1,064 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

### Feshbach Resonance Cooling of Trapped Atom Pairs

Spectroscopic studies of few-body systems at ultracold temperatures provide
valuable information that often cannot be extracted in a hot environment.
Considering a pair of atoms, we propose a cooling mechanism that makes use of a
scattering Feshbach resonance. Application of a series of time-dependent
magnetic field ramps results in the situation in which either zero, one, or two
atoms remain trapped. If two atoms remain in the trap after the field ramps are
completed, then they have been cooled. Application of the proposed cooling
mechanism to optical traps or lattices is considered.Comment: 5 pages, 3 figures; v.2: major conceptual change

### Creating Ground State Molecules with Optical Feshbach Resonances in Tight Traps

We propose to create ultracold ground state molecules in an atomic
Bose-Einstein condensate by adiabatic crossing of an optical Feshbach
resonance. We envision a scheme where the laser intensity and possibly also
frequency are linearly ramped over the resonance. Our calculations for
$^{87}$Rb show that for sufficiently tight traps it is possible to avoid
spontaneous emission while retaining adiabaticity, and conversion efficiencies
of up to 50% can be expected

### From an insulating to a superfluid pair-bond liquid

We study an exchange coupled system of itinerant electrons and localized
fermion pairs resulting in a resonant pairing formation. This system inherently
contains resonating fermion pairs on bonds which lead to a superconducting
phase provided that long range phase coherence between their constituents can
be established. The prerequisite is that the resonating fermion pairs can
become itinerant. This is rendered possible through the emergence of two kinds
of bond-fermions: individual and composite fermions made of one individual
electron attached to a bound pair on a bond. If the strength of the exchange
coupling exceeds a certain value, the superconducting ground state undergoes a
quantum phase transition into an insulating pair-bond liquid state. The gap of
the superfluid phase thereby goes over continuously into a charge gap of the
insulator. The change-over from the superconducting to the insulating phase is
accompanied by a corresponding qualitative modification of the dispersion of
the two kinds of fermionic excitations. Using a bond operator formalism, we
derive the phase diagram of such a scenario together with the elementary
excitations characterizing the various phases as a function of the exchange
coupling and the temperature.Comment: 10 pages, 5 figure

### Creating stable molecular condensate using a generalized Raman adiabatic passage scheme

We study the Feshbach resonance assisted stimulated adiabatic passage of an
effective coupling field for creating stable molecules from atomic Bose
condensate. By exploring the properties of the coherent population trapping
state, we show that, contrary to the previous belief, mean-field shifts need
not to limit the conversion efficiency as long as one chooses an adiabatic
passage route that compensates the collision mean-field phase shifts and avoids
the dynamical unstable regime.Comment: 4+\epsilon pages, 3 figure

### Three-State Feshbach Resonances Mediated By Second-Order Couplings

We present an analytical study of three-state Feshbach resonances induced by
second-order couplings. Such resonances arise when the scattering amplitude is
modified by the interaction with a bound state that is not directly coupled to
the scattering state containing incoming flux. Coupling occurs indirectly
through an intermediate state. We consider two problems: (i) the intermediate
state is a scattering state in a distinct open channel; (ii) the intermediate
state is an off-resonant bound state in a distinct closed channel. The first
problem is a model of electric-field-induced resonances in ultracold collisions
of alkali metal atoms [Phys. Rev. A 75, 032709 (2007)] and the second problem
is relevant for ultracold collisions of complex polyatomic molecules, chemical
reaction dynamics, photoassociation of ultracold atoms, and electron - molecule
scattering. Our analysis yields general expressions for the energy dependence
of the T-matrix elements modified by three-state resonances and the dependence
of the resonance positions and widths on coupling amplitudes for the
weak-coupling limit. We show that the second problem can be generalized to
describe resonances induced by indirect coupling through an arbitrary number of
sequentially coupled off-resonant bound states and analyze the dependence of
the resonance width on the number of the intermediate states.Comment: 27 pages, 4 figures; added a reference; journal reference/DOI refer
to final published version, which is a shortened and modified version of this
preprin

### 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.

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