The Nucleon-Nucleon Effective Range Expansion Parameters

Noyes, H. Pierre

doi:10.1146/annurev.ns.22.120172.002341

Cited by 121 publications

(63 citation statements)

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“…(52) - (53), Γ N * is the total width of the resonance which is introduced in the denominator term (p 2 − m 2 N * ) to account for the fact that the resonances are not the stable particles; they have a finite life time for the decay into various channels. Γ N * is a function of the center of mass momentum of the decay channel, and it is taken to be the sum of the widths for pion and rho decay (the other decay channels are considered only implicitly by adding their branching ratios to that of the pion channel)…”

Section: E Propagatorsmentioning

confidence: 99%

“…(29) and p cm πR is given by the same equation with m N * replaced by p of Eqs. (52) - (53). Γ 0 is taken to be the total on-shell width of the resonance minus the corresponding width for the nucleon-ρ meson decay channel.…”

Section: E Propagatorsmentioning

confidence: 99%

“…This allows us to express the amplitudes t i in terms of the inverse of the Jost function, J ℓi (q i ) [52,31]. In the analysis presented in this paper we assume ℓ i = 0, for all the three pairs j − k and use the modified Cini-FubiniStanghellini formula [53] for the effective range expansion of the phase-shift (δ 0i ) of the relevant pair 59) to calculate the corresponding Jost function. It may be noted that in case of the pair j − k involving uncharged particle(s), the second terms on the left hand side of Eq.…”

Section: G Final State Interactionmentioning

confidence: 99%

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pp→pK+Λreaction in an effective Lagrangian model

Shyam

1999

Phys. Rev. C

128

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We investigate the pp → pK + Λ reaction within an effective Lagrangian model where the contributions to the amplitudes are taken into account within the tree level. The initial interaction between the two nucleons is modeled by the exchange of π, ρ, ω and σ mesons and the ΛK + production proceeds via the excitation of the N * (1650), N * (1710), N * (1720) baryonic resonances. The parameters of the model at the nucleon-nucleon-meson vertices are determined by fitting the elastic nucleon-nucleon scattering with an effective interaction based on the exchange of these four mesons, while those at the resonance vertices are calculated from the known decay widths of the resonances as well as the vector meson dominance model. Available experimental data is described well by this approach. The one-pion-exchange diagram dominates the production process at both higher and lower beam energies. The ρ and ω meson exchanges make negligible contributions. However, the σ-exchange processes contribute substantially to the total cross sections at lower beam energies. The excitation of the N * (1710) and N * (1650) resonances dominate this reaction at beam momenta above and below 3 GeV/c respectively. The interference among the amplitudes of various resonance excitation processes is significant. For beam energies very close to the K + production threshold the hyperon-proton final state interaction effects are quite important. The data is selective about the model used to describe the low energy scattering of the two final state baryons.

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Section: E Propagatorsmentioning

confidence: 99%

Section: E Propagatorsmentioning

confidence: 99%

Section: G Final State Interactionmentioning

confidence: 99%

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pp→pK+Λreaction in an effective Lagrangian model

Shyam

1999

Phys. Rev. C

128

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“…The phase-shifts δ pp ( 1 S 0 ) are calculated according to the modified Cini-Fubini-Stanghellini formula including the Wong-Noyes Coulomb correction [22,23,24], [28]. In this case |M pp→pp | 2 is a dimensionless factor which approaches zero as the relative proton momentum k→0, peaks sharply at k ≈ 25 MeV/c, and asymptotically approaches unity for large relative proton-proton momentum.…”

Section: Introductionmentioning

confidence: 99%

“…The phase-shifts δ pp ( 1 S 0 ) are calculated according to the modified Cini-Fubini-Stanghellini formula including the Wong-Noyes Coulomb correction [22,23,24],…”

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confidence: 99%

S-wave η′-proton FSI; phenomenological analysis of near-threshold production of π0, η, and η′ mesons in proton-proton collisions

et al. 2000

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We describe a novel technique for comparing total cross sections for the reactions pp → ppπ 0 , pp → ppη, and pp → ppη ′ close to threshold. The initial and final state proton-proton interactions are factored out of the total cross section, and the dependence of this reduced cross section on the volume of phase space is discussed. Different models of the proton-proton interaction are compared. We argue that the scattering length of the S-wave η ′ -proton 1 interaction is of the order of 0.1 fm. PACS: 13.60. Le, 13.85.Lg, 29.20.Dh Typeset using REVT E X 2 New results on η and η ′ meson production in the reaction pp → ppX, measured very recently at the COSY-11 facility [1,2], together with previous data [3,4,5,6,7,8], determine the energy dependence of the near-threshold total cross section with a precision comparable to the measurements of the reaction pp → ppπ 0 [9,10]. These new data encouraged us to perform a phenomenological analysis similar to those of references [11,12,13]. Here we concentrate on π 0 , η, and η ′ meson production, and complete the analysis of these references by taking into account the interaction between the incident protons, and by introducing a new representation of the data. The production rates of π 0 , η, and η ′ mesons will be compared as a function of the available phase space. We will study the phase-space dependence of the quantity |M 0 | which is derived from the total cross section with the ISI and pp-FSI factored out. Consideration of the dependence of |M 0 | on phase space allows us to infer the η-proton and η ′ -proton interactions. To avoid large ambiguities due to differences in pp-FSI models, we normalize the |M 0 | for η and η ′ mesons to the one for the π 0 meson and show that the resulting η ′ -proton interaction is comparable to the π 0 -proton one.In general, the total cross section is presented as a function of the dimensionless parameter η M [9,10,12] 1 , which is defined as the maximum meson momentum in units of meson mass (η M = q max M ), or as a function of the center-of-mass excess energy Q [3,6,8], where nonrelativistically these variables are related by:with m p and M denoting the proton and meson mass, respectively. The above equationshows that the proportionality factor between the variables Q and η 2 M changes for different mesons, since the masses of the π 0 , η, and η ′ are distinct. Hence, depending which variable is selected, the relation between the cross section values changes for different mesons. For example, as shown in reference [4] the η meson production-cross-section exceeds the π 0 cross 1 In order to avoid ambiguities with the abbreviation for the eta-meson, we introduce an additional suffix M for this parameter, which usually is called η.3 section by about a factor of five using η M , whereas the π 0 meson cross section is always larger when employing the Q scale.The total cross section for pp → ppX is in general an integral over phase space, weighted by the square of the transition matrix element and normalized to the incoming fl...

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1998

Introductory Nuclear Physics

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The Nucleon-Nucleon Effective Range Expansion Parameters

Cited by 121 publications

References 1 publication

pp→pK+Λreaction in an effective Lagrangian model

pp→pK+Λreaction in an effective Lagrangian model

S-wave η′-proton FSI; phenomenological analysis of near-threshold production of π0, η, and η′ mesons in proton-proton collisions

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