The derivation of the harmonic approximation of the Hamiltonian of a model of coupled three-dimensional harmonic oscillator is presented. It is shown how the splitting of the total Hamiltonian into the intrinsic and collective Hamiltonians leads to the description of the mechanism for energy dissipation in physical systems.
KeywordsHarmonic ApproximationEnergy DissipationCoupled OscillatorsHeavy-IonsDinuclear SystemCluster Model
Diaz-Torres, A., Hinde, D.J., Dasgupta, M., Milburn, G.J. and Tostevin, J.A. (2008) Dissipative Quantum Dynamics in Low-Energy Collisions of Complex Nuclei. Physical Review C, 78, Article ID: 064604. http://dx.doi.org/10.1103/physrevc.78.064604
Diaz-Torres, A., Hinde, D.J., Dasgupta, M., Milburn, G.J. and Tostevin, J.A. (2009) Coupled-Channels Approach for Dissipative Quantum Dynamics in Near-Barrier Collisions. International Conference on New Aspects of Heavy-Ion Barrier, Chicago. http://dx.doi.org/10.1063/1.3108859
Swiatecki, W.J. and Bjфrnholm, S. (1972) Fission and Fusion Dynamics. Physics Reports, 4, 326-342. http://dx.doi.org/10.1016/0370-1573(72)90003-8
Nörenberg, W. and Weidenmüller, H.A. (1976) Introduction to the Theory of Heavy-Ion Collisions. Lecture Notes in Physics 5, Springer-Verlag, Berlin.
Hasse, R.W. (1978) Approaches to Nuclear Friction. Reports on Progress in Physics, 41, 1027-1101. http://dx.doi.org/10.1088/0034-4885/41/7/002
Weidenmüller, H.A. (1980) Transport Theories of Heavy-Ion Reactions. Progress in Particle and Nuclear Physics, 3, 49. http://dx.doi.org/10.1016/0146-6410(80)90030-7
Mshelia, E.D. (1997) Nuclear Science and Technology in Human Progress. (Unpublished University Inaugural Lecture). Abubakar Tafawa Balewa University, Bauchi.
Aritomo, Y., Hagino, K., Nishio, K. and Chiba, S. (2012) Dynamical Approach to Heavy-Ion Induced Fission Using Actinide Target Nuclei at Energies around the Coulomb Barrier. Physical Review C, 85, Article ID: 044614. http://dx.doi.org/10.1103/PhysRevC.85.044614
Liu, Z.H. and Bao, J.D. (2013) Possibility to Produce Element 120 in the 54Cr+248Cm Hot Fusion Reaction. Physical Review C, 87, Article ID: 0344616. http://dx.doi.org/10.1103/PhysRevC.87.034616
Gontchar, I.I., Bhattacharya, R. and Chushnyakova, M.V. (2014) Quantitative Analysis of Precise Heavy-Ion Fusion Data at Above-Barrier Energies Using Skyrme-Hartree-Fock Nuclear Densities. Physical Review C, 89, Article ID: 034601. http://dx.doi.org/10.1103/PhysRevC.89.034601
Wen, K., Sakata, F., Li, Z.-X., Wu, X., Zhang, Y. and Zhou, S. (2014) Energy Dependence of the Nucleus-Nucleus Potential and the Friction Parameter in Fusion Reactions. Physical Review C, 90, Article ID: 054613. http://dx.doi.org/10.1103/PhysRevC.90.054613
Mshelia, E.D., Scheid, W. and Greiner, W. (1975) Theory of Energy Dissipation in Heavy-Ion Reactions. Il Nuovo Cimento A, 30, 589-608. http://dx.doi.org/10.1007/BF02730488
Mshelia, E.D., Haln, D. and Scheid, W. (1981) Energy Dissipation in a Model of Coupled Oscillators. Il Nuovo Cimento A, 61, 28-55. http://dx.doi.org/10.1007/BF02776606
Mshelia, E.D. and Ngadda, Y.H. (1989) A Stimulation for Energy Dissipation in Nuclear Reactions. Journal of Physics G: Nuclear and Particle Physics, 15, 1281-1290. http://dx.doi.org/10.1088/0954-3899/15/8/023
Ibeh, G.J. and Mshelia, E.D. (2014) Energy Dissipation in a Model of Coupled Three-Dimensional Harmonic Oscillator. Far East Journal of Mathematical Sciences, 88, 107-136.
Corben, H.C. and Stehle, P. (1960) Classical Mechanics. John Wiley, New York, 113-131, 364-372.
Wells, D.A. (1967) Theory and Problems of Lagrangian Dynamics. Schaum Publication, New York.
Marion, J.B. and Thornton, S.T. (1995) Classical Dynamics of Particles and Systems. 4th Edition, Saunders College Publications, New York.
Goldstein, H., Poole, C. and Safko, J. (2002) Classical Mechanics. 3rd Edition, Addison-Wesley, San Francisco, 238-258.
Wilson Jr., B., Decius, J.C. and Paul, C.C. (1980) Molecular Vibrations. Dover Publications, Inc., New York.
Desloge, E.A. (1982) Classical Mechanics. Volume II, Wiley-Interscience, New York, 665-707.
Mshelia, E.D. (1995) Method of Normal Coordinates in the Formulation of a System with Dissipation: The Harmonic Oscillator. Il Nuovo Cimento A, 108, 709-721. http://dx.doi.org/10.1007/BF02813376
Schiff, L.I. (1987) Quantum Mechanics. 3rd Edition, McGraw-Hill, New York, 50-52.
Greiner, W. (1994) Quantum Mechanics: An Introduction. 3rd Edition, Springer-Verlag, New York, 97-105.
Courant, R. and Hilbert, D. (1953) Methods of Mathematical Physics. Interscience Publishers, New York, 424.
Volkov, V.V. (1978) Deep Inelastic Transfer Reaction—The New Type of Reactions between Complex Nuclei. Physics Reports, 44, 93-157. http://dx.doi.org/10.1016/0370-1573(78)90200-4
Iachello, F. and Jackson, A.D. (1982) A Phenomenological Approach to α-Clustering in Heavy Nuclei. Physics Letters B, 108, 151-154. http://dx.doi.org/10.1016/0370-2693(82)91162-5
Greiner, W., Park, J.Y. and Scheid, W. (1995) Nuclear Molecules. World Scientific, Singapore.
Buck, B., Merchant, A.C. and Perez, S.M. (1998) Systematic Study of Exotic Clustering in Even-Even Actinide Nuclei. Physical Review C, 58, 2049-2060. http://dx.doi.org/10.1103/physrevc.58.2049
Buck, B., Merchant, A.C. and Perez, S.M. (1999) Cluster Structure and Gamma Transitions in Actinides. Physical Review C, 59, 750-754. http://dx.doi.org/10.1103/PhysRevC.59.750
Adamian, G.G., Antonenko, N.V. and Scheid, W. (2000) Isotopic Dependence of Fusion Cross Sections in Reactions with Heavy Nuclei. Nuclear Physics A, 678, 24-38. http://dx.doi.org/10.1016/s0375-9474(00)00317-1
Mshelia, E.D. and Scheid, W. (2004) Collective Dynamics of a Dinuclear System. The European Physical Journal A, 20, 251-254. http://dx.doi.org/10.1140/epja/i2003-10102-7
Li, W., Nan, W., Fei, J., Hushan, X., Wei, Z., Li, Q.F., et al. (2006) Particle Transfer and Fusion Cross-Section for Super-Heavy Nuclei in Dinuclear System. Journal of Physics G, 32, 1143-1155. http://dx.doi.org/10.1088/0954-3899/32/8/006
Kalandarov, S.A., Adamian, G.G., Antonenko, N.V. and Scheid, W. (2011) Role of Angular Momentum in the Production of Complex Fragments in Fusion and Quasifission Reactions. Physical Review C, 83, Article ID: 054611. http://dx.doi.org/10.1103/PhysRevC.83.054611
Kalandarov, S.A., Adamian, G.G, Antonenko, N.V., Scheid, W., Heinz, S., Comas, V., Hofman, S., Khuyagbaatar, J., Ackermann, D., Heredia, J., HeBberger, F.P., Kindler, B., Lommel, B. and Mann, R. (2011) Emission of Cluster with Z > 2 from Excited Actinide Nuclei. Physical Review C, 84, Article ID: 054607. http://dx.doi.org/10.1103/PhysRevC.84.054607
Kalandarov, S.A., Adamian, G.G., Antonenko, N.V., Scheid, W. and Wieleczko, J.P. (2011) Role of the Entrance Channel in the Production of Complex Fragments in Fusion-Fission and Quasifission Reactions in the Framework of the Dinuclear System Model. Physical Review C, 84, Article ID: 064601. http://dx.doi.org/10.1103/PhysRevC.84.064601
Bansal, M., Sahila, C. and Rajk, G. (2012) Dynamical Cluster-Decay Model Using Various Formulations of a Proximity Potential for Compact Non-Coplanar Nuclei: Application to the 64Ni+100Mo Reaction. Physical Review C, 86, Article ID: 034604. http://dx.doi.org/10.1103/physrevc.86.034604
Adamian, G.G., Antonenko, N.V. and Lenske, H. (2015) Role of the Neck Degree of Freedom in Cold Fusion Reactions. Physical Review C, 91, Article ID: 054602. http://dx.doi.org/10.1103/PhysRevC.91.054602