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Progress of Theoretical Physics

Energy Weighted Sum Rules for Spin-Dependent Excitations of Nuclei

S. Nishizaki, K. Andō

Published May 1, 1980• 3 citations
Publisher

Abstract

An expression of the RPA-energy weighted sum rule for spin-dependent multipole operators is derived and used to relate the sum rule value to the Fermi liquid parameters in nuclear matter, including the effect of the tensor force. Numerical results for the ‘exchange’ contribution to the sum rule are presented and discussed.
DOI
10.1143/ptp.63.1599

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We present two novel relations between the quasiparticle interaction in nuclear matter and the unique low momentum nucleon-nucleon interaction in vacuum. These relations provide two independent constraints on the Fermi liquid parameters of nuclear matter. Moreover, the new constraints define two combinations of Fermi liquid parameters, which are invariant under the renormalisation group flow in the particle-hole channels. Using empirical values for the spin-independent Fermi liquid parameters, we are able to compute the major spin-dependent ones by imposing the new constraints as well as the Pauli principle sum rules.
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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A numerical method has been developed to solve the RPA equation, exchange term included, in nuclear matter. The dynamic form factor S(q, ω) is extracted for several v4 and v6 phenomenological potentials, including the d1-potential of Gogny et al. The limits of validity of the long-wavelength (Landau) approximation and the often adopted local-kernel approximation are discussed. Substantial disagreements with the exact results are found for the latter. The method is then applied to solve a Jastrow-correlated extension of the RPA equation, using the hardcore OMY potential. Results of calculations performed in two-body cluster approximation and Fermi-Hypernetted-Chain (FHNC) approximation are compared. The two-body results predict an instability against density fluctuations, which disappears at the FHNC level. The validity and consequences of employing the FHNC effective potential within the self-consistent HF/RPA framework are discussed. Future developments include applying the method to other Fermi systems such as liquid 3He and the microscopic calculation of Landau parameters.
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