Difference between stable and exotic nuclei: medium polarization effects

The bare NN-potential, parametrized so as to reproduce the nuclear phase shifts leads to a sizable Cooper pair binding energy in nuclei along the stability valley. It is a much debated matter whether this value accounts for the "empirical" value of the pairing gap or whether a similarly important contribution arises from the exchange of collective vibrations between Cooper pair partners. In keeping with the fact that two-particle transfer reactions are the specific probe of pairing in nuclei, and that exotic halo nuclei like 11Li are extremely polarizable, we find that the recent studied reaction, namely 11Li+p -> 9Li+t, provides direct evidence of phonon mediated pairing in nuclei

Vortices in Bose-Einstein condensates - finite-size effects and the thermodynamic limit

For a weakly-interacting Bose gas rotating in a harmonic trap we relate the yrast states of small systems (that can be treated exactly) to the thermodynamic limit (derived within the mean-field approximation). For a few dozens of atoms, the yrast line shows distinct quasi-periodic oscillations with increasing angular momentum that originate from the internal structure of the exact many-body states. These finite-size effects disappear in the thermodynamic limit, where the Gross-Pitaevskii approximation provides the exact energy to leading order in the number of particles N. However, the exact yrast states reveal significant structure not captured by the mean-field approximation: Even in the limit of large N, the corresponding mean-field solution accounts for only a fraction of the total weight of the exact quantum state.Comment: Phys Rev A, in pres

Nilsson diagrams for light neutron-rich nuclei with weakly-bound neutrons

Using Woods-Saxon potentials and the eigenphase formalism for one-particle resonances, one-particle bound and resonant levels for neutrons as a function of quadrupole deformation are presented, which are supposed to be useful for the interpretation of spectroscopic properties of some light neutron-rich nuclei with weakly-bound neutrons. Compared with Nilsson diagrams in text books which are constructed using modified oscillator potentials, we point out a systematic change of the shell structure in connection with both weakly-bound and resonant one-particle levels related to small orbital angular momenta $\ell$. Then, it is seen that weakly-bound neutrons in nuclei such as $^{15-19}$C and $^{33-37}$Mg may prefer to being deformed as a result of Jahn-Teller effect, due to the near degeneracy of the 1d$_{5/2}$-2s$_{1/2}$ levels and the 1f$_{7/2}$-2p$_{3/2}$ levels in the spherical potential, respectively. Furthermore, the absence of some one-particle resonant levels compared with the Nilsson diagrams in text books is illustrated.Comment: 12 pages, 5 figure

Seniority conservation and seniority violation in the g_{9/2} shell

The g_{9/2} shell of identical particles is the first one for which one can have seniority-mixing effects. We consider three interactions: a delta interaction that conserves seniority, a quadrupole-quadrupole (QQ) interaction that does not, and a third one consisting of two-body matrix elements taken from experiment (98Cd) that also leads to some seniority mixing. We deal with proton holes relative to a Z=50,N=50 core. One surprising result is that, for a four-particle system with total angular momentum I=4, there is one state with seniority v=4 that is an eigenstate of any two-body interaction--seniority conserving or not. The other two states are mixtures of v=2 and v=4 for the seniority-mixing interactions. The same thing holds true for I=6. Another point of interest is that the splittings E(I_{max})-E(I_{min}) are the same for three and five particles with a seniority conserving interaction (a well known result), but are equal and opposite for a QQ interaction. We also fit the spectra with a combination of the delta and QQ interactions. The Z=40,N=40 core plus g_{9/2} neutrons (Zr isotopes) is also considered, although it is recognized that the core is deformed.Comment: 19 pages, 9 figures; RevTeX4. We have corrected the SDI values in Table1 and Fig.1; in Sect.VII we have included an explanation of Fig.3 through triaxiality; we have added comments of Figs.10-12 in Sect.IX; we have removed Figs.7-

Rotating Bose-Einstein condensates: Closing the gap between exact and mean-field solutions

When a Bose-Einstein condensed cloud of atoms is given some angular momentum, it forms vortices arranged in structures with a discrete rotational symmetry. For these vortex states, the Hilbert space of the exact solution separates into a "primary" space related to the mean-field Gross-Pitaevskii solution and a "complementary" space including the corrections beyond mean-field. Considering a weakly-interacting Bose-Einstein condensate of harmonically-trapped atoms, we demonstrate how this separation can be used to close the conceptual gap between exact solutions for systems with only a few atoms and the thermodynamic limit for which the mean-field is the correct leading-order approximation. Although we illustrate this approach for the case of weak interactions, it is expected to be more generally valid.Comment: 8 pages, 5 figure

Direct observation of the glue pairing the halo of the nucleus 11Li

With the help of a unified description of the nuclear structure and of the direct reaction mechanism we show that a recent 1H(11Li,9Li)3H experiment provides, for the first time in nuclear physics, direct evidence of phonon mediated pairing.Comment: 9 pages, 4 figures. Major change

The Onset of Chaos with a Quadrupole--Quadrupole Interaction

The transition from order to chaos in atomic nuclei has been studied analytically and numerically using a quadrupole--quadrupole residual interaction. This interaction leads to chaotic behaviour, but the critical energy $E_C\simeq 12.6$ MeV, corresponding to the onset of chaos, is higher than that of the experimental one.Comment: 14 pages, 5 figures (available upon request to the authors), LaTex, DFPD/93/TH/73, to be published in Nuovo Cimento

The Yrast Spectra of Weakly Interacting Bose-Einstein Condensates

The low energy quantal spectrum is considered as a function of the total angular momentum for a system of weakly interacting bosonic atoms held together by an external isotropic harmonic potential. It is found that besides the usual condensation into the lowest state of the oscillator, the system exhibits two additional kinds of condensate and associated thermodynamic phase transitions. These new phenomena are derived from the degrees of freedom of "partition space" which describes the multitude of different ways in which the angular momentum can be distributed among the atoms while remaining all the time in the lowest state of the oscillator

Weakly Interacting Bose-Einstein Condensates Under Rotation: Mean-field versus Exact Solutions

We consider a weakly-interacting, harmonically-trapped Bose-Einstein condensed gas under rotation and investigate the connection between the energies obtained from mean-field calculations and from exact diagonalizations in a subspace of degenerate states. From the latter we derive an approximation scheme valid in the thermodynamic limit of many particles. Mean-field results are shown to emerge as the correct leading-order approximation to exact calculations in the same subspace.Comment: 4 pages, RevTex, submitted to PR