Single- and double-beta decay Fermi-transitions in an exactly solvable model

An exactly solvable model suitable for the description of single and double-beta decay processes of the Fermi-type is introduced. The model is equivalent to the exact shell-model treatment of protons and neutrons in a single j-shell. Exact eigenvalues and eigenvectors are compared to those corresponding to the hamiltonian in the quasiparticle basis (qp) and with the results of both the standard quasiparticle random phase approximation (QRPA) and the renormalized one (RQRPA). The role of the scattering term of the quasiparticle hamiltonian is analyzed. The presence of an exact eigenstate with zero energy is shown to be related to the collapse of the QRPA. The RQRPA and the qp solutions do not include this zero-energy eigenvalue in their spectra, probably due to spurious correlations. The meaning of this result in terms of symmetries is presented.Comment: 29 pages, 9 figures included in a Postsript file. Submitted to Physcal Review

Characterizing neuroanatomic heterogeneity in people with and without ADHD based on subcortical brain volumes

Background Attention-deficit/hyperactivity disorder (ADHD) is a prevalent neurodevelopmental disorder. Neuroanatomic heterogeneity limits our understanding of ADHD’s etiology. This study aimed to parse heterogeneity of ADHD and to determine whether patient subgroups could be discerned based on subcortical brain volumes. Methods Using the large ENIGMA-ADHD Working Group dataset, four subsamples of 993 boys with and without ADHD and to subsamples of 653 adult men, 400 girls, and 447 women were included in analyses. We applied exploratory factor analysis (EFA) to seven subcortical volumes in order to constrain the complexity of the input variables and ensure more stable clustering results. Factor scores derived from the EFA were used to build networks. A community detection (CD) algorithm clustered participants into subgroups based on the networks. Results Exploratory factor analysis revealed three factors (basal ganglia, limbic system, and thalamus) in boys and men with and without ADHD. Factor structures for girls and women differed from those in males. Given sample size considerations, we concentrated subsequent analyses on males. Male participants could be separated into four communities, of which one was absent in healthy men. Significant case–control differences of subcortical volumes were observed within communities in boys, often with stronger effect sizes compared to the entire sample. As in the entire sample, none were observed in men. Affected men in two of the communities presented comorbidities more frequently than those in other communities. There were no significant differences in ADHD symptom severity, IQ, and medication use between communities in either boys or men. Conclusions Our results indicate that neuroanatomic heterogeneity in subcortical volumes exists, irrespective of ADHD diagnosis. Effect sizes of case–control differences appear more pronounced at least in some of the subgroups