The stopping and range of ions in matter is physically very complex, and there are few simple approximations which are accurate. However, if modern calculations are performed, the ion distributions can be calculated with good accuracy, typically better than 10%. This review will be in several sections: 

a)

A brief exposition of what can be determined by modern calculations.




b)

A review of existing widely-cited tables of ion stopping and ranges.




c)

A review of the calculation of accurate ion stopping powers.

The stopping and range of ions in solids

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

The purpose of this chapter is to review the calculation f the stopping and the final range distribution of ions in matter. During the last thirty years there have been published scores of tables and books evaluating the parameters of energetic ion penetration of matter. Rarely have the authors of these reference works included any evaluation of the accuracy of the tabulated numbers. We have chosen to show the development of ion penetration theory by tracing how, as the theory developed through the years, various parts have been incorporated into tables and increased their accuracy. This approach restricts our comments to those theoretical advances which have made significant contributions to the obtaining of practical ion stopping powers and range distributions. The Tables reviewed were chosen because of their extensive citation in the literature.

The Stopping and Ranges of Ions in Matter

We present data which, to the best of our knowledge, includes all known nontrivial values and bounds for specific graph, hypergraph and multicolor Ramsey numbers, where the avoided graphs are complete or complete without one edge. Many results pertaining to other more studied cases are also presented. We give references to all cited bounds and values, as well as to previous similar compilations. We do not attempt complete coverage of asymptotic behavior of Ramsey numbers, but concentrate on their specific values.

Small Ramsey Numbers

The formalism for calculating the stopping of energetic light ions (H, He, and Li) at energies above 1 MeV/u, has advanced to the point that stopping powers may now be calculated with an accuracy of a few percent for all elemental materials. Although the subject has been of interest for a century, only recently have the final required corrections been understood and evaluated. The theory of energetic ion stopping is reviewed with emphasis on those aspects that pertain to the calculation of accurate stopping powers.

/pdf/stopping-of-energetic-light-ions-in-elemental-matter-3ytoitsnwc.pdf

Stopping of energetic light ions in elemental matter

Let denote the class of all graphsG which satisfyG→(G
1,G
2). As a way of measuring minimality for members of
 , we define thesize Ramsey number ř(G
1,G
2) by
 . We then investigate various questions concerned with the asymptotic behaviour ofř.

The size ramsey number

A new upper bound is given for the cycle-complete graph Ramsey number r(C,,,, K„), the smallest order for a graph which forces it to contain either a cycle of order m or a set of ri independent vertices

On cycle—Complete graph ramsey numbers

For n = 1, 2, …, let Bn = K2 + Kn. We pose the problem of determining the Ramsey numbers r(Bm, Bn) and demonstrate that in many cases critical colorings are avialable from known examples of strongly regular graphs.

On ramsey numbers for books

In a seminal paper from 1983, Burr and Erdős started the systematic study of Ramsey numbers of cliques vs. large sparse graphs, raising a number of problems. In this paper we develop a new approach to such Ramsey problems using a mix of the Szemeredi regularity lemma, embedding of sparse graphs, Turan type stability, and other structural results. We give exact Ramsey numbers for various classes of graphs, solving five — all but one — of the Burr-Erdős problems.

Ramsey goodness and beyond

Calculations of $\ensuremath{\alpha}$-particle stopping cross sections based on the theories of Lindhard et al. using the Hartree-Fock-Slater atomic-charge distribution provide generally good agreement with previously obtained experimental results. In particular, the calculations are helpful in understanding the structure which results when, for fixed energy of the $\ensuremath{\alpha}$ particle, the stopping cross section is plotted against the atomic number of the stopping medium.

Cecil C. Rousseau

Papers

The size ramsey number

On cycle—Complete graph ramsey numbers

On ramsey numbers for books

Ramsey goodness and beyond

CALCULATIONS OF STOPPING CROSS SECTIONS FOR 0.8- TO 2.0-MeV ALPHA PARTICLES.