K-shell Ionization Probability Research Articles

Nuclear Reaction Times in the Deep-Inelastic U + U Collision Deduced fromK-Shell Ionization Probabilities

The K-shell ionization probability P/sub K/ of the uranium-like products has been measured in the deep-inelastic reaction U+U at a beam energy of 7.5 MeV/u as a function of the total kinetic energy loss -Q. P/sub K/ was determined for Q values down to -190 MeV. After the subtraction of the ionization induced by internal conversion of ..gamma.. rays, a strongly Q-dependent P/sub K/ is found in qualitative agreement with theoretical predictions. From the data we infer a nuclear reaction time of approximately 10/sup -21/s at Q = -100 MeV.

Compound elastic cross sections in the isobaric analog resonances 88Sr(p,p 0) at 5.06 MeV and 86Sr(p,p 0) at 6.02 MeV

We have measured the K-shell ionization probability P K across the isobaric analog resonances in the elastic channel of the reactions 88Sr(p,p 0) 88Sr at 5.06 MeV and 86Sr(p,p 0) 86Sr at 6.02 MeV. The dependence of P K on the beam energy for two scattering angles 90° and 155° is analysed in the framework of the theory developed by Anholt et al. taking into account the effect of compound-nucleus scattering. A compound elastic cross section ( dσ dω ) CE = 40 ± 10 mb/sr at the peak of the resonance is deduced in the reaction 88Sr + p at 5.06 MeV, while the experimental results agree with a negligible value of ( dσ dω ) CE for the resonance in 86Sr + p at 6.02 MeV.

Probabilities for K-shell ionization and capture by light ions: Scaling properties

Theoretical approximate scaling relations for the probability of K-shell ionization and K-shell capture in collisions between moderately heavy target atoms (C, Ne and Ar) and light bare ions (H +, He 2+ and Li 3+) have been tested experimentally. The scaling with respect to the projectile charge was studied only at one intermediate scaled velocity whereas the scaling with respect to the target atomic number has been tested at several intermediate or high velocities. The scaling laws are obeyed fairly well by the present set of experimental data. The measured K-shell ionization and capture probabilities, which are smoothly decreasing functions of impact parameter, can each be characterized to a first approximation by two velocity-dependent parameters: the probability at small impact parameters, P( b≅0), and the impact parameter, b 1 2 , defined by P(b 1 2 = 1 2 P(b≅0) . The width, b 1 2 , characterizing the K-shell ionization process increases with increasing collision velocity and becomes even larger than the K-shell radius at large velocities. In contrast, the width characterizing the K-shell capture process exhibits a broad maximum of about the same size as the K-shell radius at intermediate velocities and becomes significantly smaller than this radius at large velocities.

Effects of a Polarized Wave Function in Calculations of Inner-Shell Ionization Probability

Theoretical calculations for the proton-induced K-shell ionization probability in which the ground-state electron wave function is allowed to be polarized under the influence of the incident projectile are described. These calculations extend the results of a previous theoretical model in which the wave function is allowed only a spherically symmetric distortion. The model is based upon lowest-order perturbed-stationary-state theory. Comparisons between calculations performed with different wave functions as well as between calculations performed with the polarized wave function and experimental data are shown for 0.3 to 2.4 MeV protons in titanium.

K-shell ionization across isobaric analog resonances

K-shell ionization probabilities P K near isobaric analog resonances are calculated including contributions from compound-nucleus scattering. For projectile scattering angles less than 90°, compound-nucleus scattering has a negligible effect on P K, but at large angles P K is affected considerably if compound-nucleus scattering is included.

Theory ofK-shell ionization during nuclear resonance scattering

Recently the measured proton-induced C K-shell ionization probability was found to vary significantly near the 0.461-MeV j = 1/2+ elastic resonance in /sup 12/C. Since the resonance was so wide that time-delay effects on K-shell ionization should be very small, it was hypothesized that this effect was due to the exchange of angular momentum between the projectile motion and electron. Assuming a potential description of the nuclear scattering, we make a completely quantum-mechanical calculation of the ionization probability in the distorted-wave Born approximation and show that angular momentum effects do not account for these results. We also show how the amplitude for monopole excitation is augmented by the ''shake-off'' or ''sticking'' term found in the semiclassical theory of Ciocchetti and Molinari, and display the formal correspondence between the semiclassical and quantum-mechanical theories. Numerical calculations of the ionization probability show only a slight dip at the minimum in the p-C elastic cross section, opposite in sign and of much smaller magnitude than the reported variation.

Trajectory, binding and relativistic effects in the K-shell ionization process investigated by particle-photon coincidences

The influence of the projectile trajectory on the K-shell ionization probability has been investigated by proton and deuteron impact on Ni and Ag by using particle-photon coincidence techniques. Good agreement with calculations in first order peturbation theory is obtained also at very large scattering angles, where higher multipole transitions and the recoil effect have an important influence on the ionization probability. The importance of the increased K-electron binding energy due to the influence of the projectile nuclear charge is demonstrated in the Ne on Ni and Cl on Pb collision systems. Even in the Cl on Pb collision system good agreement is obtained between the first order peturbation theory and experiment, if relativistic united-atom wave functions are used for the 1s electrons.

Role of relativistic and binding-energy effects in the Pb K-shell ionisation by Cl projectiles

The K-shell ionisation probabilities of Pb in collisions with 86.9 and 135.6 MeV Cl ions have been measured. A comparison with various calculations demonstrates the importance of the relativistic effect and the binding-energy effect in this heavy system.

K-shell ionization probability in close collisions of 7-12-MeV protons with targets ofZ=24−83

K-shell ionization probabilities were measured by the particle--x-ray coincidence technique for 7-MeV protons of 15 to 39 fm impact parameter on 24 targets from Cr to Bi. For 22 of these targets, total K-shell ionization cross sections are also reported. Additional K-shell ionization probabilities were measured for 7-, 10-, and 12-MeV protons on Mo, Cd, and Sn, at impact parameters down to 2 fm. While the total K-shell cross sections closely follow relativistic semiclassical (RSCA) calculations supplemented by minor binding-plus-polarization corrections, significant discrepancies of up to 70% occur for the K-shell ionization probabilities at small impact parameters, particularly for the targets from Cr to Zr. They can be traced back to the use of hydrogenic wave functions in the RSCA calculation, whereas nuclear recoil may account only for a few percent of the discrepancies. The data on both K-shell total cross sections and ionization probabilities exhibit the pattern characteristic for small distortions of the K-electron binding energy by the projectile charge: adiabatic binding for xi/sub K/ 1. The perturbed-stationary-state approximation somewhat underestimates these distortion effects.

Impact-Parameter Dependence of K-Shell Ionization Probabilities for 150 keV Protons on a Titanium Target

Absolute impact-parameter dependence of K-shell ionization probabilities of Ti has been measured for 150-keV protons by a coincidence measurement between the characteristic X-rays and the scattered protons. Comparison of the measured K-vacancy production probabilities with predictions from the low energy SCA (semiclassical Coulomb approximation) shows reasonable agreement for 150-keV proton-on-Ti system.

Projectile charge and mass dependence of large angle K-shell ionization probabilities on copper

The dependence on the scattering angle of the K-shell ionization probability has been measured with 0.5 MeV H +, 1 MeV D + and 2 MeV He + on copper targets. The experimental values are compared to SCA calculations corrected for binding, retardation and relativistic effects. The angular dependences are in good agreement with the theoretical predictions if the rapid variation of the nuclear relative velocity at the distance of closet approach is correctly taken into account (“hair-spin curve” effect).

Impact-parameter dependence of Ni K-shell ionisation by p, α,7Li and16O projectiles

The Ni K-shell ionisation probabilities induced by p, alpha 7Li and 16O projectiles have been measured as a function of the impact parameter for two sets of incident energies (E1=1.25 MeV amu-1 and E2=2.19 MeV amu-1). The data are compared with the scaling law of the semiclassical approximation (SCA) where binding-energy corrections are included. Reasonable agreement for all impact parameters and for all projectiles is obtained using the universal function experimentally derived from proton on copper data published in the literature. With the SCA universal functions the agreement is worse at large impact parameters. For 16O projectiles the K-vacancy sharing between the projectile and targets was found to be not negligible at large impact parameters.

K- and L-shell ionization cross sections of superheavy elements and fission probabilities of the actinides in micas by a few MeV protons

K- and L-shell ionization cross sections for a number of superheavy elements have been calculated for incident proton energies of a few MeV. It is noted that the K-shell ionization probability for an incident energy of about 15 MeV is of the same order of magnitude as that for the L shell with about 5 MeV protons. In additions, should such superheavies exist in a monazite sample K X-rays from the fission fragments from the actinides might be a competing factor with the L X-rays of superheavy elements.

Effect of particle identity on the observed impact parameter dependence of inner-shell ionization in symmetric heavy-ion collisions

The decrease in K-shell ionization probability at small impact parameters predicted by a molecular promotion model with rotational coupling cannot be unambigously tested by experiment if the target and projectile are indistinguishable.