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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This article is concerned with the construction of the general algorithm for evaluating twocenter, two-and three-electron integrals occurring in matrix elements of one-electron operators in the basis of variational correlated functions. This problem has been solved here in prolate spherical coordinates, using the modified and extended form of the Neumann expansion of the interelectronic distance function rt derived in Part I of this series for k = -1,O, 1,2. This work expands the method proposed by one of us in the preceding paper for integrals of the types mentioned above. The results of numerical calculaticns for different types of the two-and threeelectron integrals are presented. The problem of convergence of the proposed procedures used is also discussed.

The modified and extended version of the Neumann expansion of the interelectronic distance function i$ for u = -1,0, 1,2, using the set of orthogonal polynomials normalized to unity, is presented. This expansion has been utilized to obtain analytical expressions for evaluating twocenter two-and three-electron integrals in the Slater orbital basis occurring if variational correlated functions are used.