Nuclear Fusion via Triple Collisions in Solar Plasma

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 figure

Triple collisions (e+p+Be7) in solar plasma

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.

Three-body resonances Lambda-n-n and Lambda-Lambda-n

Possible bound and resonant states of the hypernuclear systems $\Lambda nn$ and $\Lambda\Lambda n$ are sought as zeros of the corresponding three-body Jost functions calculated within the framework of the hyperspherical approach with local two-body S-wave potentials describing the $nn$, $\Lambda n$, and $\Lambda\Lambda$ interactions. Very wide near-threshold resonances are found for both three-body systems. The positions of these resonances turned out to be sensitive to the choice of the $\Lambda n$-potential. Bound $\Lambda nn$ and $\Lambda\Lambda n$ states only appear if the two-body potentials are multiplied by a factor of $\sim 1.5$.Comment: 12 pages, 5 figures. Acknowledgments are added in the new versio

Coherent Photoproduction of eta-mesons on Three-Nucleon Systems

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.

Analytic structure of the multichannel Jost matrix for potentials with Coulombic tails

A quantum system is considered that can move in N two-body channels with the potentials that may include the Coulomb interaction. For this system, the Jost matrix is constructed in such a way that all its dependencies on the channel momenta and Sommerfeld parameters are factorized in the form of explicit analytic expressions. It is shown that the two remaining unknown matrices are single-valued analytic functions of the energy and therefore can be expanded in the Taylor series near an arbitrary point within the domain of their analyticity. It is derived a system of firstorder differential equations whose solutions determine the expansion coefficients of these series. Alternatively, the unknown expansion coefficients can be used as fitting parameters for parametrizing experimental data similarly to the effective-range expansion. Such a parametrization has the advantage of preserving proper analytic structure of the Jost matrix and can be done not only near the threshold energies, but around any collision or even complex energy. As soon as the parameters are obtained, the Jost matrix (and therefore the S-matrix) is known analytically on all sheets of the Riemann surface, and thus enables one to locate possible resonances.http://jmp.aip.org/am201

Analytic structure and power series expansion of the Jost function for the two-dimensional problem

For a two-dimensional quantum-mechanical problem, we obtain a generalized power series expansion of the S-matrix that can be done near an arbitrary point on the Riemann surface of the energy, similar to the standard effective-range expansion. In order to do this, we consider the Jost function and analytically factorize its momentum dependence that causes the Jost function to be a multivalued function. The remaining single-valued function of the energy is then expanded in the power series near an arbitrary point in the complex energy plane. A systematic and accurate procedure has been developed for calculating the expansion coefficients. This makes it possible to obtain a semi-analytic expression for the Jost function (and therefore for the S-matrix) near an arbitrary point on the Riemann surface and use it, for example, to locate the spectral points (bound and resonant states) as the S-matrix poles. The method is applied to a model similar to those used in the theory of quantum dots.http://www.iop.org/EJ/journal/JPhysAnf201

A method for extracting the resonance parameters from experimental cross-sections

Within the proposed method, a set of experimental data points are fitted using a multi-channel S-matrix. Then the resonance parameters are located as its poles on an appropriate sheet of the Riemann surface of the energy. The main advantage of the method is that the S-matrix is constructed in such a way that it has proper analytic structure, i.e. for any number of two-body channels, the branching at all the channel thresholds is represented via exact analytic expressions in terms of the channel momenta. The way the S-matrix is constructed makes it possible not only to locate multi-channel resonances but also to extract their partial widths as well as to obtain the scattering cross-section in the channels for which no data are available. The efficiency of the method is demonstrated by two model examples of a single-channel and a two-channel problems, where known resonance parameters are rather accurately reproduced by fitting the pseudo-data artificially generated using the corresponding potentials.http://www.worldscinet.com/ijmpehb201

Threshold scattering of the eta-meson off light nuclei

The scattering lengths of eta-meson collisions with light nuclei d,t,3He, and 4He are calculated on the basis of few-body equations in coherent approximation. It is found that the eta-nucleus scattering length depends strongly on the number of nucleons and the potential-range parameter. By taking into account the off-shell behavior of the eta-N amplitude, the eta-4He scattering length increases considerably.Comment: 8 pages, no figures, RevTeX, submitted to Phys.Lett.

The η\eta-3N problem with separable interactions

The $\eta$-3N-interaction is studied within the four-body Faddeev-Yakubovsky theory adopting purely separable forms for the two- and three-body subamplitudes, limiting the basic two-body interactions to s-waves only. The corresponding separable approximation for the integral kernels is obtained by using the Hilbert-Schmidt procedure. Results are presented for the $\eta$-$^3$H scattering amplitude and for the total elastic cross section for energies below the triton break-up threshold.Comment: revised version accepted for Phys. Rev. C, 16 pages revtex including 6 eps-figures, formal part shortene

eta d scattering in the region of the S11 resonance

We have studied the reaction eta d -> eta d close to threshold within a nonrelativistic three-body formalism. We considered several eta N and NN models, in particular potentials with separable form, fitted to the low-energy eta N and NN data to represent the two-body interactions. We found that with realistic two-body interactions a quasibound state does not exist in this system, although there is an enhancement of the cross section by one order of magnitude, in the region near threshold, which is a genuine three-body effect not predicted within the impulse approximation.Comment: 18 pages Revtex, 2 figure