BEVATRON RESEARCH MEETING V - HIGH ENERGY NUCLEAR INTERACTION Page: 2 of 5
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UCRL-2396
where thb total number of states is the integral of (2). The density of states per
) unit energy for n particles is then:
S dEF )
TT)This is now integrated over those regions
conservation of momentum, conservation of
gravity. Applying those restrictions oneof phase space which are compatible with
energy, and conservation of the center of
has:S, E P,
Now for convenience, define the function.
JJ ) f(E - EQ )O
Introduce a dummy varia e da and write:UC
4,
r 47,here the contour is just below the real axis. Also
Then one hap for the density of states.
Ce
3-?
C)ciNG-LJCJ ~
(7)
it
s; i
Csf6. ,
C.-) 3( + (9)
Now consider the case for n non-relativistic particles; since the integral is of tho
same form for each particle, suppress the subscripts. Non recall that energy isOne has:
Fl
on(10)
(11)
4-) ~
N QThis loads to tho familiar Gaussian integral:
.Iut.
(5)
(6)
(2)
d. (id-
e tIE -
J<d
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Lepore, Joseph. BEVATRON RESEARCH MEETING V - HIGH ENERGY NUCLEAR INTERACTION, report, November 3, 1953; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc1012123/m1/2/: accessed April 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.