Sheelagh O'Rourke

Investigation of various growth mechanisms of solid tumour growth within the linear-quadratic model for radiotherapy

The standard linear-quadratic survival model for radiotherapy is used to investigate different schedules of radiation treatment planning to study how these may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al (1977 Br. J. Radiol. 50 681), which was concerned with the case of exponential re-growth between treatments. Here we also consider the restricted exponential model. This has been successfully used by Panetta and Adam (1995 Math. Comput. Modelling 22 67) in the case of chemotherapy treatment planning. Treatment schedules investigated include standard fractionation of daily treatments, weekday treatments, accelerated fractionation, optimized uniform schedules and variation of the dosage and alpha/beta ratio, where alpha and beta are radiobiological parameters for the tumour tissue concerned. Parameters for these treatment strategies are extracted from the literature on advanced head and neck cancer, prostate cancer, as well as radiosensitive parameters. Standardized treatment protocols are also considered. Calculations based on the present analysis indicate that even with growth laws scaled to mimic initial growth, such that growth mechanisms are comparable, variation in survival fraction to orders of magnitude emerged. Calculations show that the logistic and exponential models yield similar results in tumour eradication. By comparison the Gompertz model calculations indicate that tumours described by this law result in a significantly poorer prognosis for tumour eradication than either the exponential or logistic models. The present study also shows that the faster the tumour growth rate and the higher the repair capacity of the cell line, the greater the variation in outcome of the survival fraction. Gaps in treatment, planned or unplanned, also accentuate the differences of the survival fraction given alternative growth dynamics.

Longitudinal momentum distributions in single ionization of He by ions

The final-state longitudinal momentum distributions of the ejected electron, recoil-ion and the projectile momentum transfer in single ionization of helium by ions are presented. The CDW and CDW-EIS approximations are used throughout. Calculations for the electron energy spectrum and total cross sections are also presented. The present results are found to be in good qualitative agreement with recent experimental data and with the predictions of the CTMC calculations.

Local saddles and local maxima in double differential cross sections of single ionization in ion-atom collisions

The ejected-electron spectrum for H+ incident on H2 and He at 40 keV is examined experimentally and theoretically. The continuum-distorted-wave eikonal-initial-state (CDW-EIS) model is adopted to study the ionization process. Experimentally a 260 mm diameter hemispherical analyser with half-angle acceptance of 1.5° and energy resolution E /E of 0.012, is used to measure the velocity distribution of the emitted electrons. The analyser and the surrounding interaction region are double shielded against the Earths magnetic field by use of µ-metal enclosures. The observations and calculations, for double differential cross sections (differential with respect to electron momentum and emission angle), are in very good agreement and show a spectrum dominated by a well defined electron capture to the continuum (ECC) peak although existence of saddle-point electrons at 0° is not confirmed.

Differential cross sections in antiproton and proton-helium collisions

Cross sections are presented for the first time for antiproton-helium collisions at an energy of 945 keV differential in longitudinal electron and recoil-ion momenta. The longitudinal momentum distributions for antiproton impact are compared with 1 MeV proton-helium collision. The electron and the recoil-ion momentum distributions for antiprotons agree with those for protons to within 10%. We did not observe a difference between antiproton impact and proton impact. A comparison with CDW and CTMC theories is presented.

New studies of the mechanism of electron emission at zero degrees in collisions of 100 KeV protons wirth H2 and He

Measurements of double differential cross sections for electron emission at zero degrees arising from collisions of 100 keV protons with H2 and He have been carried out. Calculations based on a continuum-distorted-wave eikonal-initial-state model have also been carried out and shown to provide a good description of the measurements. In addition, classical-trajectory Monte Carlo calculations have been employed to illustrate the evolution of electron emission at different times during the collision. The present measurements, which use a well defined gas target, provide no evidence of the existence of a significant saddle-point ionization mechanism at the energy considered.

Ion-atom /neon - calculation of ionization cross sections by fast ion-impact for neutral target atoms ranging from lithium to neon

The program presented calculates the total cross sections, and the electron energy spectra of the singly and doubly differential cross sections for the single target ionization of neutral atoms ranging from lithium up to and including neon. The code is applicable for the case of both high and low Z projectile impact in fast ion-atom collisions. The theoretical descriptions provided for the program user are based on two quantum mechanical models which have proved to be very successful in the study of ionization in ion-atom collisions. These are the continuum-distorted-wave (CDW) and continuum-distorted-wave eikonal-initial-state (CDW-EIS) approximations respectively.

LMD : Calculation of longitudinal momentum distributions in the single ionization of helium by ion impact

A program is presented which calculates the final-state longitudinal momentum distributions of the ejected electron and recoil-ion for the single ionization of helium-like targets by both light and heavy-ion impact. The longitudinal momentum distributions are evaluated within a wave treatment. The continuum-distorted-wave (CDW) and continuum-distorted-wave eikonal-initial-state (CDW-EIS) approximations are used throughout. The program considered here extends a previously published program ION (D.S.F. Crothers, M. McCartney, Comput. Phys. Commun. 72 (1992) 288) which calculated the total, singly and doubly differential cross sections for the ionization of hydrogen-like targets by fully stripped projectile ions.

Ion-atom wave -Calculation of single ionization cross sections in ion-atom collisions

A Fortran 90 program is presented, namely Ion-Atom-Wave (IAW), which calculates total, single and double differential cross sections for the single ionization of atomic and molecular hydrogen-like targets and helium-like targets by both light-and-heavy-ion impact. The cross sections are evaluated within the continuum distorted-wave final-state (CDW) and the continuum distorted-wave eikonal-initial-state (CDW-EIS) approximations. IAW calculates cross sections within the wave treatment. This program extends a previously published program ION (D.S.F. Crothers and M. McCartney, Comput. Phys. Commun. 72 (1992) 288) which calculated the total, single and double differential cross sections for the ionization of hydrogen-like targets by fully stripped ions.

Analytic continuation of the Nikitin exponential model to non-zero impact parameters

Numerical results for the Nikitin exponential model at non-zero impact parameters are presented. It is confirmed that in order to derive the correct strong-coupling approximation of the transition probability, one need only include the leading terms of the asymptotic expansions of the confluent hypergeometric functions. Development beyond leading order is inappropriate to the particular model, because by construction the non-analytic wavefunction is discontinuous in its second-order derivative at the turning point, which follows from the cusp-like discontinuity in the first-order derivative of at least the off-diagonal Hamiltonian potential matrix elements. It is therefore concluded that the Stueckelberg phase-integral derivations of Crothers are essential if transition probabilities and cross sections are not to be underestimated at large impact parameters, due to neglecting the bending of the double Stokes line.

Multi-state CDW approximation to electron capture during slow p-H collisions

The first complete multi-state CDW close coupling calculations which use a fully normalized basis set are performed. The results obtained at impact energies in the region of 10 keV for total and n = 2 capture cross sections are in reasonably good accord with experiment despite the fact that only the ground states of both species and the n = 2 states of the projectile are incorporated into the model. The theory has significant advantages over other atomic and molecular expansions which may require extensive bases to obtain similar accuracy.