1 - Sociedade Brasileira de Física

The first order curves E(m,w) area gccdapproximatial
to the envelopes of the exact poles E(n;miu).-To lmateEn ,
no.
look for the point on each curve with horizontal tangent,
i.e. Write
0 dE dW JP (w) dJP dW + m
du dm 2n 2m dW dw
t f
-1 T
hence J P = 2am
Eq. (2) then shows E = W, therefore: the approximate energy
levels are those values of W which satisfy
JP (W) = 2ffm (m integer)
This is the Bohr-Sommerfeld-like quantization rule of Levit,
Negele, and Paltiel (Phys. Rev. C21, 1603 (1980)) derived.
in a completely new way.
Higher-order corrections have been worked out by
summing classes of diagrams. This is the subject of next
section. But first I show numerical results for the Lipkin
model, N = 8, and two values of x, x = 0.8 and x = 0.95.
The column on the right shows the exact answer, while that
on the left gives the results of the above quantization ru
25
no
I