[bar.P] = (Q[eta](Q+[zeta]))[1 + exp(-([zeta] + Q)/[Q.sup.2][eta])/[E.sub.[beta]](([zeta] + Q)/[Q.sup.2][eta])] + (([zeta] 1)/([zeta] + Q)) is the dimensionless power, is the nonlinear damping coefficient, [eta] is the effective noise power, and [zeta] is the supercriticality
parameter defined as (7/Jth).
The largest [[mu].sub.1] such that 1/[[mu].sub.1] is an eigenvalue of the system equation is a measure for the criticality of a reactor, with [[mu].sub.1] < 1 representing subcriticality and [[mu].sub.1] > 1 representing supercriticality
. The aim is to maintain the reactor in the critical phase with [[mu].sub.1] = 1.
Manhattan scientists devised the implosion method of assembly, in which high explosives (lenses) were arranged to form an imploding (inward) shock wave that compressed the fissile material to supercriticality
. The core of fissile material is formed into such a supercritical mass by the chemical high explosives (HE) or propellants.
In Section 4, the results and discussions and the plots constructed by using Mathematica Software are commented and the energy values are given numerically; moreover, the transmission resonance condition for the scattering states and supercriticality are derived and the data obtained in this work are compared with the results achieved in earlier studies.
Conditions for Transmission Resonance and Supercriticality. The aim of this section is to obtain the conditions describing a transmission resonance (providing the requirement that the transmission coefficient is unity) and supercriticality (while the bound state of the Dirac particle is at E = -[m.sub.0]).