Context :

Aims : We aim to reveal the physical properties and chemical composition of the cores in the California molecular cloud ( CMC ) , so as to better understand the initial conditions of star formation .

Methods : We made a high-resolution column density map ( 18.2 ” ) with Herschel data , and extracted a complete sample of the cores in the CMC with the fellwalker algorithm .
We performed new single-pointing observations of molecular lines near 90 GHz with the IRAM 30m telescope along the main filament of the CMC .
In addition , we also performed a numerical modeling of chemical evolution for the cores under the physical conditions .

Results : We extracted 300 cores , of which 33 are protostellar and 267 are starless cores .
About 51 % ( 137 of 267 ) of the starless cores are prestellar cores .
Three cores have the potential to evolve into high-mass stars .
The prestellar core mass function ( CMF ) can be well fit by a log-normal form .
The high-mass end of the prestellar CMF shows a power-law form with an index \alpha = -0.9 \pm 0.1 that is shallower than that of the Galactic field stellar mass function .
Combining the mass transformation efficiency ( \varepsilon ) from the prestellar core to the star of 15 \pm 1 \% and the core formation efficiency ( CFE ) of 5.5 % , we suggest an overall star formation efficiency of about 1 % in the CMC .
In the single-pointing observations with the IRAM 30m telescope , we find that 6 cores show blue-skewed profile , while 4 cores show red-skewed profile .
The molecular line detection rates of C _ { 2 } H ( 1 - 0 ) , HCN , HCO ^ { + } ( 1 - 0 ) , and HNC in the protostellar cores are higher than those in the prestellar cores .
The detection rates of the H ^ { 13 } CO ^ { + } ( 1 - 0 ) , HN ^ { 13 } C ( 1 - 0 ) , and N _ { 2 } H ^ { + } ( 1 - 0 ) in the cores are higher than reference positions that are offset from the cores .
[ HCO ^ { + } ] / [ HNC ] and [ HCO ^ { + } ] / [ N _ { 2 } H ^ { + } ] in protostellar cores are higher than those in prestellar cores ; this can be used as chemical clocks .
The best-fit chemical age of the cores with line observations is \sim 5 \times 10 ^ { 4 } years .

Conclusions :