We correlate annual ultraviolet dose estimates with age specific and age adjusted incidence data for non-melanoma skin cancer in the United States, United Kingdom, Canada and Australia. We first examine (1) a reciprocity or photographic model in which incidence rates (R) are related to exposure (E) which is the product of age (T) and annual dose (D). We also test several models which violate reciprocity including models identified by the labels: (2) Dose potency; (3) Double cause; (4) Age-exposure and (5) separable. Our analyses together with the recent National Cancer Institute study favors the age-exposure model and/or the double cause models. All models lead to biological amplification factors (defined as the ratio of the percent increase in skin cancer incidence due to a 1% increase in dose) greater than unity. For the U.S. we find the biological amplification to be approximately 1.8 for the population center hut greater in regions of higher UV annual dose, and less in regions of lower annual UV dose.

When only a few partial waves are substantially phase shifted and yet many partial waves are slightly phase shifted, it is possible to use the direct Born approximation, provided that one projects out the inaccurate lower partial waves and replaces them by accurate theoretical or phenomenological phase shifts. We test this technique for central potentials with two different well strengths, i.e., one which will fail to bind the 1S wave, and one which can bind the 1S state. We compare numerically generated angular distributions and total cross sections with those obtained from a modified form of the direct Born approximation. The technique would be useful for weak forces, e.g., the nucleon-nucleon and electron-atom interactions, but inapplicable for strong forces, e.g., atom-atom interaction.