Possible solution of the Coriolis attenuation problem

The most consistently useful simple model for the study of odd deformed nuclei, the particle-rotor model (strong coupling limit of the core-particle coupling model) has nevertheless been beset by a long-standing problem: It is necessary in many cases to introduce an ad hoc parameter that reduces the size of the Coriolis interaction coupling the collective and single-particle motions. Of the numerous suggestions put forward for the origin of this supplementary interaction, none of those actually tested by calculations has been accepted as the solution of the problem. In this paper we seek a solution of the difficulty within the framework of a general formalism that starts from the spherical shell model and is capable of treating an arbitrary linear combination of multipole and pairing forces. With the restriction of the interaction to the familiar sum of a quadrupole multipole force and a monopole pairing force, we have previously studied a semi-microscopic version of the formalism whose framework is nevertheless more comprehensive than any previously applied to the problem. We obtained solutions for low-lying bands of several strongly deformed odd rare earth nuclei and found good agreement with experiment, except for an exaggerated staggering of levels for K=1/2 bands, which can be understood as a manifestation of the Coriolis attenuation problem. We argue that within the formalism utilized, the only way to improve the physics is to add interactions to the model Hamiltonian. We verify that by adding a magnetic dipole interaction of essentially fixed strength, we can fit the K=1/2 bands without destroying the agreement with other bands. In addition we show that our solution also fits 163Er, a classic test case of Coriolis attenuation that we had not previously studied.Comment: revtex, including 7 figures(postscript), submitted to Phys.Rev.

Derivation and assessment of strong coupling core-particle model from the Kerman-Klein-D\"onau-Frauendorf theory

We review briefly the fundamental equations of a semi-microscopic core-particle coupling method that makes no reference to an intrinsic system of coordinates. We then demonstrate how an intrinsic system can be introduced in the strong coupling limit so as to yield a completely equivalent formulation. It is emphasized that the conventional core-particle coupling calculation introduces a further approximation that avoids what has hitherto been the most time-consuming feature of the full theory, and that this approximation can be introduced either in the intrinsic system, the usual case, or in the laboratory system, our preference. A new algorithm is described for the full theory that largely removes the difference in complexity between the two types of calculation. Comparison of the full and approximate theories for some representative cases provides a basis for the assessment of the accuracy of the traditional approach. We find that for well-deformed nuclei, e.g. 157Gd and 157Tb, the core-coupling method and the full theory give similar results.Comment: revtex, 3 figures(postscript), submitted to Phys.Rev.

Kerman-Klein-Donau-Frauendorf model for odd-odd nuclei: formal theory

The Kerman-Klein-Donau-Frauendorf (KKDF) model is a linearized version of the Kerman-Klein (equations of motion) formulation of the nuclear many-body problem. In practice, it is a generalization of the standard core-particle coupling model that, like the latter, provides a description of the spectroscopy of odd nuclei in terms of the properties of neighboring even nuclei and of single-particle properties, that are the input parameters of the model. A divers sample of recent applications attest to the usefulness of the model. In this paper, we first present a concise general review of the fundamental equations and properties of the KKDF model. We then derive a corresponding formalism for odd-odd nuclei that relates their properties to those of four neighboring even nuclei, all of which enter if one is to include both multipole and pairing forces. We treat these equations in two ways. In the first we make essential use of the solutions of the neighboring odd nucleus problem, as obtained by the KKDF method. In the second, we relate the properties of the odd-odd nuclei directly to those of the even nuclei. For both choices, we derive equations of motion, normalization conditions, and an expression for transition amplitudes. We also solve the problem of choosing the subspace of physical solutions that arises in an equations of motion approach that includes pairing interactions.Comment: 27 pages, Late

Application of the Kerman-Klein method to the solution of a spherical shell model for a deformed rare-earth nucleus

Core-particle coupling models are made viable by assuming that core properties such as matrix elements of multipole and pairing operators and excitation spectra are known independently. From the completeness relation, it is seen, however, that these quantities are themselves algebraic functions of the calculated core-particle amplitudes. For the deformed rare-earth nucleus 158Gd, we find that these sum rules are well-satisfied for the ground state band, implying that we have found a self-consistent solution of the non-linear Kerman-Klein equations.Comment: revtex and postscript, including 1 figure(postscript), submitted to Phys.Rev.Let

Application of a semi-microscopic core-particle coupling method to the backbending in odd deformed nuclei

In two previous papers, the Kerman-Klein-Donau-Frauendorf (KKDF) model was used to study rotational bands of odd deformed nuclei. Here we describe backbending for odd nuclei using the same model. The backbending in the neighboring even nuclei is described by a phenomenological two band model, and this core is then coupled to a large single-particle space, as in our previous work. The results obtained for energies and M1 transition rates are compared with experimental data for 165Lu and for energies alone to the experimental data for 179W. For the case of 165Lu comparison is also made with previous theoretical work.Comment: 16 pages including 8 figure(postscript), submitted to Phys.Rev.

An investigation into the Multiple Optimised Parameter Estimation and Data compression algorithm

We investigate the use of the Multiple Optimised Parameter Estimation and Data compression algorithm (MOPED) for data compression and faster evaluation of likelihood functions. Since MOPED only guarantees maintaining the Fisher matrix of the likelihood at a chosen point, multimodal and some degenerate distributions will present a problem. We present examples of scenarios in which MOPED does faithfully represent the true likelihood but also cases in which it does not. Through these examples, we aim to define a set of criteria for which MOPED will accurately represent the likelihood and hence may be used to obtain a significant reduction in the time needed to calculate it. These criteria may involve the evaluation of the full likelihood function for comparison.Comment: 5 pages, 8 figures; corrections and additions to match version published in MNRAS Letters; added reference to published versio

Further application of a semi-microscopic core-particle coupling method to the properties of Gd155,157, and Dy159

In a previous paper a semi-microscopic core-particle coupling method that includes the conventional strong coupling core-particle model as a limiting case, was applied to spectra and electromagnetic properties of several well-deformed odd nuclei. This work, coupled a large single-particle space to the ground state bands of the neighboring even cores. In this paper, we generalize the theory to include excited bands of the cores, such as beta and gamma bands, and thereby show that the resulting theory can account for the location and structure of all bands up to about 1.5 MeV.Comment: 15 pages including 9 figure(postscript), submitted to Phys.Rev.

The expansion rate of the intermediate universe in light of Planck

We use cosmology-independent measurements of the expansion history in the redshift range 0.1≲z<1.20.1≲z<1.2 and compare them with the Cosmic Microwave Background-derived expansion history predictions. The motivation is to investigate if the tension between the local (cosmology independent) Hubble constant H0H0 value and the Planck-derived H0H0 is also present at other redshifts. We conclude that there is no tension between Planck and cosmology independent-measurements of the Hubble parameter H(z)H(z) at 0.1≲z<1.20.1≲z<1.2 for the ΛΛCDM model (odds of tension are only 1:15, statistically not significant). Considering extensions of the ΛΛCDM model does not improve these odds (actually makes them worse), thus favouring the simpler model over its extensions. On the other hand the H(z)H(z) data are also not in tension with the local H0H0 measurements but the combination of all three data-sets shows a highly significant tension (odds ∼1:400). Thus the new data deepen the mystery of the mismatch between Planck and local H0H0 measurements, and cannot univocally determine whether it is an effect localised at a particular redshift. Having said this, we find that assuming the NGC4258 maser distance as the correct anchor for H0H0, brings the odds to comfortable values. Further, using only the expansion history measurements we constrain, within the ΛΛCDM model, H0=68.5±3.5H0=68.5±3.5 and Ωm=0.32±0.05Ωm=0.32±0.05 (at 68% confidence) without relying on any CMB prior. We also address the question of how smooth the expansion history of the Universe is given the cosmology independent data and conclude that there is no evidence for deviations from smoothness on the expansion history, neither variations with time in the value of the equation of state of dark energy