Effect of shell structure on energy dissipation in heavy-ion collisions

The effect of shell structure on the distribution of the excitation energy between fragments of the deep inelastic collisions is analysed in the microscopic approach. It is shown that the density of the single-particle levels of the proton and neutron subsystems near the Fermi surface determines the ratio between the excitation energies of fragments at the initial stage of the collision. It is shown also that the shell structure strongly influences the correlations between the width of the charge distributions and the total kinetic energy losses. Calculations are performed for the ^40,48Ca+²⁴⁸Cm reactions. The results obtained suggest a possible interpretation for the observed concentration of the excitation energy in the light fragment in deep inelastic collisions for a wide range of the total kinetic energy losses. Received: 27 July 1999 / Accepted: 29 March 2000     

Collective bands in even mass Sn isotopes

Positive parity bands in ^{112, 114, 116, 118}Sn have been excited up to levels with spin and parity J^π = 12⁺ using Cd(α, 2nγ)Sn reactions. The experiments consisted of γ-ray excitation function, γ-γ coincidence, lifetime, γ-ray angular distribution, γ-ray linear polarization and conversion electron measurements. The observed bands show strong resemblances with ground-state bands of transitional nuclei in this mass region. It is pointed out that the J^π = 0⁺ band-heads originate from 2p-2h excitations in the Z = 50 proton shell. The excitation energies of the band-heads are calculated by means of the macroscopic-microscopic renormalization method. Pair correlations between the 2h and 2p configurations are included separately in a phenomenological way by taking into account the pairing energies of the Cd and Te ground states with respect to the Sn ground state.     

Quenching of the electron scattering form factor of the 1+ state at 3.48 MeV in88Sr and the influence of theΔ(1232)-isobar

The form factor for excitation of the 1⁺ state at 3.48 MeV in⁸⁸Sr by inelastic electron scattering has been measured for momentum transfersq=0.24–0.62 fm^?1. Neither its magnitude nor shape can be described employing the best available nuclear wave functions. We demonstrate with a schematic model that the observed reduction of the form factor may be understood by taking into account a renormalization of theM1-operator due to virtualΔ-hole excitations.     

A possibility of asymptotic freedom without non-Abelian gauge theories

We discuss solutions of the renormalization group equations for a Yukawa field theory. For an increasing effective boson mass we find that the leading terms in the vertex functions in the high-energy region are given by diagrams which contain no internal boson lines. In e⁺e^? annihilation into hadrons we get the parton model formula R(s) = Σ_iQ_i², whereas in the deep inelastic e^?p scattering the simple parton model behaviour is modified by the (in general) non-canonical dimension of the quark field.     

K-vacancy formation in deep inelastic nuclear reactions

We investigate the dependence of inner shell vacancy production on interaction time T in deep inelastic nuclear reactions. Coupled channel calculations for Xe-Pb, Pb-Pb, and U-U collisions are presented. In the heaviest system strong interference minima for both 1sσ and 2p^1/2σ excitation are predicted at T?3.10^?21 sec.     

Giant resonance excitation by 156 MeV6Li scattering

The excitation of the giant quadrupole resonance in ²⁰⁸Pb has been observed by inelastic scattering of 156 MeV ⁶Li ions. The continuum background in the giant resonance region of the measured ⁶Li spectra proves to be strongly reduced as compared to the spectra obtained by inelastic scattering of lighter projectiles, which makes ⁶Li scattering a promising tool for more detailed studies.     

A test of iso-scalar quadrupole renormalization in the 32− → 12−(Ex = 0.478 MeV) transition in 7Li

Electromagnetic studies have established that the $\text{3}\text{2}{}^{\mathrm{?}}\text{,}\text{1}\text{2}{}^{\mathrm{?}}$ ground state doublet in ⁷Li is well described by the LS coupling shell model, provided quadrupole effective charge is introduced. The results of microscopic calculations for the excitation of the $\text{1}\text{2}{}^{\mathrm{?}}$ level in inelastic proton scattering shown within indicate that an equivalent renormalization of the ⁷Li quadrupole neutron transition densities is also necessary. This verifies the assumption which was made in a previous calculation of the cross section for the excitation of the $\text{3}\text{2}{}^{\mathrm{?}}$ level in the ⁷Li+²⁴Mg reaction.     

Neutron total and scattering cross sections of some even Mo isotopes and the optical model

Neutron total cross sections of ⁹²Mo, ⁹⁶Mo, ⁹⁸Mo and ¹⁰⁰Mo were measured at intervals of ? 10 keV from 1.6 to 5.5 MeV with resolutions of ≈ 10 keV. Neutron elastic and inelastic scattering cross sections of these isotopes were measured from 1.8 to 4.0 MeV at intervals of 0.2 MeV. Neutron groups corresponding to the excitation of forty states were identified. The experimental results were examined in the context of optical and statistical nuclear models. It was concluded that the real part of the optical potential includes a term proportional to [(N-Z)/A] and suggested that the imaginary part of the potential was shell dependent with decreasing magnitude as N = 50 is approached. Comparison of measured and calculated inelastic neutron excitation cross sections suggested a number of J^π assignments extending previous knowledge.     

Modified action glueballs

The mass of the 0⁺ glueball in 4-dimensional lattice gauge theory with a mixed SU(2)-SO(3) action is obtained via Monte Carlo. We work in a region far from the critical end point in the phase diagram, with an action partly motivated by renormalization group flows in the Migdal-Kadanoff approximation. A large-N resummation of perturbation theory is used to show that the mass gap scales as predicted by the perturbative renormalization group. Independent of this, our results show that the ratio of the glueball mass to the square root of the string tension, obtained from a previous Monte Carlo, is a renormalization group invariant.     

The shell structure and the asymmetry of nuclear fission for 140Pu in a statistical model

The dependence on excitation energy of the mass distribution of the fragments arising from the fission of ²⁴⁰Pu is studied in a statistical model. The level densities needed are calculated on the basis of the single-particle energies obtained from a deformed Woods-Saxon potential. First we investigate when and how the shell effects disappear in ²⁴⁰Pu with increasing excitation energy. Using the transition state method we then calculate some characteristic properties of the fragment mass distributions and compare the results with the experimental observations. Reasonable agreement is obtained.     

The renormalization group of the model ofA 4-coupling in the abstract approach of quantum field theory

For the model ofA ⁴-interaction the postulates of the renormalization group are stated within the abstract approach of quantum field theory. In the massive case these postulates follow if an on-shell formulation of the model is assumed to exist. For the massless model the postulates of the renormalization group imply that the propagator has a pole at momentum zero. Consequently there is no dynamic mass generation and the propagator is normalizable on the mass shell. It is shown that theS-matrix elements scale with canonical dimensions. A general method of rescaling parameter values is developed which takes into account the possibility of propagator zeros and stationary points of the effective coupling.     

Giant M2 and transversal E1 resonances in light nuclei

The cross section for inelastic backward electron scattering on 1p shell nuclei at incident energy E_e = 70 MeV is calculated in the shell model. Comparison is made with radiative pion capture and muon capture. It is shown that the T_> branch of the M2 resonance in (e, e') and the main maxima in the (π^?, γ) response function are formed by identical partial transitions. We consider the basic features of the M2 resonance excitation in 1p shell nuclei and predict configurational and isospin splitting of this mode.     

Infrared and mass regularization in AF field theories (I). φ63

In the framework of asymptotically free (AF) field theories we determine the correction terms in the renormalization group (RG) approach to deep inelastic (DI) scattering and to the Drell-Yan (DY) process. This leads us to an order g² analysis of the DI/DY parton cross sections. Some of their contributions reveal ultraviolet (UV), infrared (IR) and mass (M) divergences which, after regularization, are removed by renormalization, IR and (partially) M cancellation. The initial-state M divergences, persisting in both processes, are removed by M factorization. Consistent IR and M regularization is constrained by the double-cut rule: its meaning and implications are explained. The calculations are performed in φ₆³ theory which is AF, IR finite and technically simple. We use “on-shell”, “off-shell” and “massless” (n-dimensional) mass assignments and demonstrate explicitly the regularization independence of the correction term.     

Spin dynamics of the intermediate-valence compound EuCu<Subscript>2</Subscript>Si<Subscript>2</Subscript>

The dynamic magnetic response of the intermediate-valence compound EuCu₂Si₂ has been studied using inelastic neutron scattering. At low temperatures, strong renormalization of the ⁷ F ₀ → ⁷ F ₁ spin-orbit transition energy is detected; it is likely to be related to partial delocalization of the f electrons of Eu. An increase in the temperature increases the valence instability of europium and results in further changes in the magnetic excitation spectrum parameters and the appearance of an intense quasi-elastic component.     

Heavy-ion inelastic scattering from deformed nuclei

Theoretical and experimental methods for studying heavy-ion inelastic scattering from deformed nuclei are described. The theoretical methods involve classical-limit approximations, while particle- γ-spectroseopy techniques are employed experimentally. With these approaches, heavy-ion excitation in the Coulomb-nuclear interference region acquires a transparent interpretation, despite the apparent complexity of the multistep excitation processes involved. The examples discussed provide a good illustration of the relationship between classical and quantum physics. The sensitivity of the inelastic scattering to details of the surface ion-ion potential due to radial and angular localization is exploited to provide a method of determining the equipotential contours in a direct manner which bypasses particular model-dependent parametrizations. The method is used to construct ion-ion potentials from inelastic scattering data for the systems ⁴⁰Ar + ¹⁶⁰Gd, ¹⁵⁶Gd, ¹⁶²Dy, ¹⁶⁴Dy, and¹⁸⁰Hf. The contribution of adiabatic giant resonance polarization to this potential is discussed. The relation between the deformed ion-ion potential and nuclear shapes is illustrated by comparing the experimental potentials to deformed double-folding and deformed proximity-potential calculations.     

A study of coupled-reaction channel effects in the36S +37Cl system,hybridization between single particle orbits

Elastic and inelastic scattering as well as transfer transitions involving a valence proton in thesd- andfp- shell orbits are studied in the interaction of³⁷Cl +³⁶S at E_CM=50 MeV. Experimental angular distributions of single particle states of³⁷Cl (elastic and inelastic transfer) are presented with a CRC analysis. In the CRC calculations the effects of inelastic and transfer couplings are studied using known spectroscopic information. In the CRC analysis six single particle bound states and the collective 2⁺ excitation of³⁶S are included in the coupling scheme. Higher order coupling effects are found to be important. A distinct effect, the mixing of single particle states (of different parity) due to direct and transfer interactions is observed to produce an enhancement of the transfer cross section to the low lying states. This feature is due to a change of the asymptotically defined single nucleon orbits via polarization in the field of the other nucleus, an effect which is analogous to hybridization, known from atomic physics.     

Fission of238U induced by136Xe for energies close to the Coulomb barrier

Excitation functions and angular distributions have been measured for fission of²³⁸U induced by¹³⁶Xe ions with bombarding energies between 4.5 and 5.9 MeV/N. Structures expected theoretically as characteristic for Coulomb fission have not been observed. The Q-value of ?(7.5±1.0) MeV measured for bombarding energies below 4.7MeV/N, however, appears to be compatible with inelastic scattering (e.g. Coulomb excitation) rather than subcoulomb transfer followed by fission. The total kinetic energy of deep inelastic events at 5.9 MeV/N is consistent with the current knowledge about mass diffusion, but also (for the highest excitation energies) with a fast fission process in the presence of the projectile.     

Resonance inelastic scattering of an x-ray photon by a Ne-like atomic ion

The absolute values and the shape of the double differential cross sections of the resonance inelastic scattering of a linearly polarized x-ray photon in the energy region of the ionization threshold of the deep 1s shell of the Ne atom and the Si⁴⁺ and Ar⁸⁺ neon-like ions are calculated in the nonrelativistic approximation for the wave functions of one-electron states and in the dipole approximation for the scattering probability amplitude. The multiparticle effects of radial relaxation of electronic shells in the field of a deep vacancy and of stabilization of the deep vacancy as a neutral atom transforms to a multiply charged positive ion, as well as the effect of the spin-orbit splitting of the 2p valence shell, are taken into account. The calculation results are predictive in character.     

Electron scattering in the interacting boson model

It is suggested that the interacting boson model be used in the analysis of electron scattering data. Qualitative features of the expected behavior of the inelastic excitation of some 2⁺ states in the transitional SmNd region are discussed.