Medium corrections to nucleon-nucleon interactions

Dortmans, P. J.; Amos, K.

doi:10.1088/0954-3899/17/6/012

Cited by 19 publications

(12 citation statements)

References 31 publications

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“…In this circumstance, the "on-shell momentum, " k can be treated as a variational parameter. By so doing, a number of studies [25,26] with uncoupled potentials, and one now with coupled interactions [27], have found excellent agreement between exact three-body binding energy calculations and those made using optimal WM separable representations. The optimal choice being with that value of k for which the remainders to the original rank-1 (rank-2) W matrices are minimal.…”

Section: Coupled Channels Rank-nmentioning

confidence: 84%

Separable expansions of theNNtmatrix via exact half-off-the-energy-shell methods

et al. 1993

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Recently a method was proposed by which one can obtain rank-1 (for uncoupled channels) and rank-2 (for coupled channels) energy-dependent separable t-matrix representations which are e~act on and half ofF of the energy shell. Fully ofF shell, this representation, though accurate at low energies, is flawed. For uncoupled channels, if the phase shift passes through zero, the representation has a pathology. Here we investigate two methods which overcome this; one due to Haberzettl which we extend to coupled channels, and the second which is based upon selective combination of the elements of Sturmian expansions. We investigate and compare all methods of separation over a range of energies up to 250 MeV for the So and Sq channels with the Paris interaction. Special attention is paid to the convergence of the higher-order Haberzettl expansion and to the comparison of the extended methods for energies around the zero-phase-shift pathology for the So channel. PACS number(s): 21.30.+y I. INTR, ODUCTIONDespite the fact that the three-body problem can be solved exactly [1,2], separable forms remain essential for solution of many-body problems [3 -7]. Even so, it has been known for many years that separable representations of the two-nucleon (NN) t matrix facilitate convenient and quite accurate solutions of the Faddeev equations for bound and scattering three-nucleon problems [8 -10]. That spurred studies to find separable representations of most sophisticated, particle exchange model, NN interactions (among which those of the Paris [11]and Bonn [12] groups are noteworthy). One reason for such developments was that phenomenological interactions of the past, while parametrized to give correct on-shell NN t matrices (and so agree with measured NN data) were arbitrary with regard to off-energy-shell properties of the t matrix; properties which are directly involved in threebody problem calculations. It has long been hoped that such dependences, along with determination of realistic three-body forces, would permit the use of data from three-nucleon systems to discriminate between the diverse postulates of the basic NN interaction. Indeed such was the case when the Ernst-Shakin-Thaler (EST) separable expansion procedure [13] was used [14] to define the PEST (for the Paris force) and BEST (for the Bonn force) separable interactions [15,16] at a low rank (usually ( 6). But there are many techniques one can Permanent address: now apply to obtain useful separable representations (of t matrices, for example) and an excellent review of them is to be found in Ref. [17].Herein we are concerned with two specific methods of defining very low rank (( 4) separable expansions of a realistic t matrix, and with the link between those methods. The first, a W-matrix expansion, is based upon the formalism of Bartnik, Haberzettl, and Sandhas [18]. In that formalism, the Lippmann-Schwinger equation is so modified that solutions can be found for both bound and continuum cases in terms of solutions (the W matrices) of nonsingular, real but inhomogen...

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Section: Coupled Channels Rank-nmentioning

confidence: 84%

Separable expansions of theNNtmatrix via exact half-off-the-energy-shell methods

et al. 1993

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“…In principle, the number of strengths and inverse ranges (n i ) chosen can be as large as one likes, though for all operators n i = 4 seems to be sufficient to reproduce accurately the half-off-shell g matrices for laboratory energies between 50 and 400 MeV [1]. Singular valued decomposition was used to optimise those inverse ranges and coefficients so that double Bessel transforms of the effective interaction map accurately to an appropriate set of infinite nuclear matter g matrices [17,18] obtained from solution of the Bethe-Brueckner-Goldstone (BBG) equation,…”

Section: B the Effective Interactionmentioning

confidence: 99%

Microscopic model analyses of the elastic scattering of 65 MeV protons from targets of diverse mass

et al. 1998

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Nonlocal coordinate space optical potentials for the scattering of 65 MeV protons from nuclei ranging in mass from 6 Li to 238 U have been defined by folding a complex, medium dependent effective interaction with the density matrix elements of each target. The effective interaction is based upon solutions of the Lippmann-Schwinger and Brueckner-Bethe-Goldstone equations having the Paris potential as input. The nuclear structure information required in our folding model are the one body density matrix elements for the target and the single nucleon bound state wave functions that they weight. For light mass nuclei, very large basis shell model calculations have been made to obtain the one body density matrix elements. For medium and heavy mass nuclei, a very simple shell model prescription has been used. The bound state single particle wave functions that complete the nuclear density matrices are either Woods-Saxon or harmonic oscillator functions. The former are employed in most cases when large basis structure is available. For light nuclei (A ≤ 16) Woods-Saxon potential parameters and harmonic oscillator lengths are determined from fits to electron scattering form factors. For all other nuclei, we use harmonic oscillator functions with the oscillator lengths set from an A 1/6 mass law. Using this microscopic model, optical potentials result from which differential cross sections, analyzing powers and spin rotations are found. In general the calculated results compare very well with data when the effective interactions are determined from a mapping of nucleon-nucleon g matrices. This is not the case when effective interactions built from a mapping of (free) t matrices are used.

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“…whereinQ(q, K; k f ) is the (angle averaged) Pauli operator and K is the average centre of mass momentum as defined previously [3,4], with the latter specified at a laboratory incident momentum p 0 and for a Fermi momentum k f . The energies in the propagators of the BBG equations include (real) auxiliary potentials U , and are defined bȳ…”

Section: The N N T and G Matricesmentioning

confidence: 99%

“…Details of the calculations have been given previously [4] and the result is tables of complex numbers for each incident energy, Fermi momentum value and set of relative momenta for each NN channel. In a free NN collision the struck nucleon initially has zero momentum.…”

Section: The N N T and G Matricesmentioning

confidence: 99%

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Signatures of Medium Effects on NN Interactions in Proton Scattering from Nuclei

Amos¹,

Dortmans²,

Karataglidis³

1997

Aust. J. Phys.

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Effective two nucleon (NN) interactions in the nuclear medium have been defined from an accurate mapping of NN g matrices obtained by solving the Brueckner–Bethe–Goldstone (BBG) equations for infinite nuclear matter. Those effective interactions have been used in fully microscopic calculations of proton-light nuclei (nonlocal) effective interactions from which predictions of the elastic scattering differential cross sections and analysing powers have been obtained. Results for incident proton energies of 65 and 200 MeV are considered in particular herein. The associated relative motion wave functions have been used as the distorted waves in distorted wave approximation (DWA) studies of select inelastic scattering events. The same effective interactions were used as the transition operators in those calculations. The relevant nuclear spectroscopy for the elastic and DWA (p, p′) calculations has been found from full (0 + 2)hϖ shell model evaluations of the nuclear structure; wave functions of which give good descriptions of form factors obtained from electron scattering.

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Medium corrections to nucleon-nucleon interactions

Cited by 19 publications

References 31 publications

Separable expansions of theNNtmatrix via exact half-off-the-energy-shell methods

Separable expansions of theNNtmatrix via exact half-off-the-energy-shell methods

Microscopic model analyses of the elastic scattering of 65 MeV protons from targets of diverse mass

Signatures of Medium Effects on NN Interactions in Proton Scattering from Nuclei

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