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critical density cagâli-ye paržani Fr.: densité critique 1) c is the → speed of light,
G is the → gravitational constant, and
H the → _{t}Hubble parameter.
The critical density is currently 9.3 × 10^{-30}g cm^{-3},
about 6 hydrogen atoms per cubic meter
(for H = 70 km s_{0}^{-1} Mpc^{-1}). 2) In → gravitational lensing, the minimum density that
would be needed by an intervening object to bend light rays.
It is expressed by:
Σ = (c^{2}/4πG)(d),
where _{os}/d_{ol}d_{ls}c is the speed of light, G is
the gravitational constant,
d, _{os}d, and _{ol}d
represent angular diameter distances between the observer and the source,
the observer and the lens, and the lens and the source respectively.
It has units of mass per unit solid angle. _{ls}3) Radiative processes: The density at which the collisional
→ de-excitation rate
equals the → radiative transition rate.
The critical density for level j is given by:
n,
where _{c} = Σ_{i < j} A_{ji} = Σ_{i ≠ j} q_{ji}A is the → _{ji}Einstein coefficient of
→ spontaneous emission
and q is the rate for collisional de-excitation
of → _{ji}energy level j, summed over all possible processes.
This expression often simplifies to the ratio
of two numbers, since in many cases there is a single
important path for emission and a dominant collisional de-excitation process.
In the low density limit the → emissivity
is proportional to the product
N (electron density) x _{e}N (ion density),
whereas for densities exceeding the critical density, the emissivity is proportional to
_{i}N. Thus, line emission in a nebula occurs most efficiently near
the critical density._{i} |