Antiproton stopping at low energies: confirmation of velocity-proportional stopping power

The stopping power for antiprotons in various solid targets has been measured in the low-energy range of 1-100 keV. In agreement with most models, in particular free-electron gas models, the stopping power is found to be proportional to the projectile velocity below the stopping-power maximum. Although a stopping power proportional to velocity has also been observed for protons, the interpretation of such measurements is difficult due to the presence of charge exchange processes. Hence, the present measurements constitute the first unambiguous support for a velocity-proportional stopping power due to target excitations by a pointlike projectile.     

A method for determination of nuclear and electronic stopping power parameters

It is shown that by use of Doppler-shift attenuation measurements of γ-rays and by use of range measurements, the correction factors for the nuclear and electronic stopping power equations can be determined.     

On the theory of slowing down gracefully

We discuss the transport of a tracer particle through the Bose?CEinstein condensate of a Bose gas. The particle interacts with the atoms in the Bose gas through two-body interactions. In the limiting regime where the particle is very heavy and the Bose gas is very dense, but very weakly interacting (??mean-field limit??), the dynamics of this system corresponds to classical Hamiltonian dynamics. We show that, in this limit, the particle is decelerated by emission of gapless modes into the condensate (Cerenkov radiation). For an ideal gas, the particle eventually comes to rest. In an interacting Bose gas, the particle is decelerated until its speed equals the propagation speed of the Goldstone modes of the condensate. This is a model of ??Hamiltonian friction??. It is also of interest in connection with the phenomenon of ??decoherence?? in quantum mechanics. This note is based on work we have carried out in collaboration with D Egli, I M Sigal and A Soffer.     

A simple universal fit formula to experimental nuclear stopping power data

Recent experimental data was fitted by using a simple universal relation between nuclear stopping power and particle energy in the range of about 10^?4≦?≦10². Comparison with previous and recent theoretical predictions is made.     

From nuclear stopping to interatomic potential via the power law formalism

A general method for inverting the energy-dependent nuclear stopping cross sections S_n(?) to derive the interatomic potential V(x) is described. A correspondence between ? and x is derived for mapping S_n(?) to V(x) and vice versa. The method is illustrated by using the recent range-energy data of keV indium and xenon ions in amorphous silicon to self-consistently deduce the In-Si and Xe-Si potentials.     

Critical slowing down exponents of mode coupling theory

A method is provided to compute the exponent parameter λ yielding the dynamic exponents of critical slowing down in mode coupling theory. It is independent from the dynamic approach and based on the formulation of an effective static field theory. Expressions of λ in terms of third order coefficients of the action expansion or, equivalently, in terms of six point cumulants are provided. Applications are reported to a number of mean-field models: with hard and soft variables and both fully connected and dilute interactions. Comparisons with existing results for the Potts glass model, the random orthogonal model, hard and soft-spin Sherrington-Kirkpatrick, and p-spin models are presented.     

Nonlinear critical slowing down of the one-component Ginzburg-Landau field

We discuss nonlinear relaxation processes of the one-component Ginzburg-Landau field that occur near the critical point after a sudden change in temperature or in the symmetry breaking field. A universal form of the equation of motion for the order parameter at the one-loop level is derived and integrated for several cases of interest. From the results some characteristic universal amplitude ratios can be extracted.     

Quantitative investigation of critical slowing down in all-optical bistability

We have observed optical bistability in rubidium vapor enclosed in a Fabry-Perot cavity for λ ～ 7779 Å (two-photon transition) and λ ～ 7800 Å (one-photon transition). We have measured the switching time τ_S as a function of (l?l_c) where l_c is the last value of the length of the cavity for which switching occurs. In all the experimental situations, we have found a similar law τ_S ～ (l?l_c)^-α with α ～ 0.5. This result is in agreement with theoretical predictions.     

Detailed balance and critical slowing down for classical lattice systems

For classical lattice systems we prove rigorously a relation between the fluctuations and the relaxation times for a dynamics given by a detailed balance semigroup. In particular we give a rigorous proof of the conventional theory of critical slowing down.On leave of absence from Institute of Theoretical Physics and Astrophysics, Gdansk University, Poland.     

Forward a production and nuclear stopping power in d+Au collisions at RHIC

Using the forward time projection chambers of STAR we measure the centrality dependent A and ā yields in d+Au collisions at √s _NN =200 GeV at forward and backward rapidities. The contributions of different processes to particle production and baryon transport are probed exploiting the inherent asymmetry of the d+Au system. While the d side appears to be dominated by multiple independent nucleon-nucleon collisions, nuclear effects contribute significantly on the Au side. Using the constraint of baryon number conservation, the rapidity loss of baryons in the incoming deuteron can be estimated as a function of centrality. This is compared to a model and to similar measurements in Au+Au, which gives insights into the nuclear stopping power at relativistic energies.     

Effective stopping charges and stopping power calculations for heavy ions

In this study the model suggested by Sugiyama has been developed and applied for the calculation of the stopping powers for nonrelativistic heavy ions in various target materials. Sugiyama's model has been expanded to low and high energy regions in our work. Analytical expressions are obtained in the modified BB stopping power formula for the effective charge and effective mean excitation energies. In the modified LSS formula, a quasi-molecule criterion has been applied to both the projectiles and the target atoms. Electronic excitation contribution, S _e0, and quasi-molecule contribution, S _ei , to stopping power were found for a wide energy region. It is observed that in intermediate energy region both contributions have maxima. The stopping power due to excitation-ionization in the intermediate and higher energy region is found to be dominant, whereas quasi-molecule contribution is dominant in the lower energy region. The calculated results of stopping power are in good agreement with experimental data for various ions and targets within a few percent in a wide projectile energy range.     

Monte-Carlo calculations of keV electron and positron slowing down in solids

A Monte-Carlo simulation technique based on the screened Rutherford differential cross section for the elastic scattering and Gryzinski's semiempirical expression for the inelastic core and valence electron excitation is used to describe electrons and positrons slowing down in solids. The theoretical results are compared with the experimental backscattering, absorption and transmission results for aluminum, silicon, copper, and gold thin film and semi-infinite targets and good agreement is observed. The simulated stopping profiles are fitted with a simple analytic expression. The profiles are Laplace-transformed to give a useful data base for analyzing phenomena associated with slow positron re-emission from solids.     

The role of curvature in the slowing down acceleration scenario

We introduce the curvature _Ωk${\Omega }_k$ as a new free parameter in the Bayesian analysis using SNIa, BAO and CMB data, in a model with variable equation of state parameter w(z)$w(z)$. We compare the results using both the Constitution and Union 2 data sets, and also study possible low redshift transitions in the deceleration parameter q(z)$q(z)$. We found that, incorporating _Ωk${\Omega }_k$ in the analysis, it is possible to make all the three observational probes consistent using both SNIa data sets. Our results support dark energy evolution at small redshift, and show that the tension between small and large redshift probes is ameliorated. However, although the tension decreases, it is still not possible to find a consensus set of parameters that fit all the three data set using the Chevalier–Polarski–Linder CPL parametrization.     

Critical slowing down of space-charge field relaxation in photorefractive sillenites

We propose a theoretical model for the recently reported anomalously long decay of a space-charge field that was resonantly excited in a photorefractive sillenite crystal [Phys. Rev. Lett. 79, 67 (1997)]. The model is based on the conventional concept of charge transfer and does not require excessively large values of the quality factor for space-charge waves. The effect in question is qualified as a critical slowing of the relaxation process as the threshold of optical oscillation is approached.     

The slowing down of fast neutrons in thin hydrogeneous moderators

The slowing down of neutrons in thin hydrogeneous moderators of different thickness and finite lateral dimensions is studied using two experimental methods, a) the direct method of measuring the time distribution of neutrons slowed down to a specified energy and leaving the moderator, b) an indirect method which consists of determining the influence of such a moderator on the resonance width of a known neutron resonance at low energy measured by the time-of-flight neutron spectrometer. The experimental results are compared with Monte Carlo calculations and with theoretical expressions derived elsewhere. Fairly good agreement is obtained between experiment and the Monte Carlo calculations. The theoretical predictions are seen to be of limited range of validity only and especially a great difference between the theoretical and experimental time variance of the slowing-down time is observed.The author would like to thank Dr. R. Joly and Dr. A. Michaudon for their suggestion that this work be performed in CEN Saclay as well as for their support and interest during the measurements in Saclay. He would also like to acknowledge the help of Dr. P. Ribon, Mr. Paya, Mr. Derrien, his wife Jarmila and Mr. Girard and the accelerator group in CEN Cadarache under the direction of Mr. Leroy during the measurements on the Van de Graaff accelerator. He is very obliged to the International Atomic Energy Agency in Vienna for having offered a stipend in France without which the present work could not have been done.     

The stopping of slow75As recoil atoms in He,Ne and H2

Recent measurements of the 2p—1s X-ray line in theK ^? p atom indicate that the 1s level shift is very different from the theoretical prediction based on the extrapolation from theK ^? p scattering data. Deloff and Law have suggested that an anomalously large Coulomb effect could be responsible for this discrepancy. We examine this possibility by carrying out an explicit model calculation, using the method by which Sauer demonstrated the possible existence of an anomalously large Coulomb effect in the proton-proton system. Our conclusion is that if there exists an anomalous Coulomb effect which explains theK ^? p atomic level shift result, then the same effect would cause a serious conflict with theK ^? p scattering data above threshold.     

Computer simulations of slowing down of heavy ions in polycrystalline materials

A fast computer code is constructed to simulate the slowing down of ions in crystalline materials. The programme is used to study the range distributions of 120 keV Pb in polycrystalline Al and 60 keV Al in polycrystalline Ta. Good agreement with experiment is found, when partial preferred orientation of the microcrystals is assumed.