Regularities with random interactions in energy centroids defined by group symmetries

Regular structures generated by random interactions in energy centroids defined over irreducible representations (irreps) of some of the group symmetries of the interacting boson models $sd$IBM, $sdg$IBM, $sd$IBM-$T$ and $sd$IBM-$ST$ are studied by deriving trace propagations equations for the centroids. It is found that, with random interactions, the lowest and highest group irreps in general carry most of the probability for the corresponding centroids to be lowest in energy. This generalizes the result known earlier, via numerical diagonalization, for the more complicated fixed spin ($J$) centroids where simple trace propagation is not possible.Comment: 18 pages, 3 figure

Shell model and deformed shell model spectroscopy of 62^{62}Ga

In the present work we have reported comprehensive analysis of recently available experimental data [H.M. David et al., Phys. Lett. B {\bf 726}, 665 (2013)] for high-spin states up to $17^+$ with $T=0$ in the odd-odd $N=Z$ nucleus $^{62}$Ga using shell model calculations within the full $f_{5/2}pg_{9/2}$ model space and deformed shell model based on Hartee-Fock intrinsic states in the same space. The calculations have been performed using jj44b effective interaction developed recently by B.A. Brown and A.F. Lisetskiy for this model space. The results obtained with the two models are similar and they are in reasonable agreement with experimental data. In addition to the $T=0$ and $T=1$ energy bands, band crossings and electromagnetic transition probabilities, we have also calculated the pairing energy in shell model and all these compare well with the available theoretical results.Comment: 9 pages, 4 figure

A Note On Line Graphs

In this note we define two generalizations of the line graph and obtain some results. Also, we mark some open problems

O(12) limit and complete classification of symmetry schemes in proton-neutron interacting boson model

It is shown that the proton-neutron interacting boson model (pnIBM) admits new symmetry limits with O(12) algebra which break F-spin but preserves the quantum number M_F. The generators of O(12) are derived and the quantum number `v' of O(12) for a given boson number N is determined by identifying the corresponding quasi-spin algebra. The O(12) algebra generates two symmetry schemes and for both of them, complete classification of the basis states and typical spectra are given. With the O(12) algebra identified, complete classification of pnIBM symmetry limits with good M_F is established.Comment: 22 pages, 1 figur

Half-lives and pre-supernova weak interaction rates for nuclei away from the stability line

A detailed model for the calculation of beta decay rates of the $fp$ shell nuclei for situations prevailing in pre-supernova and collapse phases of evolution of the core of massive stars leading to supernova explosion has been extended for electron-capture rates. It can also be used to determine the half-lives of neutron-rich nuclei in the $fp/fpg$ shell. The model uses an averaged Gamow-Teller (GT) strength function. But it can also use the experimental log ft values and GT strength function from $(n,p)$ reaction studies wherever available. The calculated rate includes contributions from each of the low-lying excited states of the mother including some specific resonant states ("back resonance") having large GT matrix elements.Comment: 11 pages; Latex; no figs; version to appear in J. Phys.

Testable Implications of Translation Invariance and Homotheticity: Variational, Maxmin, CARA and CRRA preferences

We provide revealed preference axioms that characterize models of translation invariant preferences. In particular, we characterize the models of variational, maxmin, CARA and CRRA utilities. In each case we present a revealed preference axiom that is satisfied by a dataset if and only if the dataset is consistent from the corresponding utility representation. Our results complement traditional exercises in decision theory that take preferences as primitive

Testing theories of financial decision making

We describe the observable content of some of the most widely used models of decision under uncertainty: models of translation invariant preferences. In particular, we characterize the models of variational, maxmin, constant absolute risk aversion, and constant relative risk aversion utilities. In each case we present a revealed preference axiom that is satisfied by a dataset if and only if the dataset is consistent with the corresponding utility representation. We test our axioms using data from an experiment on financial decisions