Comment on ``Structure of exotic nuclei and superheavy elements in a relativistic shell model''

A recent paper [M. Rashdan, Phys. Rev. C 63, 044303 (2001)] introduces the new parameterization NL-RA1 of the relativistic mean-field model which is claimed to give a better description of nuclear properties than earlier ones. Using this model ^{298}114 is predicted to be a doubly-magic nucleus. As will be shown in this comment these findings are to be doubted as they are obtained with an unrealistic parameterization of the pairing interaction and neglecting ground-state deformation.Comment: 2 pages REVTEX, 3 figures, submitted to comment section of Phys. Rev. C. shortened and revised versio

Cross-Document Pattern Matching

We study a new variant of the string matching problem called cross-document string matching, which is the problem of indexing a collection of documents to support an efficient search for a pattern in a selected document, where the pattern itself is a substring of another document. Several variants of this problem are considered, and efficient linear-space solutions are proposed with query time bounds that either do not depend at all on the pattern size or depend on it in a very limited way (doubly logarithmic). As a side result, we propose an improved solution to the weighted level ancestor problem

Strong dineutron correlation in 8He and 18C

We study the spatial structure of four valence neutrons in the ground state of $^8$He and $^{18}$C nuclei using a core+4$n$ model. For this purpose, we employ a density-dependent contact interaction among the valence neutrons, and solve the five-body Hamiltonian in the Hartree-Fock-Bogoliubov (HFB) approximation. We show that two neutrons with the coupled spin of $S$=0 exhibit a strong dineutron correlation around the surface of these nuclei, whereas the correlation between the two dineutrons is much weaker. Our calculation indicates that the probability of the (1p$_{3/2})^4$ and [(1p$_{3/2})^2$ (p$_{1/2})^2$] configurations in the ground state wave function of $^8$He nucleus is 34.9% and 23.7%, respectively. This is consistent with the recent experimental finding with the $^8$He($p,t)^6$He reaction, that is, the ground state wave function of $^8$He deviates significantly from the pure (1p$_{3/2})^4$ structure.Comment: 10 pages, 9 figures, 3 table

Pairing gaps from nuclear mean-field models

We discuss the pairing gap, a measure for nuclear pairing correlations, in chains of spherical, semi-magic nuclei in the framework of self-consistent nuclear mean-field models. The equations for the conventional BCS model and the approximate projection-before-variation Lipkin-Nogami method are formulated in terms of local density functionals for the effective interaction. We calculate the Lipkin-Nogami corrections of both the mean-field energy and the pairing energy. Various definitions of the pairing gap are discussed as three-point, four-point and five-point mass-difference formulae, averaged matrix elements of the pairing potential, and single-quasiparticle energies. Experimental values for the pairing gap are compared with calculations employing both a delta pairing force and a density-dependent delta interaction in the BCS and Lipkin-Nogami model. Odd-mass nuclei are calculated in the spherical blocking approximation which neglects part of the the core polarization in the odd nucleus. We find that the five-point mass difference formula gives a very robust description of the odd-even staggering, other approximations for the gap may differ from that up to 30% for certain nuclei.Comment: 17 pages, 8 figures. Accepted for publication in EPJ

Consequences of the center-of-mass correction in nuclear mean-field models

We study the influence of the scheme for the correction for spurious center-of-mass motion on the fit of effective interactions for self-consistent nuclear mean-field calculations. We find that interactions with very simple center-of-mass correction have significantly larger surface coefficients than interactions for which the center-of-mass correction was calculated for the actual many-body state during the fit. The reason for that is that the effective interaction has to counteract the wrong trends with nucleon number of all simplified schemes for center-of-mass correction which puts a wrong trend with mass number into the effective interaction itself. The effect becomes clearly visible when looking at the deformation energy of largely deformed systems, e.g. superdeformed states or fission barriers of heavy nuclei.Comment: 12 pages LATeX, needs EPJ style files, 5 eps figures, accepted for publication in Eur. Phys. J.

Prospects for direct detection of circular polarization of gravitational-wave background

We discussed prospects for directly detecting circular polarization signal of gravitational wave background. We found it is generally difficult to probe the monopole mode of the signal due to broad directivity of gravitational wave detectors. But the dipole (l=1) and octupole (l=3) modes of the signal can be measured in a simple manner by combining outputs of two unaligned detectors, and we can dig them deeply under confusion and detector noises. Around f~0.1mHz LISA will provide ideal data streams to detect these anisotropic components whose magnitudes are as small as ~1 percent of the detector noise level in terms of the non-dimensional energy density \Omega_{GW}(f).Comment: 5 pages, 1 figure, PRL in pres

Regularization of second-order scalar perturbation produced by a point-particle with a nonlinear coupling

Accurate calculation of the motion of a compact object in a background spacetime induced by a supermassive black hole is required for the future detection of such binary systems by the gravitational-wave detector LISA. Reaching the desired accuracy requires calculation of the second-order gravitational perturbations produced by the compact object. At the point particle limit the second-order gravitational perturbation equations turn out to have highly singular source terms, for which the standard retarded solutions diverge. Here we study a simplified scalar toy-model in which a point particle induces a nonlinear scalar field in a given curved spacetime. The corresponding second-order scalar perturbation equation in this model is found to have a similar singular source term, and therefore its standard retarded solutions diverge. We develop a regularization method for constructing well-defined causal solutions for this equation. Notably these solutions differ from the standard retarded solutions, which are ill-defined in this case.Comment: 14 page

Effective Operator Treatment of the Anharmonic Oscillator

We analyse the one dimensional quartic oscillator using the effective operator methodology of Lee and Suzuki. We reproduce known results for low lying energy eigenvalues.Comment: 9 Pages, Extended version with new references. To appear in Phys.ReV.

Geometry of PT-symmetric quantum mechanics

Recently, much research has been carried out on Hamiltonians that are not Hermitian but are symmetric under space-time reflection, that is, Hamiltonians that exhibit PT symmetry. Investigations of the Sturm-Liouville eigenvalue problem associated with such Hamiltonians have shown that in many cases the entire energy spectrum is real and positive and that the eigenfunctions form an orthogonal and complete basis. Furthermore, the quantum theories determined by such Hamiltonians have been shown to be consistent in the sense that the probabilities are positive and the dynamical trajectories are unitary. However, the geometrical structures that underlie quantum theories formulated in terms of such Hamiltonians have hitherto not been fully understood. This paper studies in detail the geometric properties of a Hilbert space endowed with a parity structure and analyses the characteristics of a PT-symmetric Hamiltonian and its eigenstates. A canonical relationship between a PT-symmetric operator and a Hermitian operator is established. It is shown that the quadratic form corresponding to the parity operator, in particular, gives rise to a natural partition of the Hilbert space into two halves corresponding to states having positive and negative PT norm. The indefiniteness of the norm can be circumvented by introducing a symmetry operator C that defines a positive definite inner product by means of a CPT conjugation operation.Comment: 22 Page

What can be learned from binding energy differences about nuclear structure: the example of delta V_{pn}

We perform an analysis of a binding energy difference called delta V_{pn}(N,Z) =- 1/4(E(Z,N)-E(Z,N-2)-E(Z-2,N)+ E(Z-2,N-2) in the framework of a realistic nuclear model. Using the angular-momentum and particle-number projected generator coordinate method and the Skyrme interaction SLy4, we analyze the contribution brought to delta V_{pn} by static deformation and dynamic fluctuations around the mean-field ground state. Our method gives a good overall description of delta V_{pn} throughout the chart of nuclei with the exception of the anomaly related to the Wigner energy along the N=Z line. The main conclusions of our analysis are that (i) the structures seen in the systematics of delta V_{pn} throughout the chart of nuclei can be easily explained combining a smooth background related to the symmetry energy and correlation energies due to deformation and collective fluctuations; (ii) the characteristic pattern of delta V_{pn} around a doubly-magic nucleus is a trivial consequence of the asymmetric definition of delta V_{pn}, and not due to a the different structure of these nuclei; (iii) delta V_{pn} does not provide a very reliable indicator for structural changes; (iv) \delta V_{pn} does not provide a reliable measure of the proton-neutron interaction in the nuclear EDF, neither of that between the last filled orbits, nor of the one summed over all orbits; (v) delta V_{pn} does not provide a conclusive benchmark for nuclear EDF methods that is superior or complementary to other mass filters such as two-nucleon separation energies or Q values.Comment: 19 pages and 12 figure