  We consider entangled state production utilizing a full optomechanical
arrangement, based on which we create entanglement between two far three-level
V-type atoms using a quantum repeater protocol. At first, we consider eight
identical atoms (1; 2;...; 8), while adjacent pairs (i; i + 1) with i = 1; 3;
5; 7 have been prepared in entangled states and the atoms 1, 8 are the two
target atoms. The three-level atoms (1,2,3,4) and (5,6,7,8) distinctly become
entangled with the system including optical and mechanical modes by performing
the interaction in optomechanical cavities between atoms (2,3) and (6,7),
respectively. Then, by operating appropriate measurements, instead of Bell
state measurement which is a hard task in practical works, the entangled states
of atoms (1,4) and (5,8) are achieved. Next, via interacting atoms (4,5) of the
pairs (1,4) and (5,8) and operating proper measurement, the entangled state of
target atoms (1,8) is obtained. In the continuation, entropy and success
probability of the produced entangled state are then evaluated. It is observed
that the time period of entropy is increased by increasing the mechanical
frequency and by decreasing optomechanical coupling strength to the field
modes. Also, in most cases, the maximum of success probability is increased by
decreasing G and via decreasing.
