The spectra of mixed 3^3He-4^4He droplets

The diffusion Monte Carlo technique is used to calculate and analyze the excitation spectrum of $^3$He atoms bound to a cluster of $^4$He atoms, by using a previously determined optimum filling of single-fermion orbits with well defined orbital angular momentum $L$, spin $S$ and parity quantum numbers. The study concentrates on the energies and shapes of the three kinds of states for which the fermionic part of the wave function is a single Slater determinant: maximum $L$ or maximum $S$ states within a given orbit, and fully polarized clusters. The picture that emerges is that of systems with strong shell effects whose binding and excitation energies are essentially determined over configuration at fixed number of particles and spin, i.e., by the monopole properties of an effective Hamiltonian.Comment: 14 pages, 15 figure

Nilsson-SU3 selfconsistency in heavy N=Z nuclei

It is argued that there exist natural shell model spaces optimally adapted to the operation of two variants of Elliott' SU3 symmetry that provide accurate predictions of quadrupole moments of deformed states. A selfconsistent Nilsson-like calculation describes the competition between the realistic quadrupole force and the central field, indicating a {\em remarkable stability of the quadruplole moments}---which remain close to their quasi and pseudo SU3 values---as the single particle splittings increase. A detailed study of the $N=Z$ even nuclei from $^{56}$Ni to $^{96}$Cd reveals that the region of prolate deformation is bounded by a pair of transitional nuclei $^{72}$Kr and $^{84}$Mo in which prolate ground state bands are predicted to dominate, though coexisting with oblate ones,Comment: Replacement I) Title simplified. II) Major revision: structure of paper kept but two thirds totally rewritten (same number of pages); 20 references adde

Coulomb displacement energies, energy differenced and neutron skins

A Fock space representation of the monopole part of the Coulomb potential is presented. Quantum effects show through a small orbital term in $l(l+1)$. Once it is averaged out, the classical electrostatic energy emerges as an essentially exact expression, which makes it possible to eliminate the Nolen-Schiffer anomaly, and to estimate neutron skins and the evolution of radii along yrast states of mirror nuclei. The energy differences of the latter are quantitatively reproduced by the monopole term and a schematic multipole one.Comment: 4 pages, 3 figures, Revte

Three-body monopole corrections to the realistic interactions

It is shown that a very simple three-body monopole term can solve practically all the spectroscopic problems--in the $p$, $sd$ and $pf$ shells--that were hitherto assumed to need drastic revisions of the realistic potentials.Comment: 4 pages, 5figure

Mirror displacement energies and neutron skins

A gross estimate of the neutron skin [0.80(5)$(N-Z)/A$ fm] is extracted from experimental proton radii, represented by a four parameter fit, and observed mirror displacement energies (CDE). The calculation of the latter relies on an accurately derived Coulomb energy and smooth averages of the charge symmetry breaking potentials constrained to state of the art values. The only free parameter is the neutron skin itself. The Nolen Schiffer anomaly is reduced to small deviations (rms=127 keV) that exhibit a secular trend. It is argued that with state of the art shell model calculations the anomaly should disappear. Highly accurate fits to proton radii emerge as a fringe benefit.Comment: 4 pages 3 figures, superseeds first part of nucl-th/0104048 Present is new extended version: 5 pages 4 figures. Explains more clearly the achievements of the previous on

Binomial level densities

It is shown that nuclear level densities in a finite space are described by a continuous binomial function, determined by the first three moments of the Hamiltonian, and the dimensionality of the underlying vector space. Experimental values for $^{55}$Mn, $^{56}$Fe, and $^{60}$Ni are very well reproduced by the binomial form, which turns out to be almost perfectly approximated by Bethe's formula with backshift. A proof is given that binomial densities reproduce the low moments of Hamiltonians of any rank: A strong form of the famous central limit result of Mon and French. Conditions under which the proof may be extended to the full spectrum are examined.Comment: 4 pages 2 figures Second version (previous not totally superseeded

Quantification of the differences between quenched and annealed averaging for RNA secondary structures

The analytical study of disordered system is usually difficult due to the necessity to perform a quenched average over the disorder. Thus, one may resort to the easier annealed ensemble as an approximation to the quenched system. In the study of RNA secondary structures, we explicitly quantify the deviation of this approximation from the quenched ensemble by looking at the correlations between neighboring bases. This quantified deviation then allows us to propose a constrained annealed ensemble which predicts physical quantities much closer to the results of the quenched ensemble without becoming technically intractable.Comment: 9 pages, 14 figures, submitted to Phys. Rev.

Analytical description of finite size effects for RNA secondary structures

The ensemble of RNA secondary structures of uniform sequences is studied analytically. We calculate the partition function for very long sequences and discuss how the cross-over length, beyond which asymptotic scaling laws apply, depends on thermodynamic parameters. For realistic choices of parameters this length can be much longer than natural RNA molecules. This has to be taken into account when applying asymptotic theory to interpret experiments or numerical results.Comment: 10 pages, 13 figures, published in Phys. Rev.

An Improved Algorithm for RNA Secondary Structure Prediction

Though not as abundant in known biological processes as proteins,RNA molecules serve as more than mere intermediaries betweenDNA and proteins, e.g. as catalytic molecules. Furthermore,RNA secondary structure prediction based on free energyrules for stacking and loop formation remains one of the few majorbreakthroughs in the field of structure prediction. We present anew method to evaluate all possible internal loops of size at mostk in an RNA sequence, s, in time O(k|s|^2); this is an improvementfrom the previously used method that uses time O(k^2|s|^2).For unlimited loop size this improves the overall complexity ofevaluating RNA secondary structures from O(|s|^4) to O(|s|^3) andthe method applies equally well to finding the optimal structureand calculating the equilibrium partition function. We use ourmethod to examine the soundness of setting k = 30, a commonlyused heuristic