Collective excitations in the unitary correlation operator method and relativistic QRPA studies of exotic nuclei

The collective excitation phenomena in atomic nuclei are studied in two different formulations of the random-phase approximation (RPA): (i) RPA based on correlated realistic nucleon-nucleon interactions constructed within the unitary correlation operator method (UCOM) and (ii) relativistic RPA derived from effective Lagrangians with density-dependent meson-exchange interactions. The former includes the dominant interaction-induced short-range central and tensor correlations by means of unitary transformation. It is shown that UCOM-RPA correlations induced by collective nuclear vibrations recover a part of the residual long-range correlations that are not explicitly included in the UCOM Hartree-Fock ground state. Both RPA models are employed in studies of the isoscalar giant monopole resonance in closed-shell nuclei across the nuclide chart, with an emphasis on the sensitivity of its properties on the constraints for the range of the UCOM correlation functions. Within the relativistic quasiparticle RPA (RQRPA) based on the relativistic Hartree-Bogolyubov model, the occurrence of pronounced low-lying dipole excitations is predicted in nuclei towards the proton drip line. From the analysis of the transition densities and the structure of the RQRPA amplitudes, it is shown that these states correspond to the proton pygmy dipole resonance. The text was submitted by the authors in English.     

Mass Predictions from Mean-Field Calculations

Several methods based on effective interactions or Lagrangians are available today. Although different in many respects (use of zero range or finite range interactions, relativistic or non relativistic framework, different treatments of pairing correlations), their applications to nuclei far from stability have shown converging results which still have to be incorporated in macroscopic approaches. Many efforts are also actually devoted to the improvements of the effective interactions, especially of the pairing force. Finally, developments are performed to include in a microscopic framework correlations beyond a mean-field (in particular, the correlations generated by rotation and vibration in the deformed nuclear potential). I shall review some key aspects of these developments and show how they affect the determination of nuclear masses in particular at the limits of stability. This revised version was published online in July 2006 with corrections to the Cover Date.     

General survey of polarization observables in deuteron electrodisintegration

Polarization observables in inclusive and exclusive electrodisintegration of the deuteron using a polarized beam and an oriented target are systematically surveyed using the standard nonrelativistic framework of nuclear theory but with leading-order relativistic contributions included. The structure functions and the asymmetries corresponding to the various nucleon polarization components are studied in a variety of kinematic regions with respect to their sensitivity to realistic NN-potential models, to subnuclear degrees of freedom in terms of meson exchange currents, isobar configurations and to relativistic effects in different kinematical regions, serving as a benchmark for a test of present standard nuclear theory with effective degrees of freedom.     

Some contributions from SSNTD towards nuclear science: from multifragmentation towards accelerator driven systems (ADS)

Three examples are chosen to show the importance of SSNTD as one of the essential tools in nuclear science:

(1) Multifragmentation into more than two heavy reaction products: Starting with the observation of three heavy reaction products in the interaction of relativistic protons or 414 MeV ⁴⁰Ar with actinides in the early 1960s, up to the observation of five heavy reaction products in the interaction of 2400 MeV ²³⁸U with uranium, SSNTD had a leading role in this research.

(2) In the search for superheavy elements (SHE: Z around 114): Many different techniques are used. However, SSNTD are exclusively decisive in the possible observation of SHE within the heavy element component of galactic cosmic rays.

(3) Accelerator driven systems: They are increasingly important in the discussion of energy producing nuclear power stations and in the corresponding ability to transmute long-lived poisonous radioactive materials (above all plutonium) into shorter lived fission fragments or stable nuclides. SSNTDs play an important role in the determination of the energy dependent neutron fluence in small volumes (≈cm³) or in the exact beam profile determinations of the primary proton beams.

This contribution ends with an outlook into possible future fields of physics research: With the advent of a new generation of relativistic heavy ion accelerators, such as the NUCLOTRON at the JINR in Dubna, Russia, and RHIC in Brookhaven in the United States, one can continue to study (and finally confirm or disprove) all phenomena mentioned already, as well as additional controversial phenomena, such as “enhanced nuclear cross-sections over short distances”, called colloquially “anomalons”. Again SSNDT can be used in at least a twofold manner as an important tool: (a) the enhanced neutron production with ¹²C ions or heavier ions in thick targets at energies above approximately 50 GeV and (b) the reduced “mean-free-path” of secondary fragments produced by the same heavy and energetic ions.     

Wave Node Dynamics and Revival Symmetry in Quantum Rotors

Symmetries and dynamics of wave nodes in space and time expose principles of quantum theory and its relativistic underpinning. Among these are key principles behind recently discovered dephasing and rephasing phenomena known as revivals. A reexamination of basic Eberly revivals, Berry “quantum fractal” landscapes, and the “quantum carpets” of Schleich and co-workers reveals a simple Farey arithmetic and C_n-group revival structure in one of the earliest quantum wave models, the Bohr rotor. These principles may be useful for interpreting modern time-dependent rovibrational spectra. The nodal dynamics of the Bohr rotor is seen to have a quasi-fractal structure similar to that of earlier systems involving chaotic circle maps. The fractal structure is an overlay of discrete versions of Bohr's rotor model. Each N-point Bohr rotor acts like a base-N quantum “odometer” which performs rational fraction arithmetic. Such systems may have applications for optical information technology and quantum computing.     

Cutting DNA: Mechanics of the topoisomerase

The framework of relativistic self-consistent mean-field models is extended to include correlations related to restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angular-momentum and particle-number projected relativistic wave functions. The model, currently restricted to axially symmetric shapes, employs a relativistic point-coupling (contact) nucleon-nucleon effective interaction in the particle-hole channel, and a δ-interaction in the pairing channel. Both bulk and spectroscopic nuclear properties are explored.     

Participant intimacy : A cluster analysis of the intranuclear cascadet

The intranuclear cascade for relativistic nuclear collisions is analyzed in terms of “clusters” consisting of groups of nucleons which are dynamically linked to each other by violent interactions. The formation cross sections for the different cluster types as well as their intrinsic dynamics are studied and compared with the predictions of the linear cascade model (“rows-on-rows”).     

Damage growth in random fuse networks

The correlations among elements that break in random fuse network fracture are studied, with disorder strong enough to allow for volume damage before final failure. The growth of microfractures is found to be uncorrelated above a lengthscale, that increases as the final breakdown approaches. Since the fuse network strength decreases with sample size, asymptotically the process resembles more and more mean-field-like (“democratic fiber bundle”) fracture. This is found from the microscopic dynamics of avalanches or microfractures, from a study of damage localization via entropy, and from the final damage profile. In particular, the last one is statistically constant, except exactly at the final crack zone, in spite of the fact that the fracture surfaces are self-affine. This also implies that the correlations in damage are not extensive.     

Relativistic Consistent Angular-Momentum Projected Shell-Model:Relativistic Mean Field

We develop a relativistic nuclear structure model, relativistic consistent angular-momentum projected shell-model (RECAPS), which combines the relativistic mean-field theory with the angular-momentum projection method. In this new model, nuclear ground-state properties are first calculated consistently using relativistic mean-field (RMF) theory. Then angular momentum projection method is used to project out states with good angular momentum from a few important configurations. By diagonalizing the hamiltonian, the energy levels and wave functions are obtained. This model is a new attempt for the understanding of nuclear structure of normal nuclei and for the prediction of nuclear properties of nuclei far from stability. In this paper, we will describe the treatment of the relativistic mean field. A computer code, RECAPS-RMF, is developed. It solves the relativistic mean field with axial-symmetric deformation in the spherical harmonic oscillator basis. Comparisons between our calculations and existing relativistic mean-field calculations are made to test the model. These include the ground-state properties of spherical nuclei ¹⁶O and ²⁰⁸Pb, the deformed nucleus ²⁰Ne. Good agreement is obtained.     

Multiparticle correlations in resonance-matter formation

The effect of multiparticle correlations on resonance and pion populations, in relativistic nuclear reactions, is calculated in the context of an intranuclear cascade model which includes N-body (N > 2) collisional processes. The resonance-matter population present in the highly-compressed phase of nucleus-nucleus collisions is investigated, in reactions between different intermediate-mass nuclear systems. Received: 29 December 1998 / Revised version: 20 December 1999     

Radial wave functions of a discrete spectrum

The system of equations for radial wave functions is written in a form allowing both relativistic and non relativistic wave functions to be obtained. In the case of a discrete spectrum, an asymptotic solution of this system is obtained for a potential which includes not only a Coulomb term but also terms corresponding to dipole and quadrupole polarization. The normalizing factor of the asymptote is determined in the approximation of the relativistic quantum-defect method, which offers the possibility, in principle, of using the functions in semiempirical calculations analogous to nonrelativistic calculations by the Bates — Damgaard — Seaton method. The calculation scheme is illustrated for the example of the calculation of Si IV wave functions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 39–44, December, 1978.     

Scaling laws in high-energy electron-nuclear scattering

The approximate scaling behavior suggested by recent measurements of electron scattering form factors and inelastic structure functions of few-body nuclei (mass 2, 3, 4) is discussed in a relativistic impulse approximation model. The model is a straightforward extension incorporating spin of a nucleon parton model introduced in recent works. We present results for electric and magnetic form factors as well as inelastic structure functions near threshold. The important corrections to scaling which are present in the preasymptotic regions are found to be well accounted for by the type of binding effects included in the phenomenologically constructed infinite-momentum frame nuclear wave functions. While predicted form factors are very sensitive to the parameters in the wave functions it does not appear possible to associate unambiguous dynamical meaning to these parameters. We find that spin effects bring significant and useful corrections.     

Nuclear effects in the F3 structure function for finite and asymptotic Q

We study nuclear effects in the structure function F₃ which describes the parity violating part of the charged-current neuitrino nucleon deep inelastic scattering. Starting from a covariant approach we derive a factorized expression for the nuclear structure function in terms of the nuclear spectral function and off-shell nucleon structure functions valid for arbitrary momentum transfer Q and in the limit of weak nuclear binding, i.e. when a nucleus can be treated as a non-relativistic system. We develop a systematic expansion of nuclear structure functions in terms of a Q⁻² series caused by nuclear effects (“nuclear twist” series). Basing ourselves on this expansion we calculate nuclear corrections to the Gross-Llewellyn-Smith sum rule as well as to higher moments of F₃. We show that corrections to the GLS sum rule due to nuclear effects cancel out in the Bjorken limit and calculate the corresponding Q⁻² correction. Special attention is paid to the discussion of the off-shell effects in the structure functions. A sizable impact of these effects both on the Q² and x dependence of nuclear structure functions is found.     

Relativistic many-body theory with radioactive ion beams: Surface pion condensation

We critically review the present relativistic mean-field theory from the viewpoint of missing pions. We introduce the interesting experimental data on pionic states taken at RCNP. These data seem to suggest the occurrence of pion condensation in the nuclear surface. Qualitative discussion is made on the consequence of surface pion condensation on Gamow-Teller transitions and spin response functions and others. The radioactive ion beams are the tools of studying the unstable nuclei, which have extended nuclear surfaces. We shall start with radioactive ion beams the nuclear surface science, which includes the surface pion condensation as the important ingredient in addition to spin-orbit splitting and surface pairing. Received: 1 May 2001 / Accepted: 4 December 2001     

High-energy phenomena,short-range nuclear structure and QCD

A systematic review and theoretical analysis of the experimental data on multi GeV lepton, photon, hadron, deuteron (nucleus) reactions from nuclei forbidden in the case of scattering from free nucleons is presented. It is shown that all these data can be quantitatively described as a manifestation of short-range few nucleon correlations. Calculations for elastic and (deep)inelastic electromagnetic and weak form factors of the deuteron and other nuclei, are given. The inclusive production of leading particles in the nucleus fragmentation region in high-energy lepton, hadron or nucleus-induced collisions is analyzed. The straightforward correspondence between the Weinberg equation for the light-cone wave functions of the deuteron and the non-relativistic Schrödinger equation is found. It is shown that the predictions of quantum chromodynamics for short-distance phenomena in nuclei are in agreement both with experimental data and theoretical expectations due to short range correlations in nuclei. Several feasible experiments are considered which could establish the existence of relativistic nuclear physics.     

Schlieren “PIV” for turbulent flows

The possibility of using commercial PIV equipment combined with schlieren optics to measure the velocity fields of turbulent flows is explored. Given a sufficiently high Reynolds number and adequate refractive flow differences, turbulent eddies can serve as the PIV “particles” in a schlieren image or shadowgram. The PIV software analyzes motion between consecutive schlieren or shadowgraph frames to obtain velocity fields. Velocimetry examples of an axisymmetric sonic helium jet in air and a 2D turbulent boundary layer at Mach 3 are shown. Due to optical path integration, axisymmetric flows require the inverse Abel transform to extract center-plane velocity data. Conditions for optimum schlieren sensitivity are examined. In its present embodiment, “schlieren PIV” is not useful for laminar flows nor for fully 3D flows. Otherwise it functions much like standard PIV under conditions where individual particles are not resolved and velocimetry is instead based on correlation of the motion of turbulent structures. “Schlieren PIV” shows significant promise for general refractive turbulent flow velocimetry if its integrative nature can be overcome through sharp-focusing optics.     

EMC and polarized EMC effects in nuclei

We determine nuclear structure functions and quark distributions for ⁷Li, ¹¹B, ¹⁵N and ²⁷Al. For the nucleon bound state we solve the covariant quark–diquark equations in a confining Nambu–Jona-Lasinio model, which yields excellent results for the free nucleon structure functions. The nucleus is described using a relativistic shell model, including mean scalar and vector fields that couple to the quarks in the nucleon. The nuclear structure functions are then obtained as a convolution of the structure function of the bound nucleon with the light-cone nucleon distributions. We find that we are readily able to reproduce the EMC effect in finite nuclei and confirm earlier nuclear matter studies that found a large polarized EMC effect.