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Nuclear Physics A

An exact microscopic multiphonon approach to collective modes in nuclei

F. Andreozzi, Nicola Lo Iudice, A. Porrino, F. Knapp, J. Kvasil

Published Jan 13, 2007• 0 citations
Publisher
DOI
10.1016/j.nuclphysa.2007.01.003

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Collective excitations are one of the most common and interesting features of many-body systems. Of particular interest are those collective modes which can be interpreted in terms of vibrations. Nuclei show a large variety of such modes, both low-lying and high-lying. In particular the giant dipole resonance is due to the coherent motion of protons against neutrons. Its analogue in metal clusters is the dipole plasmon excitation, due to the oscillation of electrons against the positive ions. The Random Phase Approximation (RPA) is extensively used as a microscopic theory to study the basic properties of these collective excitations. In the derivation of RPA use is made of the Quasi Boson Approximation (QBA). It consists in replacing the expectation values in the correlated ground state with those in the uncorrelated (Hartree-Fock) one. Strictly related to QBA is the feature of RPA of predicting a harmonic spectrum. On the other hand, the existence of anharmonicities in the multiphonon spectra of nuclei and their relevance in various physical processes are well established. Overcoming QBA has represented the starting point of many attempts aiming at improving RPA. A recently developed approach in this line will be presented and discussed. A very nice property of RPA is to satisfy Energy Weighted Sum Rules (EWSR). However, some violations are present in several extensions of RPA. We will show how to cure this shortcoming.

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Progress of Theoretical Physics Vol. 55 No. 5 (1976) pp. 1680–1683Representation of Nucleon Operators in the Product Space Composed of Pairing Bosons and “Quasi-Particles” Tōru Suzuki Progress of Theoretical Physics Vol. 56 No. 4 (1976) pp. 1140–1155Structure of the Anomalous 0+' Excited States in Spherical Even-Even Nuclei with N or Z ≈40 Saburo Iwasaki, Toshio Marumori, Fumihiko Sakata and Kenjiro Takada Progress of Theoretical Physics Vol. 56 No. 6 (1976) pp. 1786–1801A Semi-Microscopic Derivation of Coupling between Rotational and Intrinsic Motions. I Atsushi Kuriyama Progress of Theoretical Physics Vol. 60 No. 5 (1978) pp. 1366–1382Interplay of Pairing and Intrinsic Modes of Excitation in Nuclei. II Tōru Suzuki Progress of Theoretical Physics Vol. 61 No. 2 (1979) pp. 680–681Spurious Mode Due to Number Non-Conservation and the RPA Ground States Yoshinao Miyanishi and Goro Watanuki Progress of Theoretical Physics Vol. 61 No. 4 (1979) pp. 1082–1092Property of Many-Phonon Norm Matrix Tōru Suzuki, Masahiko Fuyuki and Kenichi Matsuyanagi Progress of Theoretical Physics Vol. 61 No. 6 (1979) pp. 1682–1696Dynamical Interplay of Pairing and Quadrupole Modes in Transitional Nuclei. I Tōru Suzuki, Masahiko Fuyuki and Kenichi Matsuyanagi Progress of Theoretical Physics Vol. 62 No. 3 (1979) pp. 690–705Dynamical Interplay of Pairing and Quadrupole Modes in Transitional Nuclei. II Tōru Suzuki, Masahiko Fuyuki and Kenichi Matsuyanagi Progress of Theoretical Physics Vol. 65 No. 5 (1981) pp. 1667–1683Dynamical Interplay of Pairing and Quadrupole Modes in Transitional Nuclei. III Tōru Suzuki, Masahiko Fuyuki and Kenichi Matsuyanagi Progress of Theoretical Physics Vol. 67 No. 5 (1982) pp. 1441–1455Attenuation Factors for B(E2) in the Microscopic Description of Multiphonon States Kenichi Matsuyanagi Progress of Theoretical Physics Supplement No.71 (1981) pp. 1–47Chapter 1. Present Status of the Microscopic Study of Low-Lying Collective States in Spherical and Transitional Nuclei Toshio Marumori, Kenjiro Takada and Fumihiko Sakata Progress of Theoretical Physics Supplement No.71 (1981) pp. 48–70Chapter 2. Outline of the Mode-Mode Coupling Theory Fumihiko Sakata, Toshio Marumori and Kenjiro Takada Progress of Theoretical Physics Supplement No.71 (1981) pp. 123–179Chapter 4. Dynamical Interplay between Pairing and Quadrupole Correlations Shigeru Tazaki, Kenjiro Takada, Kazunari Kaneko and Fumihiko Sakata Progress of Theoretical Physics Supplement No.71 (1981) pp. 180–220Chapter 5. Dynamical Interplay between Pairing and Quadrupole Correlations in Odd-Mass Nuclei Kazunari Kaneko, Kenjiro Takada, Fumihiko Sakata and Shigeru Tazaki

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Collective excitations are one of the most common and interesting features of many-body systems. Of particular interest are those collective modes which can be interpreted in terms of vibrations. Nuclei show a large variety of such modes, both low-lying and high-lying. In particular the giant dipole resonance is due to the coherent motion of protons against neutrons. Its analogue in metal clusters is the dipole plasmon excitation, due to the oscillation of electrons against the positive ions. The Random Phase Approximation (RPA) is extensively used as a microscopic theory to study the basic properties of these collective excitations. In the derivation of RPA use is made of the Quasi Boson Approximation (QBA). It consists in replacing the expectation values in the correlated ground state with those in the uncorrelated (Hartree-Fock) one. Strictly related to QBA is the feature of RPA of predicting a harmonic spectrum. On the other hand, the existence of anharmonicities in the multiphonon spectra of nuclei and their relevance in various physical processes are well established. Overcoming QBA has represented the starting point of many attempts aiming at improving RPA. A recently developed approach in this line will be presented and discussed. A very nice property of RPA is to satisfy Energy Weighted Sum Rules (EWSR). However, some violations are present in several extensions of RPA. We will show how to cure this shortcoming.
Progress of Theoretical Physics Vol. 55 No. 5 (1976) pp. 1680–1683Representation of Nucleon Operators in the Product Space Composed of Pairing Bosons and “Quasi-Particles” Tōru Suzuki Progress of Theoretical Physics Vol. 56 No. 4 (1976) pp. 1140–1155Structure of the Anomalous 0+' Excited States in Spherical Even-Even Nuclei with N or Z ≈40 Saburo Iwasaki, Toshio Marumori, Fumihiko Sakata and Kenjiro Takada Progress of Theoretical Physics Vol. 56 No. 6 (1976) pp. 1786–1801A Semi-Microscopic Derivation of Coupling between Rotational and Intrinsic Motions. I Atsushi Kuriyama Progress of Theoretical Physics Vol. 60 No. 5 (1978) pp. 1366–1382Interplay of Pairing and Intrinsic Modes of Excitation in Nuclei. II Tōru Suzuki Progress of Theoretical Physics Vol. 61 No. 2 (1979) pp. 680–681Spurious Mode Due to Number Non-Conservation and the RPA Ground States Yoshinao Miyanishi and Goro Watanuki Progress of Theoretical Physics Vol. 61 No. 4 (1979) pp. 1082–1092Property of Many-Phonon Norm Matrix Tōru Suzuki, Masahiko Fuyuki and Kenichi Matsuyanagi Progress of Theoretical Physics Vol. 61 No. 6 (1979) pp. 1682–1696Dynamical Interplay of Pairing and Quadrupole Modes in Transitional Nuclei. I Tōru Suzuki, Masahiko Fuyuki and Kenichi Matsuyanagi Progress of Theoretical Physics Vol. 62 No. 3 (1979) pp. 690–705Dynamical Interplay of Pairing and Quadrupole Modes in Transitional Nuclei. II Tōru Suzuki, Masahiko Fuyuki and Kenichi Matsuyanagi Progress of Theoretical Physics Vol. 65 No. 5 (1981) pp. 1667–1683Dynamical Interplay of Pairing and Quadrupole Modes in Transitional Nuclei. III Tōru Suzuki, Masahiko Fuyuki and Kenichi Matsuyanagi Progress of Theoretical Physics Vol. 67 No. 5 (1982) pp. 1441–1455Attenuation Factors for B(E2) in the Microscopic Description of Multiphonon States Kenichi Matsuyanagi Progress of Theoretical Physics Supplement No.71 (1981) pp. 1–47Chapter 1. Present Status of the Microscopic Study of Low-Lying Collective States in Spherical and Transitional Nuclei Toshio Marumori, Kenjiro Takada and Fumihiko Sakata Progress of Theoretical Physics Supplement No.71 (1981) pp. 48–70Chapter 2. Outline of the Mode-Mode Coupling Theory Fumihiko Sakata, Toshio Marumori and Kenjiro Takada Progress of Theoretical Physics Supplement No.71 (1981) pp. 123–179Chapter 4. Dynamical Interplay between Pairing and Quadrupole Correlations Shigeru Tazaki, Kenjiro Takada, Kazunari Kaneko and Fumihiko Sakata Progress of Theoretical Physics Supplement No.71 (1981) pp. 180–220Chapter 5. Dynamical Interplay between Pairing and Quadrupole Correlations in Odd-Mass Nuclei Kazunari Kaneko, Kenjiro Takada, Fumihiko Sakata and Shigeru Tazaki