Correlated Gaussian hyperspherical method for few-body systems

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 80, Issue 2, 2009, Pages

  Von Stecher, Javier ^a   Greene, Chris H ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHANNEL FUNCTIONS; CORRELATED GAUSSIAN BASIS; FERMION SYSTEMS; FEW BODY SYSTEMS; FOUR-BODY SYSTEMS; GAUSSIANS; HYPERSPHERICAL; HYPERSPHERICAL METHOD; NUMERICAL TECHNIQUES; SHORT RANGE INTERACTIONS; TWO-COMPONENT; UNITARITY;

ELEMENTARY PARTICLES;

EID: 68849097652     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.80.022504     Document Type: Article

References (91)

1. E. Braaten and H. W. Hammer, Phys. Rep. 428, 259 (2006). 10.1016/j.physrep.2006.03.001
2. V. Efimov, Yad. Fiz. 12, 1080 (1970)
3. V. Efimov, [Sov. J. Nucl. Phys. 12, 589 (1971)].
4. B. D. Esry, C. H. Greene, and J. P. Burke, Jr., Phys. Rev. Lett. 83, 1751 (1999). 10.1103/PhysRevLett.83.1751
5. T. Kraemer, Nature (London) 440, 315 (2006). 10.1038/nature04626
6. D. M. Eagles, Phys. Rev. 186, 456 (1969). 10.1103/PhysRev.186.456
7. A. J. Leggett, in Modern Trends in the Theory of Condensed Matter, edited by, A. Pekalski, and, J. Przystawa, (Springer, Berlin, 1980).
8. P. Nozières and S. Schmitt-Rink, J. Low Temp. Phys. 59, 195 (1985). 10.1007/BF00683774
9. M. Greiner, C. A. Regal, and D. S. Jin, Nature (London) 426, 537 (2003). 10.1038/nature02199 (Pubitemid 37526703)
10. S. Jochim, M. Bartenstein, A. Altmeyer, G. Hendl, S. Riedl, C. Chin, J. Hecker Denschlag, and R. Grimm, Science 302, 2101 (2003). 10.1126/science. 1093280 (Pubitemid 38017938)
11. M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, S. Gupta, Z. Hadzibabic, and W. Ketterle, Phys. Rev. Lett. 91, 250401 (2003). 10.1103/PhysRevLett.91.250401
12. T. Bourdel, L. Khaykovich, J. Cubizolles, J. Zhang, F. Chevy, M. Teichmann, L. Tarruell, S. J. J. M. F. Kokkelmans, and C. Salomon, Phys. Rev. Lett. 93, 050401 (2004). 10.1103/PhysRevLett.93.050401
13. C. A. Regal, M. Greiner, and D. S. Jin, Phys. Rev. Lett. 92, 040403 (2004). 10.1103/PhysRevLett.92.040403
14. M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, A. J. Kerman, and W. Ketterle, Phys. Rev. Lett. 92, 120403 (2004). 10.1103/PhysRevLett.92.120403
15. M. W. Zwierlein, J. R. Abo-Shaeer, A. Schirotzek, C. H. Schunck, and W. Ketterle, Nature (London) 435, 1047 (2005). 10.1038/nature03858 (Pubitemid 40910506)
16. D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. 81, 3108 (1998). 10.1103/PhysRevLett.81.3108
17. B. Paredes, A. Widera, V. Murg, O. Mandel, S. Fölling, I. Cirac, G. Shlyapnikov, T. Hänsch, I. Bloch, and N. Contact, Nature (London) 429, 277 (2004). 10.1038/nature02530 (Pubitemid 38684809)
18. T. Kinoshita, T. Wenger, and D. Weiss, Science 305, 1125 (2004). 10.1126/science.1100700 (Pubitemid 39100318)
19. I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. 80, 885 (2008). 10.1103/RevModPhys.80.885
20. D. S. Petrov, Phys. Rev. Lett. 93, 143201 (2004). 10.1103/PhysRevLett.93. 143201
21. D. S. Petrov, Phys. Rev. A 67, 010703 (R) (2003). 10.1103/PhysRevA.67. 010703
22. D. S. Petrov, C. Salomon, and G. V. Shlyapnikov, Phys. Rev. Lett. 93, 090404 (2004). 10.1103/PhysRevLett.93.090404
23. A. Deltuva and A. Fonseca, Phys. Rev. Lett. 98, 162502 (2007). 10.1103/PhysRevLett.98.162502 (Pubitemid 46626888)
24. J. von Stecher and C. H. Greene, Phys. Rev. Lett. 99, 090402 (2007). 10.1103/PhysRevLett.99.090402 (Pubitemid 47358540)
25. J. P. D'Incao, S. T. Rittenhouse, N. P. Mehta, and C. H. Greene, Phys. Rev. A 79, 030501 (R) (2009). 10.1103/PhysRevA.79.030501
26. Y. Wang and B. D. Esry, Phys. Rev. Lett. 102, 133201 (2009). 10.1103/PhysRevLett.102.133201
27. L. D. Faddeev, Zh. Eksp. Teor. Fiz. 39, 1459 (1960).
28. Y. Suzuki and K. Varga, Stochastic Variational Approach to Quantum-Mechanical Few-Body Problems (Springer-Verlag, Berlin, 1998).
29. R. A. Malfliet and J. A. Tjon, Nucl. Phys. A. 127, 161 (1969). 10.1016/0375-9474(69)90775-1
30. O. A. Yakubovsky, Yad. Fiz. 5, 1312 (1967)
31. O. A. Yakubovsky, [Sov. J. Nucl. Phys. 5, 937 (1967)].
32. J. Macek, J. Phys. B 1, 831 (1968). 10.1088/0022-3700/1/5/309
33. K. Singer, Proc. R. Soc. London, Ser. A 258, 412 (1960). 10.1098/rspa.1960.0196
34. S. F. Boys, Proc. R. Soc. London, Ser. A 258, 402 (1960). 10.1098/rspa.1960.0195
35. V. I. Kukulin and V. Krasnopol'sky, J. Phys. G 3, 795 (1977). 10.1088/0305-4616/3/6/011
36. K. Varga and Y. Suzuki, Phys. Rev. A 53, 1907 (1996). 10.1103/PhysRevA.53.1907
37. K. Varga and Y. Suzuki, Phys. Rev. C 52, 2885 (1995). 10.1103/PhysRevC.52.2885 (Pubitemid 126012991)
38. K. Varga and Y. Suzuki, Comput. Phys. Commun. 106, 157 (1997). 10.1016/S0010-4655(97)00059-3
39. K. Varga, Y. Suzuki, and R. G. Lovas, Nucl. Phys. A. 571, 447 (1994). 10.1016/0375-9474(94)90221-6
40. D. Blume, J. von Stecher, and C. H. Greene, Phys. Rev. Lett. 99, 233201 (2007). 10.1103/PhysRevLett.99.233201 (Pubitemid 350231916)
41. J. von Stecher and C. H. Greene, Phys. Rev. A 75, 022716 (2007). 10.1103/PhysRevA.75.022716 (Pubitemid 46294507)
42. J. von Stecher, C. H. Greene, and D. Blume, Phys. Rev. A 77, 043619 (2008). 10.1103/PhysRevA.77.043619 (Pubitemid 351555236)
43. J. Mezei, A. Kruppa, and K. Varga, Few-Body Syst. 41, 233 (2007). 10.1007/s00601-007-0176-4
44. J. Y. Zhang, J. Mitroy, and K. Varga, Phys. Rev. A 78, 042705 (2008). 10.1103/PhysRevA.78.042705
45. K. Varga, J. Mitroy, J. Z. Mezei, and A. T. Kruppa, Phys. Rev. A 77, 044502 (2008). 10.1103/PhysRevA.77.044502
46. J. Mitroy, J. Y. Zhang, and K. Varga, Phys. Rev. Lett. 101, 123201 (2008). 10.1103/PhysRevLett.101.123201
47. L. M. Delves, Nucl. Phys. 9, 391 (1959). 10.1016/0029-5582(58)90372-9
48. L. M. Delves, Nucl. Phys. 20, 275 (1960). 10.1016/0029-5582(60)90174-7
49. C. D. Lin, Phys. Rep. 257, 1 (1995). 10.1016/0370-1573(94)00094-J
50. Y. F. Smirnov and K. V. Shitikova, Sov. J. Part. Nucl. 8, 44 (1977).
51. X. Chapuisat, Phys. Rev. A 45, 4277 (1992). 10.1103/PhysRevA.45.4277
52. M. Aymar, C. H. Greene, and E. Luc-Koenig, Rev. Mod. Phys. 68, 1015 (1996). 10.1103/RevModPhys.68.1015
53. O. Zatsarinny and K. Bartschat, J. Phys. B 37, 2173 (2004). 10.1088/0953-4075/37/10/013
54. A. Sunderland, C. Noble, V. Burke, and P. Burke, Comput. Phys. Commun. 145, 311 (2002). 10.1016/S0010-4655(02)00140-6 (Pubitemid 34552150)
55. R. T. Pack and G. A. Parker, J. Chem. Phys. 87, 3888 (1987). 10.1063/1.452944
56. Y. Zhou, C. D. Lin, and J. Shertzer, J. Phys. B 26, 3937 (1993). 10.1088/0953-4075/26/21/026
57. B. D. Esry, C. D. Lin, and C. H. Greene, Phys. Rev. A 54, 394 (1996). 10.1103/PhysRevA.54.394
58. H. Suno, B. D. Esry, C. H. Greene, and J. P. Burke, Jr., Phys. Rev. A 65, 042725 (2002). 10.1103/PhysRevA.65.042725
59. F. Werner and Y. Castin, Phys. Rev. A 74, 053604 (2006). 10.1103/PhysRevA.74.053604 (Pubitemid 44707443)
60. S. Y. Chang and G. F. Bertsch, Phys. Rev. A 76, 021603 (R) (2007). 10.1103/PhysRevA.76.021603 (Pubitemid 47223014)
61. J. von Stecher, C. H. Greene, and D. Blume, Phys. Rev. A 76, 053613 (2007). 10.1103/PhysRevA.76.053613 (Pubitemid 350128793)
62. Y. Alhassid, G. F. Bertsch, and L. Fang, Phys. Rev. Lett. 100, 230401 (2008). 10.1103/PhysRevLett.100.230401
63. I. Stetcu, B. R. Barrett, U. van Kolck, and J. P. Vary, Phys. Rev. A 76, 063613 (2007). 10.1103/PhysRevA.76.063613 (Pubitemid 350276562)
64. H. H. Sørensen, D. V. Fedorov, and A. S. Jensen, AIP Conf. Proc. 777, 12 (2005). 10.1063/1.1996868 (Pubitemid 44520385)
65. H. H. Sørensen, M.S. thesis, University of Aarhus, 2005
66. H. H. Sørensen, [e-print arXiv:cond-mat/0502126].
67. U. Fano, Phys. Rev. A 24, 2402 (1981). 10.1103/PhysRevA.24.2402
68. Even though μ is arbitrary, there is one preferable selection μ= [i mi / (i mi)] 1/ (N-1) that conserves the volume element of the coordinate transformation. In this paper, we will only present results for equal-mass systems for which it is simpler to simply choose μ=m.
69. H. T. Coelho and J. E. Hornos, Phys. Rev. A 43, 6379 (1991). 10.1103/PhysRevA.43.6379
70. N. P. Mehta, S. T. Rittenhouse, J. P. D'Incao, and C. H. Greene, e-print arXiv:0706.1296.
71. The (3 NP -7) numerical integration results from the following reasoning: initially, we have 3 NP numerical integration but three dimensions are removed by decoupling the center of mass motion, three dimensions are removed fixing the Euler angles, and one dimension is removed by fixing R.
72. J. von Stecher, Ph.D. thesis, University of Colorado, 2008
73. available at http://jilawww.colorado.edu/pubs/thesis/vonstecher/ vonstecherthesis.pdf.
74. J. Macek, Z. Phys. D: At., Mol. Clusters 3, 31 (1986). 10.1007/BF01442345
75. D. Blume and C. H. Greene, J. Chem. Phys. 112, 8053 (2000). 10.1063/1.481404
76. J. von Stecher, J. P. D'Incao, and C. H. Greene, Nat. Phys. 5, 417 (2009). 10.1038/nphys1253
77. J. P. D'Incao, J. von Stecher, and C. H. Greene, Phys. Rev. Lett. 103, 033004 (2009). 10.1103/PhysRevLett.103.033004
78. S. Tan, e-print arXiv:cond-mat/0412764.
79. The coefficients pν can be easily related with the sν of Ref. by sν = pν-1 -1/2.
80. N. P. Mehta, S. T. Rittenhouse, J. P. D'Incao, J. von Stecher, and C. H. Greene, e-print arXiv:0903.4145.
81. F. Ferlaino, S. Knoop, M. Berninger, W. Harm, J. P. D'Incao, H. C. Nägerl, and R. Grimm, Phys. Rev. Lett. 102, 140401 (2009). 10.1103/PhysRevLett.102.140401
82. S. B. Papp, J. M. Pino, and C. E. Wieman, Phys. Rev. Lett. 101, 040402 (2008). 10.1103/PhysRevLett.101.040402
83. C. J. Myatt, E. A. Burt, R. W. Ghrist, E. A. Cornell, and C. E. Wieman, Phys. Rev. Lett. 78, 586 (1997). 10.1103/PhysRevLett.78.586
84. G. Thalhammer, G. Barontini, L. De Sarlo, J. Catani, F. Minardi, and M. Inguscio, Phys. Rev. Lett. 100, 210402 (2008). 10.1103/PhysRevLett.100.210402 (Pubitemid 351777239)
85. C. Weber, G. Barontini, J. Catani, G. Thalhammer, M. Inguscio, and F. Minardi, Phys. Rev. A 78, 061601 (R) (2008). 10.1103/PhysRevA.78.061601
86. G. Modugno, G. Roati, F. Riboli, F. Ferlaino, R. Brecha, and M. Inguscio, Science 297, 2240 (2002). 10.1126/science.1077386
87. S. Inouye, J. Goldwin, M. L. Olsen, C. Ticknor, J. L. Bohn, and D. S. Jin, Phys. Rev. Lett. 93, 183201 (2004). 10.1103/PhysRevLett.93.183201
88. M. L. Olsen, J. D. Perreault, T. D. Cumby, and D. S. Jin, e-print arXiv:0810.1965.
89. T. B. Ottenstein, T. Lompe, M. Kohnen, A. N. Wenz, and S. Jochim, Phys. Rev. Lett. 101, 203202 (2008). 10.1103/PhysRevLett.101.203202
90. J. H. Huckans, J. R. Williams, E. L. Hazlett, R. W. Stites, and K. M. O'Hara, Phys. Rev. Lett. 102, 165302 (2009). 10.1103/PhysRevLett.102.165302
91. D. Blume, S. T. Rittenhouse, J. von Stecher, and C. H. Greene, Phys. Rev. A 77, 033627 (2008). 10.1103/PhysRevA.77.033627