Universal Expression for the Lowest Excitation Energy of Natural Parity Even Multipole States

We present a new expression for the energy of the lowest collective states in even-even nuclei throughout the entire periodic table. Our empirical formula is extremely valid and holds universally for all of the natural parity even multipole states. This formula depends only on the mass number and the valence nucleon numbers with six parameters. These parameters are determined easily and unambiguously from the data for each multipole state. We discuss the validity of our empirical formula by comparing our results with those of other studies and also by estimating the average and the dispersion of the logarithmic errors of the calculated excitation energies with respect to the measured ones.Comment: 10 pages, 5 figure

Singular Character of Critical Points in Nuclei

The concept of critical points in nuclear phase transitional regions is discussed from the standpoints of Q-invariants, simple observables and wave function entropy. It is shown that these critical points very closely coincide with the turning points of the discussed quantities, establishing the singular character of these points in nuclear phase transition regions between vibrational and rotational nuclei, with a finite number of particles.Comment: 12 pages, 7 figures, elsart, revised version, considerable changes and addition

Trust and glycemic control in black patients with diabetic retinopathy: A pilot study

Diabetic retinopathy (DR) is more prevalent in blacks than whites because, compared to whites, blacks on average have worse glycemic control. Both of these racial disparities reflect differences in sociocultural determinants of health, including physician mistrust. This randomized, controlled 6-month pilot trial compared the efficacy of a culturally tailored behavioral health/ophthalmologic intervention called Collaborative Care for Depression and Diabetic Retinopathy (CC-DDR) to enhanced usual care (EUC) for improving glycemic control in black patients with DR (n = 33). The mean age of participants was 68 years (SD 6.1 years), 76% were women, and the mean A1C was 8.7% (SD 1.5%). At baseline, 14 participants (42%) expressed mistrust about ophthalmologic diagnoses. After 6 months, CC-DDR participants had a clinically meaningful decline in A1C of 0.6% (SD 2.1%), whereas EUC participants had an increase of 0.2% (SD 1.1%) (f [1, 28] = 1.9; P = 0.176). Within CC-DDR, participants with trust had a reduction in A1C (1.4% [SD 2.5%]), whereas participants with mistrust had an increase in A1C (0.44% [SD 0.7%]) (f [1, 11] = 2.11; P = 0.177). EUC participants with trust had a reduction in A1C (0.1% [SD 1.1%]), whereas those with mistrust had an increase in A1C (0.70% [SD 1.1%]) (f [1, 16] = 2.01; P = 0.172). Mistrust adversely affected glycemic control independent of treatment. This finding, coupled with the high rate of mistrust, highlights the need to target mistrust in new interventions to improve glycemic control in black patients with DR. © 2019 by the American Diabetes Association

Basic Concepts Underlying Singular Perturbation Techniques

In many singular perturbation problems multiple scales are used. For instance, one may use both the coordinate x and the coordinate x^* = ε^(-1)x. In a secular-type problem x and x^* are used simultaneously. This paper discusses layer-type problems in which x^* is used in a thin layer and x outside this layer. Assume one seeks approximations to a function f(x,ε), uniformly valid to some order in ε for x in a closed interval D. In layer-type problems one uses (at least) two expansions (called inner and outer) neither of which is uniformly valid but whose domains of validity together cover the interval D. To define "domain of validity" one needs to consider intervals whose endpoints depend on epsilon. In the construction of the inner and outer expansions, constants and functions of e occur which are determined by comparison of the two expansions "matching." The comparison is possible only in the domain of overlap of their regions of validity. Once overlap is established, matching is easily carried out. Heuristic ideas for determining domains of validity of approximations by a study of the corresponding equations are illustrated with the aid of model equations. It is shown that formally small terms in an equation may have large integrated effects. The study of this is of central importance for understanding layer-type problems. It is emphasized that considering the expansions as the result of applying limit processes can lead to serious errors and, in any case, hides the nature of the expansions

Parameter Symmetry of the Interacting Boson Model

We discuss the symmetry of the parameter space of the interacting boson model (IBM). It is shown that for any set of the IBM Hamiltonian parameters (with the only exception of the U(5) dynamical symmetry limit) one can always find another set that generates the equivalent spectrum. We discuss the origin of the symmetry and its relevance for physical applications.Comment: Minor changes; Revtex, 14 pages with 1 figur

Generalization of the NpNnN_pN_n Scheme and the Structure of the Valence Space

The $N_pN_n$ scheme, which has been extensively applied to even-even nuclei, is found to be a very good benchmark for odd-even, even-odd, and doubly-odd nuclei as well. There are no apparent shifts in the correlations for these four classes of nuclei. The compact correlations highlight the deviant behavior of the Z=78 nuclei, are used to deduce effective valence proton numbers near Z=64, and to study the evolution of the Z=64 subshell gap.Comment: 10 pages, 4 figure

Two-neutron separation energies, binding energies and phase transitions in the interacting boson model

In the framework of the interacting boson model the three transitional regions (rotational-vibrational, rotational-$\gamma$-unstable and, vibrational-$\gamma$-unstable transitions) are reanalyzed. A new kind of plot is presented for studying phase transitions in finite systems such as atomic nuclei. The importance of analyzing binding energies and not only energy spectra and electromagnetic transitions, describing transitional regions is emphasized. We finally discuss a number of realistic examples.Comment: 34 pages, TeX (ReVTeX). 12 ps figures. 3 tables. Submitted to Nucl. Phys.