AbstractsI t is shown that any expectation value of any observable associated with a molecule is the sum of loge contributions and of loge pair contributions. This result provides a rigorous theoretical basis for the study of additive properties of molecules.I t is demonstrated that molecular wave functions (exact or approximate) can be expressed as a sum of functions corresponding to the various electronic events. Furthermore any of these event functions can be expressed in terms of correlated loge functions. This expression suggests many kinds of variational procedures of calculating wave functions (known methods and new ones).The case in which noncorrelated completely localized loge functions are used is discussed. If continuous functions are used the variational equation reduces to a sum of independent variational equations, each one corresponding to a particular electronic event. This is not so when discontinuous functions are used or when a delocalized function is added to replace the correlation interloge function.The noncorrelated completely localized loge model is analyzed in more detail. I t is seen that local spin operators can be introduced and that each event density operator is the product of the loge density operators. Therefore that model is an independent loge model. The corresponding generalized self-consistent field equations are derived. This treatment helps us to understand how a localized state of a molecule can produce an ion containing a deIocalized region, a phenomenon which is sometimes at the origin of some misunderstanding in photoelectron spectroscopy. Finally it is seen how virtual loge functions can be introduced to describe excited states. I1 est dtmontrt que chaque valeur moyenne d'un observable associt B une moltcule est la somme de contributions de loges et de paires de loges. Ce rtsultat fournit une base thtorique rigoureuse pour l'ttude des proprittts additives des moltcules. I1 est dtmontrk, que les fonctions d'onde moltculaires (exactes ou approchtes) peuvent itre exprimtes comme une somme de fonctions qui correspondent aux tvhements
The creation of an electron–positron pair in the collision of two real photons, namely the linear Breit–Wheeler process, has never been detected directly in the laboratory since its prediction in 1934 despite its fundamental importance in quantum electrodynamics and high energy astrophysics. In the last few years, several experimental setup have been proposed to observe this process in the laboratory, relying either on thermal radiation, Bremsstrahlung, linear or multiphoton inverse Compton scattering photons sources created by lasers or by the mean of a lepton collider coupled with lasers. In these propositions, the influence of the photons’ energy distribution on the total number of produced pairs has been taken into account with an analytical model only for two of these cases. We hereafter develop a general and original, semi-analytical model to estimate the influence of the photons energy distribution on the total number of pairs produced by the collision of two such photon beams, and give optimum energy parameters for some of the proposed experimental configurations. Our results shows that the production of optimum Bremsstrahlung and linear inverse Compton sources are, only from energy distribution considerations, already reachable in today’s facilities. Despite its less interesting energy distribution features for the linear Breit–Wheeler pair production, the photon sources generated via multiphoton inverse Compton scattering by the propagation of a laser in a micro-channel can also be interesting, thank to the high collision luminosity that could eventually be reached by such configurations. These results then gives important insights for the design of experiments intended to detect linear Breit–Wheeler produced positrons in the laboratory for the first time.
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