We present Green Bank Telescope ( GBT ) observations of the 3 _ { \mbox { 12 } } -3 _ { \mbox { 13 } } ( 29 GHz ) and 4 _ { \mbox { 13 } } -4 _ { \mbox { 14 } } ( 48 GHz ) transitions of the H _ { \mbox { 2 } } CO molecule toward a sample of 23 well-studied star-forming regions .
Analysis of the relative intensities of these transitions can be used to reliably measure the densities of molecular cores .
Adopting kinetic temperatures from the literature , we have employed a Large Velocity Gradient ( LVG ) model to derive the average hydrogen number density [ n ( H _ { \mbox { 2 } } ) ] within a 16 \arcsec beam toward each source .
Densities in the range of 10 ^ { \mbox { 5.5 } } –10 ^ { \mbox { 6.5 } } cm ^ { \mbox { -3 } } and ortho-formaldehyde column densities per unit line width between 10 ^ { \mbox { 13.5 } } and 10 ^ { \mbox { 14.5 } } cm ^ { \mbox { -2 } } ( km s ^ { \mbox { -1 } } ) ^ { \mbox { -1 } } are found for most objects , in general agreement with existing measurements .
A detailed analysis of the advantages and limitations to this densitometry technique is also presented .
We find that H _ { \mbox { 2 } } CO 3 _ { \mbox { 12 } } -3 _ { \mbox { 13 } } /4 _ { \mbox { 13 } } -4 _ { \mbox { 14 } } densitometry proves to be best suited to objects with T _ { \mbox { K } } \gtrsim 100 K , above which the H _ { \mbox { 2 } } CO LVG models become relatively independent of kinetic temperature .
This study represents the first detection of these H _ { \mbox { 2 } } CO K -doublet transitions in all but one object in our sample .
The ease with which these transitions were detected , coupled with their unique sensitivity to spatial density , make them excellent monitors of density in molecular clouds for future experiments .
We also report the detection of the 9 _ { \mbox { 2 } } –8 _ { \mbox { 1 } } A ^ { \mbox { - } } ( 29 GHz ) transition of CH _ { \mbox { 3 } } OH toward 6 sources .