Particle Lifetimes and Energy Production Rates

The variation of the number of particles "X" in a volume unity due to interactions with particles "a" is (—d nX/dt)a. One defines the lifetime Ta (X) of particles "X" bombarded by "a" as d nx > - nx (9.8)

which means that in a time Ta (X), the number of particles "X" is reduced by a factor e. According to (9.6), one also has (—dnX/dt)a = (1 + 5aX) rax (if "a" = "X" each time there is a reaction, two particles disappear). The particle lifetime is nX 1 Aa mu

where the partial concentration na is expressed in terms of the mass fraction Xa of the particle of atomic mass Aa, na = pXa/(Aamu). If an element "X" is destroyed by several reactions "i", the lifetime of element "X" is given by

because the reactions rates add to each other. The energy production rate £ is the power produced by unit of mass ( 3.40),

where Q(erg) is the energy in ergs liberated by one reaction (1 erg= 1.6022 10—6 Mev, cf. Appendix A.1). Xa and XX are the mass fractions of the elements of atomic mass Aa and AX.

Analytical formulas were provided by Caughlan and Fowler [100]. In practice nowadays, one uses the tabulated values of A^v AaX (= AaX/mu), where NAV is the Avogadro number. The advantage of multiplying by Aav is that the tabulated values are not too small numbers. The values Aav AaX are given in the NACRE Library, available at: http://pntpm.ulb.ac.be/nacre.htm. The reaction rates must be corrected by the effects of screening (cf. Sect. 9.4). There are other web sites providing nuclear reaction rates and cross sections such as http://www-phys.llnl.gov/Research/RRSN.

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