H2+, HD+, D2+ cутегі молекулалық иондар
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Ключевые слова:
молекулалық ион, спектроскопия, Шредингер теңдеуіАннотация
Бұл жұмыста H2+, HD+, D2+ молекулалық иондарының статистикалық поляризациясы есептелген, соның ішінде релятивисттік емес жақындатуында DC Штарк эффектісі (тұрақты электр өрісінде) есептелген. Біздің есептеулер айналмалы-тербелмелі күйлер тәуелділігімен қоса деңгейлердің аса нәзік ыдырауының тәуелділігін ескереді. Бұрыштық момент алгебрасымен байланысты аналитикалық шешімдер қабылдай алатын жеке жағдайлар қарастырылды.
Жұмыс нәтижелері метрологияда үлкен маңызы бар. Біріншіден, іргелі физикалық тұрақтыларды айқындауға, бірінші кезекте протон массасының электрон массасына қатынасын me/mp жақсарту. Статикалық поляризациялану мәндерін аса дәл есептеу, іргелі тұрақтыларды тексеру варияциларын лаборатория шарттары уақытында тәжірибелерде аса маңызды. Жуырда сутегі молекулалық ионын H2+ және HD+ аса дәл сағаттарды бөлме температурасында салыстырмалы тиянақтылықпен 10-18 іске асыруда. Салыстыру үшін ең жақсы дәлдік цезиден жасалған сағаттарда (қазіргі уақыт үлгісі), 2011 жылы АҚШ Ұлттық стандарттар және технологиялар институтында іске асырылды: 2.3*10-16.
Библиографические ссылки
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.
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Как цитировать
Tasmurat, A., Bekbaev, A., & Aznabayev, D. (2017). H2+, HD+, D2+ cутегі молекулалық иондар. Вестник. Серия Физическая (ВКФ), 62(3), 73–79. извлечено от https://bph.kaznu.kz/index.php/zhuzhu/article/view/567
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Теоретическая физика. Физика ядра и элементарных частиц. Астрофизика
