Integral–differential equations approach to atomic three-body systems

Vibrational excitation of simple molecular ions in resonant and under-resonant strong laser fields: Dissociation and ionization of ppe and pde; laser-enhanced nuclear fusion in ddμ and dtμ

“…5. Muon-field following and enhanced nuclear fusion in ddl and dtl in strong X-ray fields: under-resonant vs. resonant excitation on the attosecond timescale Since the first idea of Frank [45] in 1947 and experimental discovery of Alvarez and co-workers [46] in 1957, the muon-catalysed nuclear fusion has become a very important field of research attracting much current interest both in theory and experiment [34][35][36][47][48][49][50][51]. Due to a very small internuclear distances in muonic molecules, e.g.…”

Nuclear effects in protonium formation low-energy three-body reaction: p̄ + (pμ)1s→ (p̄p)α+μ−: Strong p̄–p interaction in p̄ + (pμ)1s

“…Each of these blocks should have sub-blocks depending on the quantum numbers α = nlλ and α = n l λ . The second order differential operators produce three-diagonal sub-matrixes [31]. However, there is no need to keep the whole matrix A in computer's operating (fast) memory.…”

“…This means to carry out an expansion of the Faddeev-type components into eigenfunctions of the subsystem Hamiltonians. This technique provides an infinite set of one-dimensional integral-differential equations [30,31]. Within this formalism the asymptotic of the full three-body wave function contains two parts corresponding to two open channels [32].…”

Resonance energies and fusion rates of mass‐nonsymmetric dtμ* molecule

“…The resulting set of coupled second-order differential equations is solved by using numerical method [13,14]. In fact, the molecular parameters are optimized to stabilize the eigenvalues.…”