mass shell

In mathematically modeling stellar structure (and in 1D models of other spherically-symmetric bodies), the term shell (sometimes termed a mass shell) is used for the region with all the mass within a certain distance interval from the center, a concept useful in constructing differential equations for the model. The shell may be considered "infinitely thin" for the purposes of differential equations, and "thin enough that its thickness doesn't appreciably affect the outcome" for difference equations used in computation.

The term mass shell (often written as mass-shell) is also used with an entirely different meaning in quantum mechanics: a phenomena or concept is referred to as on the shell or off the shell depending upon whether it follows certain classical ("every day") rules regarding the relationship of energy and momentum. This "shell" is the ellipsoid shape of the 3D graph of an equation that shows the possibilities, i.e., the graph of quantities when the rules are followed.