Absorption intensities of the multipole-field-induced double transitions involving a homonuclear-heteronuclear pair of hydrogen molecules in condensed phase

Abstract

Theoretical expressions are derived for the integrated absorption coefficients of various zero-phonon double transitions involving a homonuclear-heteronuclear pair of hydrogen molecules in condensed phase. The formulas given in this paper can be applied to transitions in the absorption spectra of solid parahydrogen ͑or orthodeuterium, or solid HD, HT, etc.͒ matrices that contain a low concentration of impurity molecules which do not possess a permanent dipole moment ͑e.g., N 2 ).

Absorption intensities of multipole-field-induced double transitions involving orthohydrogen pairs in a solid parahydrogen crystal

“…Consequently, there are degeneracies involved in the final composite rovibrational state. Considering only the radial part of ͉f͘ we find that ͉1v 1 , 24 These features have been kept track of in the intensity derivation. The intensity formulas of Table I are derived for the line as a whole, without considering the details of fine structure components.…”

“…The orientation of the intermolecular axis does not affect the value of absorption coefficient, ␣ ͑1,k͒, for a double transition. [22][23][24] We exploit this freedom to locate a laboratory fixed coordinate system XYZ whose origin is at the center of mass (CM) of molecule 1 and the Z axis passes through the CM of the lone ortho-H 2 molecule k, say, nearest neighbor. Thus the location of the CM of molecule k is specified by the position vector R 1k = k R 1k (R 1k = a, lattice constant, k unit vector along Z axis).…”

Effect of orthohydrogen impurity on the absorption intensities of single transitions in a solid parahydrogen crystal

“…(1) and (2) are to be multiplied by the appropriate phonon renormalization factors n 2 s or n d , which correct the rigid lattice sums for the zero-point motions [13][14][15][16][17][18][19][20]. The phonon renormalization factors are not easily amenable for calculations, a priori and it is customary to set them equal to unity.…”

“…In solid hydrogen, since the transitions originate due to multipolar induction, the internal energy of a single molecule (single transition) or a pair of molecules (double transitions) is changed upon absorption of a single photon. The expressions for the intensity of single and double transitions involve sums over the entire lattice [13][14][15][16][17][18][19][20]. In case of single transitions, the lattice sums are affected by the cancellation effect due to crystal-symmetry.…”

“…Study of absorption intensity of multipole field-induced transitions in solid hydrogen has provided, over the years, a fundamental testing ground for both theory and experiment [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. In solid hydrogen, since the transitions originate due to multipolar induction, the internal energy of a single molecule (single transition) or a pair of molecules (double transitions) is changed upon absorption of a single photon.…”