Damping of high-lying single-particle modes in heavy nuclei

The recent experimental and theoretical results on the damping of high-lying single-particle modes in heavy nuclei are reviewed. In one-nucleon transfer reactions these states manifest themselves as broad “resonance”-like structures superimposed on a large continuum. The advantages and the limitations of the transfer reaction approach will be presented using the results from neutron and proton pick-up and stripping reactions. The problem raised by the subtraction of the underlying background, the assumptions made to describe the reaction process and the method used to extract the strength distributions are presented. The existing empirical systematics is summarized for nuclei ranging from ⁹⁰Zr to ²⁰⁸Pb.The theoretical approaches used to explain the damping of the high-lying single-particle modes are based on the coupling between collective and single-particle degrees of freedom. In a first step the bare single-particle mode is spread over several doorway collective states due to the interaction with surface vibrations. In a second step the doorway states spread their strengths over many other degrees of freedom. These two steps of the damping mechanism are discussed in detail within the framework of the quasiparticle-phonon nuclear model. A large-scale comparison between the measured and calculated average energies, spreading widths and spectroscopic strengths of the high-lying single-particle (hole) states in heavy nuclei is presented. The systematic features of the damping (energy, angular momentum and isotopic dependence) are discussed. Recent advances of the experimental approaches, such as the γ-decay of the high-lying states or the use of heavy-ion transfer reactions at intermediate energies, are outlined.The detailed study of the damping mechanism of high-lying single-particle modes reveals new features and leads us to a new field in nuclear structure: “the spectroscopy of inner and outer subshells”.     

Dispersive effects for the nuclear paramagnetic susceptibility

Dispersive effects coming from pionic degrees of freedom (virtual magnetic pion photoproduction) are shown to reproduce the nucleonic magnetic susceptibility and to yield a parallel quenching in nuclei. The relative importance of low lying nuclear vs.Δ-excitations is discussed and the difference of their role for the magnetic and electric polarizability is pointed out.     

The contribution of reflections to the Lorentz-Lorenz effect

We use the static limit and delta isobar dominance to calculate the contribution to the optical potential of pionic atoms of those terms in which a pion or a rho meson are exchanged any number of times between two nucleons, which constitute the ρ² term of the Lorentz-Lorenz effect. By suppressing the spin and isospin degrees of freedom, we are able to express the Lorentz-Lorenz parameter ξ in analytical form. In the general case when we include fully the spin and isospin variables, we obtain the Lorentz-Lorenz parameter ξ in numerical form. Our results show that ξ can not be larger than one and more likely is close to zero.     

Wavelet analysis and Arnold web picture for detecting energy transfer in a Hamiltonian dynamical system

Our motivation is to understand how, in chemical reactions, the reaction coordinate effectively gains dynamical energy from the other degrees of freedom (i.e., bath coordinates) avoiding thermalization of the redistributed energy. In such a system, the phase space structure should be not homogeneous; i.e., the system is never ergodic. In this study, we introduce a way to capture the inhomogeneity of the phase space and to monitor energy transfers among their partial degrees of freedom in nonergodic systems using wavelet analysis and a picture of the Arnold web. First, we examine several simple energy transfer processes, i.e., a motion on a resonance line, between resonance lines, and around a resonance junction in a simple three-degree-of-freedom (DOF) system and show how the elemental processes of the intramolecular vibrational energy redistribution (IVR) are detected by our tools. We especially note that the structure of the higher order resonance of the system can be detected by wavelet analysis and motion in the action space. Next, we analyze a reaction process in a simple Hamiltonian system of 3 DOF with a double-well potential, i.e., a system with a transition state of the center-saddle-center type, and detect energy transfers in the reactive process. The aim of the study is to propose a way to characterize the inhomogeneity of the phase space, e.g., the reactive doorway, which leads to controllability of the chemical reaction by light, i.e., control of the reaction by selectively preparing an initial state in the reactive doorway by optical excitation.     

Non-linear density dependence of the Δ-self-energy in nuclear matter and its implications in pionic atoms

The $\text{Δ(}\text{3}\text{2}\text{,}\text{3}\text{2}$) self-energy in a nuclear medium is shown to be highly non-linear in density, when proper care is taken of the virtual meson propagation in the medium and retardation effects. As a consequence the p-wave absorptive potential for pionic atoms diverges appreciably from the standard ρ² form. A fit to the existing data on pionic atoms is carried out with the new functional of the density and turns out to be as good as those with the ρ² functional. The successful fits with such different density functionals are due to a very narrow range of nuclear effective densities felt by the pion in the observed pionic atoms. The influence of these effects in related problems is discussed along with the suggestion to widen the range of nuclear densities felt by the pions by looking at other nuclear phenomena.     

Virtual and real pions in nuclei

The role of pionic degrees of freedom in photoreactions on nuclei is investigated. It is shown that the enhancement of the nuclear photoabsorption dipole cross section, given by exchange effects due to virtual pions, is accompanied by a parallel, almost compensating, hindrance with respect to the free case in the photoproduction of real pions above threshold.     

Doorway-state analysis of the fragmentation of the magnetic-dipole strength in SU58 NI observed in high-resolution inelastic electron scattering

The fine structure of the magnetic-dipole strength in ⁵⁸Ni observed in high-resolution inelastic electron scattering at the DALINAC has been analysed under the assumption that the measured distribution of the strong fragmented M1 strength results from a coupling of two doorway states to a large number of more complicated states. From the doorway-state analysis one obtains the coupling matrix elements between doorway states |d〉 and complicated states |q〉. This allows the calculation of the escape width Γ^↑ and the spreading width Γ^↓ of the assumed doorway states. The influence of a coupling between the doorway states via the complicated states (internal mixing) is discussed. An estimate of a mean coupling matrix element between the two doorway states is given.     

Emission properties of fission fragments and their isomeric ratios

The properties of neutron emission from fragments formed in the spontaneous fission of ²⁵²Cf and in the thermal-neutron-induced fission of ²³⁵U are analyzed on the basis of the statistical model of nuclear reactions. Upon extracting the mean excitation energies of fission fragments from experimental data on the mean multiplicities of neutrons, the observables of neutron emission can be described over wide ranges of total kinetic energies and masses. The observed values of mean fragment spins are also reproduced. A method for calculating the isomeric ratios of the independent yields of fission fragments that is based on the cascade-evaporation model of excited-nucleus decay is employed to describe experimental data on ²³⁵U fission induced by thermal neutrons and on ²³⁸U fission induced by alpha particles. The effect exerted on the isomeric ratios for fission fragments by two different assumptions on the spin distributions of primary-fragment populations—the assumption of the distribution associated with rotational degrees of freedom and the assumption of the distribution associated with the internal degrees of freedom of fully accelerated fragments—is investigated.     

Pygmy dipole resonance in nuclei

A brief survey of the state of the modern microscopic theory of the so-called pygmy dipole resonance in nuclei is given—in particular, some unresolved problems are listed. It is emphasized that, in order to explain the pygmy dipole resonance, it is necessary but not sufficient to take into account the coupling of single-particle degrees of freedom to photon degrees of freedom. The results of the calculations performed for the first time for the isovector pygmy dipole resonance and the isovector electric giant dipole resonance in ¹²⁴Sn within a self-consistent approach involving, in addition to the standard quasiparticle random-phase approximation, a single-particle continuum and quasiparticle-phonon coupling of single-particle degrees of freedom to phonon degrees of freedom are presented. The results are found to be in satisfactory agreement with experimental data. The calculation of the isoscalar strength function in the energy region of the pygmy dipole resonance revealed that the nuclear-structure mechanism does not provide the isoscalar-strength suppression observed at energies in excess of 7 MeV in (α, α′γ) reactions; therefore, this suppression may stem from the reaction mechanism.     

Pionic effects in inelastic electron-nucleus scattering

We calculate the structure functions for deep inelastic electron scattering on baryons in a two-dimensional model which incorporates pionic degrees of freedom explicitly. We analyze the behavior of these structure functions in the Bjorken limit and conclude that scaling and Regge behavior are satisfied. A trivial extension as a parton model can be achieved by just introducing the structure functions for the pion. We next generalize our calculation to nuclear matter and study the behavior of such a system under electron scattering. Scaling but not Regge behavior appears in the Bjorken limit. The diverse behavior in these two situations is carefully analyzed. Most of the results obtained in this paper are qualitatively independent of the dimensions of the model and therefore will hold in its four-dimensional generalization.     

Correlated charged pions from chiral dynamics in high-energy nuclear collisions

It is expected that chiral symmetry is approximately restored in the very excited matter produced in a high-energy nuclear collision and that the chiral order parameter will thereafter quickly relax towards its aligned vacuum value. This non-equilibrium evolution of the environment endows the pionic degrees of freedom with a time-dependent effective mass and this agency, in turn, may create correlated soft pions that could provide specific observable signatures of the chiral dynamics that are based solely on charged pions.     

The isoscalar pion-nucleus interaction from pionic atoms

The analysis of pionic atom data of 1s and 2p levels for N = Z spin-zero nuclei, in terms of an improved optical potential is presented. We find a strong (unexplained) s-wave repulsion and evidence for finite-range effects. The need for a relativistic treatment of the pion—nucleus interaction is discussed.     

Binding in velocity dependent potentials and pion-nuclear systems

Properties of bound states in velocity-dependent potentials are discussed and the WKB approximation is established and used to derive quantization conditions for such states. The most updated zero-range optical potential for pionic atoms is reviewed and employed for the calculation of strongly bound π^? nuclear states. Some of the several physical mechanisms, in particular the πN finite interaction range, which affect the whole issue of binding and critically determine the number of bound states expected, are qualitatively discussed. Unless dynamical suppression of π^? nuclear absorption occurs below threshold, the calculated states are too wide to be considered as well-defined physical states.     

Chiral condensate and chemical freeze-out

We consider a chemical freeze-out mechanism which is based on a strong medium dependence of the rates for inelastic flavor-equilibrating collisions based on the delocalization of hadronic wave functions and growing hadronic radii when approaching the chiral restoration. We investigate the role of mesonic (pion) and baryonic (nucleon) fluctuations for melting the chiral condensate in the phase diagram in the (T, μ)-plane. We apply the PNJL model beyond mean-field and present an effective generalization of the chiral perturbation theory result which accounts for the medium dependence of the pion decay constant while preserving the GMOR relation. We demonstrate within a schematic resonance gas model consisting of a variable number of pionic and nucleonic degrees of freedom that within the above model a quantitative explanation of the hadonic freeze-out curve and its phenomenological conditions can be given.     

Nondifferentiable Dynamic: Two Examples

Some nondifferentiable quantities (for example, the metric signature) can be the independent physical degrees of freedom. It is supposed that in quantum gravity these degrees of freedom can fluctuate. Two examples of such quantum fluctuation are considered: a quantum interchange of the sign of two components of the 5D metric and a quantum fluctuation between Euclidean and Lorentzian metrics. The first case leads to a spin-like structure on the throat of a composite wormhole and to a possible inner structure of the string. The second case leads to a quantum birth of the non-singular Euclidean Universe with frozen 5^th dimension. The probability for such quantum fluctuations is connected with an algorithmical complexity of the Einstein equations.     

Pion production in nuclear collisions

The production of pions in nuclear collisions is analyzed in terms of a microscopic reaction model, where the free energy of the entrance channel is transferred to the final channel through the coupling of the relative motion to the internal excitation of N^*-resonances. Such a model allows quite naturally for a consistent analysis of the exclusive and the inclusive production of pions. It turns out that the pionic fusion cross section is determined predominantly by the spectroscopic parentage between the initial target projectile combination and the final nucleus, whereas the inclusive part is dominated by the energy dependence of the phase space factor, i.e. by the number of the degrees of freedom which are relevant in a given kinematical situation. This model is applied to the analysis of available experimental data from threshold to the (1232)-region. A consistent analysis of both the inclusive and the exclusive part of the pion spectrum is presented.Dedicated to Prof. Dr. P. Kienle on the occasion of his 60th birthday     

Tripartite states Bell-nonlocality sudden death in a spin[1mm] environment with multisite interaction

Tis paper demonstrates that multipartite Bell-inequality violations can be fully destroyed in a finite time in three-qubit states coupled to a general XY spin-chain with a three-site interaction environment. The Mermin—Ardehali—Belinksii—Klyshko inequality is used to detect the degree of nonlocality, as measured by the extent of their violations. The effects of system-environment couplings, the size of degrees of freedom of the environment and the strength of the three-site interaction on the Bell-inequality violations are given. The results indicate that the Bell-inequality violations of the tripartite states will be completely destroyed by decoherence under certain conditions for the GHZ state. The decoherence-free subspaces of our model are identified and the entanglement of quantum states is also discussed.     

Pionic contribution to the scalar and longitudinal N-Δ transition quadrupole form factors

The pionic contribution to the scalar and longitudinal p → Δ⁺ transition quadrupole form factors is calculated. It is shown that the πN channel contributes +0.023 − i 0.093 fm² at photon momentum q = 400 MeV (EMR ≈ (+1.4 − i 5.7) %). This might be larger than the “core” quadrupole moment, and one should be careful in comparing experimental data and theoretical predictions. This pionic contribution makes the measurement of the phase of the quadrupole moment more interesting.     

On single-particle fragments in Hg

Single-particle fragments in ²⁰⁵Hg are discussed in terms of coupling single-particle and collective degrees of freedom.