Elsevier

Physics Letters B

Volume 441, Issues 1–4, 26 November 1998, Pages 17-26
Physics Letters B

Production of e+ e pairs in proton-deuteron capture to 3He

https://doi.org/10.1016/S0370-2693(98)01197-6Get rights and content

Abstract

The process p+d↔3He at intermediate energies is described using a covariant and gauge-invariant model, and a realistic pd3He vertex. Both photodisintegration of 3He and proton-deuteron capture with production of e+e pairs are studied, and results for cross sections and response functions are presented. The effect of time-like form factors on the dilepton cross sections is investigated as well.

Introduction

The electromagnetic probe is a well-established and powerful tool to investigate the structure of hadronic systems. In exclusive processes one can distinguish three different regimes depending on the four-momentum of the photon. First, in the space-like region (q2<0) in quasi-free kinematics the (e,ep) reaction directly probes the single-particle structure of the nuclear vertex. Second, for real photons, the (γ,p) or (p,γ) reactions are more sensitive to the details of the reaction mechanism and to meson exchange currents (MEC). Third, the rather less well-known time-like region (q2>0), which can be explored using dilepton production, addresses additional aspects as compared to real photons: (i) the coupling of longitudinally polarized photons, (ii) the time-like form factor in the “unphysical” region (4m2e<q2<4m2p). Basically there are two alternatives to explore the time-like region: virtual Compton scattering p(γ,γ)p and the bremsstrahlung processes with virtual photons, such as p+p→p+p+γ and capture reactions.

In this paper we study the capture reaction p+d→3He at intermediate energies (proton energies up to a few hundred MeV) for both real and virtual photons. The main motivation for the present work are experiments at TSL (Uppsala) which in the past have explored [1] only small photon invariant masses (q2<(10 MeV)2) and KVI (Groningen) experiments which cover larger photon invariant masses [2].

Since we feel it is important to satisfy gauge invariance, we start from the covariant impulse approximation model of [3] and make it explicitly gauge invariant by the introduction of an additional internal amplitude. An important input in this approach is the pd3He vertex function, for which recent calculations 4, 5, 6 using a realistic NN interaction (Argonne v14 and v18) are used.

Section snippets

Description of the model

At small photon energies the photon production amplitude is dominated by radiation from the external legs (first three diagrams of Fig. 1), and this consideration led to the development of low-energy theorems (LET)s 7, 8, 9. In kinematical conditions where the photon energy is not small we may still assume the dominance of the above external amplitude, without applying an expansion in powers of the photon energy.

The 4-momenta of the proton, deuteron, 3He nucleus, and (virtual) photon are

Cross section and response functions for dilepton production

The c.m. cross section for the p+d 3He+e++e reaction can be decomposed (in complete analogy to the spacelike (e,ep) reaction) into the sum of products of kinematical factors and four response functions (RFs),dσ(e+e)dΩγdmγdΩe=α2m1m3qcβ16π3mγpcs[WT(1−12β2sin2θ)+WL(1−β2cos2θ)+WTT12β2sin2θcos+WLT122β2sincosφ].Here mγ=q2 is the invariant mass of the virtual photon, s=(m1+m2)2+2m2Tp, Tp is the proton kinetic energy in the lab frame, pc and qc are the c.m. 3-momenta of the proton

Results of calculations and discussion

The model is first tested for the real photon reaction. Fig. 2 (upper panel) shows cross sections for the reaction γ3He→pd at EγLAB = 245 MeV, related to the capture process at TpLAB = 358 MeV via time reversal. Note the unsatisfactory discrepancy between the disintegration and capture reaction measurements, known for a long time and recently pointed out again in Ref. [20]. As seen from the figure the agreement with the photodisintegration data 17, 18 is quite reasonable and considerably better

Acknowledgements

We thank Robert Wiringa for calculating the 3He–d and 3He–d overlap integrals. We would also like to thank Justus Koch, Ulla Tengblad, Jan Ryckebusch and Rob Timmermans for useful discussions, and Betsy Beise for sending data file with the deuteron form factors. This work is supported by the Fund for Scientific Research-Flanders (FWO-Vlaanderen).

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    Permanent address: National Science Center `Kharkov Institute of Physics and Technology', 310108 Kharkov, Ukraine.

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