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At the saturation point, all first derivatives of the energy per nucleon
have to vanish and all second derivatives have to be positive. The first
derivative with respect to
is related to the pressure, the second
derivative with respect to
is related to the incompressibility,
and the second derivatives with respect to the I_{i} is related to the
asymmetry coefficients. For symmetric matter, the first derivatives with
respect to the I_{i} vanish because the energy per nucleon is an even
function of all I_{i}s.
The pressure is given by

(48) 
which gives
The incompressibility is defined as

(50) 
which, for the Skyrme energy functional (49) at the
saturation point (
,
)
gives
The asymmetry coefficients are:

= 



= 

(52) 

= 



= 

(53) 

= 



= 

(54) 
Here,
is the wellknown volume asymmetry coefficient of the
liquiddrop model, and
and
are its
generalizations to the spin and spinisospin channels of the interaction.
At the saturation point, all asymmetry coefficients have to be positive.
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Jacek Dobaczewski
20020315