Summary
It is shown that equations for average path length, average projected range, average number of primary recoils and a particular Boltzmann’s equation belong to the same family of equations. The solutions of Boltzmann’s equation are Green’s functions for the family. This allows us to transfer validity and theoretical support of range equations to radiation damage equations and can be used to improve our knowledge in radiation damage field.
Riassunto
Si dimostra che le equazioni per quantità medie relative al cammino percoiso, al range proiettato, al numero di primari rinculanti ed una particolare equazione lineare di Boltzmann appartengono alla stessa famiglia di equazioni. Le soluzioni dell’equazione di Boltzmann sono le funzioni di Green della famiglia. Una tale relazione trasferisce la stessa validità delle equazioni per il range alle equazioni per il danneggiamento, e pertanto può essere utilizzata per aumentare la nostra conoscenza in alcuni processi di danneggiamento.
Резюме
Показывается, что уравнения для средней длины траектории, среднего пробега, среднего числа первично смещенных атомов и линейное уравнение Ъоьцмана принадлежат одному семейству уравнений. Рещения уравнения Ъольцмана представляют функции Грина этого семейства. Указанная связь позволяет нам перенести известмые результаты для уразнений пробегов на уравнения, описывающие радиационные повреждения.
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Falcone, G. A connection among range, damage and linear Boltzmann equation. Il Nuovo Cimento D 6, 64–74 (1985). https://doi.org/10.1007/BF02451141
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DOI: https://doi.org/10.1007/BF02451141