Yes, there have been several studies on this. Here are just a few:
Coffey, L. C., Skipper, J. K., & Jung, F. D. (1988). Nurses and shift work: effects on job performance and job‐related stress. Journal of Advanced Nursing, 13(2), 245-254.
Totterdell, P., Spelten, E., Barton, J., Smith, L., & Folkard, S. (1995). On-shift and daily variations in self-report and performance measures in rotating-shift and permanent night nurses. Work & Stress, 9(2-3), 187-197.
Barker, L. M., & Nussbaum, M. A. (2011). Fatigue, performance and the work environment: a survey of registered nurses. Journal of advanced nursing, 67(6), 1370-1382.
Ugrovics, A., & Wright, J. (1990). 12-Hour Shifts: Does Fatigue Undermine ICU Nursing Judgments?. Nursing Management, 21(1), 64A-64G.
Iskera-golec, I., Folkard, S., Marek, T., & Noworol, C. (1996). Health, well-being and burnout of ICU nurses on 12-and 8-h shifts. Work & Stress, 10(3), 251-256.
We have recently completed a comprehensive scoping review about 12 hour shifts in nursing:
Harris, R, Sims, S, Parr, J and Davies, N (2015) Impact of 12 hour shift patterns in nursing: a scoping review. International Journal of Nursing Studies, 52(2), pp. 605-634. ISSN (print) 0020-7489
It includes quantitative studies and addresses the evidence of impact on nurse performance.
If looking for a good question - the impact of napping breaks needs more research, especially for across shifts. With the 12-hour shift being fairly consistent in US hospitals, both day and night nurses are dealing with sleep deprivation (for example, day shift nurses are often getting up exactly at the time that they should be in their deepest sleep cycle). The information about the benefits of organizations that have 'napping' policies is primarily anecdotal. Need to know if this can really be honored across an organization - what are the supports that need to be in place, such as staffing to cover during this type of break, and what are the measurable impacts of napping - decreased errors, etc. - over an extended (year+) implementation of the practice.