Structure of Low-Energy Collective 0−0^{-}-States in Doubly Magic Nuclei and Matrix Elements of the P-odd and P- and T-odd Weak Interaction

The structure of the collective low-energy $J^{\pi}=0^{-}$ (T=0 and T=1) modes is studied for a doubly magic nucleus in a schematic analytic model of RPA. The $0^{-}$ phonon states ($T= 0,1$) lie at energies E_{T=0}(0^{-}) \alt \omega and $E_{T=1}(0^{-}) > \omega$, where $\omega$ is the oscillator frequency. The matrix elements of P-odd and P- and T-odd weak one-body potentials connecting the ground state to these $0^{-}$-states, $W_{coll}$, are enhanced by the factor $\sim 2 (\frac{\omega}{E})^{1/2}A^{1/3} \sim 10$ as compared to the single-particle value $w_{sp}$ what can result in values $|W_{coll}| \sim 20-30 eV$ if standard values of DDH parameters are used for $w_{sp}$. Similar enhancement arises in the P- and T-odd case.Comment: 15 pages, REVTEX 3, 2 figure

Renormalization of the P- and T-odd nuclear potentials by the strong interaction and enhancement of P-odd effective field

Approximate analytical formulas for the self-consistent renormalization of P,T-odd and P-odd weak nuclear potentials by the residual nucleon-nucleon strong interaction are derived. The contact spin-flip nucleon-nucleon interaction reduces the constant of the P,T-odd potential 1.5 times for the proton and 1.8 times for the neutron. Renormalization of the P-odd potential is caused by the velocity dependent spin-flip component of the strong interaction. In the standard variant of $\pi + \rho$-exchange, the conventional strength values lead to anomalous enhancement of the P-odd potential. Moreover, the $\pi$-meson exchange contribution seems to be large enough to generate an instability (pole) in the nuclear response to a weak potential.Comment: 5 pages, Revtex3, no figure

Triplet Pairing in Neutron Matter

The separation method developed earlier by us [Nucl. Phys. {\bf A598} 390 (1996)] to calculate and analyze solutions of the BCS gap equation for $^1$S$_0$ pairing is extended and applied to $^3$P$_2$--$^3$F$_2$ pairing in pure neutron matter. The pairing matrix elements are written as a separable part plus a remainder that vanishes when either momentum variable is on the Fermi surface. This decomposition effects a separation of the problem of determining the dependence of the gap components in a spin-angle representation on the magnitude of the momentum (described by a set of functions independent of magnetic quantum number) from the problem of determining the dependence of the gap on angle or magnetic projection. The former problem is solved through a set of nonsingular, quasilinear integral equations, providing inputs for solution of the latter problem through a coupled system of algebraic equations for a set of numerical coefficients. An incisive criterion is given for finding the upper critical density for closure of the triplet gap. The separation method and its development for triplet pairing exploit the existence of a small parameter, given by a gap-amplitude measure divided by the Fermi energy. The revised BCS equations admit analysis revealing universal properties of the full set of solutions for $^3$P$_2$ pairing in the absence of tensor coupling, referring especially to the energy degeneracy and energetic order of these solutions. The angle-average approximation introduced by Baldo et al. is illuminated in terms of the separation-transformed BCS problem and the small parameter expansion..

Nodes of the Gap Function and Anomalies in Thermodynamic Properties of Superfluid 3^3He

Departures of thermodynamic properties of three-dimensional superfluid $^3$He from the predictions of BCS theory are analyzed. Attention is focused on deviations of the ratios $\Delta(T=0)/T_c$ and $[C_s(T_c)-C_n(T_c)]/C_n(T_c)$ from their BCS values, where $\Delta(T=0)$ is the pairing gap at zero temperature, $T_c$ is the critical temperature, and $C_s$ and $C_n$ are the superfluid and normal specific heats. We attribute these deviations to the momentum dependence of the gap function $\Delta(p)$, which becomes well pronounced when this function has a pair of nodes lying on either side of the Fermi surface. We demonstrate that such a situation arises if the P-wave pairing interaction $V(p_1,p_2)$, evaluated at the Fermi surface, has a sign opposite to that anticipated in BCS theory. Taking account of the momentum structure of the gap function, we derive a closed relation between the two ratios that contains no adjustable parameters and agrees with the experimental data. Some important features of the effective pairing interaction are inferred from the analysis.Comment: 17 pages, 4 figure

Effects of T- and P-odd weak nucleon interaction in nuclei: renormalizations due to residual strong interaction, matrix elements between compound states and their correlations with P-violating matrix elements

Manifestations of P-,T-odd weak interaction between nucleons in nucleus are considered. Renormalization of this interaction due to residual strong interaction is studied. Mean squared matrix elements of P-,T-odd weak interaction between compound states are calculated. Correlators between P-,T-odd and P-odd, T-even weak interaction matrix elements between compound states are considered and estimates for these quantities are obtained.Comment: Submitted to Phys. Rev. C; 21 pages, REVTEX 3, no figure

Induced Parity Nonconserving Interaction and Enhancement of Two-Nucleon Parity Nonconserving Forces

Two-nucleon parity nonconserving (PNC) interaction induced by the single-particle PNC weak potential and the two-nucleon residual strong interaction is considered. An approximate analytical formula for this Induced PNC Interaction (IPNCI) between proton and neutron is derived ($Q({\bf r} {\bf \sigma}_{p} \times {\bf \sigma}_{n}) \delta({\bf r}_{p}-{\bf r}_{n})$), and the interaction constant is estimated. As a result of coherent contributions from the nucleons to the PNC potential, IPNCI is an order of magnitude stronger ($\sim A^{1/3}$) than the residual weak two-nucleon interaction and has a different coordinate and isotopic structure (e.g., the strongest part of IPNCI does not contribute to the PNC mean field). IPNCI plays an important role in the formation of PNC effects, e.g., in neutron-nucleus reactions. In that case, it is a technical way to take into account the contribution of the distant (small) components of a compound state which dominates the result. The absence of such enhancement ($\sim A^{1/3}$) in the case of T- and P-odd interaction completes the picture.Comment: Phys. Rev. C, to appear; 17 pages, revtex 3, no figure

Oscillations of general relativistic superfluid neutron stars

We develop a general formalism to treat, in general relativity, the nonradial oscillations of a superfluid neutron star about static (non-rotating) configurations. The matter content of these stars can, as a first approximation, be described by a two-fluid model: one fluid is the neutron superfluid, which is believed to exist in the core and inner crust of mature neutron stars; the other fluid is a conglomerate of all charged constituents (crust nuclei, protons, electrons, etc.). We use a system of equations that governs the perturbations both of the metric and of the matter variables, whatever the equation of state for the two fluids. The entrainment effect is explicitly included. We also take the first step towards allowing for the superfluid to be confined to a part of the star by allowing for an outer envelope composed of ordinary fluid. We derive and implement the junction conditions for the metric and matter variables at the core-envelope interface, and briefly discuss the nature of the involved phase transition. We then determine the frequencies and gravitational-wave damping times for a simple model equation of state, incorporating entrainment through an approximation scheme which extends present Newtonian results to the general relativistic regime. We investigate how the quasinormal modes of a superfluid star are affected by changes in the entrainment parameter, and unveil a series of avoided crossings between the various modes. We provide a proof that, unless the equation of state is very special, all modes of a two-fluid star must radiate gravitationally. We also discuss the future detectability of pulsations in a superfluid star and argue that it may be possible (given advances in the relevant technology) to use gravitational-wave data to constrain the parameters of superfluid neutron stars