Re: [asa] Changing rate of radioactive decay (New Scientist) - Part 2

Reflecting on this further after my quick response this a.m., I realized
that I should nore another consideration which goes in the other direction.
Alpha decay lifetimes are very sensitive to the height of the nuclear
Coulomb barrier, the relation being an exponential one. So a relatively
small increase in the electron density in the immediate vicinity of the
nucleus could pdecrease lifetimes significantly. It all depends on what
"relatively small increase" would be needed, & that's something that's
beyond the scope of the kind of rough calculation I gave.

Shalom
George
http://web.raex.com/~gmurphy/

----- Original Message -----
From: "George Murphy" <gmurphy@raex.com>
To: <asa@calvin.edu>
Sent: Friday, October 27, 2006 9:58 AM
Subject: Re: [asa] Changing rate of radioactive decay (New Scientist)

> OK, this is going to be very crude: I've done some things with plasma
> physics but am not a solid state guy, & am just doing some back of the
> envelope calculations here. So enough pre-emptive excuses -
>
> The Debye shielding length in a plasma, using classical statistics, is
> [kT/4*pi*n*e^2]^1/2 k,T, n & e being, respectively, Boltzmann constant,
> Kelvin temperature, electron density, & electron charge. This length
> will
> give an estimate of the region in which electrons are clustered around a
> free positive charge. For a solid metal one really ought to use Fermi
> statistics but what I'm doing will, I think, give a gross
> _over_estimate of
> shielding. Assuming that all electrons in a chunk of radium are free
> - i.e,
> conduction electrons (!), & putting in numbers for Ra-226 at T = 300
> K, room
> tremperature, we get a shielding length of around 10^-9 cm. That's
> smaller
> than the Bohr radius but still lots larger than the nuclear radius, ~
> 7 x
> 10^-13 cm. If you take the temperature down to 3K as suggested, the
> Debye
> length is decreased by a factor of 1/10 to around 10^-10 cm, still
> over a
> hundred times the nuclear radius.
>
> Thus it doesn't seem that the increased electron concentration near the
> nucleus would be significant, & that's where they'd have to be to
> have an
> effect on the Coulomb barrier to decrease alpha lifetimes.
>
> It's true that nuclei are not isolated systems & their environment
> can have
> some effect on nuclear properties, including lifetimes. But these
> effects
> will generally be quite small unless conditions are really extreme.
>
> Even if cooling to a few K could decrease lifetimes significantly, the
> practical difficulties of achieving & maintaining those temperatures for
> years in a material which is generating heat via radioactive decay (&
> would
> be generating it even faster if you increased the decay rate) would be
> formidable. & of course this result would be even less relevant for
> calculations of the age of the earth, though I'm sure that if the
> YECs get
> hold of this they'll imagine some scenario in which Eve biting into
> an apple
> cooled the earth to millikelvin temperatures.
>
> Caveat: This is a theoretical calculation (& a crude one at that)
> indicating that one proposed mechanism for decreased lifetimes at low
> temperatures wouldn't work. If it turns out that the effect is real
> then
> it's real, but some other explanation will have to be sought.
>
> Shalom
> George
> http://web.raex.com/~gmurphy/
>
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Received on Fri Oct 27 15:50:52 2006