Short range exchange contributions to the cross section forpp→ppπ0near threshold

Abstract

The nuclear S-wave pion production is described by the axial charge density operator of the twonucleon system. It is shown that the short range axial exchange charge operator implied by the nucleon-nucleon interaction enhances the predicted cross section for the reaction pp-+pp7t° near threshold by factors 3-5. This suffices to explain most of the underprediction obtained with the single-nucleon and S-wave pion rescattering operator. The result implies that the cross section for pp -+ ppn° can provide direct information on the short range components of the nucleon-nucleon interaction.PACS numbers: 13.75. Cs, 11.40.Fy, 21.30.+y, 25.40.Qa Nuclear S-wave pion absorption and production reactions are conventionally described by a single nucleon and a pion rescattering mechanism, according to which the pion scatters off one nucleon by an S-wave collision, and is absorbed (produced) on a second nucleon [1][2][3][4]. The key element of this description is a phenomenological effective Hamiltonian //=4;rm n X 2 >• 0y/+4;r-^V T * f^ny/(1) m:that describes the rescattering vertex. The two coupling constants ^i and X 2 are determined by the S\\ and 531 pion nucleon scattering lengths a\ and a 3 as , _ -1 1+-m" m N (<2j+2#3) , X 2 sss -m Jl o 1 + m n m N (a\ -a?,) . (2a) (2b) With the values a\-0.245 fm and #3--0.143 fm of Hohler et al [5], one obtains \\ =0.005, ^2 = 0.05, and with Arndt, Ford, and Roper [6] values a\ =0.23 fm and a 3 = -0.11 fm, one obtains ^1 = -0.0013 and >. 2 =0.047. The notable feature of the effective interaction Eq.(1) is the smallness of the coefficient X\. The pion rescattering mechanism induced by the second larger term in Eq.(1) has an antisymmetric isospin dependence T'XT 2 , and hence does not contribute to the pp-^ppx 0 reaction. The contribution of the S-wave rescattering mechanism to the rate for pp-*ppx 0 is therefore very small. This is borne out by detailed calculations [7,8], which show that the predicted cross section for pp-^ppn 0 near threshold is 4-5 times smaller than the empirical values [9] when described by this rescattering amplitude combined with the amplitude for absorption on a single nucleon. We here show that most of this underprediction is removed when the short range two-nucleon mechanisms that are implied by the nucleon-nucleon interaction are taken into account. The result implies that the reaction of pp-*ppn° near threshold may prove useful for discrimination between different nucleon-nucleon interaction models.The most coherent framework for taking into account the short range exchange contributions is to describe the pion-nucleus interaction by the direct extension of Weinberg's effective pion-nucleon interaction [10] to nuclei:where 0 is the isovector pion field operator and A^ is the isovector axial current of the nuclear system. This extension of the Weinberg Lagrangian appears naturally, e.g., in the Skyrme model [11], and reduces the calculation of matrix elements for nuclear pion production to the construction of the axial current operator, which is formed of ...

pp→pK+Λreaction in an effective Lagrangian model

“…On the other hand, the σ meson exchange, which models the CTPE in the ππ S-wave and provides about 2/3 of this exchange in the low energy N N interaction, plays a relatively more important role. This observation has also been made in the case of N N → N N π reaction [58][59][60]30,31]. Thus, the σ meson exchange provides an efficient means of mediating the large momentum mismatch involved in the meson production reactions in N N collisions, particularly at lower beam momenta.…”

“…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.…”

The reaction pp → ppπ0 near threshold

“…Indeed the gures shown in refs. 6,7] suggest that the contributions from heavy-meson exchange modify the dependence of the cross section to the right direction. However, it is unlikely that these modi cations will be su cient to remedy the discrepancy observed in our calculation.…”

“…As a consequence it was argued in ref. 6] that the reaction pp ! pp 0 could provide direct information on the short range part of the NN force.…”

Observation of the Charge Symmetry Breakingd+d→He4+π0Reaction Near Threshold

“…On the basis of chiral power counting arguments, the leading terms are expected to be [16] those related to π − η mixing [17] and CSB π + N scattering [3]. Preliminary plane wave calculations [16] suggest that π − η mixing may be important because all four nucleons contribute coherently, especially if the η is produced by two nucleons via the exchange of a heavy meson, as in p + p → p + p + π 0 [18]. The effects of pion scattering are also expected to be enhanced by the initial-state d + d interactions [16].…”