Re: "A Universe Without Weak Interactions"

Tim Little <tim@xxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:

On 2008-05-31, Jonathan L Cunningham <spam@xxxxxxxxxxxxxxxxxxxx> wrote:
I'm still interested (as idle curiosity) about which would be the stable
isotopes

I ran some rough numbers, and they're very similar. The dominant
effect is the (residual) strong force, which doesn't change much. A
few elements end up with an extra neutron or two for stability, but
not much difference. It does mess up a few of the stellar fusion
cycles, in the unlikely event that there is significant tritium in
such a universe.
(snip)

I'd expect C-12 to decay to B-12 or even Be-12! I also wonder
whether the heaviest stable element would have more or less protons
than in our universe -- my hunch is that something like U-300 might
be stable, and that the "Island of Stability" which was conjectured
around element 120 might actually be stable.

Actually it's worse than ours. Elements with high atomic number get
double-hit by the increased proton mass and the higher energy levels
that have to be occupied by the extra neutrons. I'm not even sure
that gold has any stable isotopes, let alone superheavies.

A shame! ;-)

But allow me to raise some further questions about it. You reckon that
there mostly won't be a big excess of neutrons (beyond what we already
get).

Any nuclide with any excess of neutrons is going to be lighter, (same
energy levels, but made out of lighter particles), but stability doesn't
depend on the absolute mass of the nuclide, but the difference between
parent and daughter...

Excuse me laboriously posting my working, but it will make it easier to
spot where I'm going wrong if I'm doing something daft...

It's easy to imagine that alpha decay might be about the same, with the
same energy difference between parent and daughter, but suppose we take
a heavy nucleus which has a long half-life and decays by beta decay ...
<fx: consults table of isotopes>. Hmmm. Isotopes that decay by emitting
electrons don't *have* long half lives! I never noticed that before!

But Radium-228 is not too bad (half-life of 6.7 years). It beta decays
to Ac-228. In our universe (according to this antique, yellowing,
printed on physical paper, table), the atomic masses are 228.03123 and
228.03117 (that includes the electrons). So there is 0.00006 of a mass
unit to "propel" the beta particle out of the nucleus (less any energy
stolen by the neutrino).

If we swap proton and neutron masses, that reduces the Ra-228 mass by
52*0.0013894 = 0.0722488 amu, but the Ac-228 mass is reduced by only
50*0.0013894 = 0.06947 amu.

So: our universe, alt universe
Ra-228 228.03123 227.95898
Ac-228 228.03117 227.96170
diff: +0.00006 -0.00272

So rather than Ra-228 decaying by beta- decay rather slowly to Ac-228,
in the alternate universe, any Ac-228 ought to decay rather fast by
beta+ decay to Ra-228.

The Ra-228 is stable relative to alpha decay (my old table doesn't even
list Rn-224 which would be the daughter product if it could).

So, I can't see how the Ra-228 could decay. And if it can't decay...
it's stable, isn't it?

I suppose there could be some exotic modes, like emitting a Ne nucleus
(an unusual, very rare, mode which has been detected in our universe)
but that sort of process would be slooooow! And probably just as rare as
Ne instead of He nuclide emission is in our universe.

Jonathan
.

Relevant Pages

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