The three-nucleon system

A brief review is given of the recent progress made in the study of the three-nucleon problem with local interactions. In particular, it is pointed out that the presence of meson exchange currents can contribute significantly to the³He charge form factor at high momentum transfer.Invited talk at the symposium Theory of lightest nuclei, Liblice, Czechoslovakia, May 1974.     

The state of an atomic-molecular system near the stability threshold

The state of an atomic-molecular system near its stability threshold with regard to the detachment of one of the particles is studied. The decay of the system upon a decrease in the charge of a binding particle, as well upon an increasasymmetry of masses of like-charged particles, is considered. A special variational principle that allows one to directly calculate the threshold state of the system without repeatedly calculating its energy for different values of masses and charges of particles is used. With the motion of all particles fully taken into account, the threshold states of two-electron atoms with different nuclear charges and of atomic-molecular systems corresponding to the attachment of a positron of variable mass to a neutral atom are calculated. On the basis of calculation of quantum-mechanical expectation values of the kinetic energy of particles and the potential energy of their interaction, the rearrangement of the wave function upon passage of the system through the decay threshold is examined. The threshold characteristics of a purely adiabatic system containing infinitely heavy particles are considered separately.     

Relativity in the three-nucleon system

A Poincaré-invariant formulation of the three-body system is used. The two-body force embedded in the three-particle Hilbert space is generated out of the high-precision NN forces by solving a nonlinear equation. The solution of the relativistic 3N Faddeev equation for ³H reveals less binding energy than for the nonrelativistic one. The effect of the Wigner spin rotation on the binding energy is very small.     

The three-nucleon system with the Reid and Gammel-Brueckner potentials

We report preliminary results for an extension of our calculations to the Reid and Gammel-Brueckner nucleon-nucleon potentials. The results for the Reid potential appear to disagree with those of some other calculations.     

Off-shell effects in the three-nucleon system

The triton binding energy and the neutron-deuteron doublet scattering length have been studied with phase-equivalent rank-2 separable potentials in S-waves. The potentials have been constructed from the phase shifts using the solution of the inverse scattering problem. Large off-shell effects are connected with the appearance of additional nodes in the deuteron or the low-energy singlet wave functions.     

Nucleon-nucleon interaction in the three-nucleon system

The three-nucleon system is reconsidered. The Faddeev equations are given leading to a set of integral equations. Solving these integral equations, suitable forms are considered for the nucleon-nucleon interaction. In the bound state of three-nucleon system, the form of the nuclear forces from the nucleon-nucleon interaction is important. In the present calculations, we consider the nuclear forces resulting from the nucleon-nucleon interaction by the exchange of a scalar meson, a pseudoscalar meson, and a massless vector meson. With this different meson exchange nucleon-nucleon interaction, the binding energy of the three-nucleon system is calculated by solving the Faddeev integral equations giving a value of 8.452 MeV.     

Binary scattering and breakup in the three-nucleon system

We present the further development of the three-particle formalism for differential Faddeev equations. The asymptotic boundary conditions in the hyperspherical adiabatic representation have been constructed. We prove that these conditions are asymptotically equivalent to the standard Merkuriev boundary conditions. With these boundary conditions we have formulated the boundary-value problem for Faddeev equations which has the property that the binary channel and the breakup channel are explicitly orthogonal. The effective numerical scheme for solving the formulated boundary-value problem is given.     

Bag-model inspired nucleon-nucleon potentials and the three-nucleon system

Several examples of short-range energy-dependentN-N potentials derived in the quark-compound-bag (QCB) model are presented. They all satisfy the classical causality condition. We show that for radii of theN-N interactions ofb1.4 fm thes-wave QCB potentials reproduce fairly well the trinucleon binding energy and other three-nucleon observables.     

Hadron production near threshold

Final state interaction effects inpp→ pΛK ⁺ andpd →³Heη reactions are explored near threshold to study the sensitivity of the cross-sections to thepΛ potential and theηN scattering matrix. The final state scattering wave functions between Λ andp andη and³He are described rigorously. The Λ production is described by the exchange of one pion and aK-meson between two protons in the incident channel. Theη production is described by a two-step model, where in the first step a pion is produced. This pion then produces anη by interacting with another nucleon     

Disordered magnet near the percolation threshold

A disordered Potts magnet containing a random mixture of ferromagnetic exchange constants J_a and J_b (J_a?J_b) near the percolation threshold is considered. The scaling form for the free energy contains two crossover exponents. Duality arguments in two dimensions show that these exponents are equal. They are also shown to be equal to unity in d = 6 ? ? dimensions to order ?.     

Gamow-Teller strength near the pion threshold

The Gamow-Teller strength at high energy, in the vicinity of the pion mass, is linked to the absorption of p wave pions. It is not subject to Pauli blocking and increases linearly with the nucleon number.     

The plasma oscillations spectrum of a periodically inhomogeneous 2D electron system near the perforation threshold

The transformation of the spectrum of plasma oscillations with the zero reduced wave vector in the spatially modulated two-dimensional electron system moving to the regime of isolated quasi-one-dimensional electron channels is theoretically investigated. The results provide an explanation of the well-known experimental observations of the plasma resonance transformation when a two-dimensional electron system crosses the continuity violation threshold.     

Exchange magnetic moment form factor of the three-nucleon system

The exchange magnetic moment form factor of ³H and ³He is derived from experiment, regarding the D state probability P_D as free parameter. The isoscalar part is roughly constant. The rms radius corresponding to the isovector part increases as P_D increases.     

The complex Kohn variational method applied to N-d scattering

The three-nucleon ground state and the N-d scattering states are obtained using variational principles. The wave function of the system is decomposed into angular-spin-isospin channels and the corresponding two dimensional spatial amplitudes are expanded in a correlated polynomial basis. For the scattering states, the complex form of the Kohn variational principle is used to determine the S-matrix. Special attention is given to the convergence pattern of the phase-shift and mixing parameters. The calculations have been performed using realistic local NN potentials and three-nucleon forces. Important features of the method are anomaly-free solutions and the low dimensionality of the matrices involved allowing for the inclusion of a large number of states. Very precise and stable numerical results have been obtained.     

Direct application of the quasiparticle method to a three-nucleon system

The energy dependence of the expectation values of powers of the Lippmann-Schwinger operator,I _k (W)=〈γ|V(G ₀(W)·V) ^k |γ〉, is used to calculate the ground-state energy of the triton for a simple central two-nucleon interaction of Gaussian type. This method allows to calculate the exact energy eigenvalueE ₀ of a three-nucleon-system in principle with any desired precision. The calculations are performed untilk=3. In this approximation the valueE ₀ ⁽³=?13.25 MeV is obtained which is simultaneously an upper bound of the true groundstate energyE ₀ of the system.     

Fractal superconductivity near localization threshold

We develop a semi-quantitative theory of electron pairing and resulting superconductivity in bulk “poor conductors” in which Fermi energy E_F is located in the region of localized states not so far from the Anderson mobility edge E_c. We assume attractive interaction between electrons near the Fermi surface. We review the existing theories and experimental data and argue that a large class of disordered films is described by this model.Our theoretical analysis is based on analytical treatment of pairing correlations, described in the basis of the exact single-particle eigenstates of the 3D Anderson model, which we combine with numerical data on eigenfunction correlations. Fractal nature of critical wavefunction's correlations is shown to be crucial for the physics of these systems.We identify three distinct phases: ‘critical’ superconductive state formed at E_F = E_c, superconducting state with a strong pseudo-gap, realized due to pairing of weakly localized electrons and insulating state realized at E_F still deeper inside a localized band. The ‘critical’ superconducting phase is characterized by the enhancement of the transition temperature with respect to BCS result, by the inhomogeneous spatial distribution of superconductive order parameter and local density of states. The major new feature of the pseudo-gapped state is the presence of two independent energy scales: superconducting gap Δ, that is due to many-body correlations and a new “pseudo-gap” energy scale Δ_P which characterizes typical binding energy of localized electron pairs and leads to the insulating behavior of the resistivity as a function of temperature above superconductive T_c. Two gap nature of the pseudo-gapped superconductor is shown to lead to specific features seen in scanning tunneling spectroscopy and point-contact Andreev spectroscopy. We predict that pseudo-gapped superconducting state demonstrates anomalous behavior of the optical spectral weight. The insulating state is realized due to the presence of local pairing gap but without superconducting correlations; it is characterized by a hard insulating gap in the density of single electrons and by purely activated low-temperature resistivity ln R(T) ∼ 1/T.Based on these results we propose a new “pseudo-spin” scenario of superconductor-insulator transition and argue that it is realized in a particular class of disordered superconducting films. We conclude by the discussion of the experimental predictions of the theory and the theoretical issues that remain unsolved.