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Cataclysmic Variables (CVs) are close binary star systems with one componentan accreting white dwarf (WD) and the other a larger cooler star that fills itsRoche Lobe. One consequence of the WDs accreting material, is the possibilitythat they are growing in mass and will eventually reach the ChandrasekharLimit. This evolution could result in a Supernova Ia (SN Ia) explosion and isdesignated the Single Degenerate Progenitor (SD) scenario. One problem with thesingle degenerate scenario is that it is generally assumed that the accretingmaterial mixes with WD core material at some time during the accretion phase ofevolution and, since the typical WD has a carbon-oxygen (CO) core, the mixingresults in large amounts of carbon and oxygen being brought up into theaccreted layers. The presence of enriched carbon causes enhanced nuclear fusionand a Classical Nova (CN)explosion. Thus, the WD in a Classical Nova system isdecreasing in mass and cannot be a SN Ia progenitor. In new calculationsreported here, the consequences to the WD of no mixing of accreted materialwith core material have been investigated and the material involved in theexplosion has only a Solar composition. I find that once sufficient materialhas been accreted, nuclear burning continues until a thermonuclear runaway(TNR) occurs and the WD either ejects a small amount of material or its radiusgrows to about $10^{12}$ cm and the calculations are stopped. In all caseswhere mass ejection occurs, the mass of the ejecta is far less than the mass ofthe accreted material. Therefore, all the WDs are growing in mass. (Abridged)

The Accretion of Solar Material onto White Dwarfs: No Mixing with Core Material Implies that the Mass of the White Dwarf is Increasing