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Based on the accurate singlet and triplet state interatomic potentials for Na2, a theoretical study of elastic scattering properties of sodium atoms at ultracold temperatures is reported in this paper. The s-wave scattering length, effective range, the p-wave scattering length and the number of bound states are calculated. The singlet and triplet elastic scattering cross section between sodium aotms at ultracold temperatures are dominated by s-wave scattering, and shape resonances occur with collision energy increasing. There exist pronounced f-wave and i-wave shape resonances for the singlet and triplet cross section. In addition, s-wave scattering length is calculated by using the degenerate internet state approximation for selected hyperfine states of sodium atoms. The results are in agreement with calculated values obtained by close-coupling method.
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Keywords:
- scattering parameters /
- elastic scattering cross section /
- degenerate internet state approximation
[1] Weiner J, Bagnato V S, Zilio S, Julienne P S 1999 Rev. Mod. Phys. 71 1
[2] Chin C, Grimm R, Julienne P S, Tiesinga E 2010 Rev. Mod. Phys. 82 125
[3] Burnett K, Julienne P S, Lett P D, Tiesinga E, Williams C J 2002 Nature 416 225
[4] Kagan Yu, Shlyapnikov G V, Walraven J T M 1996 Phys. Rev. Lett. 76 2670
[5] Jeung G H, Hagebaum-Reignier D, Jamieson M J 2010 J. Phys. B 43 235208
[6] Zhang J C, Zhu Z L, Liu Y F, Sun J F 2011 Chin. Phys. Lett. 28 123401
[7] Davis K B, Mewes M-O, Andrews M R, van Druten N J, Durfee D S, Kurn D M, Ketterle W 1995 Phys. Rev. Lett. 75 3969
[8] McKenzie C, Denschlag J H , Häffner H , Browaeys A, de Araujo L E E, Fatemi F K, Jones K M, Simsarian J E, Cho D, Simoni A, Tiesinga E, Julienne P S, Helmerson K, Lett P D, Rolston S L, Phillips W D 2002 Phys. Rev. Lett. 88 120403
[9] Côté R, Dalgarno A 1995 Phys. Rev. A 50 4827
[10] Zemke C J, Stwalley W C 1994 J. Chem. Phys. 100 2661
[11] van Abeelen F A, Verhaar B J 1999 Phys. Rev. A 59 578
[12] Samuelis C, Tiesinga E, Laue T, Elbs M, Knöckel H, Tiemann E 2000 Phys. Rev. A 63 012710
[13] Knoop S, Schuster T, Scelle R, Trautmann A, Appmeier J, Oberthaler M K 2011 Phys. Rev. A 83 042704
[14] Zhang J C, Zhu Z L, Sun J F 2012 Acta Phys. Sin. 61 093401 (in Chinese) [张计才, 朱遵略, 孙金锋 2012 61 093401]
[15] Dalgarno A, Rudge M R H 1965 Proc. R. Soc. London Ser. A 286 519
[16] Simos T E 1997 Computers Chem. 21 125
[17] Mott N F, Massey H S W 1965 The Theory of Atomic Collisons (Oxford: Clarendon)
[18] Flambaum V V, Gribakin G F, Harabati C 1999 Phys. Rev. A 59 1998
[19] Gribakin G F, Flambaum V V 1993 Phys. Rev. A 48 546
[20] Jamieson M J, Zygelman B 2001 Phys. Rev. A 64 032703
[21] Mount B J, Redshaw M, Myers E G 2010 Phys. Rev. A 82 042513
[22] Jamieson M J, Sarbazi-Azad H, Ouerdane H, Jeung G-H, Lee Y S, Lee W C 2003 J. Phys. B 36 1085
[23] Anderlini M, Courtade E, Cristiani M, Cossart D, Ciampini D, Sias C, Morsch O, Arimondo E 2005 Phys. Rev. A 71 061401
[24] Boesten H M J M, Tsai C C, Verhaar B J, Heinzen D J 1996 Phys. Rev. Lett. 77 5194
[25] Weiss S B, Bhattacharya M, Bigelow N P 2003 Phys. Rev. A 68 042708
-
[1] Weiner J, Bagnato V S, Zilio S, Julienne P S 1999 Rev. Mod. Phys. 71 1
[2] Chin C, Grimm R, Julienne P S, Tiesinga E 2010 Rev. Mod. Phys. 82 125
[3] Burnett K, Julienne P S, Lett P D, Tiesinga E, Williams C J 2002 Nature 416 225
[4] Kagan Yu, Shlyapnikov G V, Walraven J T M 1996 Phys. Rev. Lett. 76 2670
[5] Jeung G H, Hagebaum-Reignier D, Jamieson M J 2010 J. Phys. B 43 235208
[6] Zhang J C, Zhu Z L, Liu Y F, Sun J F 2011 Chin. Phys. Lett. 28 123401
[7] Davis K B, Mewes M-O, Andrews M R, van Druten N J, Durfee D S, Kurn D M, Ketterle W 1995 Phys. Rev. Lett. 75 3969
[8] McKenzie C, Denschlag J H , Häffner H , Browaeys A, de Araujo L E E, Fatemi F K, Jones K M, Simsarian J E, Cho D, Simoni A, Tiesinga E, Julienne P S, Helmerson K, Lett P D, Rolston S L, Phillips W D 2002 Phys. Rev. Lett. 88 120403
[9] Côté R, Dalgarno A 1995 Phys. Rev. A 50 4827
[10] Zemke C J, Stwalley W C 1994 J. Chem. Phys. 100 2661
[11] van Abeelen F A, Verhaar B J 1999 Phys. Rev. A 59 578
[12] Samuelis C, Tiesinga E, Laue T, Elbs M, Knöckel H, Tiemann E 2000 Phys. Rev. A 63 012710
[13] Knoop S, Schuster T, Scelle R, Trautmann A, Appmeier J, Oberthaler M K 2011 Phys. Rev. A 83 042704
[14] Zhang J C, Zhu Z L, Sun J F 2012 Acta Phys. Sin. 61 093401 (in Chinese) [张计才, 朱遵略, 孙金锋 2012 61 093401]
[15] Dalgarno A, Rudge M R H 1965 Proc. R. Soc. London Ser. A 286 519
[16] Simos T E 1997 Computers Chem. 21 125
[17] Mott N F, Massey H S W 1965 The Theory of Atomic Collisons (Oxford: Clarendon)
[18] Flambaum V V, Gribakin G F, Harabati C 1999 Phys. Rev. A 59 1998
[19] Gribakin G F, Flambaum V V 1993 Phys. Rev. A 48 546
[20] Jamieson M J, Zygelman B 2001 Phys. Rev. A 64 032703
[21] Mount B J, Redshaw M, Myers E G 2010 Phys. Rev. A 82 042513
[22] Jamieson M J, Sarbazi-Azad H, Ouerdane H, Jeung G-H, Lee Y S, Lee W C 2003 J. Phys. B 36 1085
[23] Anderlini M, Courtade E, Cristiani M, Cossart D, Ciampini D, Sias C, Morsch O, Arimondo E 2005 Phys. Rev. A 71 061401
[24] Boesten H M J M, Tsai C C, Verhaar B J, Heinzen D J 1996 Phys. Rev. Lett. 77 5194
[25] Weiss S B, Bhattacharya M, Bigelow N P 2003 Phys. Rev. A 68 042708
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