In nuclear physics, what length year in seconds is used?
A "year" without qualification may refer to a Julian year (of exactly $31\,557\,600~\rm s$), a mean Gregorian year (of exactly $31\,556\,952~\rm s$), an "ordinary" year (of exactly $31\,536\,000~\rm s$), or any number of other things (not all of which are quite so precisely defined).
Radioactive decay tables tend to be compiled from multiple different sources, most of which don't clarify which definition of "year" they used, so it is unclear what definition of year is used throughout. It's quite possible that many tables aren't even consistent with the definition of "year" used to calculate the decay times.
On the other hand, the standard error is usually overwhelmingly larger than the deviation created by using any common definition of year, so it doesn't really make a difference.
A day in physics without qualification pretty universally refers to a period of exactly $86\,400~\rm s$.
Years are merely an approximation, as you pointed out, they really aren't precisely defined. In physics seconds are used as they can be calculated exactly using atomic clocks.
For instance, no application requires an exact decimal representation of years, you can round to approximate numbers and then use a remainder of seconds.
As a not necessarily representative example, the decay data in the NUCLIDES 2000 database, which is based on the JEF2.2 decay data file, use a year of 365 days and a day of 24 hours.
For example, the halflife of Co-60 is internally stored as 1.6623E+08 seconds but reported as 5.2711E+00 years.
The decay data provided in
- Endo, A., Yamaguchi, Y., Eckerman, K.F., 2005. Nuclear Decay Data for Dosimetry Calculations: Revised Data of ICRP Publication 38. JAERI 1347. Japan Atomic Energy Research Institute, Tokaimura, Naka-gun, Ibaraki.
- ICRP, 2008. Nuclear Decay Data for Dosimetric Calculations. ICRP Publication 107. Ann. ICRP 38 (3).
use a year of 365.2422 days and a day of 24 hours (which corresponds to a tropical year of 365 days, 5 hours, 48 minutes, and 46 seconds).