No, in longitudinal waves, particles of the medium do not move from one place to another; they simply oscillate back and forth about their position of rest.

Sound waves are classified as longitudinal waves because the individual particles of the medium oscillate back and forth in a direction parallel to the direction of sound propagation.

Rarefactions (R) are the regions where the coils of a slinky are further apart.

In longitudinal waves, particles of the medium move in a direction parallel to the direction of propagation of the disturbance.

The regions where the coils become closer are called compressions (C).