Semiclassical trace formula for truncated spherical well potentials: Toward the analyses of shell structures in nuclear fission processes

Trace formulas for the contributions of degenerate periodic-orbit families to the semiclassical level density in truncated spherical hard-wall potentials are derived. In addition to the portion of the continuous periodic-orbit family contribution which persists after truncation, end-point corrections to the truncated family should be taken into account. I propose a formula to evaluate these end-point corrections as separate contributions of what I call marginal orbits. Applications to the two-dimensional billiard and three-dimensional cavity systems with the three-quadratic-surfaces shape parametrization, initiated to describe the nuclear fission processes, reveal unexpectedly large effects of the marginal orbits.