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Korda, V. Yu.; Molev, A. S.; Korda, L. P.

doi:10.1103/physrevc.72.014611

“…Table 1 The best-fit parameters for the two models. The third (fourth) column taken from [36,37] to OBEP values in Table 2). All masses are in M eV , and n b = 1 except for nρ = nω = 2.…”

Section: Results Of Numerical Calculations and Their Discussionmentioning

confidence: 99%

The method of unitary clothing transformations in the theory of nucleon–nucleon scattering

Dubovyk¹

2010

EPJ Web of Conferences

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Abstract. The clothing procedure, put forward in quantum field theory (QFT) by Greenberg and Schweber, is applied for the description of nucleon-nucleon (N-N) scattering. We consider pseudoscalar (π and η), vector (ρ and ω) and scalar (δ and σ) meson fields interacting with 1/2 spin (N andN) fermion ones via the Yukawa-type couplings to introduce trial interactions between "bare" particles. The subsequent unitary clothing transformations (UCTs) are found to express the total Hamiltonian through new interaction operators that refer to particles with physical (observable) properties, the so-called clothed particles. In this work, we are focused upon the Hermitian and energy-independent operators for the clothed nucleons, being built up in the second order in the coupling constants. The corresponding analytic expressions in momentum space are compared with the separate meson contributions to the one-boson-exchange potentials in the meson theory of nuclear forces. In order to evaluate the T matrix of the N-N scattering we have used an equivalence theorem that enables us to operate in the clothed particle representation (CPR) instead of the bare particle representation (BPR) with its huge amount of virtual processes. We have derived the Lippmann-Schwinger(LS)-type equation for the CPR elements of the T -matrix for a given collision energy in the two-nucleon sector of the Hilbert space H of hadronic states and elaborated a code for its numerical solution in momentum space. Introductory remarksWe know that there are a number of high precision, bosonexchange models of the two nucleon force V NN , such [6]. Note also successful treatments based on chiral effective field theory [7,8], for a review see [9].In this talk, we would like to draw attention to the first application of unitary clothing transformations [10,11] in describing the nucleon-nucleon (N-N) scattering. Recall that such transformations W, being aimed at the inclusion of the so-called cloud or persistent effects, make it possible the transition from the bare-particle representation (BPR) to the clothed-particle representation (CPR) in the Hilbert space H of meson-nucleon states. In this way, a large amount of virtual processes induced with the meson absorption/emission, the NN-pair annihilation/production and other cloud effects can be accumulated in the creation (destruction) operators α c for the "clothed" (physical) mesons and nucleons. Such a bootstrap reflects the most significant distinction between the concepts of clothed and bare particles. a e-mail: e.a.dubovyk@mail.ru b e-mail: shebeko@kipt.kharkov.uaIn the course of the clothing procedure all the generators of the Poincaré group get one and the same sparse structure on H [10]. Here we will focus upon one of them, viz., the total Hamiltonianwith H I (α) = V(α) + mass and vertex counterterms,where free part H F (α) and interaction V(α) depend on creation (destruction) operators α † (α) in the BPR , i.e., referred to bare particles with physical masses [11], where they have been introduced via the ...

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The Method of Unitary Clothing Transformations in the Theory of Nucleon–Nucleon Scattering

Dubovyk

¹

,

Shebeko

²

2010

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Abstract. The clothing procedure, put forward in quantum field theory (QFT) by Greenberg and Schweber, is applied for the description of nucleon-nucleon (N-N) scattering. We consider pseudoscalar (π and η), vector (ρ and ω) and scalar (δ and σ) meson fields interacting with 1/2 spin (N andN) fermion ones via the Yukawa-type couplings to introduce trial interactions between "bare" particles. The subsequent unitary clothing transformations (UCTs) are found to express the total Hamiltonian through new interaction operators that refer to particles with physical (observable) properties, the so-called clothed particles. In this work, we are focused upon the Hermitian and energy-independent operators for the clothed nucleons, being built up in the second order in the coupling constants. The corresponding analytic expressions in momentum space are compared with the separate meson contributions to the one-boson-exchange potentials in the meson theory of nuclear forces. In order to evaluate the T matrix of the N-N scattering we have used an equivalence theorem that enables us to operate in the clothed particle representation (CPR) instead of the bare particle representation (BPR) with its huge amount of virtual processes. We have derived the Lippmann-Schwinger(LS)-type equation for the CPR elements of the T -matrix for a given collision energy in the two-nucleon sector of the Hilbert space H of hadronic states and elaborated a code for its numerical solution in momentum space. Introductory remarksWe know that there are a number of high precision, bosonexchange models of the two nucleon force V NN , such [6]. Note also successful treatments based on chiral effective field theory [7,8], for a review see [9].In this talk, we would like to draw attention to the first application of unitary clothing transformations [10,11] in describing the nucleon-nucleon (N-N) scattering. Recall that such transformations W, being aimed at the inclusion of the so-called cloud or persistent effects, make it possible the transition from the bare-particle representation (BPR) to the clothed-particle representation (CPR) in the Hilbert space H of meson-nucleon states. In this way, a large amount of virtual processes induced with the meson absorption/emission, the NN-pair annihilation/production and other cloud effects can be accumulated in the creation (destruction) operators α c for the "clothed" (physical) mesons and nucleons. Such a bootstrap reflects the most significant distinction between the concepts of clothed and bare particles. a e-mail: e.a.dubovyk@mail.ru b e-mail: shebeko@kipt.kharkov.uaIn the course of the clothing procedure all the generators of the Poincaré group get one and the same sparse structure on H [10]. Here we will focus upon one of them, viz., the total Hamiltonianwith H I (α) = V(α) + mass and vertex counterterms,where free part H F (α) and interaction V(α) depend on creation (destruction) operators α † (α) in the BPR , i.e., referred to bare particles with physical masses [11], where they have been introduced via the ...

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