Odd-even Nuclei Research Articles

Dynamic symmetries in deformed odd-even nuclei.

We study the dynamic symmetries in deformed odd-even nuclei and show the correspondence with a description in terms of the Nilsson model and the semi-microscopic interacting boson-fermion approximation model.

Configuration mixing and electromagnetic properties of odd-even nuclei.

The electromagnetic properties of ground and excited states of nuclei with an odd number of particles and holes outside the closed shells are described in the j-j coupling shell model. The residual interaction between the valence particles and holes causes two different configuration mixing: (a) one where the valence particles and holes are scattered to higher shell model states, and (b) ones where the valence particles and holes excite particles out of the core. The electromagnetic properties of odd-even nuclei are sensitive to the correct treatment of both types of configuration mixing. In this paper the matrix elements of the nuclear Hamiltonian evaluated using the basis of configuration mixing states of types (a) and (b), and the resulting eigenvalue equations, have been exactly calculated. The matrix elements of the electromagnetic multipole operators calculated with the resulting eigenvectors of type (b) are then related to the deviation observed between the experimental and valence expectation values.

Chemical evolution of the galaxy: Abundances of the light elements (sodium to calcium)

The abundances of the light (Na to Ca) elements in disc and halo stars are reviewed. New analyses are emphasized. Elements considered are the α-nuclei (Mg, Si, and Ca), and the odd-even nuclei (Na and Al, also25Mg and26Mg). The α-nuclei are overabundant (relative to Fe) in the old disc and halo stars. Halo stars ([Fe/H] < —1.2) have [α/Fe] ∼0.3 with extreme halo ([Fe/H] ≲ −2.0) stars showing possibly higher overabundances. The scatter in [α/Fe] at a given [Fe/H] is small. To within the observational errors, the abundance patterns for Mg, Si, and Ca are identical. For disc stars, the Na and Al abundances relative to Mg are almost independent of the [Fe/H]. Halo stars ([Fe/H] < −1) show [Na/Mg] < 0 and [AI/Mg] < 0, but the form of the mean relation and the scatter about the relation between [odd-even/Mg] and [Fe/H] remains uncertain.

Odd-odd nucleus198Au as first test of IBFFM (OTQM)

The levels of198Au have been calculated in IBFFM as a first application of the new model for odd-odd nuclei. The study of the Au (n, γ) spectrum has led to a large amount of data on the odd-odd nucleus198Au, with spin/parity assignments of numerous low-lying states /l/. In particular, fifteen 1−, 2− levels have been found below 500 keV. However, at that time a detailed comparison with nuclear structure theory was not possible. In last decade, the interacting boson model was extensively applied to description of even-even and odd-even nuclei /2,3/. Only recently, this approach was extended to odd-odd nuclei /4–8/. A new model /4,5/ for odd-odd nuclei was introduced, referred to as IBFFM or OTQM. In related development, a few dynamical symmetries and supersymmetries have been introduced, which encompass odd-odd nuclei. These supersymmetries are associated with Uν (6/4)×Uπ (6/4) /6/, Uν(6/12)×Uπ (6/4) /7/ and with a symplectic chain /8/.

Odd-even staggering of heavy cluster spontaneous emission rates

Experimentally observed enhanced14C and24Ne emission rates from even-even parents in comparison with that from even-odd or odd-even nuclei are explained in the framework of the analytical superasymmetric fission model, by taking various prescriptions for the zero point vibration energy of even-even, even-odd, odd-even and odd-odd emitters. Longer half-lives than previously computed are obtained by extrapolating the present prescriptions to emitted clusters heavier than24Ne.

A microscopic approach to the coupling of collective and individual degrees of freedom to describe low energy excitations of odd-even nuclei

A theoretical and computational framework to couple in a self-consistent microscopic fashion collective and individual degrees of freedom has been set up. Its relevance has been illustrated by successfully comparing experimental 111Cd spectroscopic data with the results of the coupling of 110Cd collective wavefunctions with one-quasiparticle states where both the collective and quasiparticle inputs have been derived from the Skyrme SIII effective interaction.

Nuclear structure information obtained from charge radii

We analyze the nuclear structure information obtained from measurements of charge radii in even-even and even-odd nuclei terms of the interacting boson model. The observed deviations from the smooth behavior, R = R 0A 1 3 , appear to be well described by this model.

Spin(6) boson-fermion dynamical symmetry for odd-odd nuclei

Abstract Spin (6) boson-fermion dynamical symmetry is extended to odd-odd nuclei. An algorithm is constructed for a subsequent reduction appropriate for the boson-fermion group chain associated with odd protons and neutrons in j = 3 2 configurations and with SO(6) boson symmetry of the core. The corresponding energy formula for the odd-odd system is constructed and discussed. The possibility of generalization to extended supersymmetry encompassing even-even, odd-even and odd-odd nuclei is pointed out.

A calculation of low-lying collective states in odd-even nuclei

We present results of a calculation of properties of low-lying collective quadrupole states in odd-even nuclei within the framework of the proton-neutron interacting boson-fermion model.

Dynamical supersymmetry and collective nuclear structure physics

The symmetry principles of the Interacting Boson Model (even-even nucleus) and the Interacting Bose-Fermi Model (even-odd nucleus) are reviewed. Dynamical supersymmetry is introduced as the unifying symmetry for the above two nuclear systems. Experimental tests of dynamical supersymmetry are discussed in detail.

New class of supersymmetry in nuclei

We suggest that a new class of supersymmetry may occur in nuclei. We construct energy formulas and classification schemes for two specific cases of this class. With this addition, supersymmetry considerations may be extended to many nuclei, thus providing a useful tool to analyze the corresponding spectra.NUCLEAR STRUCTURE Supersymmetries. Derived classification scheme and energy formulas for some odd-even nuclei. Application to $^{195}\mathrm{Pt}$.

Vers une description unifiée de la structure nucléaire : Modèles IBM, IBFM et supersymétries

This article is a review of the models introduced recently for the description of low-lying collective states in nuclei in terms of interacting bosons. The general basic ideas underlying the IBM (even-even nuclei) and IBFM (odd-even nuclei) models are first given, outlining some simple analytical results obtained using group theory. The theoretical predictions are compared with selected experimental data and the successes and limitations of these models are briefly discussed. The more recent supersymmetry model, which attempts to unify the description of even-even and odd-even nuclei within the same theoretical framework, is then introduced and existing experimental tests of it are discussed.

Landau-Migdal theory made consistent for even- and odd-particle nuclei

It is shown that a problem non-existent in infinite matter-the completely different low-energy structure of even- and odd-particle nuclei-can be handled in the spirit of Landau's theory, at least for magic nuclei and their neighbours, by using the Hamiltonian and the particle-number operator as external fields in response equations for even-odd nuclei. Thereby it is proved that the many-body T matrix, which governs the properties of even-particle nuclei, also determines completely the structure of even-odd nuclei, without the appearance of irreducible three-body interactions. The role played by Landau's amplitude in infinite matter is taken over by the completely irreducible kernel K in a set of Bethe-Salpeter equations for the many-body T matrix. The non-existence of double-counting problems is demonstrated by considering results in second-order perturbation theory.

Weak-coupling calculation on N = 83 isotones

A proton-neutron weak-coupling model calculation is performed on those N=83 isotones that are far fromZ = 50 proton closed shell. The agreement between the experimental and the calculated energy level schemes is quite good. The result suggests that the weak-coupling model proposed by McGrory is applicable not only to even-even nuclei, but also to even-odd and odd-odd nuclei.

Microscopic description of rotational spectra including band-mixing. - I. Formulation in a microscopic basis

Within the framework of the projection theory of collective motion, a microscopic description of the rotational energy with band-mixing is formulated using a method based on an inverse power perturbation expansion in a quantity related to the expectation value of the operator Jy2. The reliability of the present formulation is discussed in relation to the difference between the individual wave functions obtained from the variational equations which are established before and after projection. In addition to the various familiar quantities which appear in the phenomenological energy formula, such as the moment of inertia parameter, the decoupling factor and the band-mixing matrix element for |0394K| = 1, other unfamiliar quantities having the factors with peculiar phases, (1)J+1 J(J + 1), (1)J+3/2(J 1/2) (J + 1/2) (J + 3/2), (1)J+1/2(J + 1/2) J(J + 1), (1)J J(J + 1) (J 1) (J + 2) and [J(J + 1)]2 are obtained. The band-mixing term for |0394K| = 2 is also new. All these quantities are expressed in terms of two-body interactions and expectation values of the operator Jym, where m is an integer, within the framework of particle-hole formalism. The difference between the moment of inertia of an even-even and a neighbouring even-odd nucleus, as well as the effect of band-mixing on the moment of inertia are studied. All results are put into the forms so as to facilitate comparisons with the corresponding phenomenological terms and also for further application. J. Physique 43 (1982) 1575-1595 NOVEMBRE 1982,

U(6/4) supersymmetry in nuclei

We suggest that supergroups and superalgebras may be useful in classifying the spectra of certain even-even and even-odd nuclei. We show, in particular, that properties of many states in several nuclei, including excitation energies, electromagnetic transition rates and transfer reaction intensities, can be described by a U(6/4) supersymmetry. Our analysis provides the first evidence for the occurrence of supersymmetry in nature.

Particle-core coupling for heavy odd-odd and odd-even Sb nuclei: A shell model approach

Particle-core coupling calculations on heavy odd-odd and odd-even Sb nuclei have been carried out, starting from a shell-model description. Starting from a description of the core system (Sn nuclei) and a multipole-multipole protonneutron interaction, we have derived particle-core coupling matrix elements (applicable to odd-mass as well as to odd-odd nuclei). Detailed calculations have been carried out for $^{132,130,129}\mathrm{Sb}$. In the latter case, extensive comparison is made with macroscopic particle-core coupling calculations.NUCLEAR STRUCTURE Particle-core coupling, shell-model approach. Application to $^{132,\phantom{\rule{0ex}{0ex}}130,\phantom{\rule{0ex}{0ex}}129}\mathrm{Sb}$.

Photoneutron cross sections forMn55andCo59

Photoneutron cross sections, including sigma((..gamma..,n) + (..gamma..,pn)), sigma (..gamma..,2n), and sigma (..gamma..,3n), were measured for /sup 55/Mn and /sup 59/Co from threshold to 36.5 MeV, with a photon energy resolution which varied from 80 keV at the lowest to 170 keV at the highest energies measured. The source of radiation was the monoenergetic photon beam obtained from the annihilation in flight of fast positrons. The partial photoneutron cross sections were determined by neutron multiplicity counting, and the average neutron energies for (..gamma..,1n) and (..gamma..,2n) events were determined simultaneously with the cross-section data by the ring-ratio technique. The cross sections exhibit considerable but weak structure. Other nuclear information extracted from the data includes parameters of the giant dipole resonance, integrated cross sections and their moments, and nuclear symmetry energies. A comparison is made with previous experimental data for these nuclei as well as with theoretical predictions based upon hydrodynamic, vibrational, and dynamic collective models. None of these models fits the data for these odd-even nuclei satisfactorily; more theoretical work is needed for this nuclear mass region.

Spin and Spin-Isospin Distribution in Some Medium-Heavy Nuclei

Pairs of odd-even nuclei with the wave functions of the valence nucleons different simply by an interchange of neutrons and protons (pseudo mirror pairs) have been identified and mirror symmetry in the subspace of valence nucleons conjectured. Isoscalar and isovector magnetic moments have been studied, for a given shell and for an increasing number of odd nucleons. Impressive regularities become evident.

New parameters of the deformed Woods-Saxon potential for A=110-210 nuclei

Two parameters of the spin-orbit part of the deformed Woods-Saxon potential, namely the strength parameter lambda and the radius parameter (r0)so, were adjusted to reproduce the spins and parities of even-odd and odd-even nuclei in the range 51<or=Z<or=83 and 61<or=N<or=127. Experimental evidence for the values of the nuclear deformation parameters beta 2 and beta 4 was taken into account. The parameters lambda and (r0)so were subjected to smooth variations in order to preserve the overall character of the single-particle spectrum and not to disturb the sequences of spins and parities of the neighbouring nuclei. The choice of the spin-orbit potential parameters for transitional nuclei is based essentially on the interpolation between the corresponding values for spherical and well deformed nuclei for which interpretation of the experimental data is more certain.