# Effect of pressure on electron wave orbitals

1. Apr 1, 2014

### markr2

One of my nuclear physics exercises was to find out if increasing the pressure of a sample of $^{7}\textrm{Be}$ would increase the chance of electron capture to $^{7}\textrm{Li}$ occur. My reasoning was that the electron wave function is not pressure dependent and therefor it would not increase the likelihood of an electron capture.

But I know that increasing the pressure does change the likelihood of electron capture. My question is how does increasing the pressure influence the wave function of the electron in orbit? My quantum mechanics class did not cover this and I could not find anything on the web about this.

Last edited: Apr 1, 2014
2. Apr 4, 2014

### lightgrav

(try this site ... http://marvin.byu.edu/beryllium7/DecayRatePapers.php [Broken] )

My reading of the experiment papers is that they agree with each other, within 3 or 4 error bars,
and agree with multiple theories within about the same.

Modern, back-of-envelope #1: these Be atoms are not free,
so their electron wave-functions do not extend to infinity.
put the electrons in an infinite square well, width = lattice size,
then reduce the well width (via pressure, experimentally) to 96.5% of a0 .
(one issue is that in BeO2, the 10% Volume change should be mostly in the O2)

Solid State #2: essentially you fold the long tails of the electron wave-function, at the edge of the "unit cell" for the crystal lattice, to represent the neighbor's electrons (and 2nd neighbor, and 3rd...)
so the next-door neighbor's valence (outer) electrons (that are bonding the Be) can now be captured ... not just the 1s electrons. now shrink the crystal size again.

Thermo: half-life decreases at low Temperature by the same amount that sample size decreases (by thermal expansion coefficient). it's not just Pressure that increases capture likelihood.

Last edited by a moderator: May 6, 2017