708 research outputs found
Structure and decay at rapid proton capture waiting points
We investigate the region of the nuclear chart around from a
three-body perspective, where we compute reaction rates for the radiative
capture of two protons. One key quantity is here the photon dissociation cross
section for the inverse process where two protons are liberated from the
borromean nucleus by photon bombardment. We find a number of peaks at low
photon energy in this cross section where each peak is located at the energy
corresponding to population of a three-body resonance. Thus, for these energies
the decay or capture processes proceed through these resonances. However, the
next step in the dissociation process still has the option of following several
paths, that is either sequential decay by emission of one proton at a time with
an intermediate two-body resonance as stepping stone, or direct decay into the
continuum of both protons simultaneously. The astrophysical reaction rate is
obtained by folding of the cross section as function of energy with the
occupation probability for a Maxwell-Boltzmann temperature distribution. The
reaction rate is then a function of temperature, and of course depending on the
underlying three-body bound state and resonance structures. We show that a very
simple formula at low temperature reproduces the elaborate numerically computed
reaction rate.Comment: 4 pages, 3 figures, conference proceedings, publishe
Computation of local exchange coefficients in strongly interacting one-dimensional few-body systems: local density approximation and exact results
One-dimensional multi-component Fermi or Bose systems with strong zero-range
interactions can be described in terms of local exchange coefficients and
mapping the problem into a spin model is thus possible. For arbitrary external
confining potentials the local exchanges are given by highly non-trivial
geometric factors that depend solely on the geometry of the confinement through
the single-particle eigenstates of the external potential. To obtain accurate
effective Hamiltonians to describe such systems one needs to be able to compute
these geometric factors with high precision which is difficult due to the
computational complexity of the high-dimensional integrals involved. An
approach using the local density approximation would therefore be a most
welcome approximation due to its simplicity. Here we assess the accuracy of the
local density approximation by going beyond the simple harmonic oscillator that
has been the focus of previous studies and consider some double-wells of
current experimental interest. We find that the local density approximation
works quite well as long as the potentials resemble harmonic wells but break
down for larger barriers. In order to explore the consequences of applying the
local density approximation in a concrete setup we consider quantum state
transfer in the effective spin models that one obtains. Here we find that even
minute deviations in the local exchange coefficients between the exact and the
local density approximation can induce large deviations in the fidelity of
state transfer for four, five, and six particles.Comment: 12 pages, 7 figures, 1 table, final versio
A combined mean-field and three-body model tested on the O-nucleus
We combine few- and many-body degrees of freedom in a model applicable to
both bound and continuum states and adaptable to different subfields of
physics. We formulate a self-consistent three-body model for a core-nucleus
surrounded by two valence nucleons. We treat the core in the mean-field
approximation and use the same effective Skyrme interaction between both core
and valence nucleons. We apply the model to O where we reproduce the
known experimental data as well as phenomenological models with more
parameters. The decay of the ground state is found to proceed directly into the
continuum without effect of the virtual sequential decay through the well
reproduced -resonance of O.Comment: 5 pages, 5 figures, under revie
Combining few-body cluster structures with many-body mean-field methods
Nuclear cluster physics implicitly assumes a distinction between groups of
degrees-of-freedom, that is the (frozen) intrinsic and (explicitly treated)
relative cluster motion. We formulate a realistic and practical method to
describe the coupled motion of these two sets of degrees-of-freedom. We derive
a coupled set of differential equations for the system using the
phenomenologically adjusted effective in-medium Skyrme type of nucleon-nucleon
interaction. We select a two-nucleon plus core system where the mean-field
approximation corresponding to the Skyrme interaction is used for the core. A
hyperspherical adiabatic expansion of the Faddeev equations is used for the
relative cluster motion. We shall specifically compare both the structure and
the decay mechanism found from the traditional three-body calculations with the
result using the new boundary condition provided by the full microscopic
structure at small distance. The extended Hilbert space guaranties an improved
wave function compared to both mean-field and three-body solutions. We shall
investigate the structures and decay mechanism of C (C+n+n). In
conclusion, we have developed a method combining nuclear few- and many-body
techniques without losing the descriptive power of each approximation at
medium-to-large distances and small distances respectively. The coupled set of
equations are solved self-consistently, and both structure and dynamic
evolution are studied.Comment: 4 pages, 3 figures, conference proceedings, publishe
Emergence of clusters: Halos, Efimov states, and experimental signals
We investigate emergence of halos and Efimov states in nuclei by use of a
newly designed model which combines self-consistent mean-field and three-body
descriptions. Recent interest in neutron heavy calcium isotopes makes Ca
(Ca+n+n) an ideal realistic candidate on the neutron dripline, and we
use it as a representative example that illustrates our broadly applicable
conclusions. By smooth variation of the interactions we simulate the crossover
from well-bound systems to structures beyond the threshold of binding, and find
that halo-configurations emerge from the mean-field structure for three-body
binding energy less than keV. Strong evidence is provided that Efimov
states cannot exist in nuclei. The structure that bears the most resemblance to
an Efimov state is a giant halo extending beyond the neutron-core scattering
length. We show that the observable large-distance decay properties of the wave
function can differ substantially from the bulk part at short distances, and
that this evolution can be traced with our combination of few- and many-body
formalisms. This connection is vital for interpretation of measurements such as
those where an initial state is populated in a reaction or by a beta-decay.Comment: 5 pages, 5 figures, under revie
Two-proton capture on the Se nucleus with a new self-consistent cluster model
We investigate the two-proton capture reaction of the prominent rapid proton
capture waiting point nucleus, Se, that produces the borromean nucleus
Kr (Se). We apply a recently formulated general model where
the core nucleus, Se, is treated in the mean-field approximation and the
three-body problem of the two valence protons and the core is solved exactly.
The same Skyrme interaction is used to find core-nucleon and core
valence-proton interactions. We calculate electromagnetic two-proton
dissociation and capture cross sections, and derive the temperature dependent
capture rates. We vary the unknown resonance energy without changing any
of the structures computed self-consistently for both core and valence
particles. We find rates increasing quickly with temperature below ~GK
after which we find rates varying by less than a factor of two independent of
resonance energy. The capture mechanism is sequential through the
proton-core resonance, but the continuum background contributes
significantly.Comment: 7 pages, 4 figure
Combined few-body and mean-field model for nuclei
The challenging nuclear many-body problem is discussed along with
classifications and qualitative descriptions of existing methods and models. We
present detailed derivations of a new method where cluster correlations
co-exist with an underlying mean-field described core-structure. The variation
of an antisymmetrized product of cluster and core wave functions and a given
nuclear interaction, provide sets of self-consistent equations of motion.
After the applications on dripline nuclei we discuss perspectives with
improvements and applications. In the conclusion we summarize while emphasizing
the merits of consistently treating both short- and large-distance properties,
few- and many-body correlations, ordinary nuclear structure, and concepts of
halos and Efimov states
Universal properties of Fermi gases in arbitrary dimensions
We consider spin-1/2 Fermi gases in arbitrary, integer or non-integer spatial
dimensions, interacting via a Dirac delta potential. We first generalize the
method of Tan's distributions and implement short-range boundary conditions to
arbitrary dimension and we obtain a set of universal relations for the Fermi
gas. Three-dimensional scattering under very general conditions of transversal
confinement is described by an effectively reduced-dimensional scattering
length, which we show depends on the three-dimensional scattering length in a
universal way. Our formula for non-integer dimensions interpolates between the
known results in integer dimensions 1, 2 and 3. Without any need to solve the
associated multichannel scattering problem, we find that confinement-induced
resonances occur in all dimensions different from D=2, while
reduced-dimensional contacts, related to the tails of the momentum
distributions, are connected to the three-dimensional contact by a correction
factor of purely geometric origin.Comment: 6 pages, 0 figure
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