H2+, HD+, D2+ hydrogen molecular ions
70 26
Keywords:
Molecular hydrogen ion, spectroscopy, Schrodinger equationAbstract
The article is devoted to the study of statistical polarizability of molecular ions H2+, HD+, D2+ . Particularly DC Stark effect (at constant electric field) in the nonrelativistic approximation was calculated. Our calculation takes into account the dependence of the rotational-vibrational states, and the dependence of the hyperfine splitting of levels. We have considered special cases that allow obtain explicit analytical solutions associated with the algebra of angular momentum.
The results of the work have a great importance in metrology. At first to clarify the fundamental physical constants, primarily to improve the value of the mass ratio of the electron to the proton me/mp. Precise calculations of the values of static polarizabilities will be of a great importance for verification experiments of variations of fundamental constants in time in a laboratory. Recently has been proposed to use molecular hydrogen ions H2+ and HD+ for development of high-precision clock with a relative stability of order of 10-18 at room temperature. For comparison, the best accuracy achieved in cesium clocks (the current standard time) implemented by the National Institute of Standards and Technology in 2011: 2.3 * 10-16.
References
1. Schiller S., Bakalov D., and Korobov V.I. Simplest Molecules as Candidates for Precise Optical Clocks // Phys. Rev. Lett. – 2014. – Vol.113. – P.023004.
2. Hilico L., Billy N., Grөemaud B., and Delande D. Polarizabilities, light shifts and two-photon transition probabilities between J= 0 states of the H2+ and D2+ molecular ions // J. Phys. B: At. Mol. Opt. Phys. – 2001. – Vol. 34. – P. 491; Karr J.-Ph., Kilic S., and Hilico L. Energy levels and two-photon transition probabilities in the HD+ ion // J. Phys. B: At. Mol. Opt. Phys. – 2005. – Vol. 38. – P. 853.
3. Pilon H.O. and Baye D. Static and dynamic polarizabilities of the non-relativistic hydrogen molecular ion // J. Phys. B: At. Mol. Opt. Phys. – 2012. – Vol. 45. – P.235101.
4. Quan-Long Tian, Li-Yan Tang, Zong-Chao Yan, and Ting-Yun Shi, Static Dipole Polarizabilities for Low-Lying Rovibrational States of HD+* // Chin. Phys. Lett. – 2015. – Vol.32. – P.083101.
5. Schiller S., Bakalov D., Bekbaev A.K., and Korobov V.I. Static and dynamic polarizability and the Stark and blackbody-radiation frequency shifts of the molecular hydrogen ions H2+, HD+, and D2+ // Phys. Rev. A. – 2014. – Vol. 89. – P.052521.
6. Korobov V.I. Relativistic corrections to the dipole polarizability of the ground state of the molecular ion H5+ // Phys. Rev. A. – 2001. – Vol. 63. – P.044501.
7. Koelemeij J.C.J., Roth B., Wicht A., Ernsting I., and Schiller S. Vibrational Spectroscopy of HD+ with 2-ppb Accuracy // Phys. Rev. Lett. – 2007. – Vol.98. – P.173002.
8. Biesheuvel J., Karr J.-Ph., Hilico L., Eikema K.S.E., Ubachs W., and Koelemeij J.C.J., Probing QED and fundamental constants through laser spectroscopy of vibrational transitions in HD+ // Nature Comm. – 2016. – Vol.7. – P.10385.
9. Shen J., Borodin A., Hansen M., and Schiller S. Observation of a rotational transition of trapped and sympathetically cooled molecular ions // Phys. Rev. A. – 2012. – Vol.85. – P.032519.
10. Bressel U., Borodin A., Shen J., Hansen M., Ernsting I., and Schiller S.,Manipulation of Individual Hyperfine States in Cold Trapped Molecular Ions and Application to HD+ Frequency Metrology // Phys. Rev. Lett. – 2012. – Vol.108. – P.183003.
11. Korobov V.I., Hilico L., and Karr J.-Ph. Theoretical transition frequencies beyond 0.1 ppb accuracy in H2+, HD+, and antiprotonic helium // Phys. Rev. A. – 2014. – Vol.89. – P.032511; Korobov V.I., Hilico L., and Karr J.-P. Bound-state QED calculations for antiprotonic helium // Hyperfine Interactions. – 2015. – Vol. 233. – P.75-82.
12. Korobov V.I., Koelemeij J.C.J., Karr J.-Ph., and Hilico L. Theoretical Hyperfine Structure of the Molecular Hydrogen Ion at the 1 ppm Level // Phys. Rev. Lett. – 2016. – Vol.116. – P.053003.
13. Pachucki K. and Sapirstein J. Relativistic and QED corrections to the polarizability of helium // Phys. Rev. A. – 2000. – Vol.63. – P.012504.
14. Lach G., Jeziorski B., and Szalewicz K. Radiative Corrections to the Polarizability of Helium Phys. Rev. Lett. – 2004. – Vol.92. – P.233001; Piszczatowski K., Puchalski M., Komasa J., Jeziorski B., and Szalewicz K. Frequency-Dependent Polarizability of Helium Including Relativistic Effects with Nuclear Recoil Terms // Phys. Rev. Lett. – 2015. – Vol.114. – P.173004.
15. Landau L.D. and Lifshitz E.M. Quantum Mechanics. Nonrelativistic Theory. – Oxford: Pergamon, 1977.
16. Berestetsky V.B., Lifshitz E.M. and Pitaevsky L.P. Relativistic Quantum Theory. – Oxford: Pergamon, 1982.
17. Korobov V.I. Leading-order relativistic and radiative corrections to the rovibrational spectrum of H2+ and HD+ molecular ions // Phys. Rev. A. – 2006. – Vol.74. – P.052506.
18. Mohr P.J., Taylor B.N., and Newell D.B. CODATA Recommended Values of the Fundamental Physical Constants: 2010 // Rev. Mod. Phys. – 2012. – Vol.84. – P.1527-1605.
19. Li-Yan Tang, Zong-Chao Yan, Ting-Yun Shi, and Babb J.F. High-precision nonadiabatic calculations of dynamic polarizabilities and hyperpolarizabilities for low-lying vibrational-rotational states of hydrogen molecular ions // Phys. Rev. A. – 2014. – Vol.90. – P.012524.
20. Zong-Chao Yan, Jun-Yi Zhang, and Yue Li. Energies and polarizabilities of the hydrogen molecular ions // Phys. Rev. A. – 2003. – Vol.67. – P.062504.
References
1. S. Schiller, D. Bakalov, and V.I. Korobov, Phys. Rev. Lett. 113, 023004 (2014). doi.org/10.1103/PhysRevLett.113.023004
2. L. Hilico, N. Billy, B. Grөemaud, and D. Delande, J. Phys. B: At. Mol. Opt. Phys. 34, 491 (2001); J.-Ph. Karr, S. Kilic, and L. Hilico, J. Phys. B: At. Mol. Opt. Phys. 38, 853 (2005).
3. H. Olivares Pilon and D. Baye, J. Phys. B: At. Mol. Opt. Phys. 45, 235101 (2012).
4. Quan-Long Tian, Li-Yan Tang, Zong-Chao Yan, and Ting-Yun Shi, Chin. Phys. Lett. 32, 083101 (2015).
5. S. Schiller, D. Bakalov, A.K. Bekbaev, and V.I. Korobov, Phys. Rev. A 89, 052521 (2014). doi.org/10.1103/PhysRevA.89.052521
6. V.I. Korobov, Phys. Rev. A 63, 044501 (2001). doi.org/10.1103/PhysRevA.63.044501
7. J.C.J. Koelemeij, B. Roth, A. Wicht, I. Ernsting, and S. Schiller, Phys. Rev. Lett. 98, 173002 (2007). doi.org/10.1103/PhysRevLett.98.173002
8. J. Biesheuvel, J.-Ph. Karr, L. Hilico, K.S.E. Eikema, W. Ubachs, and J.C.J. Koelemeij, Nature Comm. 7, 10385 (2016). doi:10.1038/ncomms10385
9. J. Shen, A. Borodin, M. Hansen, and S. Schiller, Phys. Rev. A 85, 032519 (2012). doi.org/10.1103/PhysRevA.85.032519
10. U. Bressel, A. Borodin, J. Shen, M. Hansen, I. Ernsting, and S. Schiller, Phys. Rev. Lett. 108, 183003 (2012).
11. V.I. Korobov, L. Hilico, and J.-Ph. Karr, Phys. Rev. A 89, 032511 (2014) doi.org/10.1103/PhysRevA.89.032511; V.I. Korobov, L. Hilico, and J.-P. Karr, Hyperfine Interactions 233, 75-82 (2015) DOI 10.1007/s10751-015-1149-5 .
12. V.I. Korobov, J.C.J. Koelemeij, J.-Ph. Karr, and L. Hilico, Phys. Rev. Lett. 116, 053003 (2016).
13. K. Pachucki and J. Sapirstein, Phys. Rev. A 63, 012504 (2000).
14. G. Lach, B. Jeziorski, and K. Szalewicz, Phys. Rev. Lett. 92, 233001 (2004) doi.org/10.1103/PhysRevLett.92.233001; K. Piszczatowski, M. Puchalski, J. Komasa, B. Jeziorski, and K. Szalewicz, Phys. Rev. Lett. 114, 173004 (2015) doi.org/10.1103/PhysRevLett.114.173004.
15. L.D. Landau and E.M. Lifshitz, Quantum Mechanics. Nonrelativistic Theory (Pergamon, Oxford, 1977).
16. V.B. Berestetsky, E.M. Lifshitz and L.P. Pitaevsky, Relativistic Quantum Theory, (Oxford, Pergamon, 1982).
17. V.I. Korobov, Phys. Rev. A 74, 052506 (2006) doi.org/10.1103/PhysRevA.74.052506.
18. P.J. Mohr, B.N. Taylor, and D.B. Newell, Rev. Mod. Phys. 84, 1527 (2012) doi:10.1103/RevModPhys.84.1527
19. Li-Yan Tang, Zong-Chao Yan, Ting-Yun Shi, and J.F. Babb, Phys. Rev. A 90, 012524 (2014). doi.org/10.1103/PhysRevA.90.012524
20. Zong-Chao Yan, Jun-Yi Zhang, and Yue Li, Phys. Rev. A 67, 062504 (2003). doi.org/10.1103/PhysRevA.67.062504.
2. Hilico L., Billy N., Grөemaud B., and Delande D. Polarizabilities, light shifts and two-photon transition probabilities between J= 0 states of the H2+ and D2+ molecular ions // J. Phys. B: At. Mol. Opt. Phys. – 2001. – Vol. 34. – P. 491; Karr J.-Ph., Kilic S., and Hilico L. Energy levels and two-photon transition probabilities in the HD+ ion // J. Phys. B: At. Mol. Opt. Phys. – 2005. – Vol. 38. – P. 853.
3. Pilon H.O. and Baye D. Static and dynamic polarizabilities of the non-relativistic hydrogen molecular ion // J. Phys. B: At. Mol. Opt. Phys. – 2012. – Vol. 45. – P.235101.
4. Quan-Long Tian, Li-Yan Tang, Zong-Chao Yan, and Ting-Yun Shi, Static Dipole Polarizabilities for Low-Lying Rovibrational States of HD+* // Chin. Phys. Lett. – 2015. – Vol.32. – P.083101.
5. Schiller S., Bakalov D., Bekbaev A.K., and Korobov V.I. Static and dynamic polarizability and the Stark and blackbody-radiation frequency shifts of the molecular hydrogen ions H2+, HD+, and D2+ // Phys. Rev. A. – 2014. – Vol. 89. – P.052521.
6. Korobov V.I. Relativistic corrections to the dipole polarizability of the ground state of the molecular ion H5+ // Phys. Rev. A. – 2001. – Vol. 63. – P.044501.
7. Koelemeij J.C.J., Roth B., Wicht A., Ernsting I., and Schiller S. Vibrational Spectroscopy of HD+ with 2-ppb Accuracy // Phys. Rev. Lett. – 2007. – Vol.98. – P.173002.
8. Biesheuvel J., Karr J.-Ph., Hilico L., Eikema K.S.E., Ubachs W., and Koelemeij J.C.J., Probing QED and fundamental constants through laser spectroscopy of vibrational transitions in HD+ // Nature Comm. – 2016. – Vol.7. – P.10385.
9. Shen J., Borodin A., Hansen M., and Schiller S. Observation of a rotational transition of trapped and sympathetically cooled molecular ions // Phys. Rev. A. – 2012. – Vol.85. – P.032519.
10. Bressel U., Borodin A., Shen J., Hansen M., Ernsting I., and Schiller S.,Manipulation of Individual Hyperfine States in Cold Trapped Molecular Ions and Application to HD+ Frequency Metrology // Phys. Rev. Lett. – 2012. – Vol.108. – P.183003.
11. Korobov V.I., Hilico L., and Karr J.-Ph. Theoretical transition frequencies beyond 0.1 ppb accuracy in H2+, HD+, and antiprotonic helium // Phys. Rev. A. – 2014. – Vol.89. – P.032511; Korobov V.I., Hilico L., and Karr J.-P. Bound-state QED calculations for antiprotonic helium // Hyperfine Interactions. – 2015. – Vol. 233. – P.75-82.
12. Korobov V.I., Koelemeij J.C.J., Karr J.-Ph., and Hilico L. Theoretical Hyperfine Structure of the Molecular Hydrogen Ion at the 1 ppm Level // Phys. Rev. Lett. – 2016. – Vol.116. – P.053003.
13. Pachucki K. and Sapirstein J. Relativistic and QED corrections to the polarizability of helium // Phys. Rev. A. – 2000. – Vol.63. – P.012504.
14. Lach G., Jeziorski B., and Szalewicz K. Radiative Corrections to the Polarizability of Helium Phys. Rev. Lett. – 2004. – Vol.92. – P.233001; Piszczatowski K., Puchalski M., Komasa J., Jeziorski B., and Szalewicz K. Frequency-Dependent Polarizability of Helium Including Relativistic Effects with Nuclear Recoil Terms // Phys. Rev. Lett. – 2015. – Vol.114. – P.173004.
15. Landau L.D. and Lifshitz E.M. Quantum Mechanics. Nonrelativistic Theory. – Oxford: Pergamon, 1977.
16. Berestetsky V.B., Lifshitz E.M. and Pitaevsky L.P. Relativistic Quantum Theory. – Oxford: Pergamon, 1982.
17. Korobov V.I. Leading-order relativistic and radiative corrections to the rovibrational spectrum of H2+ and HD+ molecular ions // Phys. Rev. A. – 2006. – Vol.74. – P.052506.
18. Mohr P.J., Taylor B.N., and Newell D.B. CODATA Recommended Values of the Fundamental Physical Constants: 2010 // Rev. Mod. Phys. – 2012. – Vol.84. – P.1527-1605.
19. Li-Yan Tang, Zong-Chao Yan, Ting-Yun Shi, and Babb J.F. High-precision nonadiabatic calculations of dynamic polarizabilities and hyperpolarizabilities for low-lying vibrational-rotational states of hydrogen molecular ions // Phys. Rev. A. – 2014. – Vol.90. – P.012524.
20. Zong-Chao Yan, Jun-Yi Zhang, and Yue Li. Energies and polarizabilities of the hydrogen molecular ions // Phys. Rev. A. – 2003. – Vol.67. – P.062504.
References
1. S. Schiller, D. Bakalov, and V.I. Korobov, Phys. Rev. Lett. 113, 023004 (2014). doi.org/10.1103/PhysRevLett.113.023004
2. L. Hilico, N. Billy, B. Grөemaud, and D. Delande, J. Phys. B: At. Mol. Opt. Phys. 34, 491 (2001); J.-Ph. Karr, S. Kilic, and L. Hilico, J. Phys. B: At. Mol. Opt. Phys. 38, 853 (2005).
3. H. Olivares Pilon and D. Baye, J. Phys. B: At. Mol. Opt. Phys. 45, 235101 (2012).
4. Quan-Long Tian, Li-Yan Tang, Zong-Chao Yan, and Ting-Yun Shi, Chin. Phys. Lett. 32, 083101 (2015).
5. S. Schiller, D. Bakalov, A.K. Bekbaev, and V.I. Korobov, Phys. Rev. A 89, 052521 (2014). doi.org/10.1103/PhysRevA.89.052521
6. V.I. Korobov, Phys. Rev. A 63, 044501 (2001). doi.org/10.1103/PhysRevA.63.044501
7. J.C.J. Koelemeij, B. Roth, A. Wicht, I. Ernsting, and S. Schiller, Phys. Rev. Lett. 98, 173002 (2007). doi.org/10.1103/PhysRevLett.98.173002
8. J. Biesheuvel, J.-Ph. Karr, L. Hilico, K.S.E. Eikema, W. Ubachs, and J.C.J. Koelemeij, Nature Comm. 7, 10385 (2016). doi:10.1038/ncomms10385
9. J. Shen, A. Borodin, M. Hansen, and S. Schiller, Phys. Rev. A 85, 032519 (2012). doi.org/10.1103/PhysRevA.85.032519
10. U. Bressel, A. Borodin, J. Shen, M. Hansen, I. Ernsting, and S. Schiller, Phys. Rev. Lett. 108, 183003 (2012).
11. V.I. Korobov, L. Hilico, and J.-Ph. Karr, Phys. Rev. A 89, 032511 (2014) doi.org/10.1103/PhysRevA.89.032511; V.I. Korobov, L. Hilico, and J.-P. Karr, Hyperfine Interactions 233, 75-82 (2015) DOI 10.1007/s10751-015-1149-5 .
12. V.I. Korobov, J.C.J. Koelemeij, J.-Ph. Karr, and L. Hilico, Phys. Rev. Lett. 116, 053003 (2016).
13. K. Pachucki and J. Sapirstein, Phys. Rev. A 63, 012504 (2000).
14. G. Lach, B. Jeziorski, and K. Szalewicz, Phys. Rev. Lett. 92, 233001 (2004) doi.org/10.1103/PhysRevLett.92.233001; K. Piszczatowski, M. Puchalski, J. Komasa, B. Jeziorski, and K. Szalewicz, Phys. Rev. Lett. 114, 173004 (2015) doi.org/10.1103/PhysRevLett.114.173004.
15. L.D. Landau and E.M. Lifshitz, Quantum Mechanics. Nonrelativistic Theory (Pergamon, Oxford, 1977).
16. V.B. Berestetsky, E.M. Lifshitz and L.P. Pitaevsky, Relativistic Quantum Theory, (Oxford, Pergamon, 1982).
17. V.I. Korobov, Phys. Rev. A 74, 052506 (2006) doi.org/10.1103/PhysRevA.74.052506.
18. P.J. Mohr, B.N. Taylor, and D.B. Newell, Rev. Mod. Phys. 84, 1527 (2012) doi:10.1103/RevModPhys.84.1527
19. Li-Yan Tang, Zong-Chao Yan, Ting-Yun Shi, and J.F. Babb, Phys. Rev. A 90, 012524 (2014). doi.org/10.1103/PhysRevA.90.012524
20. Zong-Chao Yan, Jun-Yi Zhang, and Yue Li, Phys. Rev. A 67, 062504 (2003). doi.org/10.1103/PhysRevA.67.062504.
Downloads
Published
2017-09-25
How to Cite
Tasmurat, A., Bekbaev, A., & Aznabayev, D. (2017). H2+, HD+, D2+ hydrogen molecular ions. Recent Contributions to Physics (Rec.Contr.Phys.), 62(3), 73–79. Retrieved from https://bph.kaznu.kz/index.php/zhuzhu/article/view/567
Issue
Section
Theoretical Physics. Nuclear and Elementary Particle Physics. Astrophysics
