Momentum distributions in fragmentation reactions with relativistic heavy ions

The momentum distribution (or angular distribution) in inelastic heavy ion reactions is calculated by using a two-step model (abrasion and ablation). First, all nucleons in the volume element where projectile and target overlap spatially during the collision are sheared away. The remaining prefragment (the projectile minus the sheared off nucleons) has a recoil momentum proportional to the Fermi momentum. The prefragment is left in an excited state and emits nucleons, the recoil momentum given to the final fragment is proportional to the nuclear temperature. This two-step model reproduces the overall trend and the isotopic dependence for the widths of the experimental momentum distributions. Contrary to previous theoretical studies we find that surface and friction phenomena lead to an anisotropy: The momentum distributions in transverse direction are always broader than in the longitudinal direction by about 5 to 10%.     

Origin of projectile-like fragments from40Ar +68Zn collisions between 15 and 35 MeV/nucleon: Direct transfer of nucleons and projectile fragmentation

The projectile-like fragments emitted in the⁴⁰Ar +⁶⁸Zn reaction performed at 14.6, 19.6, 27.6 and 35 MeV/nucleon are studied. Their energy spectra and angular distributions have been measured. Velocities, widths of the linear momentum distributions and cross sections have been deduced. The results are discussedi) in terms of transfer of a few nucleons and analysed with a diffractional model. They are consistent, for stripping reactions, with a direct transfer of nucleons and a target excitation yielding multiparticlemultihole configurations,ii) In terms of projectile fragmentation-like process with a modified abrasion model taking into account the energy separation of the participant nucleons. The projectile fragmentation-like process appears above 20 MeV/nucleon and strongly competes with transfer of nucleons at 35 MeV/nucleon. The evolution of the mechanisms with incident energy is discussed on the basis of the reduced widths of the linear momentum distributions and on those of velocities and cross sections.     

Recoil effects in peripheral nucleus-nucleus collisions at E/A=84 MeV

Azimuthal angular correlations between projectile fragments and light particles have been measured in ¹⁸O induced reactions on ^58.64Ni and ¹⁹⁷Au targets at E/A=84 MeV. Neither sequential projectile decay nor evaporation from an equilibrated target-like recoil can explain the observed correlations. The data are well described in terms of a sideways-moving source suggesting emission of midrapidity light particles from a subset of nucleons which carries a major part of the transverse recoil momentum imparted by the projectile fragment.     

Target fragmentation in hadron-nucleus collisions at high energy

We discuss target fragmentations in hadron-nucleus collisions at high energy (5–400 GeV). A model is developed which is based on the two-step (fast and slow) processes. A high-energy hadron drills a linear hole inside the nucleus, kicking out several nucleons (fast process). Along the linear hole, the target breaks up into a few pieces. One of the fragments forms an observed nucleus, absorbing some of the recoil nucleons (slow process). During the breakup, the Coulomb interaction between the fragment and the rest is taken into account. This leads to the consideration of a three-body breakup process which influences significantly the low-energy part of the energy distribution in the h+A → B+X reaction. The model is applied to the angular and the energy distributions in this collision. It achieves a nice agreement with experiment.     

Momentum distributions of projectile fragments produced in the cold and hot fragmentation of relativistic136Xe and197Au projectiles

The longitudinal-momentum distributions of projectile fragments from 0.8 A GeV¹³⁶Xe and 1 A GeV¹⁹⁷Au projectiles impinging on targets of beryllium and aluminium, respectively, have been measured using the projectile-fragment separator FRS at GSI. Different momentum distributions have been found for two different classes of fragmentation processes: the abundant hot fragmentation with several nucleons evaporated from the prefragments, and the rare cold fragmentation with only protons removed from the projectile, but no nucleons evaporated. The data are compared to model calculations.This article comprises part of the Ph.D. thesis of B. Voss     

THE STUDY OF MOMENTUM DISTRIBUTION OF HIGH ENERGY HEAVY ION INCLUSIVE REACTIONS

In this paper, we consider nucleus-nucleus collisions on the basis of nucleon-nucleon elastic scattering and give a formula for the projectile fragment momentumdistribution of high energy heavy ion inclusive reactions using Glauber's approxima-tion. According to the experimental momentum distribution, we obtain a relativemomentum distribution between the various prefragments of the projectile. The theo-retical results show that if the bond of the prefragment is tighter, the relative mo-mentum distribution of the preframents in the nucleus is more narrow, so that the re-lative distance between them is larger.     

Abrupt rise of the longitudinal recoil ion momentum distribution for ionizing collisions

We report on the experimental observation of an abrupt rise in the longitudinal momentum distribution of recoil ions created in proton helium collision. The details of this structure can be related to electrons traveling with the velocity of the projectile [electron capture to the continuum (ECC)]. The longitudinal as well as the transverse distribution of the recoil ions can be explained as a continuation of the momentum distribution from ions resulting from electron capture illustrating the smooth transition from the capture to bound states of the projectile to the ECC.     

Spin alignment in the particle-rotor and cranking models

It is shown that the cranking model normally gives a smaller rotation-aligned spin for an odd quasiparticle than the particle-rotor model, especially at low rotational frequencies. The basic reason is found to be that the rotational frequency vector of the cranking model is “sharp”. This is an unphysical model property, and in the presence of a particle whose rotational motion is partly decoupled from the rotational motion of the average field its consequences become serious. A “sharp” rotational frequency corresponds to a neglect of the recoil effect that establishes coherence between the motion of the decoupled nucleon and the other nucleons and therefore is a prerequisite for the conservation of angular momentum. In conclusion the cranking model cannot be invoked to explain the so-called “Coriolis attenuation”, relative to the particle-rotor model, that is observed experimentally. Particle-rotor calculations are carried out into the backbending region of some well-deformed rare-earth nuclei, and the results indicate that the “Coriolis attenuation” effect is weak or absent at high rotational frequencies. However, the experimental $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$, unfavoured band of ¹⁶⁷Yb is found to exhibit an anomalous “downbending” behaviour.     

Angular momentum population in fragmentation reactions

Using a relativistic transport model followed by a statistical sequential binary emission model, the population of metastable high-spin isomeric states are studied in relativistic projectile fragmentation reactions. The initial angular momentum distribution are generated from hole excitations. We find that the angular momentum distribution of the excited prefragments are considerably broadened due to light particle evaporation. The model reproduces the experimentally measured population of relatively low-lying states and underpredicts states with high angular momentum I?17?$I?17?$. We propose that coupling the spin of the excited and hole states in the prefragment will give a better understanding of the data.     

Simple estimates for Fermi jets

The phenomenon of Fermi jets is investigated in the approximation of two colliding potential wells filled with degenerate Fermi gases of nucleons. A model is formulated which largely bypasses the explicit treatment of the relative motion of the nuclei, assumed to be governed by the window friction mechanism. Formulae for the velocity distributions and differential cross sections for neutrons and protons jetting through either target or projectile are derived. The numerical results are investigated systematically over a wide range of nuclear reactions. It is shown that the net linear momentum carried away by Fermi jets accounts for only a rather minor fraction of the observed missing momentum in typical heavy-ion fusion reactions.     

Projectile fragment emission in the fragmentation of ~(56)Fe on C,Al and CH_2 targets at 471 A MeV

The emission angle and the transverse momentum distributions of projectile fragments produced in the fragmentation of ⁵⁶Fe on CH₂, C and Al targets at 471 A MeV are measured. It is found that for the same target, the average value and width of the angular distribution decrease with an increase of the projectile fragment charge; for the same projectile fragment, the average value of the distribution increases and the width of the distribution decreases with increasing the target charge number. The transverse momentum distribution of a projectile fragment can be explained by a single Gaussian distribution and the averaged transverse momentum per nucleon decreases with the increase of the charge of projectile fragment. The cumulated squared transverse momentum distribution of a projectile fragment can be explained well by a single Rayleigh distribution. The temperature parameter of the emission source of the projectile fragment, calculated from the cumulated squared transverse momentum distribution, decreases with the increase of the size of the projectile fragment.     

A model for pion absorption in nuclei

To describe pion absorption in nuclei, we introduce a model which assumes that incident pion is absorbed by the row of target nucleons along the beam direction. The momentum distribution of these nucleons after absorbing the pion is assumed to be determined by the phase space. The experimental data on the inclusive proton cross section are well reproduced.     

Semiphenomenological Model Approach to Continuous Spectrum States. I

The Semiphenomenological Model of the Nucleus (SPM) is applied to describing the mechanisms of the inelastic and elastic scattering of nucleons by nuclei. Perturbation theory for the SPM “residual” interaction (including the first and second order) is used as calculational method. Cross sections, angular distributions, widths of resonant states and the imaginary part of optical potential are considered in a unified manner (one-step and two-step transitions being taken into account). Numerical estimates are given for the target nucleus ⁴¹Ca, quasiparticle states being taken as intermediate ones.     

Phenomenological analysis of fission induced by high-energy protons

High-energy proton induced fission is studied in the framework of a two-step model. In the first step, the projectile penetrates the target nucleus, knocks out few nucleons and leaves the residual nucleus with a spectrum of excitation energies depending upon the number of projectile-nucleon collisions. This stage is described in terms of a simplified version of Glauber's multiple-scattering theory. The second stage in which the residual nucleus fissions, is treated by assuming phenomenological expressions for the dependence of the fission probability on excitation energy which take into account the onset of fragmentation at a certain “crack” energy. Comparison with experimental data suggests that high energy fission of heavy nuclei proceeds in a way similar to low-energy fission. Light nuclei, however, require a more violent fission mechanism.     

Recoil corrections for single-nucleon transfer reactions

A formalism is developed for approximately treating the recoil of the projectile in single-nucleon transfer reactions. The “no-recoil” term is evaluated exactly by rotating the nuclear matrix element to a coordinate system where the lighter projectile lies along the z-axis relative to the target nucleus. Recoil terms are constructed by expanding the “recoil phase factor” in terms of spherical harmonic and Bessel functions, and they are again evaluated exactly. Numerical results are then obtained for some representative light-ion reactions of high incident energies. For these reactions, we find that although the first-order recoil term may be very large, higher order terms are correspondingly less important, and convergence is always easily obtained. However, absolute magnitudes of cross sections at forward angles predicted by the present theory and by the local energy approximation differ by up to 50% for the reactions we consider.     

Average Energy Loss Measured in Single and Double Electron Capture Collisions of He^2＋ on Ar at Low Velocities ＊

Employing the recoil ion momentum spectroscopy we investigate the collision between He^2＋ and argon atoms. By measuring the recoil longitudinal momentum the energy losses of projectile are deduced for capture reaction channels. It is found that in most cases for single- and double-electron capture, the inner electron in the target atom is removed, the recoil ion is in singly or multiply excited states （hollow ion is formed）, which indicates that electron correlation plays an important role in the process. The captured electrons prefer the ground states of the projectile. It is experimentally demonstrated that the average energy losses are directly related to charge transfer and electronic configuration     

MULTIPLICITY DISTRIBUTIONS OF PRODUCED PARTICLES IN α-α COLLISIONS AT HIGH ENERGIES

We analyse the multiplicity distributions of negative particles produced in α-α collisions at S_NN=31.2GeV by using a Glauber-type multiple collision model in which the projectile nucleons degrade in energy as they make collisions with target nucleons.The energy loss suffered by the projectile nucleons in the passage through the target nucleus is explicitly considered in the calculation.The agreement with experiments is good.     

Nuclear shadowing effect in relativistic heavy-ion collisions

Two complementary approaches are used in studying the nuclear shadowing effect in heavy-ion collisions at SIS/GSI beam energies within a hadronic transport model. By analysing simultaneously the average transverse momentum of nucleons and pions in the reaction plane as a function of rapidity, the shadowing effect is revealed as an anticorrelation of the average transverse momentum distributions of nucleons and pions in semicentral and peripheral collisions. While by studying the azimuthal angle distribution of pions with respect to the reaction plane, the shadowing effect appears as an azimuthal anisotropy with a preferential emission of pions perpendicular to the reaction plane. The dependence of the nuclear shadowing effect on the impact parameter and the beam energy is also studied.     

Capture into rydberg states and momentum distributions of ionized electrons

The yield of neutral excited atoms and low-energy photoelectrons generated by the electron dynamics in the combined Coulomb and laser field after tunneling is investigated. We present results of Monte-Carlo simulations built on the two-step semiclassical model, as well as analytic estimates and scaling relations for the population trapping into the Rydberg states. It is shown that mainly those electrons are captured into bound states of the neutral atom that due to their initial conditions (i) have moderate drift momentum imparted by the laser field and (ii) avoid strong interaction (“hard” collision) with the ion. In addition, it is demonstrated that the channel of capture, when accounted for in semiclassical calculations, has a pronounced effect on the momentum distribution of electrons with small positive energy. For the parameters that we investigated its presence leads to a dip at zero momentum in the longitudinal momentum distribution of the ionized electrons.     

Possibilities of revealing collective pion degrees of freedomin nuclei by means of quasielastic pion knockout by high-energy electrons

The kinematics of quasielastic pion knockout by longitudinal virtual photons in the electroproduction process is presented. The possibility of directly investigating pion momentum distributions in specific channels owing to pole-amplitude dominance is considered. It is shown that, taking into account the final-state interaction of the knock-on pion and the nucleus involved, one can reveal the existence of a pion condensate in nuclei, since the momentum distribution of collective pions has a pronounced maximum at a momentum in excess of 0.3 GeV/c and since the excitation spectrum of the final recoil nucleus is concentrated in the low-energy region E* ≈ K ²/(2AM _N ) ≤ 1 MeV. The picture of pion knockout from meson clouds of individual nucleons is totally different. The analogous rho-mesonmomentum distributions for the process ρ + γT* → π are also presented.