582 research outputs found
Interference effects in the Coulomb dissociation of 15,17,19C
In this work the semiclassical model of pure Coulomb excitation was applied
to the breakup of 15,17,19C. The ground state wave functions were calculated in
the particle-rotor model including core excitation. The importance of
interference terms in the dipole strength arising after including core degrees
of freedom is analyzed for each isotope. It is shown that Coulomb interference
effects are important for the case of 17C.Comment: 17 pages, 5 figures accepted to Physical Review
A generalized Tullock contest
We construct a generalized Tullock contest under complete information where contingent upon winning or losing, the payoff of a player is a linear function of prizes, own effort, and the effort of the rival. This structure nests a number of existing contests in the literature and can be used to analyze new types of contests. We characterize the unique symmetric equilibrium and show that small parameter modifications may lead to substantially different types of contests and hence different equilibrium effort levels
Breakup reaction models for two- and three-cluster projectiles
Breakup reactions are one of the main tools for the study of exotic nuclei,
and in particular of their continuum. In order to get valuable information from
measurements, a precise reaction model coupled to a fair description of the
projectile is needed. We assume that the projectile initially possesses a
cluster structure, which is revealed by the dissociation process. This
structure is described by a few-body Hamiltonian involving effective forces
between the clusters. Within this assumption, we review various reaction
models. In semiclassical models, the projectile-target relative motion is
described by a classical trajectory and the reaction properties are deduced by
solving a time-dependent Schroedinger equation. We then describe the principle
and variants of the eikonal approximation: the dynamical eikonal approximation,
the standard eikonal approximation, and a corrected version avoiding Coulomb
divergence. Finally, we present the continuum-discretized coupled-channel
method (CDCC), in which the Schroedinger equation is solved with the projectile
continuum approximated by square-integrable states. These models are first
illustrated by applications to two-cluster projectiles for studies of nuclei
far from stability and of reactions useful in astrophysics. Recent extensions
to three-cluster projectiles, like two-neutron halo nuclei, are then presented
and discussed. We end this review with some views of the future in
breakup-reaction theory.Comment: Will constitute a chapter of "Clusters in Nuclei - Vol.2." to be
published as a volume of "Lecture Notes in Physics" (Springer
Helium in superstrong magnetic fields
We investigate the helium atom embedded in a superstrong magnetic field
gamma=100-10000 au. All effects due to the finite nuclear mass for vanishing
pseudomomentum are taken into account. The influence and the magnitude of the
different finite mass effects are analyzed and discussed. Within our full
configuration interaction approach calculations are performed for the magnetic
quantum numbers M=0,-1,-2,-3, singlet and triplet states, as well as positive
and negative z parities. Up to six excited states for each symmetry are
studied. With increasing field strength the number of bound states decreases
rapidly and we remain with a comparatively small number of bound states for
gamma=10^4 au within the symmetries investigated here.Comment: 16 pages, including 14 eps figures, submitted to Phys. Rev.
The all-pay-auction with complete information
In a (first price) all-pay auction, bidders simultaneously submit bids for an item. All players forfeit their bids, and the high bidder receives the item. This auction is widely used in economics to model rent seeking, R&D races, political contests, and job promotion tournaments. We fully characterize equilibrium for this class of games, and show that the set of equilibria is much larger than has been recognized in the literature. When there are more than two players, for instance, we show that even when the auction is symmetric there exists a continuum of asymmetric equilibria. Moreover, for economically important configurations of valuations, there is no revenue equivalence across the equilibria; asymmetric equilibria imply higher expected revenues than the symmetric equilibrium
Hierarchy of QM SUSYs on a Bounded Domain
We systematically formulate a hierarchy of isospectral Hamiltonians in
one-dimensional supersymmetric quantum mechanics on an interval and on a
circle, in which two successive Hamiltonians form N=2 supersymmetry. We find
that boundary conditions compatible with supersymmetry are severely restricted.
In the case of an interval, a hierarchy of, at most, three isospectral
Hamiltonians is possible with unique boundary conditions, while in the case of
a circle an infinite tower of isospectral Hamiltonians can be constructed with
two-parameter family of boundary conditions.Comment: 15 pages, 3 figure
Boundary Conditions on Internal Three-Body Wave Functions
For a three-body system, a quantum wave function with definite
and quantum numbers may be expressed in terms of an internal wave
function which is a function of three internal coordinates. This
article provides necessary and sufficient constraints on to
ensure that the external wave function is analytic. These
constraints effectively amount to boundary conditions on and its
derivatives at the boundary of the internal space. Such conditions find
similarities in the (planar) two-body problem where the wave function (to
lowest order) has the form at the origin. We expect the boundary
conditions to prove useful for constructing singularity free three-body basis
sets for the case of nonvanishing angular momentum.Comment: 41 pages, submitted to Phys. Rev.
Asymmetric first-price auctions with uniform distributions: analytic solutions to the general case
While auction research, including asymmetric auctions, has grown significantly in recent years, there is still little analytical solutions of first-price auctions outside the symmetric case. Even in the uniform case, Griesmer et al. (1967) and Plum (1992) find solutions only to the case where the lower bounds of the two distributions are the same. We present the general analytical solutions to asymmetric auctions in the uniform case for two bidders, both with and without a minimum bid. We show that our solution is consistent with the previously known solutions of auctions with uniform distributions. Several interesting examples are presented including a class where the two bid functions are linear. We hope this result improves our understanding of auctions and provides a useful tool for future research in auctions
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