Cranked Relativistic Mean Field Description of Superdeformed Rotational Bands

The cranked relativistic mean field theory is applied for a detailed investigation of eight superdeformed rotational bands observed in $^{151}$Tb. It is shown that this theory is able to reproduce reasonably well not only the dynamic moments of inertia $J^

a r X i v :n u c l -t h /9710025v 1 11 O c t 1997Cranked Relativistic Mean Field Description of

Superdeformed Rotational Bands

A.V.Afanasjev 1,2,http://www.51wendang.comlazissis 1,3and P.Ring 1

1

Physik Department der Technischen Universit¨a t M¨u nchen

D-85747,Garching,Germany

2Nuclear Research Center,Latvian Academy of Sciences

LV-2169,Salaspils,Miera str.31,Latvia

3Department of Theoretical Physics,Aristotle University of Thessaloniki,

GR-54006,Thessaloniki,Greece Abstract The cranked relativistic mean ?eld theory is applied for a detailed inves-tigation of eight superdeformed rotational bands observed in 151Tb.It is shown that this theory is able to reproduce reasonably well not only the dynamic moments of inertia J (2)of the observed bands but also the alignment properties of the single-particle orbitals.In the relativistic mean ?eld (RMF)theory the nucleus is described as a system of point-like nucleons,Dirac spinors,coupled to the meson and Coulomb ?elds.The nucleons interact via the exchange of several mesons,namely a scalar σ-meson,which provides a strong intermediate range attraction,the isoscalar-vector ω-meson responsible for a very strong repulsion at short distances and the isovector-vector ρ-meson which takes care of the symmetry energy.This theory with only seven parameters ?tted to the proper-ties of several spherical nuclei provides an economic and accurate way to describe many properties of ?nite nuclei throughout the periodic table [1].The RMF theory formulated in the rotating frame -cranked RMF theory [2,3](further CRMF)-has been recently applied for a systematic investigation of superdeformed (SD)rotational bands observed in the A ?140?150mass region [4].It was shown that this theory provides a rather good agreement with the available experimental data on the

dynamic moments of inertia J (2).It reproduces the trend of the changes of the charge quadrupole moments Q 0.Moreover,the classi?cation of the SD bands in terms of the number of ?lled high-N intruder orbitals,originally suggested within the cranked Nilsson (further CN)model [5],is supported by the CRMF theory.

As the linking transitions from superdeformed states have not been identi?ed in this mass region,the relative properties of di?erent SD bands play an important role in our understanding of their structure.One way to identify the single-particle orbital by which two SD bands di?er is to compare the di?erence in their dynamic moments of inertia J (2)observed in experiment with the ones obtained in calculations.However,the de-?ciency of this approach is that di?erent (especially,non-intruder)orbitals have rather similar contributions to the total J (2).This prevents a unique de?nition of the underly-ing con?guration in terms of non-intruder orbitals due to the uncertainty related to the single-particle energies in the SD minimum.

An alternative way to analyse the contributions coming from speci?c orbitals and thus to identify the con?guration is the e?ective alignment approach suggested by I.Ragnars-son [6].The e?ective alignment of two bands is de?ned as the di?erence between their spins at constant rotational frequency ?x :i B,A

eff (?x )=I B (?x )?I A (?x ).The notation

1

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