Ground State of 4-7H Considering Internal Collective Rotation


The g.s. of heavy and superheavy hydrogen isotopes, namely 4-7 H, are successfully examined by applying the Isomorphic Shell Model. Properties examined are binding energies and effective radii. The novelty of the present work is that, due to the small number of nucleons involved and the subsequently large deformation, an internal collective rotation appears which is inseparable from the usual internal motion even in the ground states of these nuclei, i.e., for such nuclei the adiabatic approximation is not valid. This extra degree of freedom leads to a reduction of binding energies, an increase of effective radii, and an increase of level widths.

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S. Paschalis and G. S. Anagnostatos, "Ground State of 4-7H Considering Internal Collective Rotation," Journal of Modern Physics, Vol. 4 No. 5B, 2013, pp. 66-77. doi: 10.4236/jmp.2013.45B012.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] D. V. Aleksandrov, E. A. Ganza, Yu. A. Glukhov et al., “Observation of An Unstable Superheavy Hydrogen Isotope 6H in the Reaction 7Li(7Li, 8B)”, Soviet Journal of Nuclear Physics, Vol. 39, 1984, pp. 323-325.
[2] A. V. Belozyorov, C. Borcea, Z. Dlouhy et al., “Search for 4H, 5H, and 6H Nuclei in the 11B-Induced Reaction on 9Be”, Nuclear Physics A, Vol. 460, 1986, pp. 352-360. doi:10.1016/0375-9474(86)90131-4
[3] G. Audi and A. H. Wapstra, “The 1995 Update to the Atomic Mass Evaluations,” Nuclear Physics A, Vol. 595. 1995. pp. 409-480.doi:10.1016/0375-9474(95)00445-9
[4] N. B. Shul’gina, B. V. Danilin, L. V. Grigorenko et al., “Nuclear Structure of 5H in a Three-Body 3H + n + n model,” Physical Review C, Vol. 62, 2000, pp. 014312-1 – 014312-4.
[5] A. A. Korsheninnikov, M. S. Golovkov, I. Tanihata et al., “Super-heavy Hydrogen 5H,” Physical Review Letters, 87, No. 9, 2001, pp. 092501-1 – 092501-4.
[6] P. Descouvemont and A. Kharbach, “Microscopic Cluster Study of the 5H Nucleus,” Physical Review C, Vol. 63, 2001, pp. 027001-1 – 027001-4.
[7] M. Meister, L. V. Chulkov, H. Simon et al., “The t + n + n System and 5H,” Physical Review Letters, Vol. 91, No. 16, 2003, pp. 162504-1 – 162504-4.
[8] M. Meister, L. V. Chulkov, H. Simon et al., “Searching for the 5H Resonance in the t + n + n System,” Nuclear Physical A, Vol. 723, 2003, pp. 13-31. doi:10.1016/S0375-9474(03)01312-5
[9] M. G. Gornov, M. N. Ber, Yu. B. Gurov, et al., “Spectroscopy of the 5H Super-heavy Hydrogen Isotope,” Journal of Experimental and Theo-retical Physics Letters, Vol. 77, No. 7, 2003, pp. 344-348. doi:10.1134/1.1581957
[10] A. A. Korsheninnikov, E. Yu. Nikolskii, E. A. Kuzmin et al., “Experimental Evidence for the Existence of 7H and for a Specific Structure of 8He,” Physical Review Letters, Vol. 90, No. 8, 2003, pp. 082501-1 – 082501-4.
[11] G. M. Tel-Akopian, D. D. Bogdanov, A. S. Fomichev et al., “Resonance States of Hydrogen Nuclei 4H and 5H Obtained in Transfer Reactions with Exotic Beams,” Physical of Atomic Nuclei, Vol. 66, No. 8, 2003, pp. 1544-1551. doi:10.1134/1.1601763
[12] Koji Arai, “Resonance States of 5H and 5Be in a Microscopic Three-Cluster Model,” Physical Review C, Vol. 68, 2003, pp. 034303-1 – 034303-7.
[13] S. I. Sidorchuk, D. D. Bogdanov, A. S. Fomichev et al., “Experi-mental Study of 4H in the Reactions 2H(t, p) and 3H(t, d),” Physical Letters B, Vol. 594, 2004, pp. 54-60. doi:10.1016/j.physletb.2004.05.007
[14] L. V. Grigorenko, N. K. Timofeyuk and M. V. Zhukov, “Broad States beyond the Neutron Drip Line,” The Europen Physical Journal A-Hadrons and Nuclei, Vol. 19, 2004, pp. 187-201. doi:10.1140/epja/i2003-10124-1
[15] M. Caamano, D. Cortina-Gil, W. Mitting et al.,“Resonance State in 7H,” Physical Review Letters, Vol. 99, 2007, pp. 062502-1 – 062502-4.
[16] Yu. B. Gurov, S. V. Lapushkin, B. A. Chernyshev, at al., “Search for Superheavy Hydrogen Isotopes in Pion Absorption Reactions,” Physical of Particles and Nuclei, Vol. 40, No. 4, 2009, pp. 558-581. doi:10.1134/S1063779609040054
[17] C. W. Sherwin, “In-troduction to Quantum Mechanics,” Holt, Rinehart and Winston, New York, 1959, p. 205.
[18] J. Leech, “Equilibrium of Sets of Particles on a Sphere,” Mathematical Gazette, Vol. 41, 1957, pp. 81-90. doi:10.2307/3610579
[19] G. S. Anagnostatos and C. N. Panos, “Simple Static Central Potentials as Effective Nucleon-Nucleon Interactions”, Lettere Nuovo Cimento, Vol. 41, No. 12, 1984, pp. 409-414. doi:10.1007/BF02739593
[20] G. S. Anagnostatos, “The Geometry of the Quantization of Angular Momentum (?, s, j) in Fields of Central Symmetry,” Lettere Nuovo Cimento, Vol. 28, No. 17, 1980, pp. 573-576. doi:10.1007/BF02776343
[21] G. S. Anagnostatos, J. Giapitzakis, A. Kyritsis, “Rotational Invariance of Orbital-Angular-Momentum Quantization of Direction for Degenerate States,” Lettere Nuovo Cimento, Vol. 32, No. 11, 1981, pp. 332-335. doi:10.1007/BF02745301
[22] G. S. Anagnostatos, “Magic Numbers in Small Clusters of Rare-Gas and Alkali Atoms,” Physics Letters A, Vol. 124, No. 1-2, 1987, pp. 85-89.
[23] G. S. Anagnostatos, “Fermion /Boson Classification in Microclusters,” Physics Letters A, Vol. 157, No. 1, 1991, pp. 65-72. doi:10.1016/0375-9601(91)90410-A
[24] G. S. Anagnostatos, P. Ginis, and J. Giapitzakis, “α-Planar States in 28Si,” Physical Review C, Vol. 58, No. 6, 1998, pp. 3305-3315.doi:10.1103/PhysRevC.58.3305
[25] P. K. Kakanis and G. S. Anagnostatos, “Persisting α-Planar Structure in 20Ne,” Physical Review C, Vol. 54, No. 6, 1996, pp. 2996-3013. doi:10.1103/PhysRevC.54.2996
[26] G. S. Anagnostatos, “Alpha-Chain States in 12C,” Physical Review C, Vol. 51, No. 1, 1999, pp. 152-159.
[27] G. S. Anagnostatos, A. N. Antonov, P. Ginis, et al., “Nucleon Μomentum and Density Distributions in 4He Considering Internal Rotation,” Physical Review C, Vol. 58, No. 4, 1998, pp. 2115-2119
[28] M. K. Gaidarov, A. N. Antonov, G. S. Anagnostatos, S. E. Massen, M. V. Stoitsov and P. E. Hodgson, “Proton Momentum Distribution in Nuclei beyond 4He,” Physical Review C, Vol. 52, No. 6, 1995, pp. 3026-3031. doi:10.1103/PhysRevC.52.3026
[29] G. S. Anagnostatos, “A New Look at Super-Heavy Niuclei,” Int. J. Mod. Phys. B, Vol. 22, No. 25-26, 2008, pp. 4511-4523. doi:10.1142/S0217979208050267
[30] E. Merzbacher, “Quantum Mechanics,” John Wiley and Sons, Inc., New York, 1961, p.42.
[31] C. Cohen-Tannoudji, B. Diu and F. Laloe, “Quantum Mechanics,” John Wiley & Sons, New York, 1977, p.240.
[32] G. S. Anagnostatos and C. N. Panos, “Effective Two-Nucleon Potential for High-Energy Heavy-Ion Collisions,” Physical Review C, Vol. 26, No. 1, 1982, pp. 260-264.doi:10.1103/PhysRevC.26.260
[33] C. N. Panos and G. S. Anagnostatos, “Comments on á Relation between Average Kinetic Energy and Mean-Square Radius in Nuclei’ ,” Journal of Physics G: Nuclear Physics, Vol. 8, No. 12, 1982, pp. 1651-1658. doi:10.1088/0305-4616/8/12/007
[34] W. F. Hornyak, “Nuclear Structure,” Academic, New York, 1975, p.13.
[35] G. S. Anagnostatos, “Classical Equations-of-Motion Model for High-Energy Heavy-Ion Collisions”, Phys. Rev. C, Vol. 39, No. 3, 1989, pp. 877-883. doi:10.1103/PhysRevC.39.877
[36] G. S. Anagnostatos and C. N. Panos, “Semiclassical Simulation of Finite Nuclei,” Physical Review C, Vol. 42, No. 3, 1990, pp. 961-965. doi:10.1103/PhysRevC.42.961
[37] A. Bohr, B. R. Mottelson, “Nuclear Structure,” W. A. Benjamin, Inc., Advanced Book Program, Reading, Massachusetts, London, Vol. 2, 1975.
[38] A. G. Sitenko and V. K. Tartakovskii, “Lectures on the Theory of the Nucleus,” Pergamon Press, Oxford, 1975 p. 210.
[39] D. J. Rowe, “Nuclear Collective Motion (Models and Theory)”, Methuen and Co. Ltd., 11 New Fetter Lane, London EC4, 1970, p.78.
[40] G. S. Anagnostatos, “Intrinsic-collective coupling in 6He and 8He,” In: Yu,E. Penionzhkevich and R. Kalpakchieva, Eds., Proceedings of the International Conference. on Exotic Nuclei, Foros, Crimea, 1-5 October, 1991. World Scientific, London, 1993, p. 104.
[41] C. W. de Jager, H. de Vries, and C. de Vries, “Nuclear Charge and Momentum Distributions,” Atomic Data and Nuclear Data Tables, Vol. 14, No. 5-6, 1974, 479-665. doi:10.1016/S0092-640X(74)80002-1
[42] G. S. Anagnostatos, “Symmetry Description of the Independent Particle Model,” Lettere Nuovo Cimento, Vol. 29, No. 6, 1980, pp. 188-192. doi:10.1007/BF02743377
[43] J. Giapitzakis, “Σummxtriεz στην Πυρηνικh Uλη και στουz Σ Υπερπυρhνεz,” Ph.D. Dissertation, University of Patras, General Section, Patras, Greece, 2003.
[44] G. S. Anagnostatos, “On the Possible Stability of Tetraneutrons and Hexaneutrons,” International Journal of Modern Physics E, Vol. 17, No. 8, 2008, pp. 1557-1575.doi:10.1142/S0218301308010568

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