Selfconsistent generator coordinate method for giant monopole resonances

doi:10.1016/0375-9474(76)90400-0

Nuclear Physics A

Volume 269, Issue 1, 28 September 1976, Pages 112-124

https://doi.org/10.1016/0375-9474(76)90400-0 Get rights and content

Abstract

A generator coordinate method based on selfconsistent Hartree-Fock determinants is applied to the description of monopole modes in ¹⁶O, ⁴⁰Ca, ⁹⁰Zr and ²⁰⁸Pb, using the MD I4 interaction. Cross sections for the electro-excitation of the breathing mode are evaluated in DWBA and compared with other approaches.

References (32)

L. Zamick
Phys. Lett.
(1973)
R.W. Sharp et al.
Nucl. Phys.
(1973)
Th. Walcher
S.K.M. Wong et al.
Nucl. Phys.
(1971)
Y.M. Engel et al.
Nucl. Phys.
(1975)
J. Blomqvist
Nucl. Phys.
(1967)
P. Ring et al.
Nucl. Phys.
(1974)
S. Krewald et al.
Phys. Lett
(1974)
S. Krewald et al.
Phys. Rev. Lett.
(1974)
G.F. Bertsch et al.
Phys. Reports
(1975)
M. Sotana et al.
Phys. Lett.
(1975)
S. Krewald et al.
Phys. Lett.
(1975)

P. Löwdin

Phys. Rev.

(1955)

H.A. Bethe

Phys. Rev.

(1968)

M. Beiner et al.

Nucl. Phys.

(1975)

D. Vautherin et al.

Phys. Rev.

(1972)

T.H. Schucan

Nucl. Phys.

(1965)

D. Drechsel

Nucl. Phys.

(1966)

I. Sick et al.

Nucl. Phys.

(1970)

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This report is devoted to the studies of multiphonon excitations in nuclei, it contains in fact two reports: an experimental one presenting a review of the observation of multiphonon excitations and a theoretical one centered on the description of such states. The present knowledge about giant resonances in nuclei is first briefly presented and the relative merits of different probes to excite such states are illustrated. The existence of giant resonances built on excited states is stressed. In this context, multiphonon states, i.e. a giant resonance built on top of other giant resonances, are expected. Several paths can be followed to obtain experimental evidence for multiphonon states: inelastic nuclear and Coulomb excitations and charge exchange reactions. The status of the search for isoscalar multiphonon excitations by means of the strong nuclear potential produced by heavy ions is presented and novel experimental signatures of the double excitation of the giant quadrupole resonance are reported. Coulomb excitation induced by relativistic heavy ions is presented as another fruitful approach to the study of the double dipole and recent experimental results using the very selective (π⁺,π⁻) double charge exchange reactions are shown and discussed. Calculations for these different excitation mechanisms are presented.
A review of the theoretical descriptions of the properties of the multiphonon states is then presented. Hydrodynamical and phenomenological models are first discussed. The mean-field approaches are summarized. The random phase approximation is introduced to discuss giant resonances while several extensions of the meanfield concepts are presented in order to deal with large amplitude motion and multiphonons. Finally, boson mapping techniques are used to introduce a general treatment of multiple excitations. The different approaches consistently predict that such multiple collective excitations in nuclei should closely follow a harmonic pattern. Therefore, the energy of the phonons is predicted to be additive. This conclusion allows to discuss the properties of the width of the multiphonon strength in a simple manner and the observed width is predicted to be close to the quadratic sum of the single-phonon widths.
General conclusions are drawn and new prospects are discussed.
Studies of the generator coordinate method within the complex VAMPIR model
1992, Nuclear Physics, Section A
A set of deformed states generated with the VAMPIR approach is used for a generator coordinate method description of the 0⁺ states in ²⁸Si. As model space the 1s0d shell was used, and as effective hamiltonian the Chung-Wildenthal interaction. Thus a comparison with the “exact” shell-model solutions was possible. Potential-energy functions, overlaps between different deformation points and the hamiltonian matrices are discussed for three different types of VAMPIR solutions: with full symmetry projection, with particle-number projection only and without any projection. The validity of the “horizontal expansion” of the hamiltonian matrix is examined.
Dynamics of collective motion
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Using the framework of the Generator Coordinate Method the dynamics of the rotational motion is described by superimposing a set of well-prepared cranking states which have a common direction of the total angular momentum but distinguish in their orientation of the related deformed potential in space. New options for analysing configuration mixings in band crossings regions and for the determination of radiation amplitudes are discussed.
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Hartree-Fock-Bogoliubov (HFB) states shaped by auxiliary external fields form an appropriate basis for executing the concept of generator coordinates to large amplitude collective motion. We present a nonperturbational expansion of the Hamilton kernel which is adapted to structural changes of a local HFB vacuum state. Neglecting four quasiparticle terms in this treatment this kernal depends only on the static potential energy, the overlap between the generator states, and a cranking-like coupling term originated by the external field. The physical role of the overlap function is reconsidered. The diagonalization of the overlap matrix and subsequent removal of small-norm eigenstates is suggested to be the consistent way for constructing the proper subspace that saves the conditions of smooth and slow collective motion. Practical examples for realistic nuclear systems demonstrate that this collective subspace turns out to have in fact a surprisingly small and therefore feasible dimension compared to the huge space spanned by the multi-quasiparticle excitations referred to a fixed vacuum. The application of the “horizontal” expansion opens a new field for the exploration of the dynamics of shape transitions, pair-field fluctuations, quantal rotational motion and tunneling phenomena. The proposed method is considered as the logical extension of the potential energy calculations to obtain a quantized collective motion.
Response functions and charge transition densities for monopole excitations in (e,e') and (e,e'x) reactions of <sup>16</sup>O and <sup>40</sup>Ca
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The energy behaviour of the monopole (e, e') and (e, e'x) response functions of ¹⁶O and ⁴⁰Ca at q = 100 MeV/c is discussed in the framework of a self-consistent RPA-SK3 theory based on the 1plh energy continuum. The microscopic structure of the resonant states is inferred from the analysis of proton and neutron monopole transition densities in the most populated decay channels. The role of the RPA final-state interactions and ground state correlations is investigated.
Quasiparticle relativistic G-matrix interaction
1987, Nuclear Physics, Section A
A quasiparticle G-matrix interaction has been constructed from a three-dimensional integral equation which is a relativistic generalization of the conventional non-relativistic Bethe-Goldstone equation. Relativistic dynamical effects have been discussed by comparing the relativistic and the conventional non-relativistic G-matrices. The Landau theory and, in particular, the quasi-particle current have also been discussed within the present relativistic formulation.
As an example of application, the quasiparticle relativistic G-matrix interaction has been used in the RPA calculation which includes 2p-2h processes.

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^†: Present address: Institut für Kernphysik, Universität Mainz.

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Selfconsistent generator coordinate method for giant monopole resonances

Abstract

Phys. Lett.

Nucl. Phys.

Nucl. Phys.

Nucl. Phys.

Nucl. Phys.

Nucl. Phys.

Phys. Lett

Phys. Rev. Lett.

Phys. Reports

Phys. Lett.

Phys. Lett.

Phys. Rev.

Phys. Rev.

Nucl. Phys.

Phys. Rev.

Nucl. Phys.

Nucl. Phys.

Nucl. Phys.