Kanani K. M. Lee1,2

Gerd Steinle-Neumann2 1Department of Physics, New Mexico State University, Las Cruces, NM, USA.2Bayerisches Geoinstitut – Universität Bayreuth.

Pressure- and chemistry-dependent

electron-capture-decay in crystalline solids

Radioactive decay

Dating of rocks (235U, 238U, 232Th, 40K, 87Rb)

Heat dynamics (235U, 238U, 232Th, 40K)

Mostly α decay (U, Th)

40K decays by β+ (89%) and electron capture (11%) (emission of γ ray)

Other electron capture isotopes: 7Be, 22Na, 26Al, 53Mn

β-, there is also β+

Radioactive decay

Radioactive decay nuclear process, hence independent on environment:

true for α and β processes (on fundamental grounds but also measured)

electron capture ~ charge density at nucleus

here 7Be (τ½=53 days)22Na (τ½=2.6 years, τ½,EC=27.7 years)40K (τ½=1.25 Gyr, τ½,EC =11.9 Gyr)

dependence on chemistry and pressure (decay constant λ~1/τ½)

refecrefe

eec ,

,

1

Energetics of a solid

Schrödinger's equation [-2+V]Ψ(r1,r2,...,rN)=EΨ(r1,r2,...,rN)

Density Functional Theory (Kohn et al., 1964 ff.):electronic charge density ρ is basic quantity[- 2+VKS[ρ]]ψi(ρ)= eiψi (ρ)

VKS[ρ]= Vne+Vee+Vxc

Static computations:

Thermal excitations (and zero point motion) neglected.Use full periodicity of the lattice.

7Be chemistry

Experiments: λ[Be(OH2)42+]>λ[Be]>λ[BeO]>λ[BeF2] [Johlige et al., 1970]

Our computations: λ[Be]>λ[BeO]>λ[BeCl2]

7Be pressure

1.0

0.8

0.6

0.4

0.2

0.0

perc

ent

diff

ere

nce

, ec

50403020100

Pressure (GPa)

Be, hcp BeO, hcp BeCl2, orth

Gogarty et al., 1963 Hensley et al., 1973 Liu & Huh, 2000

40K pressure

0.02

0.01

0.00

perc

en

t d

iffere

nce

, ec

50403020100

Pressure (GPa)

K, bcc K, fcc K2O, fcc

KCl, B1 KCl, B2

5395.0

5394.5

5394.0

5393.5

tota

l ele

ctro

n c

harg

e d

ensi

ty,

e80604020

Volume (Å3)

1.0

0.8

0.6

0.4

0.2

0.0

num

ber o

f d-o

rbita

l ele

ctrons

05102550Pressure (GPa)

22Na pressure

0.3

0.2

0.1

0.0

nu

mb

er o

f d-o

rbita

l ele

ctron

s

40302010

Volume (Å3)

893

892

891

890

889

888

tota

l ele

ctro

n c

harg

e d

en

sity

, e

010251001000

Na, fcc total electron density 4th-order polynomial fit d-orbital occupancy

Pressure (GPa)

0.14

0.12

0.10

0.08

0.06

0.04

0.02

0.00

perc

en

t d

iffere

nce

, ec

100806040200Pressure (GPa)

Na, bcc Na, fcc NaCl, B1 NaCl, B2 Na2O, fcc

Conclusions

Using first principles computations for the electronic charge density of electron capture isotopes we

reproduce the chemical dependence of λ for 7Be in various chemical forms can not confirm the strong P dependence of λ for 7Be find small P dependence of λ for 22Na and 40K see transition in electronic state (s d) for 22Na and 40K

Changes in λ for alkalines are small, are they measurable (γ rays)?

22Na: ~32 billion decays/day40K: ~40 decays/day

22Na available from ORNL as Na(OH) gel

1400

1200

1000

800

600

400

200

0

cou

nts

300025002000150010005000

Energy (keV)

Background measurementsEmpty DAC at GEANIE facility at LANL

1275 keV 22Na

611 keV 137Cs 1461 keV

40K

2615 keV 232Th 208Tl …