Results and Discussion

  • Darshana Chandrakant Patel
Part of the Springer Theses book series (Springer Theses)


As described in the previous chapter a multipole deconposition analysis (MDA) is performed. In order to extract the strength distribution of various multipoles, MDA yields the coefficients, a L (E x ) (defined by Eq.  4.6), as a function of excitation energy for a given multipolarity.


Symmetry Energy Random Phase Approximation Strength Distribution High Excitation Energy Isotopic Chain 
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  1. 3.
    E. Khan, The Giant monopole resonance in Pb isotopes. (2009),
  2. 4.
    L.-G. Cao, H. Sagawa, G. Colò, Microscopic study of the isoscalar giant monopole resonance in Cd, Sn, and Pb isotopes. Phys. Rev. C 86(5), 054313 (2012). ISSN 0556-2813. doi: 10.1103/PhysRevC.86.054313
  3. 5.
    H. Sagawa, S. Yoshida, G.-M. Zeng, J.-Z. Gu, X.-Z. Zhang, Isospin dependence of incompressibility in relativistic and nonrelativistic mean field calculations. Phys. Rev. C 76(3), 034327 (2007). ISSN 0556-2813. doi: 10.1103/PhysRevC.76.034327
  4. 6.
    D. Patel, U. Garg, M. Fujiwara, T. Adachi, H. Akimune, G.P.A. Berg, A. Okamoto, K. Sault, R. Talwar, M. Uchida, M. Yosoi, Testing the mutually enhanced magicity effect in nuclear incompressibility via the giant monopole resonance in the 204, 206, 208Pb isotopes. Phys. Lett. B 726, 178–181 (2013) doi:  10.1016/j.physletb.2013.08.027 Google Scholar
  5. 24.
    T. Li, U. Garg, Y. Liu, R. Marks, B.K. Nayak, P.V. Madhusudhana Rao, M. Fujiwara, H. Hashimoto, K. Nakanishi, S. Okumura, M. Yosoi, M. Ichikawa, M. Itoh, R. Matsuo, T. Terazono, M. Uchida, Y. Iwao, T. Kawabata, T. Murakami, H. Sakaguchi, S. Terashima, Y. Yasuda, J. Zenihiro, H. Akimune, K. Kawase, M.N. Harakeh, Isoscalar giant resonances in the Sn nuclei and implications for the asymmetry term in the nuclear-matter incompressibility. Phys. Rev. C 81(3), 034309 (2010). ISSN 0556-2813. doi: 10.1103/PhysRevC.81.034309
  6. 26.
    J. Piekarewicz, Why is the equation of state for tin so soft? Phys. Rev. C 76(3), 031301 (2007). ISSN 0556-2813. doi: 10.1103/PhysRevC.76.031301
  7. 27.
    H. Morsch, C. Sükösd, M. Rogge, P. Turek, H. Machner, C. Mayer-Böricke, Giant monopole and quadrupole resonances and other multipole excitations in 208Pb studied in 43 MeV/nucleon α-particle and deuteron scattering. Phys. Rev. C 22(2), 489–500 (1980). ISSN 0556-2813. doi: 10.1103/PhysRevC.22.489 Google Scholar
  8. 29.
    T. Li, U. Garg, Y. Liu, R. Marks, B.K. Nayak, P.V.M. Rao, M. Fujiwara, H. Hashimoto, K. Kawase, K. Nakanishi, S. Okumura, M. Yosoi, M. Itoh, M. Ichikawa, R. Matsuo, T. Terazono, M. Uchida, T. Kawabata, H. Akimune, Y. Iwao, T. Murakami, H. Sakaguchi, S. Terashima, Y. Yasuda, J. Zenihiro, M.N. Harakeh, Isotopic dependence of the giant monopole resonance in the even-A 112−124Sn isotopes and the asymmetry term in nuclear incompressibility. Phys. Rev. Lett. 99(16), 162503 (2007). ISSN 0031-9007. doi: 10.1103/PhysRevLett.99.162503
  9. 31.
    J. Li, G. Colò, J. Meng, Microscopic linear response calculations based on the Skyrme functional plus the pairing contribution. Phys. Rev. C 78(6), 064304 (2008). ISSN 0556-2813. doi: 10.1103/PhysRevC.78.064304
  10. 33.
    V. Tselyaev, J. Speth, S. Krewald, E. Litvinova, S. Kamerdzhiev, N. Lyutorovich, A. Avdeenkov, F. Grümmer, Description of the giant monopole resonance in the even-A 112−124Sn isotopes within a microscopic model including quasiparticle-phonon coupling. Phys. Rev. C 79(3), 034309 (2009). ISSN 0556-2813. doi: 10.1103/PhysRevC.79.034309
  11. 34.
    P. Veselý, J. Toivanen, B.G. Carlsson, J. Dobaczewski, N. Michel, A. Pastore, Giant monopole resonances and nuclear incompressibilities studied for the zero-range and separable pairing interactions. Phys. Rev. C 86(2), 024303 (2012). ISSN 0556-2813. doi: 10.1103/PhysRevC.86.024303
  12. 35.
    J. Piekarewicz, Do we understand the incompressibility of neutron-rich matter? J. Phys. G: Nucl. Part. Phys. 37(6), 064038 (2010). ISSN 0954-3899. doi: 10.1088/0954-3899/37/6/064038 Google Scholar
  13. 36.
    E. Khan, Giant monopole resonance in Pb isotopes. Phys. Rev. C 80(5), 057302 (2009). ISSN 0556-2813. doi: 10.1103/PhysRevC.80.057302
  14. 41.
    C. Demonchy, W. Mittig, H. Savajols, P. Roussel-Chomaz, M. Chartier, B. Jurado, L. Giot, D. Cortina-Gil, M. Caamaño, G. Ter-Arkopian, A. Fomichev, A. Rodin, M. Golovkov, S. Stepantsov, A. Gillibert, E. Pollacco, A. Obertelli, H. Wang, MAYA, a gaseous active target. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 573(1–2), 145–148 (2007). ISSN 01689002. doi: 10.1016/j.nima.2006.11.025 Google Scholar
  15. 46.
    A. Willis, M. Morlet, N. Marty, R. Frascaria, C. Djalali, V. Comparat, P. Kitching, Excitation of the giant monopole resonance in 208Pb,120Sn,90Zr,58Ni and 40Ca by the scattering of 108 MeV deliterons. Nucl. Phys. A 344(1), 137–150 (1980). ISSN 03759474. doi: 10.1016/0375-9474(80)90435-2 Google Scholar
  16. 53.
    M. Uchida, H. Sakaguchi, M. Itoh, M. Yosoi, T. Kawabata, Y. Yasuda, H. Takeda, T. Murakami, S. Terashima, S. Kishi, U. Garg, P. Boutachkov, M. Hedden, B. Kharraja, M. Koss, B. Nayak, S. Zhu, M. Fujiwara, H. Fujimura, H. Yoshida, K. Hara, H. Akimune, M. Harakeh, Systematics of the bimodal isoscalar giant dipole resonance. Phys. Rev. C 69(5), 051301 (2004). ISSN 0556-2813. doi: 10.1103/PhysRevC.69.051301
  17. 96.
    Y.-W. Lui, D. Youngblood, Y. Tokimoto, H. Clark, B. John, Isoscalar multipole strength in 110Cd and 116Cd. Phys. Rev. C 69(3), 034611 (2004). ISSN 0556-2813. doi: 10.1103/PhysRevC.69.034611
  18. 97.
    M. Itoh, H. Sakaguchi, M. Uchida, T. Ishikawa, T. Kawabata, T. Murakami, H. Takeda, T. Taki, S. Terashima, N. Tsukahara, Y. Yasuda, M. Yosoi, U. Garg, M. Hedden, B. Kharraja, M. Koss, B. Nayak, S. Zhu, H. Fujimura, M. Fujiwara, K. Hara, H. Yoshida, H. Akimune, M. Harakeh, M. Volkerts, The effect of deformation in the isoscalar giant dipole resonance. Nucl. Phys. A 731, 41–48 (2004). ISSN 03759474. doi: 10.1016/j.nuclphysa.2003.11.017 Google Scholar
  19. 98.
    S. Brandenburg, W. Borghols, A. Drentje, L. Ekström, M. Harakeh, A. van der Woude, A. Hå kanson, L. Nilsson, N. Olsson, M. Pignanelli, R. De Leo, Decay of the isoscalar giant monopole resonance in 208Pb. Nucl. Phys. A 466(1), 29–69 (1987). ISSN 03759474. doi: 10.1016/0375-9474(87)90344-7 Google Scholar
  20. 99.
    U. Garg, The isoscalar giant dipole resonance: a status report. Nucl. Phys. A 731, 3–14 (2004). ISSN 03759474. doi: 10.1016/j.nuclphysa.2003.11.013 Google Scholar
  21. 102.
    M. Hunyadi, H. Hashimoto, T. Li, H. Akimune, H. Fujimura, M. Fujiwara, Z. Gácsi, U. Garg, K. Hara, M.N. Harakeh, J. Hoffman, M. Itoh, T. Murakami, K. Nakanishi, B.K. Nayak, S. Okumura, H. Sakaguchi, S. Terashima, M. Uchida, Y. Yasuda, M. Yosoi, Proton decay from the isoscalar giant dipole resonance in 58Ni. Phys. Rev. C 80(4), 044317 (2009). ISSN 0556-2813. doi: 10.1103/PhysRevC.80.044317
  22. 103.
    B. John, Y. Tokimoto, Y.-W. Lui, H. Clark, X. Chen, D. Youngblood, Isoscalar electric multipole strength in 12C. Phys. Rev. C 68(1), 014305 (2003). ISSN 0556-2813. doi: 10.1103/PhysRevC.68.014305
  23. 104.
    G.A. Lalazissis, J. König, P. Ring, New parametrization for the Lagrangian density of relativistic mean field theory. Phys. Rev. C 55(1), 540–543 (1997). ISSN 0556-2813. doi: 10.1103/PhysRevC.55.540 Google Scholar
  24. 105.
    B.G. Todd-Rutel, J. Piekarewicz, Neutron-rich nuclei and neutron stars: a new accurately calibrated interaction for the study of neutron-rich matter. Phys. Rev. Lett. 95(12), 122501 (2005). ISSN 0031-9007. doi: 10.1103/PhysRevLett.95.122501
  25. 106.
    J. Piekarewicz, Self-consistent description of nuclear compressional modes. Phys. Rev. C 64(2), 024307 (2001). ISSN 0556-2813. doi: 10.1103/PhysRevC.64.024307
  26. 107.
    U. Garg, T. Li, S. Okumura, H. Akimune, M. Fujiwara, M. Harakeh, H. Hashimoto, M. Itoh, Y. Iwao, T. Kawabata, K. Kawase, Y. Liu, R. Marks, T. Murakami, K. Nakanishi, B. Nayak, P. Madhusudhana Rao, H. Sakaguchi, Y. Terashima, M. Uchida, Y. Yasuda, M. Yosoi, J. Zenihiro, The giant monopole resonance in the Sn isotopes: why is tin so “fluffy”? Nucl. Phys. A 788(1–4), 36–43 (2007). ISSN 03759474. doi: 10.1016/j.nuclphysa.2007.01.046 Google Scholar
  27. 108.
    E. Khan, J. Margueron, G. Colò, K. Hagino, H. Sagawa, Effect of pairing correlations on incompressibility and symmetry energy in nuclear matter and finite nuclei. Phys. Rev. C 82(2), 024322 (2010). ISSN 0556-2813. doi: 10.1103/PhysRevC.82.024322
  28. 109.
    M. Centelles, X. Roca-Maza, X. Viñas, M. Warda, Nuclear symmetry energy probed by neutron skin thickness of nuclei. Phys. Rev. Lett. 102(12), 122502 (2009). ISSN 0031-9007. doi: 10.1103/PhysRevLett.102.122502
  29. 110.
    S. Patra, M. Centelles, X. Viñas, M. Del Estal, Surface incompressibility from semiclassical relativistic mean field calculations. Phys. Rev. C 65(4), 044304 (2002). ISSN 0556-2813. doi: 10.1103/PhysRevC.65.044304
  30. 111.
    L.-W. Chen, B.-J. Cai, C. Ko, B.-A. Li, C. Shen, J. Xu, Higher-order effects on the incompressibility of isospin asymmetric nuclear matter. Phys. Rev. C 80(1), 014322 (2009). ISSN 0556-2813. doi: 10.1103/PhysRevC.80.014322
  31. 112.
    D. Patel, U. Garg, M. Fujiwara, H. Akimune, G. Berg, M. Harakeh, M. Itoh, T. Kawabata, K. Kawase, B. Nayak, T. Ohta, H. Ouchi, J. Piekarewicz, M. Uchida, H. Yoshida, M. Yosoi, Giant monopole resonance in even-A Cd isotopes, the asymmetry term in nuclear incompressibility, and the “softness” of Sn and Cd nuclei. Phys. Lett. B 718(2), 447–450 (2012). ISSN 03702693. doi: 10.1016/j.physletb.2012.10.056 Google Scholar
  32. 113.
    N. Zeldes, T. Dumitrescu, H. Köhler, Mutual support of magicities and residual effective interactions near 208Pb. Nucl. Phys. A 399(1), 11–50 (1983). ISSN 03759474. doi: 10.1016/0375-9474(83)90592-4 Google Scholar
  33. 114.
    D. Lunney, C. Thibault, Recent trends in the determination of nuclear masses. Rev. Mod. Phys. 75(3), 1021–1082 (2003). ISSN 0034-6861. doi: 10.1103/RevModPhys.75.1021 Google Scholar
  34. 115.
    M. Uchida, H. Sakaguchi, M. Itoh, M. Yosoi, T. Kawabata, H. Takeda, Y. Yasuda, T. Murakami, T. Ishikawa, T. Taki, N. Tsukahara, S. Terashima, U. Garg, M. Hedden, B. Kharraja, M. Koss, B. Nayak, S. Zhu, M. Fujiwara, H. Fujimura, K. Hara, E. Obayashi, H. Yoshida, H. Akimune, M. Harakeh, M. Volkerts, Isoscalar giant dipole resonance in Pb via inelastic α scattering at 400 MeV and nuclear incompressibility. Phys. Lett. B 557(1–2), 12–19 (2003). ISSN 03702693. doi: 10.1016/S0370-2693(03)00137-0 Google Scholar
  35. 116.
    D.H. Youngblood, Y.-W. Lui, H.L. Clark, B. John, Y. Tokimoto, X. Chen, Isoscalar E0–E3 strength in 116Sn,144Sm,154Sm, and 208Pb. Phys. Rev. C 69(3), 034315 (2004). ISSN 0556-2813. doi: 10.1103/PhysRevC.69.034315
  36. 117.
    M. Harakeh, B. Van Heyst, K. Van Der Borg, A. Van Der Woude, Isoscalar excitations in the lead region observed in inelastic α-scattering at Eα = 120 MeV. Nucl. Phys. A 327(2), 373–396 (1979). ISSN 03759474. doi: 10.1016/0375-9474(79)90265-3 Google Scholar
  37. 118.
    F. Bertrand, G. Satchler, D. Horen, J. Wu, A. Bacher, G. Emery, W. Jones, D. Miller, A. van der Woude, Giant multipole resonances from inelastic scattering of 152-MeV alpha particles. Phys. Rev. C 22(5), 1832–1847 (1980). ISSN 0556-2813. doi: 10.1103/PhysRevC.22.1832 Google Scholar
  38. 119.
    M. Sharma, W. Borghols, S. Brandenburg, S. Crona, A. van der Woude, M. Harakeh, Giant monopole resonance in Sn and Sm nuclei and the compressibility of nuclear matter. Phys. Rev. C 38(6), 2562–2572 (1988). ISSN 0556-2813. doi: 10.1103/PhysRevC.38.2562 Google Scholar

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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Darshana Chandrakant Patel
    • 1
  1. 1.University of Notre DameNotre DameUSA

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