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The generalized collective model; Das generalisierte Kollektivmodell

Thesis/Dissertation:

Abstract

In this thesis a new way of proceeding, basing on the method of the finite elements, for the solution of the collective Schroedinger equation in the framework of the Generalized Collective Model was presented. The numerically reachable accuracy was illustrated by the comparison to analytically known solutions by means of numerous examples. Furthermore the potential-energy surfaces of the {sup 182-196}Hg, {sup 242-248}Cm, and {sup 242-246}Pu isotopes were determined by the fitting of the parameters of the Gneuss-Greiner potential to the experimental data. In the Hg isotopes a shape consistency of nearly spherical and oblate deformations is shown, while the Cm and Pu isotopes possess an essentially equal remaining prolate deformation. By means of the pseudo-symplectic model the potential-energy surfaces of {sup 24}Mg, {sup 190}Pt, and {sup 238}U were microscopically calculated. Using a deformation-independent kinetic energy so the collective excitation spectra and the electrical properties (B(E2), B(E4) values, quadrupole moments) of these nuclei were calculated and compared with the experiment. Finally an analytic relation between the (g{sub R}-Z/A) value and the quadrupole moment was derived. The study of the experimental data of the {sup 166-170}Er isotopes shows an in the framework of the measurement accuracy a sufficient agreement with this relation.  More>>
Authors:
Publication Date:
Jul 01, 1992
Product Type:
Thesis/Dissertation
Report Number:
GSI-92-15
Reference Number:
SCA: 663120; 663110; 663220; 663500; PA: DEN-92:016305; SN: 93000906035
Resource Relation:
Other Information: TH: Diss. (Dr.rer.nat.); PBD: Jul 1992
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; COLLECTIVE MODEL; FINITE ELEMENT METHOD; MAGNESIUM 24; EXCITED STATES; PLATINUM 190; MERCURY ISOTOPES; URANIUM 238; E2-TRANSITIONS; PLUTONIUM ISOTOPES; CURIUM ISOTOPES; ERBIUM ISOTOPES; GYROMAGNETIC RATIO; SCHROEDINGER EQUATION; HAMILTONIANS; NUCLEAR DEFORMATION; NUCLEAR STRUCTURE; ROTATIONAL STATES; VIBRATIONAL STATES; HIGH SPIN STATES; POTENTIAL ENERGY; WAVE FUNCTIONS; HARMONIC POTENTIAL; ACCURACY; THEORETICAL DATA; ENERGY SPECTRA; STRENGTH FUNCTIONS; QUADRUPOLE MOMENTS; NUCLEAR MAGNETIC MOMENTS; MAGNETIC DIPOLE MOMENTS; RARE EARTH NUCLEI; NUCLEAR ELECTRIC MOMENTS; 663120; 663110; 663220; 663500; NUCLEAR STRUCTURE MODELS AND METHODS; GENERAL AND AVERAGE PROPERTIES OF NUCLEI AND NUCLEAR ENERGY LEVELS; ELECTROMAGNETIC TRANSITIONS; NUCLEAR MASS RANGES
OSTI ID:
10106162
Research Organizations:
Gesellschaft fuer Schwerionenforschung mbH, Darmstadt (Germany); Frankfurt Univ. (Germany). Fachbereich 13 - Physik
Country of Origin:
Germany
Language:
German
Other Identifying Numbers:
Other: ON: DE93744562; TRN: DE9216305
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
DEN
Size:
165 p.
Announcement Date:
Jun 30, 2005

Thesis/Dissertation:

Citation Formats

Troltenier, D. The generalized collective model; Das generalisierte Kollektivmodell. Germany: N. p., 1992. Web.
Troltenier, D. The generalized collective model; Das generalisierte Kollektivmodell. Germany.
Troltenier, D. 1992. "The generalized collective model; Das generalisierte Kollektivmodell." Germany.
@misc{etde_10106162,
title = {The generalized collective model; Das generalisierte Kollektivmodell}
author = {Troltenier, D}
abstractNote = {In this thesis a new way of proceeding, basing on the method of the finite elements, for the solution of the collective Schroedinger equation in the framework of the Generalized Collective Model was presented. The numerically reachable accuracy was illustrated by the comparison to analytically known solutions by means of numerous examples. Furthermore the potential-energy surfaces of the {sup 182-196}Hg, {sup 242-248}Cm, and {sup 242-246}Pu isotopes were determined by the fitting of the parameters of the Gneuss-Greiner potential to the experimental data. In the Hg isotopes a shape consistency of nearly spherical and oblate deformations is shown, while the Cm and Pu isotopes possess an essentially equal remaining prolate deformation. By means of the pseudo-symplectic model the potential-energy surfaces of {sup 24}Mg, {sup 190}Pt, and {sup 238}U were microscopically calculated. Using a deformation-independent kinetic energy so the collective excitation spectra and the electrical properties (B(E2), B(E4) values, quadrupole moments) of these nuclei were calculated and compared with the experiment. Finally an analytic relation between the (g{sub R}-Z/A) value and the quadrupole moment was derived. The study of the experimental data of the {sup 166-170}Er isotopes shows an in the framework of the measurement accuracy a sufficient agreement with this relation. Furthermore it is by this relation possible to determine the effective magnetic dipole moment parameter-freely. (orig./HSI). [Deutsch] In dieser Arbeit wurde eine neue, auf der Methode der Finiten Elemente beruhende Vorgehensweise zur Loesung der kollektiven Schroedingergleichung im Rahmen des Generalisierten Kollektivmodells vorgestellt. Die numerisch erreichbare Genauigkeit wurde durch den Vergleich zu analytisch bekannten Loesungen an Hand zahlreicher Beispiele dargestellt. Weiterhin wurden die Potentialenergieflaechen der {sup 182-196}Hg-, {sup 242-248}Cm- und {sup 242-246}Pu-Isotope durch die Anpassung der Parameter des Gneuss-Greiner Potentials an die experimentellen Daten bestimmt. Bei den Hg-Isotopen zeigt sich eine Formkoexistenz von fast-sphaerischen und oblaten Deformationen, waehrend die Cm- und Pu-Isotope eine, im wesentlichen gleichbleibende, prolate Deformation besitzen. Mit Hilfe des pseudo-symplektischen Modells wurden die Potentialenergieflaechen von {sup 24}Mg, {sup 190}Pt und {sup 238}U mikroskopisch berechnet. Unter Benutzung einer deformationsunabhaengigen kinetischen Energie wurden so die kollektiven Anregungsspektren und die elektrischen Eigenschaften (B(E2)-, B(E4)-Werte, Quadrupolmomente) dieser Kerne berechnet und mit dem Experiment verglichen. Schliesslich wurde eine analytische Beziehung zwischen dem (g{sub R} - Z/A)-Wert und dem Quadrupolmoment abgeleitet. Die Untersuchung der experimentellen Daten der {sup 166-170}Er-Isotope zeigt eine, im Rahmen der Messgenauigkeit, befriedigende Uebereinstimmung mit dieser Relation. Ausserdem ist es durch diese Beziehung moeglich, den effektiven magnetischen Dipoloperator parameterfrei zu bestimmen. (orig./HSI).}
place = {Germany}
year = {1992}
month = {Jul}
}