Calculation of the probability of overlapping one family of nuclear levels with resonances of an independent family Page: 3 of 8
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Let R(6) and Q(f) deaLe Lhe proh-ihi LiLy densi.t [s to rEnd to one
side and a distance S and G from a class 1 resonance, a class 2 and a
class 1 resonance, respectively, as a first neighbor. The probability
density that a class 1 resonance has a class 2 first neighbor around 6 to
either side is given by
p(6) = 2 R(6) f Q(0) dg + 2 R(G) R(;) dl (1)
0 5
The first term in Eq. (1) states the probability of having a class 2
resonance to one side gnd a eli 1 resonance to the oLher side; the
second term states the probability of having two class 2 resonances, one
to each side of the class 1 resonance. The factor 2 appears because we
do not distinguish between class 2 resonances tihat appear to either side
of the class I resonance.
The probability distributions f1(6) and (2(0) are related to Lhe level
distributions of the two families of resonances, n (D) and I2 (D), as
follows:
R(6) = g(6,1),) nf 71(1)) dD (2)
6
and
Q(;) = sjD) f g(oh2) do , (3)
U
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Difilippo, F. C. Calculation of the probability of overlapping one family of nuclear levels with resonances of an independent family, article, January 1, 1982; Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc1056862/m1/3/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.