obtains an enormous improvement of the convergence of the hyperspherical harmonics series in calculating ground state properties, excitation energies and transitions to continuum states., LaTeX, 16 pages, 8 ps figures