Scattering Length Approximation Research Articles

Cancellation of the Sigma Mode in the Thermal Pion Gas by Quark Pauli Blocking

In this study, we calculate the pressure of the interacting pion gas using the Beth–Uhlenbeck approach to the relativistic virial expansion with Breit–Wigner phase shifts for the σ- and ϱ-meson resonances. The repulsive phase shift δ02 is taken from the quark interchange model of Barnes and Swanson, which is in very good agreement with the experimental data. In this work we show that the cancellation of the attractive (I = 0) and repulsive (I = 2) isospin channel contributions to the scalar ππ interaction in the low-energy region that is known for the vacuum phase shifts also takes place at a finite temperature. This happens despite the strong medium dependence of these phase shifts that enters our model by the temperature dependence of the σ-meson and constituent quark masses, because for these masses the relation Mσ(T)≈2mq(T) holds and the scattering length approximation is valid as long as the strong decay channel σ→ππ is open. Exploiting the Nambu–Jona-Lasinio model for describing the dynamical breaking of chiral symmetry in the vacuum and its restoration at a finite temperature, we justify with our approach that the σ-meson should be absent from the hadron resonance gas description at low temperatures because the above cancellation holds. However, since this cancellation breaks down in the vicinity of the hadronization transition, where due to chiral symmetry restoration the decay channel σ→ππ closes and the σ-meson becomes a good resonance, the latter should be included into the statistical model description of chemical freeze-out in heavy-ion collisions.

On the possible virtual state nature of the LHCb Pc (4312)+ signal

In this contribution we study the nature of the new Pc (4312)+ signal reported by LHCb collaboration in the J/ψ p spectrum. We use S-matrix principles to perform a minimum-bias analysis of the data, focusing on the analytic properties that can be related to the microscopic origin of the Pc (4312)+ peak. Using the scattering length approximation we find evidence for interpretation of the signal as a virtual state generated by the attractive effect of the channel opening.

Realization of a Resonant Fermi Gas with a Large Effective Range

We have measured the interaction energy and three-body recombination rate for a two-component Fermi gas near a narrow Feshbach resonance and found both to be strongly energy dependent. Even for de Broglie wavelengths greatly exceeding the van der Waals length scale, the behavior of the interaction energy as a function of temperature cannot be described by atoms interacting via a contact potential. Rather, energy-dependent corrections beyond the scattering length approximation are required, indicating a resonance with an anomalously large effective range. For fields where the molecular state is above threshold, the rate of three-body recombination is enhanced by a sharp, two-body resonance arising from the closed-channel molecular state which can be magnetically tuned through the continuum. This narrow resonance can be used to study strongly correlated Fermi gases that simultaneously have a sizable effective range and a large scattering length.

Three-bodyDD¯πdynamics for theX(3872)

We investigate the role played by the three-body $D\bar{D}\pi$ dynamics on the near-threshold resonance X(3872) charmonium state, which is assumed to be formed by nonperturbative $D\bar D^*$ dynamics. It is demonstrated that, as compared to the naive static-pions approximation, the imaginary parts that originate from the inclusion of dynamical pions reduce substantially the width from the $D\bar{D}\pi$ intermediate state. In particular, for a resonance peaked at 0.5 MeV below the $D^0\bar D^{*0}$ threshold, this contribution to the width is reduced by about a factor of 2, and the effect of the pion dynamics on the width grows as long as the resonance is shifted towards the $D^0\bar{D^0}\pi^0$ threshold. Although the physical width of the $X$ is dominated by inelastic channels, our finding should still be of importance for the $X$ line shapes in the $D\bar{D}\pi$ channel below $D{\bar D}^*$ threshold. For example, in the scattering length approximation, the imaginary part of the scattering length includes effects of all the pion dynamics and does not only stem from the $D^*$ width. Meanwhile, we find that another important quantity for the $X$ phenomenology, the residue at the $X$ pole, is weakly sensitive to dynamical pions. In particular, we find that the binding energy dependence of this quantity from the full calculation is close to that found from a model with pointlike $D\bar D^*$ interactions only, consistent with earlier claims. Coupled-channel effects (inclusion of the charged $D\bar{D}^*$ channel) turn out to have a moderate impact on the results.

Validity of the scattering-length approximation in strongly interacting Fermi systems

We investigate the energy spectrum of systems of two, three, and four spin-$\frac{1}{2}$ fermions with short range attractive interactions both exactly and within the scattering length approximation. The formation of molecular bound states and the ferromagnetic transition of the excited scattering state are examined systematically as a function of the two-body scattering length. Identification of the upper branch (scattering states) is discussed and a general approach valid for systems with many particles is given. We show that an adiabatic ferromagnetic transition occurs, but at a critical transition point ${k}_{F}a$ much higher than predicted from previous calculations, almost all of which use the scattering length approximation. In the four-particle system the discrepancy is a factor of 2. The exact critical interaction strength calculated in the four-particle system is consistent with that reported by experiment. To make comparisons with the adiabatic transition, we study the quench dynamics of the pairing instability using the eigenstate wave functions.

On the electromagnetic form factors of hadrons in the time-like region near threshold

Hadron electromagnetic form factor in the time-like region at the boundary of the physical region is considered. The energy behavior of the form factor is shown to be determined by the strong hadron–antihadron interaction. We propose a simple phenomenological model of the h h ¯ interaction that describes the form factor behaviour in the region where scattering length approximation fails and estimate on its basis imaginary part of the scattering lengths (volumes) for Λ Λ ¯ , Λ Σ ¯ 0 ( Λ ¯ Σ 0 ) , Σ 0 Σ ¯ 0 and D ∗ D ∗ ¯ from present experimental data. The developed approach enables us to analyze the existence of baryon–antibaryon ( B B ¯ ) near threshold resonances. The experiments to extract detailed information on the near threshold B B ¯ interaction from hadron form factor energy behavior are suggested.

Universal properties of Efimov physics beyond the scattering length approximation

We calculate the low-lying energy spectrum for three trapped identical bosons interacting via a finite-range potential. The spectrum is compared to results from the zero-range model. The thresholds for trimer binding and atom-dimer binding are extracted and related to effective range corrections. Effective range corrections to Efimov physics and Borromean binding are two aspects of the same effect, and we connect these two regions qualitatively. The Borromean window becomes slightly narrower for substantial effective ranges. The structure at the atom-dimer threshold is an atom far away from the dimer and the major energy correction is due to the change of dimer energy with effective range. This structure becomes less pronounced when the effective range increases.

INTERACTING BOSE AND FERMI GASES IN LOW DIMENSIONS AND THE RIEMANN HYPOTHESIS

We apply the S-matrix based finite temperature formalism to nonrelativistic Bose and Fermi gases in 1+1 and 2+1 dimensions. For the (2+1)-dimensional case in the constant scattering length approximation, the free energy is given in terms of Roger's dilogarithm in a way analagous to the thermodynamic Bethe ansatz for the relativistic (1+1)-dimensional case. The 1d fermionic case with a quasiperiodic two-body potential is closely connected with the Riemann hypothesis.

Pairing with polarization effects in low-density neutron matter

We study the properties of the ${}^{1}{S}_{0}$ pairing gap in low-density neutron matter. Different corrections to the lowest-order scattering length approximation are explored, resulting in a strong suppression with respect to the BCS result.

The reaction [formula omitted] and the eta–nucleon and nucleon–nucleon interactions

The π, η and ρ exchange contributions to the cross section for the reaction pp→ppη near threshold are calculated, with a phenomenological description of the intermediate S11 (N(1535)) resonance for all exchange mechanisms. The final state interaction in the pp system is described by realistic nucleon–nucleon interaction models. The sensitivity of the results to the phenomenological models for the η–nucleon transition amplitude and the nucleon–nucleon interaction is explored. The η-exchange mechanism is found to play a dominant role. The off-shell behavior of the ηN→ηN amplitude within the η exchange amplitude leads to a result significantly different from that obtained with the constant scattering length approximation. The two-nucleon amplitudes that are associated with the short-range components of the nucleon–nucleon interaction contribute significantly to the cross section.

Identical particle scattering from a weakly coupled Bose-Einstein condensed gas

We calculate the scattering states and cross sections for a Bose-Einstein condensed dilute gas trapped in a spherical square well of finite depth. The interactions are treated in the scattering length approximation. We solve the Gross-Pitaevskii equation and the Bogoliubov equations for bound and scattering states. The results show that there are transparency effects reminiscent of those conjectured to occur for strongly coupled systems. When incident particle wavelengths $\ensuremath{\lambda}$ are comparable to the well size a, exchange induced transparency enhancement is dramatic only for particular combinations of well depth, interaction strength, and particle number. For particles with large momenta $(a/\ensuremath{\lambda}\ensuremath{\gg}1),$ however, exchange with the condensate results in enhanced transmission for all coupling strengths. We calculated the rate of decay of the scattering states to leading order in anharmonic corrections to the Bogoliubov approximation and found the corresponding inelastic cross sections to be extremely small.

Total and annihilation [formula omitted] cross sections from 50 to 400 MeV/c

The recent experimental data obtained by the OBELIX Collaboration on total and annihilation cross sections are presented and analysed in terms of scattering length approximation. This analysis allowed the evaluation of the partial wave contributions to the np interaction as well as the isospin dependence in the NN total cross sections, but the most striking result is the indication of a quite unexpected, narrow structure just above the NN threshold.

P̄P partial cross sections at low energy

New measurements of the pp total annihilation cross-section at very low momenta (around 50 MeV/c) confirm the previous results obtained by the OBELIX collaboration. The measured values are in general agreement with a scattering length approximation of the annihilation cross-section where the pp scattering lengths are obtained from measurement of the protonium shifts and widths and which accounts for the Coulomb interaction. Partial annihilation cross-sections and annihilation frequencies for some channels have been measured too. The values of the total and partial cross sections at the lowest p momentum show an unexpected behaviour

Thermal collisional angular-momentum mixing of highly excited Na(n 2D) states by N 2 and CO

On the basis of the impulse approximation, an analytical wavefunction and a scattering length approximation are utilized to calculate thermal collisional l-mixing cross sections of highly excited Na( n 2D) states by N 2 and CO. Our study indicates that these results are better than other theoretical ones.

Ionization of Rydberg atoms by neutral particles. I. Mechanism of the perturber-quasifree-electron scattering

The theory of ionization of highly excited atoms by neutral particles (atoms or molecules) is developed within the framework of the quasifree electron model. General formulae relating the ionization cross section with the differential cross section for electron-perturber scattering and with the momentum distribution function of the Rydberg electron in the initial atomic state, have been derived from the impulse approximation. These formulae are applicable for any arbitrary form of the amplitude of elastic or inelastic scattering of the slow electron by a perturbing particle. In the special case of the scattering length approximation, simple analytical expressions for the ionization cross sections and the rate constants have been obtained.

Embedded cluster calculations for hydrogen chemisorption on the (111) surfaces of fcc Co, Ni, Cu, Rh, Pd and Ag

Abstract We present a muffin tin based calculation on (TM) 3 H, (TM) 7 H and (TM) 19 H clusters embedded at the surface of an effective jellium-like medium whose potential is treated in scattering length approximation. We consider the changes occurring when the d-like perturbation of the TM muffin tins is switched on. The broad chemisorption-induced resonance seen for H on the effective jellium surface is narrowed and shifted down in energy. Furthermore the occupation of this resonance is increased from about 1.1 electrons to about 1.4 (on 3d metals) or 1.8 (on 4d metals), due to d-like states dropping down from the d band to form a relatively welldefined “bonding state”. An antibonding state containing about 0.4 electrons is formed at the top of the d band. The results are compared with other calculations and with photoemission data. Implications for the metal-hydrogen distance and (for Ni) the demagnetizing effect of hydrogen chemisorption are discussed. We use the change in total single particle energy when the d-like perturbation is switched on to estimate trends in chemisorption energy along the 3d and 4d series. In the 3d case experimental data is available on the difference in chemisorption energy between Ni and Cu which is in reasonable agreement with our estimate.

Embedded cluster calculations for hydrogen chemisorption on the (111) surfaces of fcc Co, Ni, Cu, Rh, Pd and Ag

We present a muffin tin based calculation on (TM) 3H, (TM) 7H and (TM) 19H clusters embedded at the surface of an effective jellium-like medium whose potential is treated in scattering length approximation. We consider the changes occurring when the d-like perturbation of the TM muffin tins is switched on. The broad chemisorption-induced resonance seen for H on the effective jellium surface is narrowed and shifted down in energy. Furthermore the occupation of this resonance is increased from about 1.1 electrons to about 1.4 (on 3d metals) or 1.8 (on 4d metals), due to d-like states dropping down from the d band to form a relatively welldefined “bonding state”. An antibonding state containing about 0.4 electrons is formed at the top of the d band. The results are compared with other calculations and with photoemission data. Implications for the metal-hydrogen distance and (for Ni) the demagnetizing effect of hydrogen chemisorption are discussed. We use the change in total single particle energy when the d-like perturbation is switched on to estimate trends in chemisorption energy along the 3d and 4d series. In the 3d case experimental data is available on the difference in chemisorption energy between Ni and Cu which is in reasonable agreement with our estimate.

Features of the π0π0 system produced in 5π final states by 3.5 GeV/ cπ+

Angular correlations between two pions in the 5-pion final states are studied. A comparison between neutral, like-charged and unlike-charged pion-pion system is done. Evidence is shown for a strong π 0 π 0 correlation in the asymmetry parameters as well as in the mass distribution. This effect is interpreted in terms of the scattering length approximation.

2−Threshold State inBe8

The ${2}^{\ensuremath{-}}$ level in $^{8}\mathrm{Be}$ at the threshold for the reaction $^{7}\mathrm{Li}(p,n)^{7}\mathrm{Be}$ is shown to be a virtual state relative to threshold. A description of the state as an $S$-matrix pole in the scattering-length approximation gives a good account of its properties as observed in different reaction channels, and, in particular, removes an apparent contradiction about its width as observed through particle and $\ensuremath{\gamma}$-ray channels. The width of the ${2}^{\ensuremath{-}}$ state is found to be about 50 keV.

Effects of exchange, final-state interactions, and distorted waves in the reactions 2H( 3He, 3H p)p and 2H( 3He, 3He p)n

A systematic treatment of the 2H( 3He 3H p)p and 2H( 3He, 3He p)n reactions by the Born approximation is carried out for conditions at which Warner et al. (WBDFF) observed spectator peaks juxtaposed with final-state interaction (FSI) effects. WBDFF fitted the spectator peaks with plane-wave Born approximation (PWBA) using two interaction matrix elements, but encountered difficulties in predicting relative yields, absolute cross sections and the shape modifications due to FSI. We first add full antisymmetry to PWBA in order to account properly for relative yields. This step connects all reaction mechanisms (break-up, knock-out, and pick-up), and their seven distinct interaction matrix elements. Next, the FSI shape modifications are successfully accounted for by using scattering wave functions for the final free nucleons in one of the matrix elements and by inferring the FSI properties in all matrix elements through a scattering-length approximation. When juxtaposed to simple spectator poles the FSI effects are shown to be interesting interference dips and amplitude peaks which are dominated by the sign and size of the singlet and triplet nueleon-nucleon scattering lengths. Finally, the effects of distorted waves on absolute cross sections are briefly discussed.