Towards reliable calculations of the correlation function

The correlation function of two identical pions interacting via Coulomb potential is computed for a general case of anisotropic particle's source of finite life time. The effect of halo is taken into account as an additional particle's source of large spatial extension. Due to the Coulomb interaction, the effect of halo is not limited to very small relative momenta but it influences the correlation function in a relatively large domain. The relativistic effects are discussed in detail and it is argued that the calculations have to be performed in the center-of-mass frame of particle's pair where the (nonrelativistic) wave function of particle's relative motion is meaningful. The Bowler-Sinyukov procedure to remove the Coulomb interaction is tested and it is shown to significantly underestimate the source's life time.Comment: 18 pages, presented at XIth International Workshop on Correlation and Fluctuation in Multiparticle Production, Hangzhou, China, November 21-24, 200

Sum rule of the correlation function

We discuss a sum rule satisfied by the correlation function of two particles with small relative momenta. The sum rule, which results from the completeness condition of the quantum states of the two particles, is first derived and then we check how it works in practice. The sum rule is shown to be trivially satisfied by free particle pair, and then there are considered three different systems of interacting particles. We discuss a pair of neutron and proton in the s-wave approximation and the case of the so-called hard spheres with the phase shifts taken into account up to l=4. Finally, the Coulomb system of two charged particles is analyzed.Comment: 18 pages, 18 figures, revised, to appear in Phys. Rev.

Społeczne i ekologiczne aspekty zarządzania

Praca recenzowana / peer-reviewed pape

Współczesne zagadnienia zarządzania: przedsiębiorstwo - biznes - region

Praca recenzowana / peer-reviewed pape

Bishop Michał Korczyński – forgotten servant of Christ. A biographical sketch

Do tej pory brak osobnej biografii biskupa Michała Korczyńskiego, pomimo tego, że dobrze zasłużył się dla Kościoła i dla Polski. Niniejszy szkic jest pierwszą próbą opracowania takiej biografii. Zebrałem w nim rozproszone na ogół informacje doty-czące nie tylko kolejnych etapów życia, ale także obfitej twórczości M. K. Szkic daje możliwość poznania niezwykłego człowieka. Towarzysząc mu w drodze od małego przysiółka w pobliżu Mielca do rezydencji biskupiej w Przemyślu można dostrzec jego pracowitość, pokorę i poczucie obowiązku. Analizując twórczość – troskę o życie religijne i narodowe. Staranie M. K. o wiarę znajduje swój wyraz w takich pra-cach czy tłumaczeniach jak: „Katechizm dla dzieci wiejskich ku wygodzie parochów spisany…”, „Wykład nauki Kościoła katolickiego…”, „Ksiądz Pleban…” a może przede wszystkim pierwsze polskie czasopismo teologiczne „Przyjaciel Chrześcijańskiej Prawdy”. Staranie o polskość – w opracowaniu „Początków gramatyki języka polskiego”, z których obszerne cytaty z mogą zaskoczyć czytelnika.Despite of his obvious merits for the Church and Poland, a separate biography of bishop Michal Korczynski has never been written or published. This study is the first attempt to write such a biography. I gathered various, usually scat-tered, pieces of information about the subsequent phases of M. K’s life as well as his rich literary legacy. This essay provides an opportunity to meet a truly unique man. Accompanying him from a small hamlet near Mielec all the way to the bishop’s residence in Przemysl one may appreciate his work ethic, diligence, humbleness and his sense of duty. While analyzing his work it is impossible not to notice his concern about religious and national matters. M. K’s care and focus on faith is demonstrated in his writings and translations such as “The Catechism for Rural Children…”, „The Lecture of the Cath-olic Church on those articles of faith…”, The Parish Priest…”, and possibly the most visible in the first Polish theological periodical „A Friend of the Christian Truth”. His care about Polishness – in his work on „The Beginnings of the Polish Grammar” – a source of extensive quotations that some readers may find very surprising