Exact Solution of the Isovector Proton Neutron Pairing Hamiltonian

The complete exact solution of the T=1 neutron-proton pairing Hamiltonian is presented in the context of the SO(5) Richardson-Gaudin model with non-degenerate single-particle levels and including isospin-symmetry breaking terms. The power of the method is illustrated with a numerical calculation for $^{64}$Ge for a $pf+g_{9/2}$ model space which is out of reach of modern shell-model codes.Comment: To be published by Physical Review Letter

Deformations of the fermion realization of the sp(4) algebra and its subalgebras

With a view towards future applications in nuclear physics, the fermion realization of the compact symplectic sp(4) algebra and its q-deformed versions are investigated. Three important reduction chains of the sp(4) algebra are explored in both the classical and deformed cases. The deformed realizations are based on distinct deformations of the fermion creation and annihilation operators. For the primary reduction, the su(2) sub-structure can be interpreted as either the spin, isospin or angular momentum algebra, whereas for the other two reductions su(2) can be associated with pairing between fermions of the same type or pairing between two distinct fermion types. Each reduction provides for a complete classification of the basis states. The deformed induced u(2) representations are reducible in the action spaces of sp(4) and are decomposed into irreducible representations.Comment: 28 pages, LaTeX 12pt article styl

A mixed-mode shell-model theory for nuclear structure studies

We introduce a shell-model theory that combines traditional spherical states, which yield a diagonal representation of the usual single-particle interaction, with collective configurations that track deformations, and test the validity of this mixed-mode, oblique basis shell-model scheme on $^{24}$Mg. The correct binding energy (within 2% of the full-space result) as well as low-energy configurations that have greater than 90% overlap with full-space results are obtained in a space that spans less than 10% of the full space. The results suggest that a mixed-mode shell-model theory may be useful in situations where competing degrees of freedom dominate the dynamics and full-space calculations are not feasible.Comment: 20 pages, 8 figures, revtex 12p

Generalization of Richardson-Gaudin models to rank-2 algebras

A generalization of Richardson-Gaudin models to the rank-2 SO(5) and SO(3,2) algebras is used to describe systems of two kinds of fermions or bosons interacting through a pairing force. They are applied to the proton-neutron neutron isovector pairing model and to the Interacting Boson Model 2, in the transition from vibration to gamma-soft nuclei, respectively. In both cases, the integrals of motion and their eigenvalues are obtained

Polymorphisms of genes coding for ghrelin and its receptor in relation to colorectal cancer risk: a two-step gene-wide case-control study

<p>Abstract</p> <p>Background</p> <p>Ghrelin, an endogenous ligand for the growth hormone secretagogue receptor (GHSR), has two major functions: the stimulation of the growth hormone production and the stimulation of food intake. Accumulating evidence also indicates a role of ghrelin in cancer development.</p> <p>Methods</p> <p>We conducted a case-control study to examine the association of common genetic variants in the genes coding for ghrelin (GHRL) and its receptor (GHSR) with colorectal cancer risk. Pairwise tagging was used to select the 11 polymorphisms included in the study. The selected polymorphisms were genotyped in 680 cases and 593 controls from the Czech Republic.</p> <p>Results</p> <p>We found two SNPs associated with lower risk of colorectal cancer, namely SNPs rs27647 and rs35683. We replicated the two hits, in additional 569 cases and 726 controls from Germany.</p> <p>Conclusion</p> <p>A joint analysis of the two populations indicated that the T allele of rs27647 SNP exerted a protective borderline effect (P_trend= 0.004).</p