The qualitative and quantitative effects on the line profile of hard and soft velocity-changing collisions with scattering of absorbing molecules at large and small angles, respectively, are considered. It is shown that in the diffusion model of the profile, known as the model of "soft" collisions, scattering at large angles makes a significant contribution comparable to that in the model of hard collisions. The difference between these traditional models lies only in the mathematical forms of the representation of the collision integral, integral and differential, and the following analytical expressions for the profiles. Simple approximate formulas for the profile were derived and tested, which simultaneously took into account hard and soft collisions.
line profile, hard collisions, soft collisions, diffusion
1. Voigt W. Über das gesetz intensitӓtsverteilung innerhalb der linien eines gasspektrams. München, Berlin: Sitzber. Bayr Akad., 1912. 603 p.
2. Galatry L. Simultaneous effect of Doppler and foreign gas broadening on spectral lines // Phys. Rev. 1961. V. 122. P. 1218−1223.
3. Podgoretskij M.I., Stepanov A.V. K voprosu o doplerovskoj shirine linij ispuskaniya i pogloshcheniya // ZHETF. 1961. V. 40, N 2. P. 561–566.
4. Nelkin M., Ghatak A. Simple binary collision model for Van Hove's Gs(r, t) // Phys. Rev. 1964. V. 135. P. A4–A9.
5. Rautian S.G., Sobel'man I.I. Vliyanie stolknovenij na doplerovskoe ushirenie spektral'nyh linij // Uspekhi fiz. nauk. 1966. V. 90, N 2. P. 209–236.
6. Rautian S.G. Nekotorye voprosy teorii gazovyh kvantovyh generatorov // Tr. FIAN. 1968. V. 43. P. 3–115.
7. Dicke R.H. The effect of collisions upon the Doppler width of spectral lines // Phys. Rev. 1953. V. 89. P. 472–473.
8. Wittke J.P., Dicke R.H. Redetermination of the hyperfine splitting in the ground state of atomic hydrogen // Phys. Rev. 1956. V. 103. P. 620–631.
9. Duggan P., Sinclair P.M., Berman R., May A.D., Drummond J.R. Testing lineshape models: Measurements for ν = 1–0 CO broadened by He and Ar // J. Mol. Spectrosc. 1997. V. 186, N 1. P. 90–98.
10. Ciuryło R., Jaworski R., Jurkowski J., Pine A.S., Szudy J. Spectral line shapes modeled by a quadratic speed-dependent Galatry profile // Phys. Rev. A. 2001. V. 63, N 3. P. 032507−7. DOI: 10.1103/PhysRevA63.032507.
11. Duggan P., Sinclair P.M., May A.D., Drummond J.R. Line-shape analysis of speed-dependent collisional width inhomogeneities in CO broadened by Xe, N2, and He // Phys. Rev. A. 1995. V. 51, N 1. P. 218–224.
12. Ciuryło R. Shapes of pressure- and Doppler-broadened spectral lines in the core and near wings // Phys. Rev. A. 1998. V. 58, N 2. P. 1029–1039.
13. De Vizia M.D., Castrillo A., Fasci E., Moretti L., Rohart F., Gianfrani L. Speed dependence of collision parameters in the H218O near-IR spectrum: Experimental test of the quadratic approximation // Phys. Rev. A. 2012. V. 85, N 6. P. 062512–7. DOI: 10.1103/PhysRevA. 85.062512.
14. Tran H., Hartmann J.-M., Chaussard F., Gupta M. An isolated line-shape model based on the Keilson–Storer function for velocity changes. II. Molecular dynamics simulations and the Q(1) lines for pure H2 // J. Chem. Phys. 2009. V. 131, N 15. P. 154303. DOI: 10.1063/1.3247898.
15. Fertsiger Dzh., Kaper G. Matematicheskaya teoriya protsessa perenosa v gazah. M.: Mir, 1976. 554 p. // Ferziger J.H., Kaper H.G. Mathematical theory of transport processes in gases. Amsterdam–London: North–Holland publ. comp, 1972.
16. Berman P.R., Haverkort J.E.M., Woerdman J.P. Collision kernels and transport coefficients // Phys. Rev. A. 1986. V. 34, N 6. P. 4647–4656.
17. Rautian S.G. Diffuzionnoe priblizhenie v zadache o migratsii chastits v gaze // Uspekhi fiz. nauk. 1991. V. 161, N 11. P. 151–170.
18. Kochanov V.P. Proyavleniya rasseyaniya molekul na malye ugly v konture spektral'nyh linij // ZHETF. 2014. V. 145, N 3. P. 387–404.
19. Kochanov V.P. Combined effect of small- and large-angle scattering collisions on a spectral line shape // J. Quant. Spectrosc. Radiat. Transf. 2015. V. 159. P. 32–38.
20. Kochanov V.P. Speed-dependent spectral line profile including line narrowing and mixing // J. Quant. Spectrosc. Radiat. Transf. 2016. V. 177. P. 261–268.
21. Kochanov V.P. Algebraicheskaya approksimatsiya kontura spektral'nyh linij s uchetom sil'nyh i slabyh po skorostyam stolknovenij // Optika atmosf. i okeana. 2015. V. 28, N 5. P. 474–479. DOI: 10/15372/AOO20150510; Kochanov V.P. Algebraic approximation of the spectral line profile with allowance for hard and soft speed-related collisions // Atmos. Ocean. Opt. 2015. V. 28, N 5. P. 394–399. DOI: 10.1134/S1024856015050085.
22. Kochanov V.P., Ptashnik I.V. Approksimatsiya shiriny suzhennogo stolknoveniyami kontura linii // Optika i spektroskopiya. 2000. V. 89, N 5. P. 736–742.
23. Claveau C., Henry A., Hurtmans D., Valentin A. Narrowing and broadening parameters of H2O lines perturbed by He, Ne, Ar, Kr and nitrogen in the spectral range 1850–2140 cm-1 // J. Quant. Spectrosc. Radiat. Transfer. 2001. V. 68, N 3. P. 273–298. DOI: 10.1016/S0022-4073(00)00025-X.
24. Andreeva T.L. Uravnenie diffuzii dlya matritsy plotnosti // ZHETF. 1968. V. 54, N 2. P. 641–651.
25. Alekseev V.A., Andreeva T.L., Sobel'man I.I. Metod kvantovogo kineticheskogo uravneniya dlya atomov i molekul i ego prilozheniya k vychisleniyu opticheskih harakteristik gazov // ZHETF. 1972. V. 62, N 2. P. 614–626.
26. Alekseev V.A., Andreeva T.L., Sobel'man I.I. K teorii nelinejnyh rezonansov moshchnosti gazovyh lazerov // ZHETF. 1973. Т. 64, № 3. С. 813–822.
27. Berman P.R. Theory of collision effects on atomic and molecular line shapes // Appl. Phys. 1975. V. 6. P. 283–296.
28. Pestov E.G., Rautian S.G. Polevoe suzhenie spektral'nyh linij // ZHETF. 1973. V. 64, N 6. P. 2032–2045.
29. Rautian S.G., Smirnov G.I., Shalagin A.M. Nelinejnye rezonansy v spektrah atomov i molekul. Novosibirsk: Nauka, 1979. 310 p.
30. Blackmore R. A modified Boltzmann kinetic equation for line shape functions // J. Chem. Phys. 1987. V. 87. P. 791−800. DOI: 10.1063/1.453286.
31. Pestov E.G. Teoriya relaksatsii kvantovyh sistem v sil'nom elektromagnitnom pole // Tr. FIAN. 1988. V. 187. P. 60–116.
32. Kochanov V.P. Vliyanie difraktsii molekul na stolknovitel'noe suzhenie linij // Optika i spektroskopiya. 2000. V. 89, N 5. P. 743–748.
33. Chandrasekar S. Stohasticheskie problemy v fizike i astronomii. M.: Inostr. lit-ra, 1947. 168 p.
34. Spravochnik po spetsial'nym funktsiyam / pod red. M. Abramovitsa i I. Stigan. M.: Nauka, 1979. 830 p.
35. Kochanov V.P. Ekonomichnye approksimatsii konturov Fojgta i Rautiana–Sobel'mana // Optika atmosf. i okeana. 2011. V. 24, N 4. P. 275–278. DOI: 10/15372/AOO20150510; Kochanov V.P. Efficient approximations of the Voigt and Rautian–Sobelman profiles / Atmos. Ocean. Opt. 2011. V. 24, N 5. P. 432–435. DOI: 10.1134/S1024856011050071.
36. Kochanov V.P. On one-dimensional velocity approximation for speed-dependent spectral line profiles // J. Quant. Spectrosc. Radiat. Transf. 2013. V. 121. P. 105–110.
37. Berman P.R. Speed-dependent collisional width and shift parameters in spectral line profiles // J. Quant. Spectrosc. Radiat. Transf. 1972. V. 12. P. 1331–1342.
38. Kochanov V.P. On parameterization of spectral line profiles including the speed-dependence in the case of gas mixture // J. Quant. Spectrosc. Radiat. Transf. 2017. V. 189. P. 18–23. DOI: 10.1016/j.jqsrt.2016.11.007.
39. Kochanov V.P., Morino I. Methane line shapes and spectral line parameters in the 5647–6164 cm-1 region // J. Quant. Spectrosc. Radiat. Transf. 2018. V. 206. P. 313–322. DOI: 10.1016/j.jqsrt.2017.12.006.
40. Kochanov V.P. Line profiles for the description of line mixing, narrowing, and dependence of relaxation constants on speed // J. Quant. Spectrosc. Radiat. Transf. 2011. V. 112. P. 1931–1941.
41. Rautian S.G. Universal'nyj asimptoticheskij kontur spektral'noj linii pri malom doplerovskom ushirenii // Optika i spektroskopiya. 2001. V. 90, N 1. P. 36–47.