Applications of the Bargmann-Segal transform to nuclear systems of complex clusters

Seligman, T. H.; Zahn, W.

doi:10.1088/0305-4616/2/2/005

Cited by 32 publications

(11 citation statements)

References 14 publications

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“…The evaluation of the necessary interaction and norm kernels is carried out by standard techniques [36][37][38]. The 3q…”

Section: Ts: ~(Hh)st2(andt)]smentioning

confidence: 99%

The NN interaction in a quark model with quark-antiquark excitations

Fujiwara¹,

Hecht²

1985

Nuclear Physics A

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Quark-antiquark excitations inherent in the quark-gluon interaction have been incorporated into a quark model of the nucleon to study the effects of such excitations on the NN interaction within the framework of the resonating group method. The three-quark (3q) components of a single nucleon are augmented by (3q)(qq) excitations with the 24 possible spin, isospin, color combinations for the energetically lowest p-wave relative motion function. Quark exchange kernels are then calculated for the two-nucleon system described by these improved nucleon internal functions; and these exchange kernels are converted to phase-shift-equivalent effective NN potentials by the Wigner-transfo~ WKB technique. The off-shell qq pair-creation terms are derived from the one-gluon exchange diagrams in the Breit approximation in analogy with the derivation of the qq and qq potentials. The parameters of the interaction are chosen to be consistent with the experimental AN mass difference, the nucleon-vector-meson coupling constants, and the nucleon magnetic moments. Within these constraints, the predicted amplitudes of the (3q)(qq) components of the nucleon internal functions have been shown to be insensitive to the precise values of the model parameters. In particular, they pass the crucial test of being insensitive to very large changes in the magnitude of the confinement potential constant which is a necessary ingredient of the model. The qij excitations lead to the following effects in the S-wave NN potentials: (i) The repulsive core heights of the simple 3q-3q model are greatly reduced but retain their strong essentially linear energy dependence, with numerical values very similar to those of the short-range phenomenological terms of the Paris potential. (ii) The effective potentials have acquired an attractive part in the 0.8-1.5 fm range. However, this attraction is too weak to bind the deuteron or fit the extreme low-energy S-wave phase shifts.

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“…The evaluation of the necessary interaction and norm kernels is carried out by standard techniques [36][37][38]. The 3q…”

Section: Ts: ~(Hh)st2(andt)]smentioning

confidence: 99%

The NN interaction in a quark model with quark-antiquark excitations

Fujiwara¹,

Hecht²

1985

Nuclear Physics A

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“…In an early review [12] discusses the problems arising from the singularities of the transforms used, which have been analyzed in [13]. The solution in terms of the Bargmann transform [20] has been successfully applied [21] but the singular transforms have still been essential for numerical work. We shall limit our considerations to the one dimensional case as again the generalization is obvious.…”

Section: Representations Of Complex Extensions Of Canonical Transformmentioning

confidence: 99%

Observables and density matrices embedded in dual Hilbert spaces

Prosen¹,

Martignon²,

Seligman³

2015

Phys. Scr.

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The introduction of operator states and of observables in various fields of quantum physics has raised questions about the mathematical structures of the corresponding spaces. In the framework of third quantization it had been conjectured that we deal with Hilbert spaces although the mathematical background was not entirely clear, particularly, when dealing with bosonic operators. This in turn caused some doubts about the correct way to combine bosonic and fermionic operators or, in other words, regular and Grassmann variables. In this paper we present a formal answer to the problems on a simple and very general basis. We illustrate the resulting construction by revisiting the Bargmann transform and finding the known connection between L 2 (R) and the Bargmann-Hilbert space. We pursue this line of thinking one step further an discuss the representations of complex extensions of linear canonical transformations as isometries between dual Hilbert spaces. We then use the formalism to give an explicit formulation for Fock spaces involving both fermions and bosons thus solving the problem at the origin of our considerations.

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“…There are 14 possible Of states in this space. In an ((I,Z,)Z,L)O+ angular-momentum coupled basis these correspond to the (Ill,) combinations: (00), (22), (44) with I, = 0; (02), (24), (22), (44)…”

Section: The W(3) Coupled Cluster Basismentioning

confidence: 99%

Spectroscopic amplitudes for complex cluster systems

et al. 1981

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By expanding the Bargmann-Segal integral transform of norm and overlap kernels in appropriately SU(3) coupled Bargmann space functions, the calculation of norm and overlap matrix elements in a cluster model basis is reduced to purely algebraic techniques involving the algebra of SU(3) recoupling transformations. This technique has been further developed to make calculations possible for systems of two heavy fragments other than closed-shell nuclei. In one application of the method, analytic expressions are given for the norms of binary fragment systems in which a light fragment of mass number f, f < 4, is combined with a heavy fragment of mass number A-J with A-f< 24. The A-j' fragment nuclei with different p and sd-shell structure illustrate somewhat different problems in the recoupling technique. In a second application, spectroscopic amplitudes are calculated for the most important open channels of the "C+ "C resonances. Eigenvalues and eigenvectors ofthe antisymmetrizer are evaluated in a "molecular basis" of the "C+ "C system, in which each "C nucleus is assumed to have SU(3) symmetry (04) with internal rotational excitations ofO+, 2+ and 4+. Reduced width amplitudes are calculated connecting such normalized, fully antisymmetrized molecular basis states to exit channels which include: a+20Ne with *ONe internal functions of (80) SU(3) symmetry, (K = O+ band), and (82) SU(3) symmetry, (K = 2-band); 160+sBe; and 23Na+p or 23Mg+n fragments with 23Na or 23Mg excitations in K = jj and f rotational bands of SU(3) symmetry (83).

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Applications of the Bargmann-Segal transform to nuclear systems of complex clusters

Cited by 32 publications

References 14 publications

The NN interaction in a quark model with quark-antiquark excitations

The NN interaction in a quark model with quark-antiquark excitations

Observables and density matrices embedded in dual Hilbert spaces

Spectroscopic amplitudes for complex cluster systems

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