Parity Splitting Research Articles

Excitation Spectra of the Impurity Anderson Model Calculated by the Numerical Renormalization Group Method

A method to calculate the excitation spectra of the impurity Anderson model based on the numerical renormalization group technique is reviewed. The single particle and the magnetic excitation spectra are calculated for the cases of various magnitudes of the 1-1 Coulomb interaction to compare them with experimentally observed broad PES-BIS spectra in U-compounds. Excitation spectra in the Kondo limit are also examined in detail. The Kondo effect due to the magnetic ions with complex multiplet structures, such as the Sm- and the Tm·like ions, is studied. The excitation spectra of the two impurity Anderson model are calculated and roles of the parity splitting are discussed. In this paper we review our recent. calculation for the excitation spectra of the impurity Ande:r;son model. The method of calculation is developed based on the numerical renormalization group (NRG) technique which has been originally introduced by Wilson to study the thermodynamic properties of the Kondo problem. 1 >,z> The purposes of the calculation are three folds. The first one is to study the single particle excitation (SPE) spectra of the impurity Anderson model in wide energy range. 3 >' 4 > We study roles of the atomic/-/ Coulomb interaction in the origin of the broad PES-BIS spectra of U-compounds, in which the atomic interactions and the c-/ hybridization are expected to have comparable magnitude. The second one is to study the dynamical excitation spectra of the Kondo problem. Several approximation schemes have been developed to study the dynami­ cal properties of the problem, but exact excitation spectra at very low temperature have not been obtained before our calculation. We calculate the spectra of SPE, magnetic and charge excitations in the low energy region of the order of the Kondo · temperature, TK., carefully. 5 >

Hybridized bands and parity splitting in the odd-odd nucleus220Ac

The high spin state structure of the nucleus220Ac was investigated by means of the209Bi(14C, 3n) reaction. In beamγ ray spectroscopy was carried out using the Château de Cristal multidetector array. Gamma ray multipolarities were established by extracting directional correlation ratios from the Ge—Ge coincidence data and by intensity balance considerations. The level scheme, established up to 18 ħ above the lowest observed state, consists of three alternating parity bands. The data are interpreted in terms of the reflection asymmetric shapes of the nucleus. The analysis of the parity doublet candidates does not show the decrease of the parity splitting predicted for an odd-odd nucleus.

Excitation spectra of two impurity Anderson model

Magnetic and single particle excitation spectra of the two impurity Anderson model are calculated based on the numerical renormalization method. The direct f-f hoping or the realistic c-f hybridization terms cause the splitted Kondo peaks corresponding to the even and odd parity channels. The antiferromagnetic fluctuation of local spin pair shows softening when it has weak antiferromagnetic coupling. This softening, and the divergence of the staggered susceptibility previously pointed out by Jones et al. are suppressed by the parity splitting.

Evidence for a parity dependence of the ?+20Ne interaction

The anomalous features of the elastic20Ne(α, α) angular distribution recently measured by Abele et al. are analyzed within the frame of the optical model. It is shown that the introduction of a very small parity splitting in the real part of the interaction makes possible a precise description of the anomaly, and at the same time leads to a potential in line with those found for the lower mass “normal” targets. The relation of this parity effect with cluster transfer and/or coupling effects to other channels is discussed. Finally the bound and quasi-bound state properties of the derived potential are investigated in relation with theα-cluster spectroscopy of the24Mg nucleus.

Rotational bands in deformed nuclei

The authors present an alternative derivation of the strong-coupling adiabatic model for nuclear rotational bands generated by coupling particles to a rotor. They avoid as far as possible the use of symmetry arguments as well as the assumption of the motion of a particle in a static deformed field. Instead they approach the problem by diagonalising a rotationally invariant Hamiltonian using basis states of good angular momentum at all stages. This leads to the standard 'symmetrised' wavefunctions in a transparent manner, with appropriate constraints on the effective mean field for the particles emerging naturally. The cranking approximation is derived in a way which leads automatically to the relation between the total angular momentum of the system and the signature of the particles in the cranked deformed field. The advantage of such an approach is that it is easier to see how to extend this model and give as an example the application to a system where the effective mean field possesses an octupole component. The origin of the parity splitting that is observed in this case is discussed, as is its dependence on odd and even particle number.

Electric dipole collectivity in light nuclear systems.

\ensuremath{\alpha}${\mathrm{\ensuremath{-}}}^{18}$O and \ensuremath{\alpha}-Ca cluster configurations of $^{22}\mathrm{Ne}$ and the $^{46}$,48,52Ti isotopes, respectively, have been studied in a microscopically founded model, treating antisymmetrization between the clusters correctly. Depending on the respective ground state structure, these systems show rotational bands with weak (Ti isotopes) and strong ${(}^{22}$Ne) parity splitting. Irrespective of the degree of parity splitting, both cases exhibit E1 transitions between these cluster states, which are strong on the appropriate molecular scale. Though the influence of inelastic channels is discussed in qualitative terms only, both $^{22}\mathrm{Ne}$ and the Ti isotopes appear to be promising candidates for the molecular-dipole degree of freedom to be seen in light nuclei.

Microscopic study of the α-14C molecular-dipole degree of freedom in the18O nucleus

α-14C cluster configurations of the18O system have been studied in a microscopically founded model, treating antisymmetrization between the clusters exactly. A rotational band with little parity splitting and strong intrabandE1-transitions has been found, supporting Iachello's notion of the molecular-dipole degree of freedom in nuclei. Deviations from a pure molecular rotator picture are understood in terms of shell model contaminations, using the analysis of the18O spectrum by Fortune et al.

Baryon sum rules and chiral symmetry breaking

In an SVZ-type approach sum rules for baryonic currents have been investigated, without radiative QCD corrections but with the inclusion of non-perturbative terms due to the non-vanishing vacuum expectation value of the quark-antiquark condensate. We give upper bounds for baryon masses, which allow a choice of optimal interpolating operators for low-lying baryon states. The results show that the mentioned vacuum expectation value not only sets the scale for parity splitting but also for the masses of the baryons directly. The alternative way of explicit symmetry breaking by quark masses has also been investigated in the same technical framework.

Neutron blocking in elastic α-scattering on Oxygen isotopes

Elastic α- 18O scattering has been studied microscopically within the framework of the generator coordinate method. The bound states of the α- 18O system agree very well with the 22Ne ground state band. The scattering phase shifts as well as the bound states show a strong parity splitting. A comparison with the α- 16O system gives no evidence for a reduction of parity splitting due to the blocking of the 18O excess neutrons as suggested by Sünkel and Wildermuth.