Order by Rung

Main Chain Ordering

Three types of decay dictate the order for Main Chain fission fragments if we are to process all decays in one pass.

  1. The neutron emission modes (B-N, B-2N, B-Nm) require we process the heaviest decay chains first.
  2. Beta Minus (B-) decay proceeds down the energy ladder, so we count down Rungs.
  3. Internal Transforms (IT) fit between the rungs.

The rung values were developed by counting the number of neutrons in excess of the number found in the main sink for each decay chain.  The isomers were jammed in between.

Together, these factors dictate a list of nuclides sorted by AtWt (descending), followed by Rung (descending).  This sequences the major chains properly from Rung 9 to 0.  Special cases are treated by adjusting the Rung values.

Shadowed Chains

There are more than one decay chain for each atomic weight.  The minor chains are associated with the shadowed nuclei.  This NuDat graphic shows initial yields for 235-U (for fission triggered by a slow neutron).  The Main Chain fission fragments are born on the neutronheavy side of the stable valley – east of the stable isotopes (outlined in black).

NuDat (Brookhaven) graphic of Initial Yields

The most “popular” fission fragments are shown in brown.  The number of destabilizing neutrons increases to the right.  The Main Chains flow from the neutron-heavy side to the northwest.  In general, the first stable/primordial isotope encountered when decaying to the northwest is the Main Sink.  (That some of the main sinks are primordial will require some adjustment, however.)

Special Case 1

There are a few green (low yield) isotopes northwest of the stable isotopes.  These drain to the Main Sink if there is only one stable isotope at that atomic weight.  Due to the EC-m decay mode (see below), we need to process these before processing the main chain.  everything drains into it.  We therefore give them rungs 15 and 16, with +1.0 or +0.2 as needed to name the isomers.

The Pesky decay mode

Some nuclides covered by special cases 1 or 2 above can decay by the EC-m mode, which will pass the nucleus through a Rung 0.1 isomer.  This means both cases need to be processed before the main chains.  Since the main chain are processed from Nine to Zero, we need bigger numbers.

 Special Case 2

If the number of protons is even, there is often a second sink.  There can even be a third sink, but this is so far on the neutron-poor side the initial yields are zero.  Nonetheless, the second and third sinks are given rung values of 20 and 30, with 20.1 being needed for just one isomer of the second sink, 136-Ba.

When there are two sinks, there is often an Unstable Island between them.  The NuDat screenshot below highlights 86-Rb, on the 86 chain(s) between 86-Kr and 86-Sr.  These islands can decay either way.  They are shadowed on both sides, so can be processed first.  (They don’t have to be processed first, but it makes other rules easier.)  As the rungs are processed top-down, these are given a rung value of 100 (or 100.1 or 100.2).

86-Rb: Shadowed Island on its own Ladder

The caption captures three of the analogies in use here, two of which conflict vertically.  86-Rb is shadowed by 86-Kr in that no nucleus on the main chain can reach 86-Rb from the southeast.  The shadow analogy is drawn from the rain shadow of a mountain.  86-Kr is blocking the flow.  At the same time, it is energetically downhill from 86-Rb to 86-Kr.  So 86-Kr is either a mountain or a hole, depending on the analogy.

Special case 3

The graphic above also captures a primordial isotope that decays (oh so slowly) to an adjacent stable isotope (northwest: B- decays are always to the NW on the NuDat chart).  87-Rb decays directly to 87-Sr, one of only four cases of two “stable” isotopes without an island between.  These decay so slowly it matters little which is the sink, but it is more consistent to treat the primordial as a normal member of a main chain.  So the rungs for chains 87, 113, and 115, were renumbered.

However, the isomer of 87-Sr  sometimes decays “back” to 87-Rb.  This is, fortunately, the only case of a stable isotope’s isomer NOT decaying directly to the ground state.  87-Sr-1 is not shadowed from 87-Y, which is on rung 15.  87-Sr-1 needs to be processed after 87-Y, so we put it (uniquely) on Rung 14.1.

(non) Special Case 4

Five fission fragments decay (very slowly) by emitting a helium nucleus.  Their daughters are already in the proper order because we sort by AtWt.

Uncovered Case

The special cases sometimes only need attention because of our original choice for the Main Sink.  After the fact, we should have ignored the primordials when deciding where to put Rung Zero.  They don’t decay enough to matter themselves, but some have isomers that do.

Wrap up

After all the kinks and special cases, the Nuclides table was regenerated using AtWt and Rung to control the sort order and an auto-numbered ID.  So, the Nuclides are now listed in the order that the decay cascade was processed.