Formation of Neutron-Rich and Superheavy Elements in Astrophysical Objects

ABSTRACT

We calculate the reaction and the fusion cross-sections of neutron-rich heavy nuclei taking light exotic isotopes as projectiles. Results of neutron-rich Pb and U isotopes are demonstrated as the representative targets and He, B as the projectiles. The Gluaber Model and the Coupled Channel Formalism are used to evaluate the reaction and the fusion cross-sections for the cases considered. Based on the analysis of these cross-sections, we predict the formation of heavy, superheavy and super-superheavy elements through rapid neutron/ light nuclei capture r-process of the nucleosynthesis in astrophysical objects.

We calculate the reaction and the fusion cross-sections of neutron-rich heavy nuclei taking light exotic isotopes as projectiles. Results of neutron-rich Pb and U isotopes are demonstrated as the representative targets and He, B as the projectiles. The Gluaber Model and the Coupled Channel Formalism are used to evaluate the reaction and the fusion cross-sections for the cases considered. Based on the analysis of these cross-sections, we predict the formation of heavy, superheavy and super-superheavy elements through rapid neutron/ light nuclei capture r-process of the nucleosynthesis in astrophysical objects.

KEYWORDS

Total Nuclear Cross Section, Fusion Reaction Cross Section, Gluaber Model, Coupled Channel Formalism

Total Nuclear Cross Section, Fusion Reaction Cross Section, Gluaber Model, Coupled Channel Formalism

Cite this paper

nullR. Panda and S. Patra, "Formation of Neutron-Rich and Superheavy Elements in Astrophysical Objects,"*Journal of Modern Physics*, Vol. 1 No. 5, 2010, pp. 312-318. doi: 10.4236/jmp.2010.15044.

nullR. Panda and S. Patra, "Formation of Neutron-Rich and Superheavy Elements in Astrophysical Objects,"

References

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[8] A. Ozawa, T. Suzuki and I. Tanihata, “Nuclear Size and Related Topics,” Nuclear Physics A, Vol. 693, No. 1-2, 2001, pp. 32-62.

[9] L. Satpathy, S. K. Patra and R. K. Choudhury, “Fission Decay Properties of Ultra Neutron-Rich Uranium Isotopes,” PRAMANA-Journal of Physics, Vol. 70, No. 1, 2008, pp. 87-99.

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[12] B. D. Serot and J. D. Walecka, “Recent Progress in Quantum Hydrodynamics,” International Journal of Modern Physics E, Vol. 6, No. 4, 1997, pp. 515-631.

[13] R. J. Furnstahl and B. D. Serot, “Parameter Counting in Relativistic Mean-field Models,” Nuclear Physics A, Vol. 671, No. 1-4, 2000, pp. 447-460.

[14] R. J. Glauber, “Lectures on Theoretical Physics,” In: W. E. Brittin and L. C. Dunham, Eds., Interscience, Vol. 1, New York, 1959, p. 315.

[15] P. Shula, “Glauber Model and the Heavy ion Reaction Cross Section,” Physical Review C, Vol. 67, No. 5, 2003, p. 054607.

[16] M. Y. H. Farag, “Modified Glauber Model for the Total Reaction Cross-section of 12C + 12C Collisions,” European Physics Journal A, Vol. 12, No. 4, 2001, pp. 405-411.

[17] S. K. Charagi and S. K. Gupta, “Coulomb-modified Glauber Model Description of Heavy-Ion Reaction Cross Sections,” Physical Review C, Vol. 41, No. 4, 1990, pp. 1610-1618.

[18] S. K. Charagi, “Nucleus-Nucleus Reaction Cross Section at Low Energies: Modified Glauber Model,” Physical Review C, Vol. 48, No. 1, 1993, pp. 452-454.

[19] S. K. Patra, R. N. Panda, P. Arumugam and R. K. Gupta, “Nuclear Reaction Cross Sections of Exotic Nuclei in the Glauber Model for Relativistic Mean Field Densities,” Physical Review C, Vol. 80, No. 6, 2009, p. 064602.

[20] A. Shukla, B. K. Sharma, R. Chandra, P. Arumugam and S. K. Patra, “Nuclear Reaction Studies of Unstable Nuclei Using Relativistic Mean Field Formalisms in Conjunction with the Glauber Model,” Physical Review C, Vol. 76, No. 3, 2007, p. 34601.

[21] B. K. Sharma, et al., “Reaction Cross-Sections for Light Nuclei on 12C using Relativistic Mean Field Formalism,” Journal of Physics G: Nuclear Particle Physics, Vol. 32, No. 11, 2006, pp. 2089-2097.

[22] M. D. Estal, M. Centelles, X. Vinyas and S. K. Patra, “Pairing Properties in Relativistic Mean Field Models Obtained from Effective Field Theory,” Physical Review C, Vol. 63, No. 4, 2001, p. 044321.

[23] S. K. Patra, M. D. Estal, M. Centelles and X. Vi?nas, “Ground-State Properties and Spins of the Odd Z = N + 1 Nuclei 61Ga-97In,” Physical Review C, Vol. 63, No. 2, 2001, p. 024311.

[24] B. A. Ibrahim, Y. Ogawa, Y. Suzuki and I. Tanihata, “Cross Section Calculations in Glauber Model: I. Core Plus One-nucleon Case,” Computer Physics Communications, Vol. 151, No. 3, 2003, pp. 369-386.

[25] K. Hagino, N. Rowley and A. T. Kruppa, “A Program for Coupled-channel Calculations with All Order Couplings for Heavy-Ion Fusion Reactions,” Computer Physics Communications, Vol. 123, No. 1-3, 1999, pp. 143-152.

[26] L. H. Bradt and B. Peters, “The Heavy Nuclei of the Primary Cosmic Radiation,” Physical Review, Vol. 77, No. 1, 1950, pp. 54-70.

[27] S. Barshay, C. B. Dover and J. P. Vary, “Nucleus-nucleus Cross Sections and the Validity of the Factorization Hypothesis at Intermediate and High Energies,” Physical Review C, Vol. 11, No. 2, 1975, pp. 360-369.

[28] S. Barshay, C. B. Dover and J. P. Vary, “The Validity of the Factorization Hypothesis for Nucleus-nucleus Cross Sections at High Energies,” Physics Letters B, Vol. 51, No. 1, 1974, pp. 5-8.

[29] A. Ingemarsson and M. Lantz, “Geometrical Aspects of Reaction Cross Sections for 3He, 4He, and 12C Projectiles,” Physical Review C, Vol. 67, No. 6, 2003, p. 064605.

[30] A. Ingemarsson and M. Lantz, “Energy Dependence of Proton-Nucleus Reaction Cross Sections,” Physical Review C, Vol. 72, No. 6, 2005, p. 064615.

[31] C.-T. Liang, Y.-A. Luo, X.-H. Li and C.-H. Cai, “Systematic Analysis of the Reaction Cross Section for d, 3He and 4He as Projectiles,” Journal of Physics G: Nuclear Particle Physics, Vol. 36, No. 1, 2009, p. 015102.

[32] H. P. Wellisch and D. Axen, “Total Reaction Cross Section Calculations in Proton-nucleus Scattering,” Physical Review C, Vol. 54, No. 3, 1996, pp. 1329-1332.

[33] J. Y. Hostachy, et al., “Elastic and Inelastic Scattering of 12C Ions at Intermediate Energies,” Nuclear Physics A, Vol. 490, No. 2, 1988, pp. 441-470.

[34] V. Bernard, et al., “Production of Charged Pions in Intermediate-Energy Heavy-Ion Collisions,” Nuclear Physics A, Vol. 423, No. 3, 1984, pp. 511-524.

[35] J. N. De, X. Vinyas, S. K. Patra and M. Centelles, “Nuclei beyond the Drip Line,” Physical Review C, Vol. 64, No. 5, 2001, p. 057306.

[36] P. A. Mazzali, et al., “A Neutron-star-Driven X-ray Flash Associated with Supernova SN 2006aj,” Nature, Vol. 442, No. 7106, 2006, pp. 1018-1020.

[37] T. A. Thompson, P. Chang and E. Quataert, “Magnetar Spindown, Hyper-energetic Supernovae, and Gamma Ray Burst,” Astrophysics Journal, Vol. 611, No. 1, 2004, pp. 380-393.

[38] P. O. Lagage and C. J. Cesarsky, “The Maximum Energy of Cosmic Rays Accelerated by Supernova Shocks,” Astronomy and Astrophysics, Vol. 125, No. 2, 1983, pp. 249-257.

[39] J. R. Wilson and R. W. Mayle, “Report on the Progress of Supernova Research by the Livermore Group,” Physics Reports, Vol. 227, No. 1-5, 1993, pp. 97-111.

[40] B. S. Meyer, “The r-, s-, and p- Process in Nucleosynthesis,” Annual Review of Astronomy and Astrophysics, Vol. 32, 1994, pp. 153-190.

[41] J. M. Pearson, “Nuclear Physics: Energy and Matter,” Ch. II, Adam Hilger Ltd, 1986, p. 87.

[42] A. Marinov, et al., “Evidence for the Possible Existence of Long-lived Superheavy Nucleus with Atomic Mass Number A = 292 and Atomic Number Z ≈ 122 in Natural Th,” International Journal of Modern Physics E, Vol. 19, No. 1, 2010, pp. 131-140.

[43] S. K. Patra, M. Bhuyan, M. S. Mehta and R. K. Gupta, “Superdeformed and Hyperdeformed States in Z = 122 Isotopes,” Physical Review C, Vol. 80, No. 3, 2009, p. 034312.

[1] Yu. Ts. Oganessian, et al., “Synthesis of the Isotopes of Elements 118 and 116 in the 249Cf and 245Cm+48Ca Fusion Reaction,” Physical Review C, Vol. 74, No. 4, 2006, p. 044602.

[2] P. Moller and J. R. Nix, “Stability and Decay of Nuclei at the End of the Periodic System,” Nuclear Physics A, Vol. 549, No. 1, 1992, pp. 84-102.

[3] S. G. Nilsson, et al., “On the Spontaneous Fission of Nuclei with Z near 114 and N near 184,” Nuclear Physics A, Vol. 115, No. 3, 1968, pp. 545-562.

[4] S. G. Nilsson, et al., “On the Nuclear Structure and Stability of Heavy and Superheavy Elements”, Nuclear Physics A, Vol. 131, No. 1, 1969, pp. 1-66.

[5] M. Brack, J. Damgaaid, A. S. Jensen, H. C. Pauli, V. M. Strutinsky and C. Y. Wong, “Funny Hills: The Shell- Correction. Approach to Nuclear Shell Effects and Its Applications to the Fission Process,” Reviews of Modern Physics, Vol. 44, No. 2, 1972, pp. 320-405.

[6] E. O. Fiset and J. R. Nix, “Calculation of Half-Lives for Superheavy Nuclei,” Nuclear Physics A, Vol. 193, No. 2, 1972, pp. 647-671.

[7] J. R. Nix, “Calculation of Fission Barriers for Heavy and Superheavy Nuclei,” Annual Review of Nuclear Science, Vol. 22, 1972, pp. 65-120.

[8] A. Ozawa, T. Suzuki and I. Tanihata, “Nuclear Size and Related Topics,” Nuclear Physics A, Vol. 693, No. 1-2, 2001, pp. 32-62.

[9] L. Satpathy, S. K. Patra and R. K. Choudhury, “Fission Decay Properties of Ultra Neutron-Rich Uranium Isotopes,” PRAMANA-Journal of Physics, Vol. 70, No. 1, 2008, pp. 87-99.

[10] R. J. Furnstahl, B. D. Serot and H. B. Tang, “Analysis of Chiral Mean-field Models for Nuclei,” Nuclear Physics A, Vol. 598, No. 4, 1996, pp. 539-582.

[11] R. J. Furnstahl, B. D. Serot and H. B. Tang, “A Chiral Effective Lagrangian for Nuclei,” Nuclear Physics A, Vol. 615, No. 3-4, 1997, pp. 441-482.

[12] B. D. Serot and J. D. Walecka, “Recent Progress in Quantum Hydrodynamics,” International Journal of Modern Physics E, Vol. 6, No. 4, 1997, pp. 515-631.

[13] R. J. Furnstahl and B. D. Serot, “Parameter Counting in Relativistic Mean-field Models,” Nuclear Physics A, Vol. 671, No. 1-4, 2000, pp. 447-460.

[14] R. J. Glauber, “Lectures on Theoretical Physics,” In: W. E. Brittin and L. C. Dunham, Eds., Interscience, Vol. 1, New York, 1959, p. 315.

[15] P. Shula, “Glauber Model and the Heavy ion Reaction Cross Section,” Physical Review C, Vol. 67, No. 5, 2003, p. 054607.

[16] M. Y. H. Farag, “Modified Glauber Model for the Total Reaction Cross-section of 12C + 12C Collisions,” European Physics Journal A, Vol. 12, No. 4, 2001, pp. 405-411.

[17] S. K. Charagi and S. K. Gupta, “Coulomb-modified Glauber Model Description of Heavy-Ion Reaction Cross Sections,” Physical Review C, Vol. 41, No. 4, 1990, pp. 1610-1618.

[18] S. K. Charagi, “Nucleus-Nucleus Reaction Cross Section at Low Energies: Modified Glauber Model,” Physical Review C, Vol. 48, No. 1, 1993, pp. 452-454.

[19] S. K. Patra, R. N. Panda, P. Arumugam and R. K. Gupta, “Nuclear Reaction Cross Sections of Exotic Nuclei in the Glauber Model for Relativistic Mean Field Densities,” Physical Review C, Vol. 80, No. 6, 2009, p. 064602.

[20] A. Shukla, B. K. Sharma, R. Chandra, P. Arumugam and S. K. Patra, “Nuclear Reaction Studies of Unstable Nuclei Using Relativistic Mean Field Formalisms in Conjunction with the Glauber Model,” Physical Review C, Vol. 76, No. 3, 2007, p. 34601.

[21] B. K. Sharma, et al., “Reaction Cross-Sections for Light Nuclei on 12C using Relativistic Mean Field Formalism,” Journal of Physics G: Nuclear Particle Physics, Vol. 32, No. 11, 2006, pp. 2089-2097.

[22] M. D. Estal, M. Centelles, X. Vinyas and S. K. Patra, “Pairing Properties in Relativistic Mean Field Models Obtained from Effective Field Theory,” Physical Review C, Vol. 63, No. 4, 2001, p. 044321.

[23] S. K. Patra, M. D. Estal, M. Centelles and X. Vi?nas, “Ground-State Properties and Spins of the Odd Z = N + 1 Nuclei 61Ga-97In,” Physical Review C, Vol. 63, No. 2, 2001, p. 024311.

[24] B. A. Ibrahim, Y. Ogawa, Y. Suzuki and I. Tanihata, “Cross Section Calculations in Glauber Model: I. Core Plus One-nucleon Case,” Computer Physics Communications, Vol. 151, No. 3, 2003, pp. 369-386.

[25] K. Hagino, N. Rowley and A. T. Kruppa, “A Program for Coupled-channel Calculations with All Order Couplings for Heavy-Ion Fusion Reactions,” Computer Physics Communications, Vol. 123, No. 1-3, 1999, pp. 143-152.

[26] L. H. Bradt and B. Peters, “The Heavy Nuclei of the Primary Cosmic Radiation,” Physical Review, Vol. 77, No. 1, 1950, pp. 54-70.

[27] S. Barshay, C. B. Dover and J. P. Vary, “Nucleus-nucleus Cross Sections and the Validity of the Factorization Hypothesis at Intermediate and High Energies,” Physical Review C, Vol. 11, No. 2, 1975, pp. 360-369.

[28] S. Barshay, C. B. Dover and J. P. Vary, “The Validity of the Factorization Hypothesis for Nucleus-nucleus Cross Sections at High Energies,” Physics Letters B, Vol. 51, No. 1, 1974, pp. 5-8.

[29] A. Ingemarsson and M. Lantz, “Geometrical Aspects of Reaction Cross Sections for 3He, 4He, and 12C Projectiles,” Physical Review C, Vol. 67, No. 6, 2003, p. 064605.

[30] A. Ingemarsson and M. Lantz, “Energy Dependence of Proton-Nucleus Reaction Cross Sections,” Physical Review C, Vol. 72, No. 6, 2005, p. 064615.

[31] C.-T. Liang, Y.-A. Luo, X.-H. Li and C.-H. Cai, “Systematic Analysis of the Reaction Cross Section for d, 3He and 4He as Projectiles,” Journal of Physics G: Nuclear Particle Physics, Vol. 36, No. 1, 2009, p. 015102.

[32] H. P. Wellisch and D. Axen, “Total Reaction Cross Section Calculations in Proton-nucleus Scattering,” Physical Review C, Vol. 54, No. 3, 1996, pp. 1329-1332.

[33] J. Y. Hostachy, et al., “Elastic and Inelastic Scattering of 12C Ions at Intermediate Energies,” Nuclear Physics A, Vol. 490, No. 2, 1988, pp. 441-470.

[34] V. Bernard, et al., “Production of Charged Pions in Intermediate-Energy Heavy-Ion Collisions,” Nuclear Physics A, Vol. 423, No. 3, 1984, pp. 511-524.

[35] J. N. De, X. Vinyas, S. K. Patra and M. Centelles, “Nuclei beyond the Drip Line,” Physical Review C, Vol. 64, No. 5, 2001, p. 057306.

[36] P. A. Mazzali, et al., “A Neutron-star-Driven X-ray Flash Associated with Supernova SN 2006aj,” Nature, Vol. 442, No. 7106, 2006, pp. 1018-1020.

[37] T. A. Thompson, P. Chang and E. Quataert, “Magnetar Spindown, Hyper-energetic Supernovae, and Gamma Ray Burst,” Astrophysics Journal, Vol. 611, No. 1, 2004, pp. 380-393.

[38] P. O. Lagage and C. J. Cesarsky, “The Maximum Energy of Cosmic Rays Accelerated by Supernova Shocks,” Astronomy and Astrophysics, Vol. 125, No. 2, 1983, pp. 249-257.

[39] J. R. Wilson and R. W. Mayle, “Report on the Progress of Supernova Research by the Livermore Group,” Physics Reports, Vol. 227, No. 1-5, 1993, pp. 97-111.

[40] B. S. Meyer, “The r-, s-, and p- Process in Nucleosynthesis,” Annual Review of Astronomy and Astrophysics, Vol. 32, 1994, pp. 153-190.

[41] J. M. Pearson, “Nuclear Physics: Energy and Matter,” Ch. II, Adam Hilger Ltd, 1986, p. 87.

[42] A. Marinov, et al., “Evidence for the Possible Existence of Long-lived Superheavy Nucleus with Atomic Mass Number A = 292 and Atomic Number Z ≈ 122 in Natural Th,” International Journal of Modern Physics E, Vol. 19, No. 1, 2010, pp. 131-140.

[43] S. K. Patra, M. Bhuyan, M. S. Mehta and R. K. Gupta, “Superdeformed and Hyperdeformed States in Z = 122 Isotopes,” Physical Review C, Vol. 80, No. 3, 2009, p. 034312.