Two-particle spatial correlations in superfluid nuclei

We discuss the effect of pairing on two-neutron space correlations in deformed nuclei. The spatial correlations are described by the pairing tensor in coordinate space calculated in the HFB approach. The calculations are done using the D1S Gogny force. We show that the pairing tensor has a rather small extension in the relative coordinate, a feature observed earlier in spherical nuclei. It is pointed out that in deformed nuclei the coherence length corresponding to the pairing tensor has a pattern similar to what we have found previously in spherical nuclei, i.e., it is maximal in the interior of the nucleus and then it is decreasing rather fast in the surface region where it reaches a minimal value of about 2 fm. This minimal value of the coherence length in the surface is essentially determined by the finite size properties of single-particle states in the vicinity of the chemical potential and has little to do with enhanced pairing correlations in the nuclear surface. It is shown that in nuclei the coherence length is not a good indicator of the intensity of pairing correlations. This feature is contrasted with the situation in infinite matter.Comment: 14 pages, 17 figures, submitted to PR

Generalized Second-Order Thomas-Fermi Method for Superfluid Fermi Systems

Using the $\hbar$-expansion of the Green's function of the Hartree-Fock-Bogoliubov equation, we extend the second-order Thomas-Fermi approximation to generalized superfluid Fermi systems by including the density-dependent effective mass and the spin-orbit potential. We first implement and examine the full correction terms over different energy intervals of the quasiparticle spectra in calculations of finite nuclei. Final applications of this generalized Thomas-Fermi method are intended for various inhomogeneous superfluid Fermi systems.Comment: 8 pages, 10 figures, PR

Size-shrinking of deuterons in very dilute superfluid nuclear matter

It is shown within the strong-coupling BCS approach that, starting from the zero-density limit of superfluid nuclear matter, with increasing density deuterons first shrink before they start expanding.Comment: 2 pages, Latex, 1 figure included, submitted to Phys. Rev.

Generic strong coupling behavior of Cooper pairs in the surface of superfluid nuclei

With realistic HFB calculations, using the D1S Gogny force, we reveal a generic behavior of concentration of small sized Cooper pairs (2-3 fm) in the surface of superfluid nuclei. This study confirms and extends previous results given in the literature that use more schematic approaches.Comment: 5 pages, 5 figure

Cooper pair sizes in 11Li and in superfluid nuclei: a puzzle?

We point out a strong influence of the pairing force on the size of the two neutron Cooper pair in $^{11}$Li, and to a lesser extent also in $^6$He. It seems that these are quite unique situations, since Cooper pair sizes of stable superfluid nuclei are very little influenced by the intensity of pairing, as recently reported. We explore the difference between $^{11}$Li and heavier superfulid nuclei, and discuss reasons for the exceptional situation in $^{11}$Li.Comment: 9 pages. To be published in J. of Phys. G special issue on Open Problems in Nuclear Structure (OPeNST

Cooper pair sizes in superfluid nuclei in a simplified model

Cooper pair sizes are evaluated in a simple harmonic oscillator model reproducing the values of sophisticated HFB calculations. Underlying reasons for the very small sizes of 2.0-2.5 fm of Cooper pairs in the surface of nuclei are analysed. It is shown that the confining properties of the nuclear volume is the dominating effect. It is argued that for Cooper pair sizes LDA is particularly inadapted.Comment: 8 pages, 6 figure

The Consumer Class Action: An Endangered Species

In 1967, Judge Marvin Frankel of the United States District Court for Southern District of New York said of the then newly revised federal class action rule, Fed. R. Civ. P. 23, that it tends to ask more questions than it answers. Professor Benjamin Kaplan, reporter for the new civil rules, predicted that generation or so would pass before the scope, the virtues, and the vices of the new Rule 23 would be fully appreciated. But the 1973-74 Supreme Court term, with its significant class action decisions, has accelerated that process. Now, only eight years later, we know that revised Rule 23 constitutes a rather uncertain weapon for consumers with small claims. The Supreme Court has blunted its edge. Whether Rule 23 can be honed into a more useful tool remains an issue for Congress and for future class action litigants