RE: What is meant by "forbiddenness of the decay path?"

["Boyce, Dale" <DBoyce@intiso.com>]

John,

It has to do with spin and parity conservation.  In so called "allowed"
transitions the spin and parity difference of the parent and daughter nuclei
is either 0 or +/-1.  This means (in beta decay) that both the beta and the
antineutino can be emitted from a "point" and do not have to carry off any
angular momentum other than their respective spins.  The rate of transition
between a parent state and daughter state is governed by an overlap integral
of the wave functions of the parent and daughter nuclei.  Very
simplistically for an allowed transition the beta and neutrino can be
emitted from the center of the nucleus.  The larger the difference in spin
the more forbidden the transition because in order to carry off angular
momentum the beta and antineutino must be emitted further and further from
the center of the nucleus, and therefore the "overlap" of the parent and
daughter wave functions is smaller.   Beta decay normally follows a Q^5
rule.  That is the rate of two transitions that have similar change in spin
and parity will have half lives such that the ratio of the half lives will
approximately equal the inverse ratio of the decay energies to the fifth
power.  However, if you find two examples of beta emitters with similar
decay energies, but one has a greater spin change it will typically have a
much longer half-life.  

Check out Ar39, Be10, and In115 decay energies are .565, .56, and .5
respectively, but the half lives are 269, 1.6E6, and 6E14 years.  Spin
changes for them are 2, 3, and 4 with Ar39 also having a parity flip.

Please forgive the admixture of classical and quantum mechanics.  Just
trying to help give a gut feeling for why..

Dale Boyce
dboyce@intiso.com


> -----Original Message-----
> From:	Jacobus, John (OD) [SMTP:JJacobus@exchange.nih.gov]
> Sent:	Wednesday, November 10, 1999 5:33 PM
> To:	Multiple recipients of list
> Subject:	What is meant by "forbiddenness of the decay path?"
> 
> I am reviewing a manual that discusses beta decay, which indicates that
> some
> paths are forbidden?  Can anyone tell me that refers to?  Are there
> probabilistic values associated with this?
> 
> -- John 
> 
> "It isn't necessary to imagine the world ending in fire or ice-there are
> two
> other possibilities: one is paperwork, and the other is nostalgia." 
> -Frank Zap 
> 
> 
> 
> John Jacobus, MS
> Health Physicist
> National Institutes of Health
> Radiation Safety Branch, Building 21
> 21 Wilson Drive, MSC 6780
> Bethesda, MD  20892-6780
> Phone: 301-496-5774      Fax: 301-496-3544
> jjacobus@exchange.nih.gov (W)
> jenday@ix.netcom.com (H)
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