High-precision spectroscopy of hydrogen molecular ions

doi:10.1088/1674-1056/24/5/053102

Abstract In this paper, we overview recent advances in high-precision structure calculations of the hydrogen molecular ions (H₂⁺ and HD⁺), including nonrelativistic energy eigenvalues and relativistic and quantum electrodynamic corrections. In combination with high-precision measurements, it is feasible to precisely determine a molecular-based value of the proton-to-electron mass ratio. An experimental scheme is presented for measuring the rovibrational transition frequency (v,L):(0,0)→(6,1) in HD⁺, which is currently underway at the Wuhan Institute of Physics and Mathematics.

Keywords: hydrogen molecular ion rovibrational transition proton-to-electron mass ratio relativistic and QED corrections

Received: 16 November 2014
Revised: 04 December 2014
Accepted manuscript online:

PACS:	31.15.ac	(High-precision calculations for few-electron (or few-body) atomic systems)
	31.30.J-	(Relativistic and quantum electrodynamic (QED) effects in atoms, molecules, and ions)
	33.20.-t	(Molecular spectra)
	33.80.-b	(Photon interactions with molecules)

Corresponding Authors: Yan Zong-Chao, Shi Ting-Yun
E-mail: zyan@unb.ca;tyshi@wipm.ac.cn

About author: 31.15.ac; 31.30.J-; 33.20.-t; 33.80.-b

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Zhong Zhen-Xiang (钟振祥), Tong Xin (童昕), Yan Zong-Chao (严宗朝), Shi Ting-Yun (史庭云) High-precision spectroscopy of hydrogen molecular ions 2015 Chin. Phys. B 24 053102

[1]	Greiner W, Schramm S and Stein E 2004 Quantum Chromodynamics (2nd edn.) (Berline: Springer) pp. 178–182
[2]	Schiller S and Korobov V 2005 Phys. Rev. A 71 032505
[3]	Karr J Ph, Bielsa F, Valenzuela T, Douillet A, Hilico L and Korobov V I 2007 Can. J. Phys. 85 497
[4]	Salumbides E J, Koelemeij J C J, Komasa J, Pachucki K, Eikema K S E and Ubachs W 2013 Phys. Rev. D 87 112008
[5]	Salumbides E J, UbachsWand Korobov V I 2014 Journal of Molecular Spectroscopy 300 65
[6]	Mohr P J, Taylor B N and Newell D B 2012 Rev. Mod. Phys. 84 1527
[7]	Verdú J, Djekić S, Stahl S, Valenzuela T, Vogel M, Werth G, Beier T, Kluge H J and Quint W 2004 Phys. Rev. Lett. 92 093002
[8]	Sturm S, Köhler F, Zatorski J, Wagner A, Harman Z, Werth G, Quint W, Keitel C H and Blaum K 2014 Nature 506 467
[9]	Cärtner G and Klempt E 1978 Z. Physik A 287 1
[10]	Gräff G, Kalinowsky H and Traut J 1980 Z. Physik A 297 35
[11]	Van Dyck R S, Jr. and Schwinberg P B 1981 Phys. Rev. Lett. 47 395
[12]	Van Dyck R S, Jr., Moore F L, Farnham D L and Schwinberg P B 1985 Int. J. Mass Spectrosc. Ion Proc. 66 327
[13]	Farnham D L, Van Dyck R S, Jr. and and Schwinberg P B 1995 Phys. Rev. Lett. 75 3598
[14]	Wineland D J, Bollinger J J and Itano W M 1983 Phys. Rev. Lett. 50 628
[15]	Erratum 1983 Phys. Rev. Lett. 50 1333
[16]	Gabrielse G, Fei X, Orozco L A, Tjoelker R L, Haas J, Kalinowsky H, Trainor T A and Kells W 1990 Phys. Rev. Lett. 65 1317
[17]	Karshenboim S G 2005 Phys. Rep. 422 1
[18]	Karshenboim S G 2008 Lect. Notes. Phys. 745 1
[19]	Hayano R S, Hori M, Horváth D andWidmann E 2007 Pep. Prog. Phys. 70 1995
[20]	Hori M and Walz J 2013 Prog. Part. Nucl. Phys. 72 206
[21]	Hori M, Dax A, Eades J, Gomikawa K, Hayano R S, Ono N, Pirkl W, Widmann E, Torii H A, Juhász B, Barna D and Horváth D 2006 Phys. Rev. Lett. 96 243401
[22]	Hori M, Sótér A, Barna D, Dax A, Hayano R, Friedreich S, Juhász B, Pask T, Widmann E, Horváth D, Venturelli L and Zurlo N 2011 Nature 475 484
[23]	Koelemeij J C J, Roth B,Wicht A, Ernsting I and Schiller S 2007 Phys. Rev. Lett. 98 173002
[24]	Hori M and Walz J 2013 Prog. Part. Nuc. Phys. 72 206
[25]	Roth B, Koelemeij J, Schiller S, Hilico L, Karr J Ph, Korobov V I and Bakalov D 2008 Lect. Notes Phys. 745 205
[26]	Bressel U, Borodin A, Shen J, Hansen M, Ernsting I and Schiller S 2012 Phys. Rev. Lett. 108 183003
[27]	Koelemeij J C J, Noom D W E, de Jong D, Haddad M A and Ubachs W 2012 Appl. Phys. B 107 1075
[28]	Korobov V I 2003 Phys. Rev. A 67 062501
[29]	Erratum 2003 Phys. Rev. A 68 019902
[30]	Korobov V I 2006 Phys. Rev. A 74 052506
[31]	Korobov V I 2008 Phys. Rev. A 77 022509
[32]	Korobov V I 2008 Phys. Rev. A 77 042506
[33]	Blythe P, Roth B, Fröhlich U, Wenz H and Schiller S 2005 Phys. Rev. Lett. 95 183002
[34]	Bekbaev A K, Korobov V I and Dineykhan M 2011 Phys. Rev. A 83 044501
[35]	Tian Q L, Tang L Y, Zhong Z X, Yan Z C and Shi T Y 2012 J. Chem. Phys. 137 024311
[36]	Caswell W E and Lepage G P 1986 Phys. Lett. B 167 437
[37]	Nio M and Kinoshita T 1997 Phys. Rev. D 55 7267
[38]	Bates D R, Ledsham K and Stewart A L 1953 Phil. Trans. R. Soc. A 246 215
[39]	Carrington A, MacNab I R and Montgomerie C A 1989 J. Phys. B 22 3551
[40]	Leach C A and Moss R E 1995 Ann. Rev. Phys. Chem. 46 55
[41]	Bishop D M and Solunac S A 1985 Phys. Rev. Lett. 55 1986
[42]	Erratum 1985 Phys. Rev. Lett. 55 2627
[43]	Moss R E and Sadler I A 1989 Mol. Phys. 68 1015
[44]	Rebane T K and Filinsky A V 1997 Phys. At. Nucl. 60 1816
[45]	de Saavedra F A, Buendía E, Gálvez F J and Sarsa A 1998 Eur. Phys. J. D 2 181
[46]	Grémaud B, Delande D and Billy N 1998 J. Phys. B 31 383
[47]	Bhatia A K 1998 Phys. Rev. A 58 2787
[48]	Moss R E 1999 J. Phys. B 32 L89
[49]	Taylor J M, Yan Z C, Dalgarno A and Babb J F 1999 Mol. Phys. 97 25
[50]	Hilico L, Billy N, Grémaud B and Delande D 2000 Eur. Phys. J. D 12 449
[51]	Korobov V I 2000 Phys. Rev. A 61 064503
[52]	Bailey D H and Frolov A M 2002 J. Phys. B 35 4287
[53]	Yan Z C, Zhang J Y and Li Y 2003 Phys. Rev. A 67 062504
[54]	Yan Z C and Zhang J Y 2004 J. Phys. B 37 1055
[55]	Cassar M M and Drake G W F 2004 J. Phys. B 37 2485
[56]	Li H, Wu J, Zhou B L, Zhu J M and Yan Z C 2007 Phys. Rev. A 75 012504
[57]	Ning Y and Yan Z C 2014 Phys. Rev. A 90 032516
[58]	Stephen M J and Auffray J P 1959 J. Chem. Phys. 31 1329
[59]	Dalgarno A, Patterson T N L and Somerville W B 1960 Proc. R. Soc. Lond. A 259 100
[60]	Kalaghan P M and Dalgarno A 1972 Phys. Lett. A 38 485
[61]	Cohen M, McEachran R P and Schlifer I R 1977 Chem. Phys. Lett. 49 374
[62]	Ray R D and Certain P R 1977 Phys. Rev. Lett. 38 824
[63]	McEachran R P, Veenstra C J and Cohen M 1978 Chem. Phys. Lett. 59 275
[64]	Babb J F and Dalgarno A 1991 Phys. Rev. Lett. 66 880
[65]	Babb J F and Dalgarno A 1992 Phys. Rev. A 46 5317
[66]	Babb J F 1995 Phys. Rev. Lett. 75 4377
[67]	Korobov V I, Hilico L and Karr J Ph 2006 Phys. Rev. A 74 040502
[68]	Karr J Ph, Bielsa F, Douillet A, Gutierrez J P, Korobov V I and Hilico L 2008 Phys. Rev. A 77 063410
[69]	Bakalov D, Korobov V I and Schiller S 2006 Phys. Rev. Lett. 97 243001
[70]	Bekbaev A K, Korobov V I and Dineykhan M 2013 J. Phys. B 46 175101
[71]	Zhang P P, Zhong Z X and Yan Z C 2013 Phys. Rev. A 88 032519
[72]	Korobov V I, Hilico L and Karr J Ph 2009 Phys. Rev. A 79 012501
[73]	Luke S K, Hunter G, McEachran R P and Cohen M 1969 J. Chem. Phys. 50 1644
[74]	Gersten J I 1969 J. Chem. Phys. 51 3181
[75]	Bishop D M and Cheung L M 1977 Phys. Rev. A 16 640
[76]	Wolniewicz L and Poll J D 1980 J. Chem. Phys. 73 6225
[77]	Wolniewicz L and Poll J D 1985 Can. J. Phys. 63 1201
[78]	Moss R E 1993 Mol. Phys. 78 371
[79]	Zhong Z X, Yan Z C and Shi T Y 2009 Phys. Rev. A 79 064502
[80]	Zhong Z X, Zhang P P, Yan Z C and Shi T Y 2012 Phys. Rev. A 86 064502
[81]	Korobov V I and Zhong Z X 2012 Phys. Rev. A 86 044501
[82]	Korobov V I, Hilico L and Karr J Ph 2013 Phys. Rev. A 87 062506
[83]	Korobov V I, Hilico L and Karr J Ph 2014 Phys. Rev. Lett. 112 103003
[84]	Korobov V I, Hilico L and Karr J Ph 2014 Phys. Rev. A 89 032511
[85]	Antognini A, Nez F, Schuhmann K, et al. 2013 Science 339 417
[86]	Gill P 2001 Science 294 1666
[87]	Schneider T, Roth B, Duncker H, Ernsting I and Schiller S 2010 Nature Physics 6 275
[88]	Karr J Ph, Hilico L and Korobov V I 2011 Can. J. Phys. 89 103
[89]	Bhatia A K and Drachman R J 1999 Phys. Rev. A 59 205
[90]	Yan Z C and Drake G W F 1996 Chem. Phys. Lett. 259 96
[91]	Yan Z C and Drake G W F 1994 Can. J. Phys. 72 822
[92]	Harris F E, Frolov A M and Smith V H Jr. 2004 J. Chem. Phys. 121 6323
[93]	Stone A P 1961 Proc. Phys. Soc. 77 786
[94]	Stone A P 1963 Proc. Phys. Soc. 81 868
[95]	Bethe H A and Salpeter E E 1977 Quantum Mechanics of One- and Two-Electron Atoms (New York: Plenum)
[96]	Pachucki K 2005 Phys. Rev. A 71 012503
[97]	Pachucki K and Karshenboim S G 1995 J. Phys. B 28 L221
[98]	Pachucki K 1998 J. Phys. B 31 3547
[99]	Yelkhovsky A 2001 Phys. Rev. A 64 062104
[100]	Korobov V I 2004 Phys. Rev. A 70 012505
[101]	Kinoshita T and Nio M 1996 Phys. Rev. D 53 4909
[102]	Araki H 1957 Prog. Theor. Phys. 17 619
[103]	Sucher J 1958 Phys. Rev. 109 1010
[104]	Yan Z C 2000 J. Phys. B 33 2437
[105]	Bethe H A 1947 Phys. Rev. 72 339
[106]	Schwartz C 1961 Phys. Rev. 123 1700
[107]	Korobov V I and Korobov S V 1999 Phys. Rev. A 59 3394
[108]	Korobov V I 2004 Phys. Rev. A 70 012505
[109]	Korobov V I 2006 Phys. Rev. A 73 024502
[110]	Korobov V I 2012 Phys. Rev. A 85 042514
[111]	Erratum 2012 Phys. Rev. A 86 069905
[112]	Drake G W F and Goldman S P 1999 Can. J. Phys. 77 835
[113]	Zhong Z X, Yan Z C and Shi T Y 2013 Phys. Rev. A 88 052520
[114]	Eides M I, Grotch H and Shelyuto V A 2001 Phys. Rep. 342 63
[115]	Eides M I, Grotch H and Shelyuto V A 2007 Theory of Light Hydrogenic Bound States (Berlin: Springer)
[116]	Korobov V I and Tsogbayar Ts 2007 J. Phys. B 40 2661
[117]	Sapirstein J R and Yennie D R 1990 Quantum Electrodynamics (ed. Kinoshita T) (Singapore: World Scientific) p. 560
[118]	Jentschura U D, Czarnecki A and Pachucki K 2005 Phys. Rev. A 72 062102
[119]	Czarnecki A, Jentschura U D and Pachucki K 2005 Phys. Rev. Lett. 95 180404
[120]	Erratum 2005 Phys. Rev. Lett. 95 199903
[121]	Mohr P J 1975 Phys. Rev. Lett. 34 1050
[122]	Mohr P J 1982 Phys. Rev. A 26 2338
[123]	Ivanov V G and Karshenboim S G 1997 Yad. Fiz. 60 333
[124]	Ivanov V G and Karshenboim S G 1997 Phys. At. Nuclei 60 270
[125]	Layzer A J 1960 Phys. Rev. Lett. 4 580
[126]	Mohr P J 1983 At. Data Nucl. Data Tables 29 453
[127]	Pachucki K 1993 Phys. Rev. A 48 2609
[128]	Eides M I, Grotch H and Shelyuto V A 1997 Phys. Rev. A 55 2447
[129]	Dowling M, Mondéjar J, Piclum J H and Czarnecki A 2010 Phys. Rev. A 81 022509
[130]	Kinoshita T 1990 Quantum Electrodynamics (ed. Kinoshita T) (Singapore: World Scientific) p. 218
[131]	Laporta S and Remiddi E 1996 Phys. Lett. B 379 283
[132]	Eides M I and Grotch H 1995 Phys. Rev. A 52 3360
[133]	Melnikov K and van Ritbergen T 2000 Phys. Rev. Lett. 84 1673
[134]	Mohr P J, Taylor B N and Newell D B 2008 Rev. Mod. Phys. 80 633
[135]	Shen J, Borodin A, Hansen M and Schiller S 2012 Phys. Rev. A 85 032519
[136]	Drullinger R E, Wineland D J and Bergquist J C 1980 Appl. Phys. 22 365
[137]	Larson D J, Bergquist J C, Bollinger J J, Itano W M and Wineland D J 1986 Phys. Rev. Lett. 57 70
[138]	Baba T and Waki I 1996 Jpn. J. Appl. Phys. 35 L1134
[139]	Drewsen M, Jensen I, Lindballe J, Nissen N, Martinussen R, Mortensen A, Staanum P and Voigt D 2003 Int. J. Mass Spectrom. 229 83
[140]	Willitsch S, Bell M T, Gingell A D and Softley T P 2008 Phys. Chem. Chem. Phys. 10 7200
[141]	Baba T and Waki I 2002 J. Appl. Phys. 92 4109
[142]	Schiller S and Lämmerzahl C 2003 Phys. Rev. A 68 053406
[143]	Tong X,Winney A H andWillitsch S 2010 Phys. Rev. Lett. 105 143001
[144]	Tong X, Wild D and Willitsch S 2011 Phys. Rev. A 83 023415
[145]	Mackenzie S R, Merkt F, Halse E J and Softley T B 1995 Mol. Phys. 86 1283
[146]	Willitsch S and Merkt F 2005 Int. J. Mass Spectrom. 245 14
[147]	Roth B, Koelemeij J C J, Daerr H and Schiller S 2006 Phys. Rev. A 74 040501

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