arXiv subjects
Publications and source records attributed to G. F. Bertsch.
We analyze the adiabatic magnetization of ferromagnetic clusters in an intermediate coupling regime, where the anisotropic potential is comparable to other energy scales. We find a non-monotonic behavior of the magnetic susceptibility as a function of coupling with a peak. Coriolis coupling effects are calculated for the first time; they reduce the susceptibility somewhat.
The time-dependent local-density approximation (TDLDA) is applied to the optical response of conjugated carbon molecules in the energy range of 0-30 eV, with calculations given for carbon chains, polyenes, retinal, benzene and C_60. The major feature of the spectra, the collective pi-pi* transition, is seen at energies ranging from below 2 to 7 eV, and is reproduced by the theory to a few tenths of an eV with a good account of systematic trends. However, there is some indication that TDLDA predicts too much fragmentation of the strength function in large molecules. Transition strengths are reproduced with a typical accuracy of 20%. The theory also predicts a broad absorption peak in the range 15-25 eV, and this feature agrees with experiment in the one case where quantitative data is available (benzene).
We investigate the low-lying spectra of many-body systems with random two-body interactions, specifying that the ensemble be invariant under particle-hole conjugation.Surprisingly we find patterns reminiscent of more orderly interactions, such as a predominance of J=0 ground states separated by a gap from the excited states, and evidence of phonon vibrations in the low-lying spectra.
The time-dependent local-density approximation (TDLDA) is shown to remain accurate in describing the atomic response of IB elements under the additional approximation of using pseudopotentials to treat the effects of core electrons. This extends the work of Zangwill and Soven who showed the utility of the all-electron TDLDA in the atomic response problem.
An iterative algorithm is presented for solving the RPA equations of linear response. The method optimally computes the energy-weighted moments of the strength function, allowing one to match the computational effort to the intrinsic accuracy of the basic mean-field approximation, avoiding the problem of solving very large matrices. For local interactions, the computational effort for the method scales with the number of particles N_p as O(N_p^3).
We study the eikonal model for the nuclear-induced breakup of Borromean nuclei, using Li11 and He6 as examples. The full eikonal model is difficult to realize because of six-dimensional integrals, but a number of simplifying approximations are found to be accurate. The integrated diffractive and one-nucleon stripping cross sections are rather insensitive to the neutron-neutron correlation, but the two-nucleon stripping does show some dependence on the correlation. The distribution of excitation energy in the neutron-core final state in one-neutron stripping reactions is quite sensitive to the shell structure of the halo wave function. Experimental data favor models with comparable amounts of s- and p-wave in the Li11 halo.
We apply the time-dependent local density approximation (TDLDA) to calculate dipole excitations in small carbon clusters. A strong low-frequency mode is found which agrees well with observation for clusters C_n with n in the range 7-15. The size dependence of the mode may be understood simply as the classical resonance of electrons in a conducting needle. For a ring geometry, the lowest collective mode occurs at about twice the frequency of the collective mode in the linear chain, and this may also be understood in simple terms.
We discuss the calculation of collective excitations in atomic clusters using the time-dependent local density approximation. In principle there are many formulations of the TDLDA, but we have found that a particularly efficient method for large clusters is to use a coordinate space mesh and the algorithms for the operators and the evolution equations that had been developed for the nuclear time-dependent Hartree-Fock theory. The TDLDA works remarkably well to describe the strong excitations in alkali metal clusters and in carbon clusters. We show as an example the benzene molecule, which has two strong features in its spectrum. The systematics of the linear carbon chains is well reproduced, and may be understood in rather simple terms.
We derive large-amplitude collective equations of motion from the variational principle for the time-dependent Schroedinger equation. These equations reduce to the well-known diabatic formulas for vibrational frequencies in the small amplitude limit. The finite amplitude expression allows departures from harmonic behavior of giant resonances to be simply estimated. The relative shift of the second phonon falls with nuclear mass A as A^(-4/3) in the three modes we consider: monopole, dipole, and quadrupole. Numerically the effect is very small in heavy nuclei, as was found with other approaches.
We examine the magnetic response of free clusters considering the spin direction and the cluster orientation as the only active degrees of freedom. The average magnetization in small fields approaches the Langevin value for paramagnets, depending on the degree to which the Hamiltonian preserves symmetries. Superparamagnetic behavior is not achievable within models considering only these degrees of freedom.
Off-shell propagation of nucleons is neglected in one-body transport models of heavy-ion collisions, but it could be significant in processes that are limited by phase space, such as the threshold production of heavy particles. We estimate the relative magnitude of off-shell production to on-shell production of the N$^*$(1535) resonance in heavy ion collisions. In the region where the on-shell production is dominated by a~two-step mechanism with an intermediate $Δ$, we find that the contribution of off-shell scattering between projectile and target nucleons is indeed small. Beyond the latter contribution, however, correlations in the initial wave function produce off-shell contributions which can exceed those of the on-shell $Δ$ mechanism.
When the Vlasov equation is investigated numerically using the method of test particles, the particle-particle interactions that inevitably arise in the simulation (but are not present in the Vlasov equation itself) result in an accumulation of errors which eventually drive the collection of test particles toward a state of classical thermal equilibrium. We estimate the rate at which these errors accumulate.
We present Shell Model Monte Carlo calculations for nuclei within the full major shell 50-82 for both protons and neutrons. The interaction is determined solely by self-consistency and odd-even mass differences. The methods are illustrated for ${}^{124}$Sn, ${}^{128}$Te and ${}^{124}$Xe. We calculate shape distributions, moments of inertia and pairing correlations as functions of temperature and angular velocity. Our calculations are the first microscopic evidence of $γ$-softness of nuclei in this region.
Recent experiments on pion correlations, interpreted as interferometric measurements of the collision zone, are compared with models that distinguish a prehadronic phase and a hadronic phase. The models include prehadronic longitudinal expansion, conversion to hadrons in local kinetic equilibrium, and rescattering of the produced hadrons. We find that the longitudinal and outward radii are surprisingly sensitive to the algorithm used for two-body collisions. The longitudinal radius measured in collisions of 200 GeV/u sulfur nuclei on a heavy target requires the existence of a prehadronic phase which converts to the hadronic phase at densities around 0.8-1.0 GeV/fm$^3$. The transverse radii cannot be reproduced without introducing more complex dynamics into the transverse expansion.
The analysis of meson correlations by Hanbury-Brown--Twiss interferometry is tested with a simple model of meson production by resonance decay. We derive conditions which should be satisfied in order to relate the measured momentum correlation to the classical source size. The Bose correlation effects are apparent in both the ratio of meson pairs to singles and in the ratio of like to unlike pairs. With our parameter values, we find that the single particle distribution is too distorted by the correlation to allow a straightforward analysis using pair correlation normalized by the singles rates. An analysis comparing symmetrized to unsymmetrized pairs is more robust, but nonclassical off-shell effects are important at realistic temperatures.