参考文献:1. Tang ZK, Nouze Y, Goto TJ: Quantum size effect on the excited state of HgI2, PbI2 and BiI3 clusters and molecules in zeolite LTA. / J. Phys. Soc. Jpn. 1992, 61:2943. CrossRef 2. Frank KH, Didde R, Sagner HJ, Eberhardt W: Modification of the surface electronic structure of Cu (111) by monolayer Ni adsorption and the effects on H2 chemisorption. / Phys. Rev. B. 1989, 39:940鈥?48. CrossRef 3. Connerade JP, Dolmatov VK, Lakshmi PA, Manson ST: Electron structure of endohedrally confined atoms: atomic hydrogen in an attractive shell. / J. Phys. B. At. Mol. Opt. Phys. 1999, 32:L239-L244. CrossRef 4. Connerade JP, Dolmatov VK, Manson ST: A unique situation for an endohedral metallofullerene. / J. Phys. B: At. Mol. Opt. Phys. 1999, 32:L395-L403. CrossRef 5. B谩nyai L, Koch SW: / Semiconductor Quantum Dots. World Scientific, London; 1993. 6. Jask贸lski W: Confined many-electron systems. / Phys. Rep. 1996, 271:1鈥?6. CrossRef 7. Michels A, de Boer J, Bijl A: Remarks concerning molecular interaction and their influence on the polarizability. / Physica. (Amsterdam) 1937, 4:981鈥?94. CrossRef 8. Dolmatov VK, Baltenkov AS, Connerade JP, Manson S: Structure and photoionization of confined atoms. / Radiat. Phys. Chem. 2004, 70:417鈥?33. CrossRef 9. Goldman S, Joslin C: Spectroscopic properties of an isotopically compressed hydrogen atom. / J. Phys. Chem. 1992, 96:6021鈥?027. CrossRef 10. Joslin C, Goldman S: Quantum Monte Carlo studies of two-electron atoms constrained in spherical boxes. / J. Phys. B. At. Mol. Opt. Phys. 1992, 25:1965. CrossRef 11. Aquino N, Riveros AF, Rivas-Silva JF: The compressed helium atom variationally treated via a correlated Hylleraas wave function. / Phys. Lett. A. 2003, 307:326鈥?36. CrossRef 12. Patil SH, Varshni YP: A simple description of the spectra of confined hydrogen, helium, and lithium. / Can. J. Phys. 2004, 82:647鈥?59. CrossRef 13. Ten Seldam CA, de Groot SR: On the ground state of a model for compressed helium. / Physica. 1952, 18:891鈥?04. CrossRef 14. Rivelino R, Vianna JDM: A configuration interaction model to investigate many-electron systems in cavities. / J. Phys. B. At. Mol. Opt. Phys. 2001, 34:L645. CrossRef 15. Marin JL, Cruz SA: Enclosed quantum systems: use of the direct variational method. / J. Phys. B. At. Mol. Opt. Phys. 1991, 24:2899. CrossRef 16. Marin JL, Cruz SA: Use of the direct variational method for the study of one- and two-electron atomic systems confined by spherical penetrable boxes. / J. Phys. B. At. Mol. Opt. Phys. 1992, 25:4365. CrossRef 17. Lude帽a EV: SCF Hartree-Fock calculations of ground state wavefunctions of compressed atoms. / J. Chem. Phys. 1978, 69:1170. CrossRef 18. Lude帽a EV, Gregori M: Configuration interaction calculations for two鈥恊lectron atoms in a spherical box. / J. Chem. Phys. 1979, 71:2235. CrossRef 19. Flores-Riveros A, Rodr铆guez-Contreras A: Compression effects in helium-like atoms (Z = 1, 5) constrained by hard spherical walls. / Phys. Lett. A. 2008, 372:6175鈥?182. CrossRef 20. Banerjee A, Kamal C, Chowdhury A: Calculation of ground- and excited-state energies of confined helium atom. / Phys. Lett. A. 2006, 350:121鈥?25. CrossRef 21. Wen-Fang X: A study of confined helium atom. / Commun. Theor. Phys. (Beijing, China) 2007, 48:331鈥?34. CrossRef 22. Wen-Fang X: A helium atom confined by a spherical Gaussian potential well. / Commun. Theor. Phys. (Beijing, China) 2008, 49:1287鈥?290. CrossRef 23. Laughlin C, Chu S: A highly accurate study of a helium atom under pressure. / J. Phys. A. Math. Theor. 2009, 42:265004. CrossRef 24. Montgomery HE Jr, Aquino N, Flores-Riveros A: The ground state energy of a helium atom under strong confinement. / Phys. Lett. A. 2010, 374:2044. CrossRef 25. Wilson CL, Montgomery HE Jr, Sen KD, Thompson DC: Electron correlation energy in confined two-electron systems. / Phys. Lett. A. 2010, 374:4415. CrossRef 26. Doma SB, El-Gammal FN: Applications of the variational Monte Carlo method to the two-electron atom. / Appl. Math. Inf. Sci. 2011, 5:315S-325S. 27. El-Gammal FN: Variational Monte Carlo study of the three-body atomic system. / Alex. J. Math. 2011, 2:1鈥?. 28. Bressanini D, Morosi G: A compact boundary-condition determined wave function for two- electron atomic systems. / J. Phys. B. At. Mol. Opt. Phys. 2008, 41:145001. CrossRef 29. Metropolis N, Rosenbluth AW, Rosenbluth NM, Teller AM, Teller E: Equations of state calculations by fast computing machines. / J. Chem. Phys. 1953, 21:1087. CrossRef 30. Pottorf S, Puzer A, Chou MY: The simple harmonic oscillator ground state using a Variational Monte Carlo method. / Eur. J. Phys. 1999, 20:205. CrossRef 31. Ruiz MB: Hylleraas method for many-electron atoms. / Int. J. Quantum. Chem. 2005, 101:246. CrossRef 32. Foulaadvand ME, Zarenia M: Optimisation of quantum Monte Carlo wave function: steepest descent method. / Int. J. Mod. Phys. C. 2010, 21:523. CrossRef 33. Galek TA, Handy NC, Cohen AJ, Chan GK: Hartree-Fock orbitals which obey the nuclear cusp condition. / Chem. Phys. Lett. 2005, 404:156. CrossRef 34. Lin X, Zhang H, Rappe AM: Optimization of quantum Monte Carlo wave functions using analytical energy derivatives. / J. Chem. Phys. 2000, 112:2650. CrossRef
A new application of variational Monte Carlo method is presented to study the helium atom under the compression effect of a spherical box with radius (r c ). The ground-state energies of the helium atom were calculated for different values of r c . Our calculations were extended to include Li+ and Be2+ ions. The calculations were based on the use of a compact accurate trial wave function with five variational parameters. To optimize variational parameters, we used the steepest descent method. The obtained results are in good agreement with previous results.