841 research outputs found
A statistical theory of the mean field
A statistical theory of the mean field is developed. It is based on the
proposition that the mean field can be obtained as an energy average. Moreover,
it is assumed that the matrix elements of the residual interaction, obtained
after the average interaction is removed, are random with the average value of
zero. With these two assumptions one obtains explicit expressions for the mean
field and the fluctuation away from the average. The fluctuation is expanded in
terms of more and more complex excitations. Using the randomness of the matrix
elements one can then obtain formulas for the contribution to the error from
each class of complex excitations and a general condition for the convergence
of the expansion is derived. It is to be emphasized that no conditions on the
nature of the system being studied are made. Making some simplifying
assumptions a schematic model is developed. This model is applied to the
problem of nuclear matter. The model yields a measure of the strength of the
effective interaction. It turns out to be three orders of magnitude less than
that calculated using a potential which gives a binding energy of about -7
MeV/nucleon demonstrating the strong damping of the interaction strength
induced by the averaging process.Comment: 25 pages, REVTeX, 4 eps figure
Ground state energy fluctuations in nuclear matter II
Improvements are performed on a recently proposed statistical theory of the
mean field of a many-fermion system. The dependence of the predictions of the
theory upon its two basic ingredients, namely the Hartree-Fock energy and the
average energy of the two particle-two hole excitations, is explored.Comment: 16 pages, 1 figure, revte
Collisional oscillations of trapped boson-fermion mixtures approaching collapse
We study the collective modes of a confined gaseous cloud of bosons and
fermions with mutual attractive interactions at zero temperature. The cloud
consists of a Bose-Einstein condensate and a spin-polarized Fermi gas inside a
spherical harmonic trap and the coupling between the two species is varied by
increasing either the magnitude of the interspecies s-wave scattering length or
the number of bosons. The mode frequencies are obtained in the collisional
regime by solving the equations of generalized hydrodynamics and are compared
with the spectra calculated in the collisionless regime within a random-phase
approximation. We find that, as the mixture is driven towards the collapse
instability, the frequencies of the modes of fermionic origin show a blue shift
which can become very significant for large numbers of bosons. Instead the
modes of bosonic origin show a softening, which becomes most pronounced in the
very proximity of collapse. Explicit illustrations of these trends are given
for the monopolar spectra, but similar trends are found for the dipolar and
quadrupolar spectra except for the surface (n=0) modes which are essentially
unaffected by the interactions.Comment: 9 pages, 5 figures, revtex
Proton-tetraneutron elastic scattering
We analyze the elastic scattering of protons on a 4n system. This was used as
part of the detection technique of a recent experiment [1] to search for the 4n
(tetraneutron) as a bound particle. We show that it is unlikely that this
process alone could yield the events reported in ref. [1], unless the 4n has an
anomalously large backward elastic scattering amplitude.Comment: 6 pages, 2 figures, accepted for publication in Phys. Rev.
Three-body Faddeev-Alt-Grassberger-Sandhas approach to direct nuclear reactions
Momentum space three-body Faddeev-like equations are used to calculate
elastic, transfer and charge exchange reactions resulting from the scattering
of deuterons on 12C and 16O or protons on 13C and 17O; 12C and 16O are treated
as inert cores. All possible reactions are calculated in the framework of the
same model space. Comparison with previous calculations based on approximate
methods used in nuclear reaction theory is discussed.Comment: 10 pages, 13 figures, to be published in Phys. Rev.
Center of mass rotation and vortices in an attractive Bose gas
The rotational properties of an attractively interacting Bose gas are studied
using analytical and numerical methods. We study perturbatively the ground
state phase space for weak interactions, and find that in an anharmonic trap
the rotational ground states are vortex or center of mass rotational states;
the crossover line separating these two phases is calculated. We further show
that the Gross-Pitaevskii equation is a valid description of such a gas in the
rotating frame and calculate numerically the phase space structure using this
equation. It is found that the transition between vortex and center of mass
rotation is gradual; furthermore the perturbative approach is valid only in an
exceedingly small portion of phase space. We also present an intuitive picture
of the physics involved in terms of correlated successive measurements for the
center of mass state.Comment: version2, 17 pages, 5 figures (3 eps and 2 jpg
Vortex line in a neutral finite-temperature superfluid Fermi gas
The structure of an isolated vortex in a dilute two-component neutral
superfluid Fermi gas is studied within the context of self-consistent
Bogoliubov-de Gennes theory. Various thermodynamic properties are calculated
and the shift in the critical temperature due to the presence of the vortex is
analyzed. The gapless excitations inside the vortex core are studied and a
scheme to detect these states and thus the presence of the vortex is examined.
The numerical results are compared with various analytical expressions when
appropriate.Comment: 8 pages, 6 embedded figure
Control of Ultra-cold Inelastic Collisions by Feshbash Resonances and Quasi-One-Dimensional Confinement
Cold inelastic collisions of atoms or molecules are analyzed using very
general arguments. In free space, the deactivation rate can be enhanced or
suppressed together with the scattering length of the corresponding elastic
collision via a Feshbach resonance, and by interference of deactivation of the
closed and open channels. In reduced dimensional geometries, the deactivation
rate decreases with decreasing collision energy and does not increase with
resonant elastic scattering length. This has broad implications; e.g.,
stabilization of molecules in a strongly confining two-dimensional optical
lattice, since collisional decay of the highly vibrationally excited states due
to inelastic collisions is suppressed. The relation of our results with those
based on the Lieb-Liniger model are addressed.Comment: 5 pages, 1 figur
Dynamical coupled-channels analysis of 1H(e,e'pi)N reactions
We have performed a dynamical coupled-channels analysis of available
p(e,e'pi)N data in the region of W < 1.6 GeV and Q^2 < 1.45 (GeV/c)^2. The
channels included are gamma^* N, pi N, eta N, and pi pi N which has pi Delta,
rho N, and sigma N components. With the hadronic parameters of the model
determined in our previous investigations of pi N --> pi N, pi pi N reactions,
we have found that the available data in the considered W < 1.6 GeV region can
be fitted well by only adjusting the bare gamma^* N --> N^* helicity amplitudes
for the lowest N^* states in P33, P11, S11 and D13 partial waves. The
sensitivity of the resulting parameters to the amount of data included in the
analysis is investigated. The importance of coupled-channels effect on the
p(e,e' pi)N cross sections is demonstrated. The meson cloud effects, as
required by the unitarity conditions, on the gamma^* N --> N^* form factors are
also examined. Necessary future developments, both experimentally and
theoretically, are discussed.Comment: 14 pages, 11 figures. Version to appear in PR
- …