Energy-dependent potentials in the nuclear three body problem

Abdurakhmanov, A. A.; Zubarev, Alexander L.

doi:10.1007/bf01412090

Cited by 7 publications

(4 citation statements)

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“…The accuracy of the binding energy demonstrates the applicability of the 1D approximation to the off-shell T -matrix, which is important for applications to manybody problems (see also discussion in Ref. [26]). The only criteria of applicability are a < 1 and E b ≪ ω ⊥ (or E c ≪ ω ⊥ for collisions).…”

Section: Relation To the One-dimensional Problemmentioning

confidence: 84%

Properties of quasi-one-dimensional molecules with Feshbach-resonance interaction

Yurovsky

2006

Phys. Rev. A

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Bound states and collisions of atoms with two-channel two-body interactions in harmonic waveguides are analyzed. The closed-channel contributions to two-atom bound states become dominant in the case of a weak resonance. At low energies and values of the non-resonant scattering length the problem can be approximated by a one-dimensional resonant model. Three-body problem becomes nonintegrable and the properties of triatomic molecules become different from those predicted by the integrable Lieb-Liniger-McGuire model.

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Section: Relation To the One-dimensional Problemmentioning

confidence: 84%

Properties of quasi-one-dimensional molecules with Feshbach-resonance interaction

Yurovsky

2006

Phys. Rev. A

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“…This is not at variance with Stone's theorem, since, as it has been shown on the exactly solvable model, the evolution operator is not strongly continuous in this case. It satisfies only the more general continuity condition (7). We have stated correspondence between the large-momentum behaviour of the matrix elements of the evolution operator and the form of the generalized interaction operator H int (τ ) must necessarily be of the form (48), and if this large-momentum behaviour does not meet the above requirements, then H (s) int (τ ) must be of the form corresponding to the case when the interaction generating the dynamics of a quantum system is nonlocal in time.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…Indeed, nonlocality of interaction leads to the energy dependence of effective interaction operators. In recent years the possibility of using energy-dependent potentials to describe hadron-hadron interaction at low and intermediate energies has been widely discussed [3][4][5][6][7][8][9][10]. Interest in studying potentials of this type is provoked by still existing discrepancy between theory and experiment.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal interactions and quantum dynamics

Gainutdinov

1999

J. Phys. A: Math. Gen.

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The problem is considered of describing the dynamics of quantum systems generated by a nonlocal in time interaction. It is shown that the use of the Feynman approach to quantum theory in combination with the canonical approach allows one to extend quantum dynamics to describe the time evolution in the case of such interactions. In this way, using only the current concepts of quantum theory, a generalized equation of motion for state vectors is derived. In the case, where the fundamental interaction generating the dynamics in a system is local in time, this equation is equivalent to the Schrödinger equation. Explicit examples are given for an exactly solvable model. The proposed formalism is shown to provide a new insight into the problem of the description of nonlocal interactions in quantum field theory. It is shown that such a property of the equation of motion as nonlocality in time may be important for describing hadron-hadron interactions at low and intermediate energies.

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“…(11). Elimination of channels and energy-dependent potentials in 3D three-body problems were considered in [50,51,52]. However, in three-body problems effects of the eliminated channels extend beyond the interaction strength.…”

Section: B Two-body Systemmentioning

confidence: 99%