We performed bound state calculations to obtain the first few vibrational states for the Ar-3 molecular system. The equations used are of Faddeev-type and are solved directly as three-dimensional equations in configuration space, i.e. without resorting to an explicit partial wave decomposition. In addition to realistic pairwise interactions, we employ long range three-body forces. Our results are in good agreement with those obtained by other methods based on partial wave expansion and show a significant contribution of the three-body forces (> 10%) to the binding energy and thus their inclusion is, in general, warranted in studying similar triatomic systems.

Strongly interacting matter such as nuclear or quark matter leads to few-body bound states and correlations of the constituents. As a consequence quantum chromodynamics has a rich phase structure with spontaneous symmetry breaking, superconductivity, condensates of different kinds. All this appears in many astrophysical scenarios. Among them is the formation of hadrns during the early stage of the Universe, the structure of a neutron star, the formation of nuclei during a supernova explosion. Some of these extreme conditions can be simulated in heavy ion colliders. To treat such a hot and dense system we use the Green function formalism of many-body theory. It turns out that a systematic Dyson expansion of the Green functions leads to modified few-body equations that are capable to describe phase transitions, condensates, cluster formation and more. These equations include self energy corrections and Pauli blocking. We apply this method to nonrelativistic and relativistic matter. The latter one is treated on the light front. Because of the medium and the inevitable truncation of space, the few-body dynamics and states depend on the thermodynamic parameters of the medium.

We present a method based on hyperspherical harmonics to solve the nuclear many-body problem. It is an extension of accurate methods used for studying few-body systems to many bodies and is based on the assumption that nucleons in nuclei interact mainly via pairwise forces. This leads to a two-variable integro-differential equation which is easy to solve. Unlike methods that utilize effective interactions, the present one employs directly nucleon–nucleon potentials and therefore nuclear correlations are included in an unambiguous way. Three body forces can also be included in the formalism. Details on how to obtain the various ingredients entering into the equation for the A-body system are given. Employing our formalism we calculated the binding energies for closed and open shell nuclei with central forces where the bound states are defined by a single hyperspherical harmonic. The results found are in agreement with those obtained by other methods.

The manifestation of pseudospin-symmetry in proton-nucleus scattering is discussed. Constraints on the pseudospin-symmetry violating scattering amplitude are given which require as input cross section and polarization data, but no measurements of the spin rotation function. Application of these constraints to p-58Ni and p-208Pb scattering data in the laboratory energy range of 200 MeV to 800 MeV, reveals a significant violation of the symmetry at lower energies and a weak one at higher energies. Using a schematic model within the Dirac phenomenology, the role of the Coulomb potential in proton-nucleus scattering with regard to pseudospin symmetry is studied. Our results indicate that the existence of pseudospin-symmetry in proton-nucleus scattering is questionable in the whole energy region considered and that the violation of this symmetry stems from the long range nature of the Coulomb interaction.

Aspects of the inverse scattering problem and the transformation of the wave equation for elastic displacement into a Marchenko integral equation are discussed. The latter equation provides the required connection with the scattering data and from its solution the potential ('profile') that caused the scattering can be reconstructed. As an application of our method, we use reflection travel time data for synthetic seismic experiments in layered substrate models to recover the characteristic impedances of the medium.

A microscopic few-body description of near-threshold coherent photoproduction of the eta-meson on tritium and He3 targets is given. The photoproduction cross-section is calculated using the Finite Rank Approximation (FRA) of the nuclear Hamiltonian. The results indicate a strong final state interaction of the eta-meson with the residual nucleus. Sensitivity of the results to the choice of the eta-N T-matrix is investigated. The importance of obeying the two-body unitarity condition in the eta-N system is demonstrated.

We consider the multi-channel inverse scattering problem in one-dimension in the presence of thresholds and bound states for a potential of finite support. Utilizing the Levin representation, we derive the general Marchenko integral equation for N-coupled channels and show that, unlike to the case of the radial inverse scattering problem, the information on the bound state energies and asymptotic normalization constants can be inferred from the reflection coefficient matrix alone. Thus, given this matrix, the Marchenko inverse scattering procedure can provide us with a unique multi-channel potential. The relationship to supersymmetric partner potentials as well as possible applications are discussed. The integral equation has been implemented numerically and applied to several schematic examples showing the characteristic features of multi-channel systems. A possible application of the formalism to technological problems is briefly discussed.

The process of coherent photoproduction of eta-mesons on light nuclei is:investigated on the bases of microscopic Finite Rank Approximation method. Numerical calculations are performed for the He-3 and H-3 targets and different inputs for eta-nucleon interaction. Comparison with the modified optical model approach is given.

We show that the introduction of components, in the Jest function, that create new bound states while leaving the S-matrix unchanged, generates potentials behaving as r(-2) at large distances. We demonstrate that the modified Jest functions can be obtained by applying two successive supersymmetric transformations to the original potential. We further show that transparent potentials, with S-l(k) equivalent to 1, can also be obtained by successive supersymmetric transformations. They are characterized by the property that their SUSY-2 partners resemble centrifugal barriers. Finally, the relation of these transformations to the asymptotic normalization constants of the inverse scattering problem is discussed. We show that the two supersymmetric transformations that remove a bound state provide a potential which is the same as that obtained via the Marchenko inverse scattering procedure, when the asymptotic normalization constant is set to zero.

Photoproduction of eta -mesons off deuterons is studied within the Alt-Grassberger-Sandhas formalism for different parameters of the etaN interaction. The calculations revealed peaks in the energy dependence of the total cross-section.

Based on the thermodynamic Green function approach two-nucleon correlations in nuclear matter at finite temperatures are revisited. To this end, we derive phase-equivalent effective r-space potentials that include the effect of Pauli blocking at a given temperature and density. These potentials enter into a Schrodinger equation that is the r-space representation of the Galitskii-Feynman equation for two nucleons. We explore the analytical structure of the equation in the complex k-plane by means of Jost functions. We find that despite the Mott effect the correlation with deuteron quantum numbers are manifested as antibound states, i.e. as zeros of the Jost function on the negative imaginary axis of the complex momentum space. The analysis presented here is also suited for Coulombic systems.

The appearance of bound states with large binding energies of several hundred MeV in the three-body system, known as bound state collapse, is investigated. For this purpose three classes of two-body potentials are employed; local potentials equivalent to nonlocal interactions possessing a continuum bound state, in addition to the usual negative-energy bound state; local potentials with a strong attractive well sustaining a forbidden state; and supersymmetric transformation potentials. It is first shown that local potentials equivalent to the above nonlocal ones have a strong attractive well in the interior region which supports, in addition to the physical deuteron state, a second bound state (usually called a pseudobound state) with a large binding energy, which is responsible for the bound state collapse in the three-body (and in general to the N-body) system. Second, it is shown that local potentials with a forbidden state also generate a three-body bound state collapse. implying that the role played by the forbidden state is similar to the one played by the pseudobound state. Finally, it is shown that the removal of the forbidden state via supersymmetric transformations also results in the disappearance of the collapse. Thus one can safely argue that the presence of unphysical bound states with large binding energies in the two-body system is responsible for the bound state collapse in the three-body system.

Among the light nuclear clusters the α-particle is by far the strongest bound system and therefore expected to play a significant role in the dynamics of nuclei and the phases of nuclear matter. To systematically study the properties of the α-particle we have derived an effective four-body equation of the Alt–Grassberger–Sandhas (AGS) type that includes the dominant medium effects, i.e. self energy corrections and Pauli-blocking in a consistent way. The equation is solved utilizing the energy dependent pole expansion for the subsystem amplitudes. We find that the Mott transition of an α-particle at rest differs from that expected from perturbation theory and occurs at approximately 1/10 of nuclear matter densities.

Differential cross sections for the electro-disintegration process $e + {^4He} \longrightarrow {^3H}+ p + e'$ are calculated, using a model in which the final state interaction is included by means of a nucleon-nucleus (3+1) potential constructed via Marchenko inversion. The required bound-state wave functions are calculated within the integrodifferential equation approach (IDEA). In our model the important condition that the initial bound state and the final scattering state are orthogonal is fulfilled. The sensitivity of the cross section to the input $p{^3H}$ interaction in certain kinematical regions is investigated. The approach adopted could be useful in reactions involving few cluster systems where effective interactions are not well known and exact methods are presently unavailable. Although, our Plane-Wave Impulse Approximation results exhibit, similarly to other calculations, a dip in the five-fold differential cross-section around a missing momentum of $\sim 450 MeV/c$, it is argued that this is an artifact of the omission of re-scattering four-nucleon processes.

An exact method for direct calculation of the Jost function and Jost solutions for a repulsive singular potential is presented. Within this method the Schrodinger equation is replaced by an equivalent system of linear first-order differential equations, which after complex rotation, can easily be solved numerically. The Jost function can be obtained to any desired accuracy for all complex momenta of physical interest, including the spectral points corresponding to bound and resonant states. The method can also be used in the complex angular-momentum plane to calculate the Regge trajectories. The effectiveness of the method is demonstrated using the Lennard-Jones (12,6) potential. The spectral properties of the realistic inter-atomic He4-He4 potentials HFDHE2 and HFD-B of Aziz and collaborators are also investigated.

The importance of including experimental resonances in constructing effective intercluster interactions has been investigated. For this, we first address the question of how to obtain the analytical properties of the Jost function in regions of physical interest on the complex k-plane when the potential is given in a tabular form. We then employ the Marchenko inverse scattering method to construct, numerically, phase equivalent local potentials supporting the same bound state(s) but having different resonance spectra which affect the off-shell characteristics of the corresponding scattering amplitudes. This implies that the inclusion of the experimental resonances in constructing a potential would change its shape, strength, and range which in turn would modify the bound and scattering wave functions in the interior region. This is expected to have important consequences in calculations of transition amplitudes in nuclear reaction theories, which strongly depend on the behaviour of the wave functions at short distances. The influence of Supersymmetric Transformations on the position and movement of resonances has also been investigated.