Abstract
It is well-known that molecules show electronic, vibrational, and rotational degrees of freedom. In principle, by taking into account the role of these degrees of freedom, it is possible to accurately describe chemical reactions at room temperature. However, at ultracold temperatures is necessary to go one step further and include some subtle effects on the molecular Hamiltonian. In particular, it is necessary to include the fine and hyperfine splitting of the molecular states and the interaction among them [1, 2]. The interactions emerge as a consequence of diverse couplings between the nuclear spin, molecular rotation, and electron spin [1, 2].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Please, note that the \(\hat {\mathbf {r}}\) stands for the unit vector of the vector position r.
- 2.
In other words, the total angular momentum of the system and its projection on a given axis is conserved.
- 3.
The term physical here denotes the fact that the scattering wave function can be always be decomposed as an incoming plane wave plus a divergent spherical wave times the amplitude of scattering.
- 4.
Polarized molecules show a preferable angular momentum projection.
- 5.
- 6.
This is equivalent to C6; however, the superscript is omitted when dealigning for spherical symmetric potentials.
- 7.
This condition is general for scattering problems. One needs to choose the initial propagation point deeply in the classical forbidden region to ensure that the wave function is null at that point.
References
Brown J, Carrington A (2003) Rotational spectroscopy of diatomic molecules. Cambridge University Press, Cambridge
Bernath PF (2005) Spectra of atoms and molecules. Oxford University Press, Oxford
Takayanagi K (1965) The production of rotational and vibrational transitions in encounters between molecules. Academic, pp 149–194. https://doi.org/10.1016/S0065-2199(08)60282-1, http://www.sciencedirect.com/science/article/pii/S0065219908602821
Green S (1975) J Chem Phys 62(6):2271. https://doi.org/10.1063/1.430752
Zarur G, Rabitz H (1974) J Chem Phys 60:2057
Englot GF, Rabitz H (1974) Dimensionality control of coupled scattering equations using partitioning techniques: the case of two molecules. Phys Rev A 10:2187. https://doi.org/10.1103/PhysRevA.10.2187
Barreto PRP, Cruz ACPS, Barreto RLP, Palazzetti F, Albernaz AF, Lombardi A, Maciel GS, Aquilanti V (2017) The spherical-harmonics representation for the interaction between diatomic molecules: the general case and applications to COCO and COHF. J Mol Spectrosc 337:163. https://doi.org/10.1016/j.jms.2017.05.009, http://www.sciencedirect.com/science/article/pii/S0022285217300905
Varshalovich D, Moskalev A, Khersonskii V (1988) Quantum theory of angular momentum: irreducible tensors, spherical harmonics, vector coupling coefficients, 3nj symbols. World Scientific. https://books.google.de/books?id=hQx_QgAACAAJ
Edmonds AR (1974) Angular momentum in quantum mechanics. Princeton University Press, Princeton
Zare RN (1988) Angular momentum. Wiley, New York
Zhang JZH (1999) Theory and applications of quantum molecular dynamics. World Scientific, Singapore
Landau LD, Lifshitz EM (1958) Quantum mechanics. Butterworth-Heinemann
Abramowitz M, Stegun IA (1972) Handbook of mathematical functions. Dover, New York
Miller WH (1976) Dynamics of molecular collisions. Plenum Press, New York
Pérez-Ríos J, Bartolomei M, Campos-Martínez J, Hernández MI, Hernández-Lamoneda R (2009) J Phys Chem A 113:14952
Gioumousis G, Curtiss CF (1958) J Chem Phys 29:996
Krems RV, Dalgarno A (2004) “Quantum-mechanical theory of atom-molecule and molecular collisions in a magnetic field: spin depolarization. J Chem Phys 120(5):2296. https://doi.org/10.1063/1.1636691
Tscherbul TV, Suleimanov YV, Aquilanti V, Krems RV (2009) New J Phys 11(5):055021
Volpi A, Bohn JL (2002) Phys Rev A 65:052712
Tscherbul TV, Suleimanov YV, Aquilanti V, Krems R (2009) New J Phys 11:055021
Freidrich B, deCarvalho R, Kim J, Patterson D, Weinstein JD, Doyle JM (1998) J Chem Soc Faraday Trans 94:1783
Herzberg G (1950) Spectra of diatomic molecules. Van Nostrand, New York
Mizushima M (1975) The theory of rotating diatomic molecules. Wiley, New York
Gazzoli G, Espositi CD (1985) Chem Phys Lett 113:501
Avdeenkov AV, Bohn JL (2001) Phys Rev A 64:052703. https://doi.org/10.1103/PhysRevA.64.052703
Teisinga E, Verhaar BJ, Stoof HTC (1993) Phys Rev A 47:4114
Aquilanti V, Ascenzi D, Bartolomei M, Cappelletti D, Cavalli S, de Castro Vìtores M, Pirani F (1999) J Am Chem Soc 121(46):10794
Wormer PES, van der Avoird A (1984) J Chem Phys 81(4):1929. https://doi.org/10.1063/1.447867
Bussery B, Wormer PES (1993) J Chem Phys 99:1230
Pérez-Ríos J, Campos-Martínez J, Hernández MI (2011) J Chem Phys 134(12):124310. https://doi.org/10.1063/1.3573968
Bartolomei M, Carmona-Novillo E, Hernández MI, Campos-Martínez J, Hernández-Lamoneda R (2010) J Chem Phys 133(12):124311
Hutson JM (2007) New J Phys 9:152
Idziaszek Z, Julienne PS (2010) Phys Rev Lett 104(11):113202. https://doi.org/10.1103/PhysRevLett.104.113202
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Pérez Ríos, J. (2020). Ultracold Molecular Collisions. In: An Introduction to Cold and Ultracold Chemistry. Springer, Cham. https://doi.org/10.1007/978-3-030-55936-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-55936-6_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-55935-9
Online ISBN: 978-3-030-55936-6
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)