Search results for "Bound state"
showing 10 items of 235 documents
Couplings in coupled channels versus wave functions: Application to theX(3872)resonance
2010
We perform an analytical study of the scattering matrix and bound states in problems with many physical coupled channels. We establish the relationship of the couplings of the states to the different channels, obtained from the residues of the scattering matrix at the poles, with the wave functions for the different channels. The couplings basically reflect the value of the wave functions around the origin in coordinate space. In the concrete case of the $X(3872)$ resonance, understood as a bound state of ${D}^{0}{\overline{D}}^{*0}$ and ${D}^{+}{D}^{*\ensuremath{-}}$ (and $c.c.$ From now on, when we refer to ${D}^{0}{\overline{D}}^{*0}$ , ${D}^{+}{D}^{*\ensuremath{-}}$, or $D{\overline{D}}…
Couplings in coupled channels versus wave functions in the case of resonances: Application to the twoΛ(1405)states
2011
In this paper we develop a formalism to evaluate wave functions in momentum and coordinate space for the resonant states dynamically generated in a unitary coupled channel approach. The on-shell approach for the scattering matrix, commonly used, is also obtained in quantum mechanics with a separable potential, which allows one to write wave functions in a trivial way. We develop useful relationships among the couplings of the dynamically generated resonances to the different channels and the wave functions at the origin. The formalism provides an intuitive picture of the resonances in the coupled channel approach, as bound states of one bound channel, which decays into open ones. It also pr…
η′-Nucleus optical potential and possible η′ bound states
2012
Abstract Starting from a recent model of the η ′ N interaction, we evaluate the η ′ -nucleus optical potential, including the contribution of lowest order in density, t ρ / 2 m η ′ , together with the second-order terms accounting for η ′ absorption by two nucleons. We also calculate the formation cross section of the η ′ bound states from ( π + , p ) reactions on nuclei. The η ′ -nucleus potential suffers from uncertainties tied to the poorly known η ′ N interaction, which can be partially constrained by the experimental modulus of the η ′ N scattering length and/or the recently measured transparency ratios in η ′ nuclear photoproduction. Assuming an attractive interaction and taking the c…
The Z(3985) as a threshold effect from the D¯s⁎D+D¯sD⁎ interaction
2021
Abstract We study the e + e − → K + ( D s ⁎ − D 0 + D s − D ⁎ 0 ) reaction recently measured at BESIII, from where a new Z c s state has been reported. We study the interaction of D ¯ s D ⁎ with the coupled channels J / ψ K − , K ⁎ − η c , D s − D ⁎ 0 , D s ⁎ − D 0 by means of an extension to the charm sector of the local hidden gauge approach. We find that the D s − D ⁎ 0 + D s ⁎ − D 0 combination couples to J / ψ K − and K ⁎ − η c , but the D s − D ⁎ 0 − D s ⁎ − D 0 combination does not. The coupled channels help to build up strength in the D s − D ⁎ 0 + D s ⁎ − D 0 diagonal scattering matrix close to threshold and, although the interaction is not strong enough to produce a bound state or…
Energetic collisions of charged projectiles with atomic bound states
1998
Abstract Use of the multiple-scattering expansion of the three-body amplitude for atomic direct and exchange reactions requires the evaluation of multidimensional integrals involving the two-body Coulomb T-operator. We present here numerical results for the first-order terms, both for the attractive and repulsive case. Furthermore, easy-to-calculate approximations are described which in their domain of validity (i) reproduce the exact amplitudes to high accuracy, and (ii) also serve to derive interesting theoretical results.
Towards electronic g-factor measurements in medium-heavy hydrogen-like and lithium-like ions
2005
Abstract Measurements of the anomalous magnetic moment of the electron bound in hydrogen-like ions with spinless nuclei have proven to be highly sensitive tests of corresponding calculations based on bound-state quantum electrodynamics. Measurements performed on H-like carbon 12C5+ and oxygen 16O7+ together with bound-state QED calculations on the same level of accuracy have achieved sensitivities around 0.25% of the QED bound state contributions to the calculated electronic g-factors of these ions. Currently, a similar experiment on hydrogen-like calcium 40Ca19+, lithium-like calcium 40Ca17+ and other medium-heavy ions is being prepared, which is capable of increasing this sensitivity on t…
Microscopic description ofα+40Caquasimolecular resonances
2001
A multistep microscopic approach describing the dynamics of quasimolecular resonances is applied to the $\ensuremath{\alpha}{+}^{40}\mathrm{Ca}$ system. The lowest collective two-particle eigenmodes are used as building blocks of the four-particle states. The pair states are built on mean-field single-particle orbitals including also sharp resonances in continuum. The structure of ${}^{44}\mathrm{Ti}$ is analyzed and strong high-lying $\ensuremath{\alpha}$-like resonances are found in good agreement with the experimentally observed quasimolecular spectrum. The resonances turn out to be very collective and contain mostly proton-neutron pairs where the lowest proton single-particle resonance,…
Linear confinement in momentum space: singularity-free bound-state equations
2014
Relativistic equations of Bethe-Salpeter type for hadron structure are most conveniently formulated in momentum space. The presence of confining interactions causes complications because the corresponding kernels are singular. This occurs not only in the relativistic case but also in the nonrelativistic Schr\"odinger equation where this problem can be studied more easily. For the linear confining interaction the singularity reduces to one of Cauchy principal value form. Although this singularity is integrable, it still makes accurate numerical solutions difficult. We show that this principal value singularity can be eliminated by means of a subtraction method. The resulting equation is much…
On the chiral covariant approach to ρρ scattering
2017
We examine in detail a recent work (D.~G\"ulmez, U.-G.~Mei\ss ner and J.~A.~Oller, Eur. Phys. J. C 77:460 (2017)), where improvements to make $\rho\rho$ scattering relativistically covariant are made. The paper has the remarkable conclusion that the $J=2$ state disappears with a potential which is much more attractive than for $J=0$, where a bound state is found. We trace this abnormal conclusion to the fact that an "on-shell" factorization of the potential is done in a region where this potential is singular and develops a large discontinuous and unphysical imaginary part. A method is developed, evaluating the loops with full $\rho$ propagators, and we show that they do not develop singula…
Eta bound states in nuclei
2002
The energies and widths of bound states of the $\eta$ meson in different nuclei are obtained using the results for its selfenergy in a nuclear medium, which is evaluated in a selfconsistent manner using techniques of unitarized chiral perturbation theory. We find bound states in all studied nuclei (from $^{12}{C}$ on) and the half widths obtained are larger than the separation of the levels, what makes the experimental observation of peaks unlikely. We have paid a special attention to the region of nuclei where only the $1s$ state appears and the binding energies are of the order of magnitude of the half width, which would magnify the chances that some broad peak could be observed. This is …