We present a new ultra-violet spectrum of the QSO 0013 - 004 with 0.9 Å resolution obtained with the MMT Blue spectrograph .
The \upsilon = 0 - 0 , 1 - 0 , 2 - 0 and 3 - 0 Lyman bands of H _ { 2 } associated with the z = 1.9731 damped Ly \alpha absorption line system have been detected .
The H _ { 2 } column density is N ( H _ { 2 } ) = 6.9 ( \pm 1.6 ) \times 10 ^ { 19 } cm ^ { -2 } , and the Doppler parameter b = 15 \pm 2 km s ^ { -1 } .
The populations of different rotational levels are measured and used to derive the excitation temperatures .
The estimated kinetic temperature T _ { K } \sim 70 K , and the total particle number density n ( H ) \sim 300 cm ^ { -3 } .
The UV photoabsorption rate \beta _ { 0 } \sim 6.7 \times 10 ^ { -9 } s ^ { -1 } , about a factor of few times greater than that in a typical diffuse Milky Way interstellar cloud .
The total hydrogen column density is N ( H ) = 6.4 ( \pm 0.5 ) \times 10 ^ { 20 } cm ^ { -2 } .
The fractional H _ { 2 } abundance f = 2N ( H _ { 2 } ) / ( 2N ( H _ { 2 } ) + N ( H I ) ) \sim 0.22 \pm 0.05 is the highest among all observed damped Ly \alpha absorbers .
The high fractional H _ { 2 } abundance is consistent with the inferred presence of dust and strong C I absorption in this absorber .