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Three-cluster description of properties of light neutron- and proton-rich nuclei in the framework of the algebraic version of the resonating group method

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Abstract

A three-cluster microscopic approach to description of the properties of light atomic nuclei (algebraic version of the resonating group method) is presented. The approach is based on the application of oscillator functions for determination of the wave functions of each cluster and expansion of the function of relative cluster motion. Those applications of the method that are related to the study of the properties of states of the discrete and continuous spectra of neutron- and proton-rich 6He, 8He, 6Be, 5H nuclei and fusion reactions 3H(2H, 2n)4He and 3He(3He, 2p)4He are mainly considered. Technical issues of calculations are discussed to the extent necessary for understanding the presented material. The main attention is concentrated on the presentation of physical results, their comparison with experimental data, and results obtained in other theoretical approaches. Problems associated with the role of the Pauli principle, convergence of numerical results, and approximations made in the course of calculations are also discussed in sufficient detail

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References

  1. Y. Fujiwara and Y. C. Tang, “Three-Cluster Resonating-Group Method in the Coupled-Channel Formalism,” Phys. Lett. B 131, 261–264 (1983).

    Article  ADS  Google Scholar 

  2. Y. Fujiwara and Y. C. Tang, “Reaction Cross Sections in Light Nuclear Systems with the Multiconfiguration Resonating-Group Method,” Prog. Theor. Phys. 93, 711–726 (1995).

    Article  ADS  Google Scholar 

  3. Y. Fujiwara and Y. C. Tang, “Reaction Mechanisms in the Six-Nucleon System with the Multi-Configuration Resonating-Group Method,” Few-Body Syst. 12, 21–35 (1992).

    Article  ADS  Google Scholar 

  4. Y. Fujiwara and Y. C. Tang, “Multiconfiguration Resonating-Group Study of the Six-Nucleon System with Cluster-Rearrangement and Pseudo-Inelastic Configurations,” Phys. Rev. C 43, 96–104 (1991).

    Article  ADS  Google Scholar 

  5. Y. Fujiwara and Y. C. Tang, “Multiconfiguration Resonating-Group Theory of 8Li,” Phys. Rev. C 41, 28–44 (1990).

    Article  ADS  Google Scholar 

  6. P. Descouvemont and D. Baye, “7Li+p and 7Be+n Reactions in a Microscopic Three-Cluster Model,” Nucl. Phys. A 573, 28–46 (1994).

    Article  ADS  Google Scholar 

  7. P. Descouvemont and D. Baye, “Microscopic Study of the 7Li(n, γ)8Li and 7Be(p,γ)8B Reactions in a Multiconfiguration Three-Cluster Model,” Nucl. Phys. A 567, 341–353 (1994).

    Article  ADS  Google Scholar 

  8. P. Descouvemont and D. Baye, “The 7Be(p,γ)8B Reaction in a Microscopic Three-Cluster Model,” Nucl. Phys. A 487, 420–432 (1988).

    Article  ADS  Google Scholar 

  9. A. Csótó and D. Baye, “Microscopic Description of the Beta Delayed Deuteron Emission From 6He,” Phys. Rev. C 49, 818–823 (1994).

    Article  ADS  Google Scholar 

  10. A. Csótó, “Three-Body Resonances in 6He, 6Li, and 6Be, and the Soft Dipole Mode Problem of Neutron Halo Nuclei,” Phys. Rev. C 49, 3035–3041 (1994).

    Article  ADS  Google Scholar 

  11. I. F. Gutich, A. V. Nesterov, and I. P. Okhrimenko, “Study of Tetraneutron Continuum States,” Yad. Fiz. 50, 19–26 (1989) [Phys. At. Nucl. 50, 12 (1989)].

    Google Scholar 

  12. G. F. Filippov, A. V. Nesterov, I. Y. Rybkin, and S. V. Korennov, “The Realization of the Resonating Group Method Algebraic Version for Three-Cluster Systems,” Fiz. Elem. Chastits At. Yadra 25, 1347–1378 (1994) [Phys. Part. Nucl. 25, 569 (1994)].

    Google Scholar 

  13. G. F. Filippov, Yu. A. Lashko, and L. P. Shvedov, “Asymptotic-Potential Approximation and Soft Dipole Mode in the 6He Nuclear System,” Yad. Fiz. 62, 1763–1771 (1999) [Phys. At. Nucl. 62, 1642 (1999)].

    Google Scholar 

  14. G. F. Filippov, K. Kato, and S. V. Korennov, “6He as a Three-Cluster System — Investigation of the Ground State and Continuum 0+ States,” Prog. Theor. Phys. 96, 575–595 (1996).

    Article  ADS  Google Scholar 

  15. V. S. Vasilevsky, A. V. Nesterov, F. Arickx, and P. V. Leuven, “Three-Cluster Model of Six-Nucleon System,” Yad. Fiz. 60, 413–419 (1997) [Phys. At. Nucl. 60, 343 (1997)].

    Google Scholar 

  16. G. Filippov and Y. Lashko, “Structure of Light Neutron-Rich Nuclei and Nuclear Reactions Involving These Nuclei,” Fiz. Elem. Chastits At. Yadra 36, 1373–1424 (2005) [Phys. Part. Nucl. 36, 714 (2005)].

    Google Scholar 

  17. K. Wildermuth and Y. C. Tang, A Unified Theory of the Nucleus (Vieweg, Braunschweig 1977; Mir, Moscow, 1980).

    Google Scholar 

  18. G. F. Filippov and I. P. Okhrimenko, “Use of an Oscillator Basis for Solving Continuum Problems,” Yad. Fiz. 32, 932–939 (1980) [Sov. J. Nucl. Phys. 32, 480 (1980)].

    Google Scholar 

  19. G. F. Filippov, “Account of Correct Asymptotics in Decomposition by Oscillator Basis,” Yad. Fiz. 33, 928–931 (1981) [Sov. J. Nucl. Phys. 33, 488 (1981)].

    Google Scholar 

  20. G. F. Filippov, V. S. Vasilevskií and L. L. Chopovskií “Generalized Coherent States in Nuclear Physics Problems,” Fiz. Elem. Chastits At. Yadra. 15, 1338–1385 (1984) [Sov. J. Part. Nucl. 15, 600 (1984)].

    Google Scholar 

  21. G. F. Filippov, V. S. Vasilevskií, and L. L. Chopovskií “The Solution of the Nucleus Microscopic Theory Problems Based on the Generalized Coherent States Technique,” Fiz. Elem. Chastits At. Yadra. 16, 349–406 (1985) [Sov. J. Part. Nucl. 16, 153 (1985)].

    Google Scholar 

  22. G. F. Filippov, “Dynamics of the Cluster and Collective Degrees of Freedom,” J. Phys. Soc. Jpn. Suppl. 58, 118–128 (1989).

    Google Scholar 

  23. A. Sytcheva, F. Arickx, J. Broeckhove, and V. S. Vasilevsky, “Monopole and Quadrupole Polarization Effects on the α-particle Description of 8Be,” Phys. Rev. C 71, 044322 (2005).

    Article  ADS  Google Scholar 

  24. E. J. Heller and H. A. Yamani, “New L 2 Approach to Quantum Scattering: Theory,” Phys. Rev. A 9, 1201–1208 (1974).

    Article  ADS  Google Scholar 

  25. E. J. Heller and H. A. Yamani, “J-Matrix Method: Application to s-Wave Electron-Hydrogen Scattering,” Phys. Rev. A 9, 1209–1214 (1974).

    Article  ADS  Google Scholar 

  26. H. A. Yamani and L. Fishman, “J-Matrix Method: Extensions to Arbitrary Angular Momentum and to Coulomb Scattering,” J. Math. Phys. 16, 410–420 (1975).

    Article  ADS  Google Scholar 

  27. The J-Matrix Method. Developments and Applications, Ed. by A. D. Alhaidari, H. A. Yamani, E. J. Heller, and M. S. Abdelmonem (Springer, Netherlands, 2008).

    Google Scholar 

  28. V. S. Vasilevsky and F. Arickx, “Algebraic Model for Quantum Scattering: Reformulation, Analysis, and Numerical Strategies,” Phys. Rev. A 55, 265–286 (1997).

    Article  ADS  Google Scholar 

  29. W. Vanroose, J. Broeckhove, and F. Arickx, “Modified J-Matrix Method for Scattering,” Phys. Rev. Lett. 88, 10404 (2002).

    Article  ADS  Google Scholar 

  30. J. Broeckhove, F. Arickx, W. Vanroose, and V. S. Vasilevsky, “The Modified J-Matrix Method for Short Range Potentials,” J. Phys. A Math. Gen. 37, 7769–7781 (2004).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  31. V. S. Vasilevsky, A. V. Nesterov, F. Arickx, and P. V. Leuven, “Dynamics of α + n + n Channel in 6He and 6Li,” Preprint ITP-96-3E (Kiev, 1996).

  32. G. Rosensteel and D. Rowe, “Nuclear Sp(3, R) Model,” Phys. Rev. Lett. 38, 10–14 (1977).

    Article  ADS  Google Scholar 

  33. R. M. Asherova et al., “Some Group Theoretical Aspects of the Generalized Hyperspherical Function Method,” Yad. Fiz. 21, 1126–1134 (1974) [Sov. J. Nucl. Phys. 21, 580 (1974)].

    MathSciNet  Google Scholar 

  34. Y. Fujiwara, Y. C. Tang, and H. Horiuchi, “Generator Coordinate Theory of Normalization Kernels of Cluster Systems. IV: Application of Double Gel’fand Polynomials to SU 4 Symmetry of Cluster Wave Functions,” Prog. Theor. Phys. 70, 809–826 (1983).

    Article  ADS  Google Scholar 

  35. Y. Fujiwara, Y. C. Tang, and H. Horiuchi, “Application of Double Gel’fand Polynomials to the Symmetric Group and Spin-Isospin Wave Functions of Cluster Systems,” J. Math. Phys. 25, 2826–2837 (1984).

    Article  MathSciNet  ADS  Google Scholar 

  36. G. Filippov and Y. Lashko, “Peculiar Properties of the Cluster-Cluster Interaction Induced by the Pauli Exclusion Principle,” Phys. Rev. C 70, 064001 (2004).

    Article  ADS  Google Scholar 

  37. G. F. Filippov et al., “Norm Kernels and the Closeness Relation for Pauli-Allowed Basis Functions,” Few-Body Syst. 33, 173–198 (2003).

    Article  ADS  Google Scholar 

  38. H. Horiuchi, “Generator Coordinate Theory of Allowed States of Many-Cluster Systems,” Prog. Theor. Phys. 55, 1448–1461 (1976).

    Article  ADS  Google Scholar 

  39. H. Horiuchi, “Multi-Cluster Allowed States and Spectroscopic Amplitude of Cluster Transfer,” Prog. Theor. Phys. 58, 204–222 (1977).

    Article  ADS  Google Scholar 

  40. Yu. A. Simonov, “Nuclear Wave Functions for Arbitrary Number of Nucleons,” Yad. Fiz. 7, 1210–1220 (1968) [Sov. J. Nucl. Phys. 7, 722 (1968)].

    Google Scholar 

  41. A. M. Badalyan and Yu. A. Simonov, “Three Body Problem. Equation for Partial Waves,” Yad. Fiz. 3, 1032–1047 (1966) [Sov. J. Nucl. Phys. 3, 755 (1966)].

    Google Scholar 

  42. A. I. Baz’ et al., “Some Applications of the K-Harmonic Method to the Calculation of Properties of Atomic Nuclei,” Fiz. Elem. Chastits At. Yadra 3, 275–318 (1972) [Sov. J. Part. Nucl. 3, 137 (1972)].

    Google Scholar 

  43. Yu. F. Smirnov and K. V. Shitikova, “The K-Harmonics Method and Shell Models,” Fiz. Elem. Chastits At. Yadra. 8, 847–910 (1977) [Sov. J. Part. Nucl. 8, 344 (1977)].

    Google Scholar 

  44. V. D. Efros, “To K-Harmonics Method in Problem of Several Nucleons,” Yad. Fiz. 15, 226–241 (1972) [Sov. J. Nucl. Phys. 15, 128 (1972)].

    Google Scholar 

  45. V. D. Efros, “On Method of Hyperspherical Functions,” Yad. Fiz. 27, 845 (1978) [Sov. J. Nucl. Phys. 27, 448 (1978)].

    Google Scholar 

  46. R. I. Dzhibuti and N. B. Krupennikova, The Method of Hyperspherical Functions in Few-Body Quantum Mechanics (Metsniereba, Tbilisi, 1984) [in Russian].

    Google Scholar 

  47. M. Fabre de la Ripelle and J. Navarro, “First Order of the Hyperspherical Harmonic Expansion Method,” Ann. Phys. (N.Y.) 123, 185–232 (1979).

    Article  MATH  ADS  Google Scholar 

  48. M. Fabre de la Ripelle, H. Fiedeldey, and G. Weichers, “Beyond First Order of the Hyperspherical Harmonic Expansion Method,” Ann. Phys. (N.Y.) 138, 275–318 (1982).

    Article  MATH  ADS  Google Scholar 

  49. M. Fabre de la Ripelle, “Green Function and Scattering Amplitudes in Many-Dimensional Space,” Few-Body Syst. 14, 1–24 (1993).

    Article  ADS  Google Scholar 

  50. M. V. Zhukov et al., “Structure of 6He Nucleus as Three-Body System: α-Particle and Neutron Momentum Distributions,” Nucl. Phys. A 538, 375–381 (1992).

    Article  ADS  Google Scholar 

  51. B. V. Danilin and M. V. Zhukov, “Resonance 3 → 3 Scattering and Structure of the Excited States of A = 6 Nuclei,” Yad. Fiz. 56, 67–83 (1993) [Phys. At. Nucl. 56, 182 (1993)].

    Google Scholar 

  52. J. M. Bang et al., “Few-Body Aspects of Borromean Halo Nuclei,” Phys. Rep. 264, 27–37 (1996).

    Article  ADS  Google Scholar 

  53. M. V. Zhukov et al., “Bound State Properties of Borromean Halo Nuclei: 6He and 11Li,” Phys. Rep. 231, 151–199 (1993).

    Article  ADS  Google Scholar 

  54. A. Cobis, D. V. Fedorov, and A. S. Jensen, “Three-Body Halos. V. Computations of Continuum Spectra for Borromean Nuclei,” Phys. Rev. C 58, 1403–1421 (1998).

    Article  ADS  Google Scholar 

  55. B. V. Danilin et al., “Study of States of Nuclei with A = 6 (J π = 0+, 1+) in Microscopic α + 2N — Model by Method of Hyperspherical Functions,” Yad. Fiz. 53, 71–85 (1991) [Sov. J. Nucl. Phys. 53, 45 (1991)].

    Google Scholar 

  56. L. V. Grigorenko et al., “Three-Body Decay of 6Be,” Phys. Rev. C 80, 034602 (2009).

    Article  ADS  Google Scholar 

  57. A. V. Nesterov, V. S. Vasilevskií, and O. F. Chernov, “A Neutron Halo in 8He,” Yad. Fiz. 64, 1486–1492 (2001) [Phys. At. Nucl. 64, 1409 (2001)].

    Google Scholar 

  58. V. S. Vasilevsky et al., “Algebraic Model for Scattering in Three-s-Cluster Systems. I. Theoretical Background,” Phys. Rev. C 63, 034606 (2001).

    Article  ADS  Google Scholar 

  59. V. S. Vasilevsky et al., “Algebraic Model for Scattering in Three-s-Cluster Systems. II. Resonances in Three-Cluster Continuum of 6He and 6Be,” Phys. Rev. C 63, 034607 (2001).

    Article  ADS  Google Scholar 

  60. G. F. Filippov, A. D. Bazavov, and K. Kato, “Resonance States in the 5He and 6Be,” Yad. Fiz. 62, 1642–1650 (1999) [Phys. At. Nucl. 62, 1642 (1999)].

    Google Scholar 

  61. S. Korennov and P. Descouvemont, “A Microscopic Three-Cluster Model in the Hyperspherical Formalism,” Nucl. Phys. A 740, 249–267 (2004).

    ADS  Google Scholar 

  62. T. Ya. Mikhelashvili, Yu. F. Smirnov, and A. M. Shirokov, “The Continuous Spectrum Effect on Monopole Excitations of the 12C Nucleus Considered as a System of α-Particles,” Yad. Fiz. 48, 969–978 (1988) [Sov. J. Nucl. Phys. 48, 617 (1988)].

    Google Scholar 

  63. Yu. I. Nechaev and Yu. F. Smirnov, “Solution of the Scattering Problem in the Oscillator Representation,” Yad. Fiz. 35, 1385–1391 (1982) [Sov. J. Nucl. Phys. 35, 808 (1982)].

    Google Scholar 

  64. S. A. Rakityansky and S. A. Sofianos, “Jost Function for Coupled Channels,” in Proc. of the Conf. on Few-Body Problems in Physics 98, Autrans, France, 1–6 June, 1998, Ed. by B. Desplanques et al. (Wien, Springer, 1999), pp. 93–97.

    Google Scholar 

  65. H. Masui et al., “Partial Decay Widths in Coupled-Channel Systems with Complex-Scaled Jost Function Method,” Prog. Theor. Phys. 102, 1119–1131 (1999).

    Article  ADS  Google Scholar 

  66. A. Perelomov, “Coherent States for Arbitrary Lie Group,” Comm. Math. Phys. 26, 222–236 (1972).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  67. A. M. Perelomov, Generalized Coherent States and their Applications (Nauka, Moscow, 1987; Springer, Berlin, 1986).

    MATH  Google Scholar 

  68. F. Arickx et al., “The Algebraic Method for the Quantum Theory of Scattering,” Am. J. Phys. 62, 362–370 (1994).

    Article  ADS  Google Scholar 

  69. A. V. Nesterov, “Using the Technique of Multiparticle Oscillator Basis in the Study of Properties of Three Cluster Systems,” Yad. Fiz. 56, 35–46 (1993) [Phys. At. Nucl. 56, 1320 (1993)].

    Google Scholar 

  70. D. V. Fedorov, A. S. Jensen, and K. Riisager, “Three-Body Halos: Gross Properties,” Phys. Rev. C 49, 201–212 (1994).

    Article  ADS  Google Scholar 

  71. V. V. Babikov, The Method of Phase Functions in Quantum Mechanics (Nauka, Moscow, 1976) [in Russian].

    Google Scholar 

  72. F. Calogero, Variable Phase Approach to Potential Scattering (Academic, New York, 1967; Mir, Moscow, 1972).

    MATH  Google Scholar 

  73. J. Wurzer and H. M. Hofmann, “Structure of the Helium Isotopes 4He-8He,” Phys. Rev. C 55, 688–698 (1997).

    Article  ADS  Google Scholar 

  74. K. Varga, Y. Suzuki, and R. G. Lovas, “Microscopic Multicluster Description of Neutron-Halo Nuclei with a Stochastic Variational Method,” Nucl. Phys. A 571, 447–466 (1994).

    Article  ADS  Google Scholar 

  75. S. Karataglidis et al., “Alternative Evaluations of Halos in Nuclei,” Phys. Rev. C 61, 024319 (2000).

    Article  ADS  Google Scholar 

  76. P. Navrátil and B. R. Barrett, “Large-Basis Shell-Model Calculations for p-Shell Nuclei,” Phys. Rev. C 57, 3119–3128 (1998).

    Article  ADS  Google Scholar 

  77. B. V. Danilin et al., “Dynamical Multicluster Model for Electroweak and Charge-Exchange Reactions,” Phys. Rev. C 43, 2835–2843 (1991).

    Article  ADS  Google Scholar 

  78. A. Csótó, “Neutron Halo of 6He in a Microscopic Model,” Phys. Rev. C 48, 165–171 (1993).

    Article  ADS  Google Scholar 

  79. K. Varga, Y. Suzuki, and Y. Ohbayasi, “Microscopic Multicluster Description of the Neutron-Rich Helium Isotopes,” Phys. Rev. C 50, 189–195 (1994).

    Article  ADS  Google Scholar 

  80. F. Ajzenberg-Selove, “Energy Levels of Light Nuclei A = 5–10,” Nucl. Phys. A 490, 1–225 (1988).

    Article  ADS  Google Scholar 

  81. A. A. Ogloblin, “Present Status of Exotic Lightest Nuclei,” in Proc. of the Conf. on Exotic Nuclei, Foros, Crimea, 1–5 Oct. 1991, Ed. by Yu. E. Penionzhkevich and R. Kalpakchieva (World Sci., Singapore, New Jersey, London, Hong Kong, 1991), pp. 36–66.

    Google Scholar 

  82. A. B. Migdal, “Two Interacting Particles in the Potential Hole,” Yad. Fiz. 16, 427–434 (1972) [Sov. J. Nucl. Phys. 16, 238 (1972)].

    Google Scholar 

  83. V. S. VasilevskiÍ and I. Yu. Rybkin, “Astrophysical S Factor of the Reactions t(t, 2n)α and 3He(3He, 2p)α,” Yad. Fiz. 50, 662–670 (1989) [Sov. J. Nucl. Phys. 50, 411 (1989)].

    Google Scholar 

  84. P. G. Hansen and B. Jonson, “The Neutron Halo of Extremely Neutron-Rich Nuclei,” Europhys. Lett. 4, 409–414 (1987).

    Article  ADS  Google Scholar 

  85. A. B. Volkov, “Equilibrum Deformation Calculation of the Ground State Energies of 1p Shell Nuclei,” Nucl. Phys. 74, 33 (1965).

    Article  Google Scholar 

  86. D. R. Thompson, M. LeMere, and Y. C. Tang, “Systematic Investigation of Scattering Problems with the Resonating-Group Method,” Nucl. Phys. A 286, 53–66 (1977).

    Article  ADS  Google Scholar 

  87. K. Arai, Y. Suzuki, and R. G. Lovas, “Structure of 6He with an Extended Three-Cluster Model,” Phys. Rev. C 59, 1432–1439 (1999).

    Article  ADS  Google Scholar 

  88. Y. A. Lashko and G. F. Filippov, “How the Pauli Principle Governs the Decay of Three-Cluster Systems,” Nucl. Phys. A 806, 124–145 (2008).

    Article  ADS  Google Scholar 

  89. I. Tanihata et al., “Measurement of Interaction Cross Sections Using Isotope Beams of Be and B and Isospin Dependence of the Nuclear Radii,” Phys. Lett. B 206, 592–596 (1988).

    Article  ADS  Google Scholar 

  90. I. Tanihata et al., “Revelation of Thick Neutron Skins in Nuclei,” Phys. Lett. B 289, 261–266 (1992).

    Article  ADS  Google Scholar 

  91. G. D. Alkhazov et al., “Nuclear Matter Distributions in the 6He and 8He Nuclei From Differential Cross Sections for Small-Angle Proton Elastic Scattering at Intermediate Energy,” Nucl. Phys. A 712, 269–299 (2002).

    Article  ADS  Google Scholar 

  92. G. D. Alkhazov et al., “Nuclear Matter Distributions in 6He and 8He From Small Angle p-He Scattering in Inverse Kinematics at Intermediate Energy,” Phys. Rev. Lett. 78, 2313–2316 (1997).

    Article  ADS  Google Scholar 

  93. S. Neumaier et al., “Study of the Nucleon Density Distribution of 6He and 8He by Proton Elastic Scattering in Inverse Kinematics,” Nucl. Phys. A 583, 799–802 (1995).

    Article  ADS  Google Scholar 

  94. L. B. Wang et al., “Laser Spectroscopic Determination of the 6He Nuclear Charge Radius,” Phys. Rev. Lett. 93, 142501 (2004).

    Article  ADS  Google Scholar 

  95. P. Mueller et al., “Nuclear Charge Radius of 8He,” Phys. Rev. Lett. 99, 252501 (2007).

    Article  ADS  Google Scholar 

  96. E. Caurier and P. Navrátil, “Proton Radii of 4, 6, 8He Isotopes from High-precision Nucleon-Nucleon Interactions,” Phys. Rev. C 73, 021302 (2006).

    Article  ADS  Google Scholar 

  97. B. V. Danilin et al., “New Modes of Halo Excitation in 6He Nucleus,” Phys. Rev. C 55, R577–R581 (1997).

    Article  ADS  Google Scholar 

  98. A. Csótó, “Three-Body Resonances in 6He, 6Li, and 6Be, and the Soft Dipole Mode Problem of Neutron Halo Nuclei,” Phys. Rev. C 49, 3035–3041 (1994).

    Article  ADS  Google Scholar 

  99. N. Tanaka, Y. Suzuki, and K. Varga, “Exploration of Resonances by Analytic Continuation in the Coupling Constant,” Phys. Rev. C 56, 562–565 (1997).

    Article  ADS  Google Scholar 

  100. B. Jonson, “Light Dripline Nuclei,” Phys. Rep. 389, 1–59 (2004).

    Article  ADS  Google Scholar 

  101. M. S. Golovkov et al., “Correlation Studies of the 5H Spectrum,” Phys. Rev. C 72, 064612 (2005).

    Article  ADS  Google Scholar 

  102. G. M. Ter-Akopian et al., “New Insights into the Resonance States of 5H and 5He,” Eur. Phys. J. A 25(Suppl. 1), 315–320 (2005).

    Article  Google Scholar 

  103. Y. B. Gurov et al., “Spectroscopy of Superheavy Hydrogen Isotopes 4H and 5H,” Eur. Phys. J. A 24, 231–236 (2005).

    Article  ADS  Google Scholar 

  104. S. V. Stepantsov et al., “5H and 5He Nuclear Systems Studied by Means of the 6He + 2H Reaction,” Nucl. Phys. A 738, 436–439 (2004).

    Article  ADS  Google Scholar 

  105. L. V. Chulkov, “Heavy Hydrogen Isotopes 4H and 5H,” Nucl. Phys. A 734, 357 (2004).

    Article  ADS  Google Scholar 

  106. M. Meister et al., “The t + n + n System and 5H,” Phys. Rev. Lett. 91, 162504 (2003).

    Article  ADS  Google Scholar 

  107. M. S. Golovkov et al., “Evidences for Resonance States in 5H,” Phys. Lett. B 566, 70–75 (2003).

    Article  ADS  Google Scholar 

  108. M. Meister et al., “Searching for the 5H Resonance in the t + n + n System,” Nucl. Phys. A 723, 13–31 (2003).

    ADS  Google Scholar 

  109. S. I. Sidorchuk et al., “Resonance States of Hydrogen Nuclei 4H and 5H Obtained in Transfer Reactions with Exotic Beams,” Nucl. Phys. A 719, 229c–232c (2003).

    Article  ADS  Google Scholar 

  110. A. A. Korsheninnikov et al., “Superheavy Hydrogen 5H and Spectroscopy of 7He,” Yad. Fiz. 65, 690–696 (2002) [Phys. At. Nucl. 65, 664 (2002)].

    Google Scholar 

  111. A. A. Korsheninnikov et al., “Superheavy Hydrogen 5H,” Phys. Rev. Lett. 87, 092501 (2001).

    Article  ADS  Google Scholar 

  112. M. S. Golovkov et al., “Spectroscopy of 7He and Superheavy Hydrogen Isotope 5H,” Yad. Fiz. 64, 1315–1318 (2001) [Phys. At. Nucl. 64, 1244 (2001)].

    Google Scholar 

  113. N. B. Shul’gina, “Nuclear Structure of 5H in a Three-Body 3H + n + n Model,” Phys. Rev. C 62, 014312 (2000).

    Article  ADS  Google Scholar 

  114. P. Descouvemont and A. Kharbach, “Microscopic Cluster Study of the 5H Nucleus,” Phys. Rev. C 63, 027001 (2001).

    Article  ADS  Google Scholar 

  115. K. Arai, “Resonance States of 5H and 5Be in a Microscopic Three-Cluster Model,” Phys. Rev. C 68, 034303 (2003).

    Article  ADS  Google Scholar 

  116. A. Adahchour and P. Descouvemont, “Microscopic Cluster Model of 5H and 5He (T = 3/2),” Nucl. Phys. A 813, 252–261 (2008).

    Article  ADS  Google Scholar 

  117. M. S. Golovkov et al., “Observation of Excited States in 5H,” Phys. Rev. Lett. 93, 262501 (2004).

    Article  ADS  Google Scholar 

  118. V. I. Kukulin and V. M. Krasnopolsky, “A Stochastic Variational Method for Few Body Systems,” J. Phys. G 3, 795–811 (1977).

    Article  ADS  Google Scholar 

  119. V. I. Kukulin, V. M. Krasnopolsky, and J. Horacek, Theory of Resonances. Principles and Applications (Kluwer Acad., Dordrecht, Boston, London, 1989).

    MATH  Google Scholar 

  120. L. V. Grigorenko, N. K. Timofeyuk, and M. V. Zhukov, “Broad States beyond the Neutron Drip Line. Examples of 5H and 4H,” Eur. Phys. J. A 19, 187–201 (2004).

    Article  ADS  Google Scholar 

  121. L. V. Grigorenko, “Experimental Puzzle of 5H,” Eur. Phys. J. A 20, 419–427 (2004).

    Article  ADS  Google Scholar 

  122. D. R. Tilley et al., “Energy Levels of Light Nuclei A = 5, 6, 7,” Nucl. Phys. A 708, 3–163 (2002).

    Article  ADS  Google Scholar 

  123. S. Aoyama et al., “Binding Mechanism of a Neutron-Rich Nucleus 6He and Its Excited States,” Prog. Theor. Phys. 93, 99–114 (1995).

    Article  ADS  Google Scholar 

  124. S. Aoyama et al., “Theoretical Predictions of Low-Lying Three-Body Resonance States in 6He,” Prog. Theor. Phys. 94, 343–352 (1995).

    Article  ADS  Google Scholar 

  125. I. Reichstein and Y. C. Tang, Study of N + α System with the Resonating-Group Method,” Nucl. Phys. A 158, 529–545 (1970).

    Article  ADS  Google Scholar 

  126. A. Hasegawa and S. Nagata, “Ground State of 6Li,” Prog. Theor. Phys. 45, 1786–1807 (1971).

    Article  ADS  Google Scholar 

  127. F. Tanabe, A. Tohsaki, and R. Tamagaki, “α-α Scattering at Intermediate Energies,” Prog. Theor. Phys. 53, 677–691 (1975).

    Article  ADS  Google Scholar 

  128. A. Csótó, “Low-Lying Continuum Structures in 8B and 8Li in a Microscopic Model,” Phys. Rev. C 61, 024311 (2000).

    Article  ADS  Google Scholar 

  129. T. Myo et al., “Resonances and Continuum States in the Breakup of Halo Nuclei,” Nucl. Phys. A 738, 298–302 (2004).

    Article  ADS  Google Scholar 

  130. S. Aoyama, “Where Is the Ground State of 10He?,” Nucl. Phys. A 722, C474–C478 (2003).

    Article  MathSciNet  ADS  Google Scholar 

  131. P. Hellinckx et al., “User Experiences with Nuclear Physics Calculations on H2O and on the BEgrid,” Lect. Notes Comp. Sci. 3515, 1081–1088 (2005).

    Google Scholar 

  132. D. R. Tilley, H. R. Weller, and G. M. Hale, “Energy Levels of Light Nuclei A = 4,” Nucl. Phys. A 541, 1–104 (1992).

    Article  ADS  Google Scholar 

  133. T. A. Tombrello, “Phase-Shift Analysis of T(n, n)T,” Phys. Rev. 143, 772–774 (1966).

    Article  ADS  Google Scholar 

  134. A. Sytcheva et al., “Influence of Monopole and Quadrupole Channels on the Cluster Continuum of the Lightest p-Shell Nuclei,” J. Phys. G 32, 2137–2155 (2006).

    Article  ADS  Google Scholar 

  135. A. Csótó and G. M. Hale, “S-Matrix and R-Matrix Determination of the Low-Energy 5He and 5Li Resonance Parameters,” Phys. Rev. C 55, 536–539 (1997).

    Article  ADS  Google Scholar 

  136. F. E. Harris, “Expansion Approach to Scattering,” Phys. Rev. Lett. 19, 173–175 (1967).

    Article  ADS  Google Scholar 

  137. R. K. Nesbet, “Analysis of the Harris Variational Method in Scattering Theory,” Phys. Rev. 175, 134–142 (1968).

    Article  ADS  Google Scholar 

  138. Y. K. Ho, “The Method of Complex Coordinate Rotation and Its Applications to Atomic Collision Processes,” Phys. Rep. 99, 1–68 (1983).

    Article  ADS  Google Scholar 

  139. S. Typel et al., “Microscopic Study of the Low-Energy 3He(3He,2p)4He and 3H(3H,2n)4He Fusion Cross Sections,” Z. Phys. A 339, 249–253 (1991).

    Article  ADS  Google Scholar 

  140. P. Descouvemont, “Microscopic Analysis of the 3He(3He, 2p)4He and 3H(3H, 2n)4He Reactions in a Three-Cluster Model,” Phys. Rev. C 50, 2635–2638 (1994).

    Article  ADS  Google Scholar 

  141. A. Csótó and K. Langanke, “Large-Space Cluster Model Calculations for the 3He(3He, 2p)4He and 3H(3H, 2n)4He Reactions,” Nucl. Phys. A 646, 387–396 (1999).

    Article  ADS  Google Scholar 

  142. K. Varga and Y. Suzuki, “Precise Solution of Few-Body Problems with the Stochastic Variational Method on a Correlated Gaussian Basis,” Phys. Rev. C 52, 2885–2905 (1995).

    Article  ADS  Google Scholar 

  143. Z. Papp, I. N. Filikhin, and S. L. Yakovlev, “Integral Equations for Three-Body Coulombic Resonances,” Few Body Syst. 30, 31–37 (2001).

    Article  ADS  Google Scholar 

  144. V. I. Serov, S. N. Abramovich, and L. A. Morkin, “Measurement of the Total Cross Section for the Reaction 3H(t, 2n),” At. Energ. 42, 59–61 (1977).

    Article  Google Scholar 

  145. A. M. Govorov et al., “Spectra of α-Particles and Differential Cross Sections for the 3H(t, 2n)4 He Reaction at the Angle of 90°,” Zh. Eksp. Teor. Fiz. 41, 703–707 (1961) [Sov. Phys. JETP 14, 508 (1961)].

    Google Scholar 

  146. R. E. Brown and N. Jarmie, “Hydrogen Fusion-Energy Reactions,” Rad. Eff. 92, 45–57 (1986).

    Article  Google Scholar 

  147. H. M. Agnew et al., “Measurement of the Cross Section for the Reaction T + T − 4He + 2n +11.4 MeV,” Phys. Rev. 84, 862–863 (1951).

    Article  ADS  Google Scholar 

  148. A. Krauss et al., “Astrophysical S(E) Factor of 3He(3He, 2p)4He at Solar Energies,” Nucl. Phys. A 467, 273–290 (1987).

    Article  ADS  Google Scholar 

  149. R. Bonetti et al., “First Measurement of the 3He(3He, 2p)4He Cross Section Down to the Lower Edge of the Solar Gamow Peak,” Phys. Rev. Lett. 82, 5205–5208 (1999).

    Article  ADS  Google Scholar 

  150. C. Arpesella et al., “The Cross Section of 3He(3He, 2p)4He Measured at Solar Energies,” Phys. Rev. C 57, 2700–2710 (1998).

    Article  ADS  Google Scholar 

  151. M. R. Dwarakanath, H. Winkler, “3He(3He,2p)4He Total Cross-Section Measurements below the Coulomb Barrier,” Phys. Rev. C 4, 1532–1540 (1971).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Bogolyubov Institute of Theoretical Physics, Kyiv, Ukraine

    A. V. Nesterov & V. S. Vasilevsky

  2. Group of Computational Modeling and Programming, University of Antwerp, Antwerp, Belgium

    F. Arickx & J. Broeckhove

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  1. A. V. Nesterov
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Original Russian Text © A.V. Nesterov, F. Arickx, J. Broeckhove, V.S. Vasilevsky, 2010, published in Fizika Elementarnykh Chastits i Atomnogo Yadra, 2010, Vol. 41, No. 5.

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Nesterov, A.V., Arickx, F., Broeckhove, J. et al. Three-cluster description of properties of light neutron- and proton-rich nuclei in the framework of the algebraic version of the resonating group method. Phys. Part. Nuclei 41, 716–765 (2010). https://doi.org/10.1134/S1063779610050047

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