Search

We study the ground state and the low-lying excitations of a trapped Bose gas in an isotropic harmonic potential for very small ($\sim 3$) to very large ($\sim 10^7$) particle numbers. We use the correlated two-body basis functions and the shape-dependent van der Waals interaction in our many-body calculations. We present an exhaustive study of the effect of inter-atomic correlations and the accuracy of the mean-field equations considering a wide range of particle numbers. We calculate the ground state energy and the one-body density for different values of the van der Waals parameter $C_{6}$. We compare our results with those of the modified Gross-Pitaevskii results, the correlated Hartree hypernetted-chain equations (which also utilize the two-body correlated basis functions), as well as of the Diffusion Monte Carlo for hard sphere interactions. We observe the effect of the attractive tail of the van der Waals potential in the calculations of the one-body density over the truly repulsive zero-range potential as used in the Gross-Pitaevskii equation and discuss the finite-size effects. We also present the low-lying collective excitations which are well described by a hydrodynamic model in the large particle limit., Comment: Accepted in J Low Temp Phys

It is shown that the spectral points (bound states and resonances) generated by a central potential of a single-channel problem, can be found using rational parametrization of the S-matrix. To achieve this, one only needs values of the S-matrix along the real positive energy axis. No calculations of the S-matrix at complex energies or a complex rotation are necessary. The proposed method is therefore universal in that it is applicable to any potential (local, non-local, discontinuous, etc.) provided that there is a way of obtaining the S-matrix (or scattering phase-shifts) at real collision energies. Besides this, combined with any method that extracts the phase-shifts from the scattering data, the proposed rational parametrization technique would be able to do the spectral analysis using the experimental data., Comment: 20 pages, 6 figures

Consider the fixed-$\ell$ inverse scattering problem. We show that the zeros of the regular solution of the Schr\"odinger equation, $r_{n}(E)$, which are monotonic functions of the energy, determine a unique potential when the domain of the energy is such that the $r_{n}(E)$ range from zero to infinity. This suggests that the use of the mixed data of phase-shifts $\{\delta(\ell_0,k), k \geq k_0 \} \cup \{\delta(\ell,k_0), \ell \geq \ell_0 \}$, for which the zeros of the regular solution are monotonic in both domains, and range from zero to infinity, offers the possibility of determining the potential in a unique way., Comment: 9 pages, 2 figures. Talk given at the Conference of Inverse Quantum Scattering Theory, Hungary, August 2007

The universal three-body dynamics in ultra-cold binary gases confined to one-dimensional motion are studied. The three-body binding energies and the (2 + 1)-scattering lengths are calculated for two identical particles of mass $m$ and a different one of mass $m_1$, which interactions is described in the low-energy limit by zero-range potentials. The critical values of the mass ratio $m/m_1$, at which the three-body states arise and the (2 + 1)-scattering length equals zero, are determined both for zero and infinite interaction strength $\lambda_1$ of the identical particles. A number of exact results are enlisted and asymptotic dependences both for $m/m_1 \to \infty$ and $\lambda_1 \to -\infty$ are derived. Combining the numerical and analytical results, a schematic diagram showing the number of the three-body bound states and the sign of the (2 + 1)-scattering length in the plane of the mass ratio and interaction-strength ratio is deduced. The results provide a description of the homogeneous and mixed phases of atoms and molecules in dilute binary quantum gases.

The long-standing problem of constructing a potential from mixed scattering data is discussed. We first consider the fixed-$\ell$ inverse scattering problem. We show that the zeros of the regular solution of the Schr\"odinger equation, $r_{n}(E)$ which are monotonic functions of the energy, determine a unique potential when the domain of energy is such that the $r_{n}(E)$'s range from zero to infinity. The latter method is applied to the domain $\{E \geq E_0, \ell=\ell_0 \} \cup \{E=E_0, \ell \geq \ell_0 \}$ for which the zeros of the regular solution are monotonic in both parts of the domain and still range from zero to infinity. Our analysis suggests that a unique potential can be obtained from the mixed scattering data $\{\delta(\ell_0,k), k \geq k_0 \} \cup \{\delta(\ell,k_0), \ell \geq \ell_0 \}$ provided that certain integrability conditions required for the fixed $\ell$-problem, are fulfilled. The uniqueness is demonstrated using the JWKB approximation., Comment: 17 pages, 2 figures. Improved version involving an expanded introduction and additional physical considerations

We investigate the properties of 3He, 4He, 6He, 7Li and 16O nuclei in nuclear matter of finite temperature and density. A Dyson expansion of the many-body Green function leads to few-body equations that are solved using the ntegro-Differential Equation Approach (IDEA) and the Antisymmetrized Molecular Dynamics (AMD) methods. The use of the latter method allows us to trace the individual movement of the wave packet for each nucleon and the formation and disintegration of quasi-nuclei in a changing thermodynamical nuclear matter environment., Comment: 12 pages, 5 figures

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., Comment: 3 pages, Oral Contribution to the 19th European Few-Body Conference, Groningen Aug. 23-27, 2004

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., Comment: 72 pages

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., Comment: 3 pages, 2 figures, talk presented at the 19th European Conference on Few-Body Systems

We are concerned with few-particle correlations in a fermionic system at finite temperature and density. Within the many-body Green functions formalism the description of correlations is provided by the Dyson equation approach that leads to effective few-body equations. They contain the dominant medium effects, which are self energy corrections and the Pauli blocking. Hence the effective two-body interactions between quasiparticles are momentum/energy-dependent and therefore they can be usesed in the medium modified, momentum space, integral AGS equations for three- and four-body systems. To investigate correlations and clusters beyond four-body, we employ, instead, the configuration space two-variable integro-differential equations (IDEA) for $A$-body bound systems which are based on Hyperspherical Harmonics and the Faddeev decomposition of the wave function in two-body amplitudes. This requires the transformation of the energy dependent two-body interactions to equivalent local, energy independent, ones. To achieve this we use inverse scattering techniques the resulting interactions being, on-- and (to all practical purposes) off--shell equivalent to the energy dependent potentials. In this way we obtain binding energy results for the 2--, 3--, 4--, and 16--particle in a medium at a finite temperature and various densities. Several aspects of the problem are discussed and the behavior of the potential surfaces obtained in the extreme adiabatic approximation, below and above the Mott transition, is investigated., Comment: 16 pages, 7 figures, uses balkan.sty

We investigate properties and the distribution of light nuclei (A<4) in symmetric nuclear matter of finite temperature within a microscopic framework. For this purpose we have solved few-body Alt-Grassberger-Sandhas type equations for quasi-nucleons that include self-energy corrections and Pauli blocking in a systematic way. In a statistical model we find a significant influence in the composition of nuclear matter if medium effects are included in the microscopic calculation of nuclei. If multiplicities are frozen out at a certain time (or volume), we expect significant consequences for the formation of light fragments in a heavy ion collision. As a consequence of the systematic inclusion of medium effects the ordering of multiplicities becomes opposite to the law of mass action of ideal components. This is necessary to explain the large abundance of $\alpha$-particles in a heavy ion collision that are otherwise largely suppressed in an ideal equilibrium scenario., Comment: 9 pages, 9 figures, epja-style files

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., Comment: 22 pages including 9 figures, correction of 1 reference, revision of abstract and major modification of chapter 4, Fig. 6, and Fig. 7; addition of Fig. 8 and Fig. 9

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., Comment: 19 pages, 5 figures

A microscopic few-body description of near-threshold coherent photoproduction of the eta meson on tritium and 3He 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., Comment: RevTeX, 17 pages, 2 eps-figures, accepted for publication in Nucl.Phys.A

A method to calculate the bound states of three-atoms without resorting to an explicit partial wave decomposition is presented. The differential form of the Faddeev equations in the total angular momentum representation is used for this purpose. The method utilizes Cartesian coordinates combined with the tensor-trick preconditioning for large linear systems and Arnoldi's algorithm for eigenanalysis. As an example, we consider the He$_3$ system in which the interatomic force has a very strong repulsive core that makes the three-body calculations with standard methods tedious and cumbersome requiring the inclusion of a large number of partial waves. The results obtained compare favorably with other results in the field., Comment: 18 pages, 3 figures, 9 tables, revtex4

Effective interactions that fit the low energy p-$^3$He experimental data have been constructed. They are based on the Resonating Group Method and a modified Orthogonality Condition Model in which Pauli and partly Pauli forbidden states are removed from the spectrum. Partial waves up to L=3 have been considered. The LS force acting between the proton and $^3$He has been included phenomenologically, while the Coulomb interaction has been incorporated using a renormalization technique for a screened Coulomb interaction. The potentials are also given in a separable momentum space form, obtained using the Ernst-Shakin-Thaler (EST) method. In all cases the potentials generate phase shifts that fit well the low energy experimental data., Comment: 47 pages, 19 figures, 29 tables, Submitted to Physical Review C

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., Comment: 17 pages, RevTeX, 5 eps-figures, submitted to Phys. Rev. C

A microscopic four-body description of near-threshold coherent photoproduction of the $\eta$ meson on the (3N)-nuclei is given. The photoproduction cross-section is calculated using the Finite Rank Approximation (FRA) of the nuclear Hamiltonian. The results indicate that the final state interaction of the $\eta$ meson with the residual nucleus plays an important role in the photoproduction process. Sensitivity of the results to the choice of the $\eta N$ T-matrix is investigated. The importance of obeying the condition of $\eta N$ unitarity is demonstrated., Comment: 4 pages, 4 figures; talk given at the International Conference on Mesons and Light Nuclei '01, Prague, Czech Republic, July 2-6, 2001; to be published in the Proceedings (AIP press)

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 the Pauli blocking at a given temperature and density. These potentials enter into a Schr\"odinger 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., Comment: 6 pages, 1 table, 4 figures

Photoproduction of $\eta$-mesons off deuteron is studied within the Alt-Grassberger-Sandhas formalism for different parameters of $\eta N$ interaction. The calculations revealed peaks in the energy dependence of the total cross-section., Comment: 5 pages, LaTex, 4 eps figures; reference list was corrected and acknowledgements were added. Talk given at the XVIIth European conference on Few-Body Problems in Physics, Evora, Portugal, 11 - 16 September 2000

Photo-production of $\eta$-mesons and their collisions with light nuclei are studied within the Alt-Grassberger-Sandhas (AGS) formalism for different parameters of $\eta N$ interaction. A three-body resonance or a quasi-bound state is found close to the $\eta d$ threshold. Expected manifestation of this resonant behavior of $\eta d$ elastic scattering in various processes involving $\eta d$-system in their final states was found in calculations of the $\gamma d \to \eta d$ reaction in the framework of modified AGS equations. These calculations revealed peaks in the energy dependence of the total cross-section almost at the same energies as in the elastic $\eta d$ scattering. Meanwhile, such peaks did not appear in the impulse approximation (i.e. when $\eta d$ resonance was not taken into account). This sheds some light on the nature of the enhancement of $\eta$ photo-production on deuteron observed recently in the low energy experiments., Comment: 11 pages, LaTex, 9 eps figures, 1 table; reference list was corrected and acknowledgments were added. Talk given at the IX International seminar "Electromagnetic interactions of nuclei at low and medium energies", INR, Moscow, 20-22 September 2000; to be published in the proceedings

The 4He3 system is investigated using a hard-core version of the Faddeev differential equations and realistic 4He-4He interactions. We calculate the binding energies of the 4He trimer but concentrate in particular on scattering observables. The atom-diatom scattering lengths are calculated as well as the atom-diatom phase shifts for center of mass energies up to 2.45 mK., Comment: LaTeX, 3 pages, 1 figure; Contribution to Proceedings of 16th International Conference on Few-Body Problems in Physics, 6-10 March 2000, Taipei, Taiwan

A transformation of supersymmetric quantum mechanics for N coupled channels is presented, which allows the introduction of up to N degenerate bound states without altering the remaining spectrum of the Hamiltonian. Phase equivalence of the Hamiltonian can be restored by two successive supersymmetric transformations at the same energy. The method is successfully applied to the 3S1-3D1 coupled channels of the nucleon-nucleon system and a set of Moscow-type potentials is thus generated., Comment: 10 pages, 4 figures

Among the light nuclear clusters the alpha-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 alpha-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 sub system amplitudes. We find that the Mott transition of an alpha-particle at rest differs from that expected from perturbation theory and occurs at approximately 1/10 of nuclear matter densities., Comment: 9 pages RevTex file, 1 figure, submitted to Phys. Lett. B

The ^4He_3 bound states and the scattering of a ^4He atom off a ^4He dimer at ultra-low energies are investigated using a hard-core version of the Faddeev differential equations. Various realistic ^4He-^4He interactions were employed, amomg them the LM2M2 potential by Aziz and Slaman and the recent TTY potential by Tang, Toennies and Yiu. The ground state and the excited (Efimov) state obtained are compared with other results. The scattering lengths and the atom-diatom phase shifts were calculated for center of mass energies up to 2.45 mK. It was found that the LM2M2 and TTY potentials, although of quite different structure, give practically the same bound-state and scattering results., Comment: RevTeX, 14 pages, 1 eps-figure; list of references has been extended and some minor changes of the text have been done

The two-fragment electrodisintegration of 4He into proton and triton is calculated in Plane Wave Impulse Approximation (PWIA). The three- and four-nucleon wave functions involved are obtained by solving the Alt-Grassberger-Sandhas (AGS) integral equations, with the Malfliet-Tjon potential as the underlying NN-interaction. Our results are in remarkable agreement with the experimental data and, in contrast to alternative approaches, do not exhibit any dip in the five-fold differential cross section at a missing momentum of ~ 450 MeV/c., Comment: 4 pages, RevTeX, 3 Postscript figures, to be published

Elastic eta-d scattering is considered within the Alt-Grassberger-Sandhas (AGS) formalism for various eta-N input data. A three-body resonant state is found close to the eta-d threshold. This resonance is sustained for different choices of the two-body eta-N scattering length a_{\eta N}. The position of the resonance moves towards the eta-d threshold when Re a_{\eta N} is increased, and turns into a quasi-bound state at Re a_{\eta N}=0.733 fm., Comment: 13 pages, LaTeX (revtex.sty), 5 figures (epsfig), submitted to Phys.Rev.Lett

The importance of including experimental resonances in constructing effective inter-cluster 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., Comment: 21 pages, 4 figures, LaTeX, to appeard in Nuclear Physics A

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., Comment: 16 pages, 6 figures, accepted for publication by Phys.Rev.C

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., Comment: 12 pages, latex, 2 eps-figures, submitted to Phys.Rev.A

Recently, we proposed an exact method for direct calculation of the Jost function for central potentials (which may have Coulombic tails) and the Jost matrix for non-central short range potentials. This method works for all real or complex momenta of physical interest, including the spectral points corresponding to bound and Siegert states. In this work we extend it for potentials which couple channels with different thresholds. The proposed method is based on simple differential equations of the first order, which can be easily solved numerically. Thus, the spectrum generated by any given potential can be thoroughly investigated. At the same time the physical wave function can be obtained having the correct asymptotic behaviour., Comment: 5 pages, latex, no figures, talk given at XVI European Conference on Few-Body Problems in Physics, Autrans, June 1998, to appear in Few-Body Systems Suppl

The scattering length for the eta-meson collision with deuteron is calculated on the basis of rigorous few-body equations (AGS) for various eta-N input. The results obtained strongly support the existence of a resonance or quasi-bound state close to the eta-d threshold., Comment: 11 pages, ReVTeX, 2 LaTeX pseudo-figures

Photoexcitation of the nucleon is studied in the framework of the constituent quark model with nonrelativistic quark-quark interactions. Utilizing the dominance of the pairwise structure of the relevant three-quark potential, the bound and excited state wave functions have been constructed using the Faddeev-type Integrodifferential Equation Approach. The method is based on the Hyperspherical Harmonics expansion and takes two-body correlations exactly into account and therefore reliable wave functions, required in photo processes, can be obtained. The integrated photoabsorption cross sections for the E1-and M1-transitions are calculated and compared with experimental values as well as with those of other theoretical calculations. Our results, in overall, are in good to very good agreement with the experimental values., Comment: 12 pages, latex, no figures, cimento-class file and latex source, accepted by Nuovo Cimento A

The nuclear reaction e + He3 + He4 ---> e + Be7 is considered at thermonuclear energies. The motion of the electron is treated within the adiabatic approximation and the He3-He4 scattering state is calculated using an effective He3-He4 potential constructed via the Marchenko inverse scattering method. The reaction rate thus obtained for solar interior conditions is approximately 10^{-4} of the corresponding rate for the radiative capture He3 + He4 ----> Be7 + gamma. However, at the conditions corresponding to the early stages of the primordial nucleosynthesis, the non-radiative fusion is five times faster than the radiative one. The importance of the non-radiative processes for the energy balance in the sun, which for electrons is totally opaque, is discussed., Comment: 16 pages, RevTex, LaTex-pseudo-figures are included

We present a new, mathematically rigorous, method suitable for bound state and scattering processes calculations for various three atomic or molecular systems where the underlying forces are of a hard-core nature. We employed this method to calculate the binding energies and the ultra-low energy scattering phase shifts below as well as above the break-up threshold for the three He-atom system. The method is proved to be highly successful and suitable for solving the three-body bound state and scattering problem in configuration space and thus it paves the way to study various three-atomic systems, and to calculate important quantities such as the cross-sections, recombination rates etc., Comment: LaTeX, RevTeX and amssymb styles, 7 pages (25 Kb), 3 tables

Several nuclear reactions involving the Be7 nucleus, not included into the standard model of the pp-chain, are discussed. A qualitative analysis of their possible influence on the fate of the Be7 in solar plasma and of their role in the interpretation of the solar neutrino experiments is given. As an example, the reaction rate of the nonradiative production of B8 in the triple collision p + e^- + Be7 ---> B8 + e^- is estimated in the framework of the adiabatic approximation. For the solar interior conditions the triple collision reaction rate is approximately 10^{-4} of that for the binary process p + Be7 ---> B8 + gamma ., Comment: RevTeX, 15 pages, submitted to Nucl.Phys.A

Three- and four-nucleon photodisintegration processes are quite efficiently treated by means of effective two-body integral equations in momentum space. We recall some aspects of their derivation, present previous and most recent results obtained within this framework, and discuss general features, trends and effects observed in these investigations: At low energies final-state interaction plays an important role. Even more pronounced is the effect of meson exchange currents. A considerable potential dependence shows up in the low-energy peak region. The different peak heights are found to be closely correlated with the corresponding binding energies. Above the peak region only the difference between potentials with or without p-wave contributions remains relevant. In the differential cross sections the electric quadrupole contributions have to be taken into account. The remarkable agreement between theory and experiment in $p$-$d$ radiative capture is achieved only when incorporating this contribution, together with most of the above-mentioned effects. In the final part of this report we briefly review also methods developed, and results achieved in three- and four- nucleon electrodisintegration. We, in particular, compare them with a recent access to this problem, based on the construction of nucleon-nucleus potentials via Marchenko inversion theory., Comment: 20 pages LaTeX and 22 postscript figures included, uses epsfig.sty and espcrc1.sty. Invited talk at the XVth International Conference on Few-Body Problems in Physics (22-26 July, 1997, Groningen, The Netherlands). To be published in the conference proceedings in Nucl. Phys. A

We calculated the energy and the size of the three-deuteron muonic molecule (3d 2e^- \mu^-) = D_3 \mu. It turns out that this system possesses two equilibrium positions, one at distances typical for muonic molecules and a second one at the usual molecular size. We show, moreover, that the fusion probability of the three deuterons is considerably enhanced due to the existence of a ^6Li^* threshold resonance. Our estimates indicate that this probability is considerably higher than the decay rate of the competing Auger transition., Comment: 16 pages, revtex, 5 figures eps-style, submitted to Phys. Rev A

An exact method for direct calculation of the Jost functions and Jost solutions for non-central potentials which couple partial waves of different angular momenta is presented. A combination of the variable-constant method with the complex coordinate rotation is used to replace the matrix Schr\"odinger equation by an equivalent system of linear first--order differential equations. Solving these equations numerically, the Jost functions 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 effectiveness of the method is demonstrated using the Reid soft-core and Moscow nucleon-nucleon potentials which involve tensor forces., Comment: 32 pages, RevTex, only latex pseudo-figures

We present a mathematically rigorous method for solving three-atomic bound state and scattering problems. The method is well suited for applications in systems where the inter-atomic interaction is of a hard-core nature. It has been employed to obtain the ground- and excited-state energies for the Helium trimer and to calculate, for the first time, the scattering phase shifts and wave-functions for the He atom-He dimer at ultra-low energies., Comment: 9 pages, main file 21 kB, 1 eps and 4 ps figures

We consider several nuclear fusion reactions that take place at the center of the sun, which are omitted in the standard pp-chain model. More specifically the reaction rates of the nonradiative production of ^3He, ^7Be, and ^8B nuclei in triple collisions involving electrons are estimated within the framework of the adiabatic approximation. These rates are compared with those of the corresponding binary fusion reactions., Comment: 3 pages, latex (RevTex), no figures

A microscopic treatment of eta-nucleus system is presented. Using this, the poles of the amplitude describing elastic scattering of eta-meson off the light nuclei ^2H, ^3H, ^3He, and ^4He have been located in the second quadrant of the complex plane of the eta-nucleus relative momentum. The results obtained indicate that, within the existing uncertainties in the eta-Nucleon input data, a bound state could exist. By a qualitative consideration it is shown that such bound-states, cannot be narrow. It is further shown that scattering length calculations cannot provide a definite answer on the question concerning the existence of eta-nucleus bound states., Comment: 10 pages, Revtex, only latex-figures, Talk given at European Conference on ADVANCES IN NUCLEAR PHYSICS AND RELATED AREAS, Thessaloniki-Greece 8-12 July 1997

Three- and four-neutron systems are studied within the framework of the hyperspherical approach with a local S-wave nn-potential. Possible bound and resonant states of these systems are sought as zeros of three- and four-body Jost functions in the complex momentum plane. It is found that zeros closest to the origin correspond to sub-threshold (nnn) (1/2-) and (nnnn) (0+) resonant states. The positions of these zeros turned out to be sensitive to the choice of the $nn$--potential. For the Malfliet- Tjon potential they are E(nnn)=-4.9-i6.9 (MeV) and E(nnnn)=-2.6-i9.0 (MeV). Movement of the zeros with an artificial increase of the potential strength also shows an extreme sensitivity to the choice of potential. Thus, to generate ^3n and ^4n bound states, the Yukawa potential needs to be multiplied by 2.67 and 2.32 respectively, while for the Malfliet-Tjon potential the required multiplicative factors are 4.04 and 3.59., Comment: Latex, 22 pages, no PS-figures, submitted to J.Phys.G

The \eta-meson collision with light nuclei, ^2H, ^3H, ^3He, and ^4He, is considered on the basis of a microscopic approach which utilises Faddeev type and Lippmann-Schwinger equations. The nuclear hamiltonian is approximated by the finite rank approximation which amounts to the coherent approximation. The \eta-nucleus scattering length and the resonance and bound--state poles of the amplitude describing elastic scattering of \eta-meson by these nuclei are obtained. For each of the nuclei considered, the minimal factor enhancing the \eta N--attraction that moves the poles to the quasi--bound state area of the complex k--plane, is determined. It is shown that within the existing uncertainties in the elementary \eta N iteraction all these nuclei can support a quasi--bound state which can result in a formation of an eta-mesic nucleus. Various aspects of the eta-nucleus physics are discussed with specific emphasis given to the \eta--nucleus effective interaction in configuration space (constructed via the Marchenko inverse scattering method), to the Okubo--Zweig--Iizuka (OZI) rule, and to the charge symmetry breaking problem., Comment: 6 pages, latex, no PS-figures, Talk given at the International Workshop on Exciting Physics with New Accelerators Facilities (EXPAF97), SPring8, Aioi, Japan, March 11-13, 1997

We present a mathematically rigorous method suitable for solving three-body bound state and scattering problems when the inter-particle interaction is of a hard-core nature. The proposed method is a variant of the Boundary Condition Model and it has been employed to calculate the binding energies for a system consisting of three ^4He atoms. Two realistic He-He interactions of Aziz and collaborators, have been used for this purpose. The results obtained compare favorably with those previously obtained by other methods. We further used the model to calculate, for the first time, the ultra-low energy scattering phase shifts. This study revealed that our method is ideally suited for three-body molecular calculations where the practically hard-core of the inter-atomic potential gives rise to strong numerical inaccuracies that make calculations for these molecules cumbersome., Comment: RevTeX, main file 97 kB (26 pages including 6 tables) plus 3 eps and 4 ps figures; published version of the paper

The nuclear reaction e+p+d -----> He3 + e is considered at thermonuclear energies. The motion of the electron is treated within the adiabatic approximation and the pd scattering state is constructed in the form of an antisymmetrized product of the bound state wave function of the deuteron and of the wave function of the pd relative motion. The latter is calculated using an effective pd potential constructed via the Marchenko inverse scattering method. The bound state wave function of He3 is obtained using Faddeev--type integrodifferential equations. The reaction rate thus obtained for the solar interior conditions is approximately 10^{-4} of the corresponding rate for the radiative capture pd ----> He3 + gamma ., Comment: RevTeX, 18 pages, 2 figures, submitted to Nucl.Phys.A

We propose an exact method for locating the zeros of the Jost function for analytic potentials in the complex momentum--plane. We further extend the method to the complex angular--momentum plane to provide the Regge trajectories. It is shown, by using several examples, that highly accurate results for extremely wide as well as for extremely narrow resonances with or without the presence of the Coulomb interaction can be obtained., Comment: RevTeX, 19 pages, 3 figures, submitted to J.Phys.A

The position and movement of poles of the amplitude for elastic eta-meson scattering off the light nuclei d, t, ^3He, and ^4He are studied. It is found that, within the existing uncertainties for the elementary eta-N interaction, all these nuclei can support a quasi-bound state. The values of the eta-nucleus scattering lengths corresponding to the critical eta-N interaction which produces a quasi--bound state are given., Comment: 31K,RevTex, 9 pages, 1 Tex-pseudofigure, no postscript files, submitted to Phys.Rev.C Rapid Comm