[en] Explicit representations are formulated for the Faddeev components of three-body T-matrix continued analytically on unphysical sheets of the energy Riemann surface

[en] Explicit representations for the Faddeev components of three-body T-matrix continued analytically on unphysical sheets of the energy Riemann surface are proved

[en] A proof is given for the explicit representations which have been formulated in the author's previous work for the Faddeev components of three-body T-matrix continued analytically on unphysical sheets of the energy Riemann surface. Also, the analogous representations for analytical continuation of the three-body scattering matrices and resolvent are proved. An algorithm to search for the three-body resonances on the base of the Faddeev differential equations is discussed. 13 refs., 2 figs

[en] The spectral problem (A + V(z))ψ = zψ is considered where main Hamiltonian A is a self-adjoint operator of sufficiently arbitrary nature. The perturbation V(z) = -B(A'-z)^-1 B^* depends on the energy z as resolvent of another self-adjoint operator A'. The latter is usually interpreted as Hamiltonian describing an internal structure of physical system. The operator B is assumed to have a finite Hilbert-Schmidt norm. The conditions are formulated when one can replace the perturbation V(z) with an energy independent 'potential' W such that the Hamiltonian H = A + W has the same spectrum (more exactly a part of spectrum) and the same eigenfunctions as the initial spectral problem. The Hamiltonian H is constructed as a solution of the non-linear operator equation H = A + V(H). It is established that this equation is closely connected with the problem of searching for invariant subspaces for the Hamiltonian H = A_B^* B_A'. The orthogonality and expansion theorems are proved for eigenfunction systems of the Hamiltonian H = A+W. Scattering theory is developed for this Hamiltonian in the case when operator A has continuous spectrum. (author). 26 refs

[en] Algorithm, based on explicit representations for analytic continuation of the T-matrix Faddeev components on unphysical sheets, is worked out for calculations of resonances in the three-body quantum problem. According to the representations, poles of T-matrix, scattering matrix and Green function on unphysical sheets, interpreted as resonances, coincide with those complex energy values where appropriate truncations of the scattering matrix have zero as eigenvalue. Scattering amplitudes on the unphysical sheet, necessary to construct scattering matrix, are calculated on the basis of the Faddeev differential equations. The algorithm developed is applied to search for the resonances in the nnp system and in a model three-boson system. 31 refs., 4 figs., 1 tab

[en] Explicit representations are formulated for the Faddeev components of three-body T-matrix continued analytically on unphysical sheets of the energy Riemann surface. According to the representations, the T-matrix is obviously expressed in terms of its components taken on the physical sheet only. The representations for T-matrix are used then to construct similar representations for analytical continuation of three-body scattering matrices and resolvent. Domains on unphysical sheets are described where the irepresentations obtained can be applied. 43 refs

[en] A mechanism of disappearance and formation of the Efimov levels of the helium ⁴He₃ trimer is studied when the force of interatomic interaction is changed. It is shown that these levels arise from virtual levels which are in turn formed from (quasi)resonances settled on the real axis. The resonances including virtual levels are calculated by the method based on the solution of the boundary value problem, at complex energies, for the Faddeev differential equations describing the scattering processes (2 + 1 → 2 + 1; 1 + 1 + 1). All the calculations are performed with the known interatomic Aziz He-He-potential HFD-B. A very strong repulsive component of this potential at short distances between helium atoms is approximated by a hard core. A special attention is paid to the substantiation of the method used for computing resonances and to the investigation of its applicability range

[en] We consider finite linear or cyclic crystalline structures with molecular cells having narrow prethreshold nuclear resonance. We prove that, if the real part of such a nuclear resonance lies within the energy band (the convex hull of the energy levels) of the crystalline structure arising from a separated molecular level, then there exist molecular crystalline states that decay exponentially in time and the decay rate Γ_R^(m) of these states in the main order is described by the formula Γ_R^(m) ≅ 4(Rea/Γ_R⁽ⁿ⁾, where a is the value of the residue of the molecular channel transfer function at the nuclear resonance

[en] The case of quantum-mechanical system (including electronic molecules) is considered where Hamiltonian allows a separation, in particular by the Faddeev method, of a weakly coupled channel. Width (i.e. the imaginary part) of the resonance generated by a discrete spectrum eigenvalue of the separated channel is studied in the case where main part of the Hamiltonian gives itself another resonance. It is shown that if real parts of these resonances coincide and, at the same time, a coupling between the separated and main channels is sufficiently small then the width of the resonance generated by the separated (molecular) channel is inversely proportional to the width of the main (nuclear) channel resonance. This phenomenon being a kind of universal law, may play an important role increasing the 'cold fusion' probability in electronic molecules whose nuclear constituents have narrow pre-threshold resonances. 21 refs

[en] The probability of nuclear transitions p+p+¹⁶O→¹⁸Ne(4.522,1^-) in molecular water is estimated. Due to a practically exact agreement of the energy of the Ne resonance and of the p+p+¹⁶O threshold, the transition probability is found to be considerably enhanced. This indicates the possibility of nuclear fusion in rotationally excited H₂O molecules of angular momentum 1^-