Раэделяемые Раэложения Для Релятивистских Многоканальных Проблем Рассеяния

Canton, L.; Cattapan, G.; Pisent, G.

doi:10.1007/bf02734941

Cited by 11 publications

(8 citation statements)

References 30 publications

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“…The diagonalizing matrix Q then can be chosen orthogonal, with the Γ × N 1 eigenvalues η (1) p being purely real quantities. Then, a completeness relation [4,5,6] for the potential V cc ′ can be established, namely…”

Section: A Sturmian Expansion Of a Multichannel Interactionmentioning

confidence: 99%

“…have been discussed in detail elsewhere [4,5,6,7,8]. With Φ cn (r), the Weinberg (or sturmian) functions in coordinate space, those form factors then are given by…”

Section: A Sturmian Expansion Of a Multichannel Interactionmentioning

confidence: 99%

“…However, a more promising multichannel coupling theory of the scattering of neutrons from nuclei has been developed by the Padova group [3,4,5,6,7,8]; a theory based upon the work of Rawitscher and Delic [9,10]. The approach is predicated upon making finite-rank separable representations of realistic interaction potentials and the properties of scattering matrices for such Schrödinger interactions.…”

Section: Introductionmentioning

confidence: 99%

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An algebraic solution of the multichannel problem applied to low energy nucleon–nucleus scattering

et al. 2003

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Compound resonances in nucleon-nucleus scattering are related to the discrete spectrum of the target. Such resonances can be studied in a unified and general framework by a scattering model that uses sturmian expansions of postulated multichannel interactions between the colliding nuclei. Associated with such expanded multichannel interactions are algebraic multichannel scattering matrices. The matrix structure of the inherent Green functions not only facilitates extraction of the sub-threshold (compound nucleus) bound state spin-parity values and energies but also readily gives the energies and widths of resonances in the scattering regime. We exploited also the ability of the sturmian-expansion method to deal with non-local interactions to take into account the strong non-local effects introduced by the Pauli principle. As an example, we have used the collective model (to second order) to define a multichannel potential matrix for low energy neutron-12 C scattering allowing coupling between the 0 + 1 (ground), 2 + 1 (4.4389 MeV), and 0 + 2 (7.64 MeV) states. The algebraic S matrix for this system has been evaluated and the sub-threshold bound states as well as cross sections and polarizations as functions of energy are predicted. The results are reflected in the actual measured data, and are shown to be consistent with expectations as may be based upon a shell model description of the target and of the compound nucleus.

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Section: A Sturmian Expansion Of a Multichannel Interactionmentioning

confidence: 99%

“…have been discussed in detail elsewhere [4,5,6,7,8]. With Φ cn (r), the Weinberg (or sturmian) functions in coordinate space, those form factors then are given by…”

Section: A Sturmian Expansion Of a Multichannel Interactionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An algebraic solution of the multichannel problem applied to low energy nucleon–nucleus scattering

et al. 2003

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“…The model, though simple, has very general features. In particular, the restriction to multirank interactions is no limitation, since it has been demonstrated that any interaction can be reduced to a multirank one by the Sturrnian expansion [7] or as in the work of the Gratz group [8].…”

Section: Introductionmentioning

confidence: 99%

Analysis of compound and quasicompound resonances in a multichannel, finite-rank model

Pisent

Svenne

1995

Phys. Rev. C

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Within a multichannel, multirank model of wide applicability, resonances in complex systems are studied. In particular, compound resonances, which are well observed in nuclear systems can be clearly examined as arising from bound states in subsystems of the coupled-channel system. A less well known, and until now little understood, form of resonance is the quasicompound resonance (or structure). These are seen as arising from resonances in subsystems of the multichannel system. The nature of the two types of resonances is contrasted, in their behavior as the strength of coupling increases. Compound resonances arise in6nitely narrow; but of fixed height and increase in width, whereas quasicompound structures arise as small "bumps" of finite width, and increase in height. After presentation of the general theory, these properties are illustrated in a simple numerical model calculation.PACS number(s): 25.40. Ny, 24. 10.Eq

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“…Negative-energy Weinberg states (NEWS) have been similarly used with good success for generating a separable representation of the two-body T matrix for many years [7]. Renewed activity with NEWS has more recently provided a separable representation for the T matrix for modern potentials [8], and also for obtaining the energy dependence of the dynamic polarization potential due to channel coupling at the threshold of the opening of a new channel [9]. NEWS are also used in atomic scattering situations [10],or for including the efFects of breakup in deuteron-nucleus transfer reactions [11].…”

Section: Intrc)ductionmentioning

confidence: 99%

Numerical quasiparticle representation of the nucleon-nucleonTmatrix

Rawitscher

Canton

1991

Phys. Rev. C

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In this paper we develop a practical "hybrid" numerical representation of the nucleon-nucleon T matrix. Part of the expression contains nonseparable terms which are easily calculated, and the rest consists of a separable representation of small rank in terms of Weinberg states. The method rests on the observation that when a set of positive-energy %'einberg states is used to obtain a separable representation of the potential V then the residue 6 V, due to the basis-set truncation, has very special properties:(1) The contribution 6T to the T matrix due to AVis identical to the undistorted T matrix for 6 V alone, T&, i.e. , the usual Moeller distortion factors in the two-potential formula are unity in this case. (2) A perturbative-iterative treatment of Tz in powers of 5 V is found to be equivalent to the finite-rank representation of operators of the type T, T -V, T -V -VGo V, and so on. This equivalence has both practical and theoretical implications. On the one hand, it provides a reliab1e method for calculating the T matrix and for analyzing the corresponding accuracy properties. On the other hand, a connection is established between each order of the quasiparticle method and the different variational principles which underlie the finite-rank representation of operators such as T, T -V, T -V -VGO V, etc. Numerical examples are provided for two difterent nucleon-nucleon singlet potentials (Reid soft core and MalflietTjon). In the Malffiet-Tjon case, for instance, two Weinberg states are found to be sufhcient in order to give an accuracy of 0.1% for the calculation of T -V -VGOV, while for T -V and T the same two states give an accuracy of 1% and 10%, respectively, in an interval of 6 fm ' around the on-shell point. I. INTRC)DUCTIONPositive-energy Weinberg states [1] (PEWS) are a useful basis for solving scattering problems because these functions asymptotically obey the appropriate outgoing wave boundary condition. They have been used for the solution of the Schrodinger wave function (coupled or uncoupled) [1,2], for the solution of a many-particle shellmodel system with one nucleon in the continuum [3], for obtaining a representation of the two-nucleon T matrix [4,5], and for obtaining a nonlocal dynamic polarization potential which expresses the e6'ect of channel coupling [6]. Negative-energy Weinberg states (NEWS) have been similarly used with good success for generating a separable representation of the two-body T matrix for many years [7]. Renewed activity with NEWS has more recently provided a separable representation for the T matrix for modern potentials [8], and also for obtaining the energy dependence of the dynamic polarization potential due to channel coupling at the threshold of the opening of a new channel [9]. NEWS are also used in atomic scattering situations [10],or for including the efFects of breakup in deuteron-nucleus transfer reactions [11]. Many applications, however, require good accuracy with low rank, while the convergence with the number of Weinberg basis states can be rather slow, esp...

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Раэделяемые Раэложения Для Релятивистских Многоканальных Проблем Рассеяния

Cited by 11 publications

References 30 publications

An algebraic solution of the multichannel problem applied to low energy nucleon–nucleus scattering

An algebraic solution of the multichannel problem applied to low energy nucleon–nucleus scattering

Analysis of compound and quasicompound resonances in a multichannel, finite-rank model

Numerical quasiparticle representation of the nucleon-nucleonTmatrix

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