Three-nucleon calculations with local potentials

Sandhas, W.

doi:10.1007/bf03158000

Cited by 5 publications

(6 citation statements)

References 31 publications

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“…which in the zero density limit coincides with the usual definition of the transition operator with the correct reduction formula to calculate cross sections [19]. After proper three-body algebra we arrive at the following equation for the transition operator in medium, viz.…”

Section: Finite Temperature Three-body Equationsmentioning

confidence: 57%

Deuteron formation in nuclear matter

Kuhrts¹,

Beyer²,

Röpke³

2000

Nuclear Physics A

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We investigate deuteron formation in nuclear matter at finite temperatures within a systematic quantum statistical approach. We consider formation through three-body collisions relevant already at rather moderate densities because of the strong correlations. The three-body in-medium reaction rates driven by the break-up cross section are calculated using exact three-body equations (Alt-Grassberger-Sandhas type) that have been suitably modified to consistently include the energy shift and the Pauli blocking. Important quantities are the lifetime of deuteron fluctuations and the chemical relaxation time. We find that the respective times differ substantially while using in-medium or isolated cross sections. We expect implications for the description of heavy ion collisions in particular for the formation of light charged particles at low to intermediate energies.Comment: 19 pages, 5 figure

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Section: Finite Temperature Three-body Equationsmentioning

confidence: 57%

Deuteron formation in nuclear matter

Kuhrts¹,

Beyer²,

Röpke³

2000

Nuclear Physics A

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“…In the zero density limit, this definition coincides with the usual definition of the transition operator with the correct reduction formula to calculate cross sections [30]. Inserting this definition into Eq.…”

Section: Finite Temperature Green Function and Three-body Equationsmentioning

confidence: 62%

Deuteron lifetime in hot and dense nuclear matter near equilibrium

Beyer

Röpke

1997

Phys. Rev. C

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We consider deuteron formation in hot and dense nuclear matter close to equilibrium and evaluate the life-time of the deuteron fluctuations within the linear response theory. To this end we derive a generalized linear Boltzmann equation where the collision integral is related to equilibrium correlation functions. In this framework we then utilize finite temperature Green functions to evaluate the collision integrals. The elementary reaction cross section is evaluated within the Faddeev approach that is suitably modified to reflect the properties of the surrounding hot and dense matter.PACS numbers: 21.65.+f,24.60.-k,25.70.-z 21.45.+v I. INTRODUCTIONThe complicated dynamics of heavy-ion collisions provides a great challenge for many-particle theory. In particular at intermediate energies where the elementary ingredients are rather well known -in terms of constituents and their respective interactions -the main problem arises from a sufficient description of the many-particle aspect. To provide single-particle distribution functions such reactions can be simulated on the basis of kinetic equations as, e.g., supplied by the Boltzmann-Uhlenbeck-Uhling (BUU) approach (see, e.g., Refs. [1][2][3][4][5][6]).However, the formation of light clusters such as deuterons, helium, α-particles, etc., is an important phenomenon of heavy-ion collisions at intermediate energies, see, e.g., Ref. [7]. Empirical evidence, including recent experimental data on cluster formation [8,9], indicate that a large fraction of deuterons can be formed in heavy-ion collisions of energies below E/A ≤ 200 MeV. Also, during the expansion of the system the density can drop below the Mott-density of deuteron dissociation [10][11][12].The description of the formation of such bound states (clusters) during the expansion of hot and dense matter is not as well elaborated as the single-particle distribution. The main obstacle is that the formation of bound states requires the notion of few-body reactions within the medium. Even the simplest case, i.e., the abundances of deuterons that are determined by the deuteron formation via N N N → dN (N nucleon, d deuteron) and break-up, dN → N N N , reactions, requires a proper treatment of the effective three-body problem. Previous studies of the kinetics of deuteron production have utilized the impulse approximation to calculate the reaction cross section at energies above 200 MeV [13]. For lower energies, viz. E/A ≤ 200 MeV, the impulse approximation fails badly and a full three-body treatment of the scattering problem is necessary [14]. Furthermore, a consistent treatment of cluster formation in expanding hot and dense matter requires the inclusion of medium effects into the respective elementary reaction cross sections as has been done in the nucleon nucleon (NN)-case and proven to be substantial in BUUsimulations of heavy-ion reactions [6]. Therefore we present an exact treatment of the three-body problem including medium modifications in mean-field approximation.The cluster formation during the expansion ...

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“…where ḟ (ib) = df (k)/dk provide us with a short-range unique potential (see [24] for a discussion). We mention here that once the rational fit (11) is achieved the extraction of f (k) is obtained from the procedure described by Massen et al [22].…”

Section: Inverse Scattering Methodsmentioning

confidence: 99%

“…A powerful formalism for a systematic treatment of correlations is provided by the Dyson equations approach, for a review see [1]. This approach has been used to derive effective in-medium equations that can be solved rigorously with few-body techniques [2][3][4][5][6][7][8][9][10][11][12][13]. For two-body correlations it leads to equations known as Galitskii-Feynman or Bethe-Goldstone equations [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

In-medium nucleon-nucleon potentials in configuration space

Beyer¹,

Sofianos

2001

J. Phys. G: Nucl. Part. Phys.

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Based on the thermodynamic Green function approach two-nucleon correlations in nuclear matter at finite temperatures are revisited. To this end, we derive phase equivalent effective r-space potentials that include the effect of the Pauli blocking at a given temperature and density. These potentials enter into a Schrödinger equation that is the r-space representation of the Galitskii-Feynman equation for two nucleons. We explore the analytical structure of the equation in the complex k-plane by means of Jost functions. We find that despite the Mott effect the correlation with deuteron quantum numbers are manifested as antibound states, i.e., as zeros of the Jost function on the negative imaginary axis of the complex momentum space. The analysis presented here is also suited for Coulombic systems.

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Three-nucleon calculations with local potentials

Abstract: The integral equations approach to the three-nucleon problem is reviewed. The results of different calculations with local potentials are compare&

Cited by 5 publications

References 31 publications

Deuteron formation in nuclear matter

Deuteron formation in nuclear matter

Deuteron lifetime in hot and dense nuclear matter near equilibrium

In-medium nucleon-nucleon potentials in configuration space

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