1. Change of 7Be decay rate under compression
A.Ray1, Arindam Kr. Sikdar1, S. Pathak1 , P. Das1 and J. Datta2
1Variable Energy Cyclotron Centre, 1/AF Bidhannagar, Kolkata
2Analytical Chemistry Division, BARC, Variable Energy Cyclotron Centre, 1/AF Bidhannagar, Kolkata

2. λ(electron capture decay rate)∝ 𝜓(0) 2
Unstable nuclei
Fission
Radioactive decay mostly independent of temperature, pressure and chemical environment
e- capture decay is susceptible to environment change. 7Be have 3.3 % contribution of 2s electron in e- capture decay.
λ(electron capture decay rate)∝ 𝜓(0) 2

3. 7Be electron capture Decay in different chemical environment
Electron affinity of surrounding medium affects decay rate of 7Be
Host atoms of high electron affinity takes away valence 2s electrons of 7Be.
Decay rate reduced.
Results could be understood by Density Functional calculations.
P. Das and A. Ray, Phys. Rev. C71, (2005).
T. Ohtsuki et al., Phys. Rev. Lett. 93, (2004).
E. B. Norman et al., Phys. Lett. B 519, 15 (2001).

4. Effect of compressing 7Be ion on its decay rate
2s valence electrons pushed in towards nucleus.
Increases 2s electron density at nucleus.
1s electrons see less nuclear charge due to more screening by 2s electrons.
1s electron density at nucleus decreases.
Net result: Total electron density at nucleus generally increases under compression
For 7Be implanted in a lattice, both electron affinity and lattice compression play their roles.
Want to disentangle compressional effect to understand it.

5. Astrophysical Significance
7Be electron capture reaction takes place at the solar core.
8B neutrino flux f(8B)∝1/𝑅(𝑒) ; R(e)7Be electron
Capture decay rate
At solar core, density =150 gm/cc, Pressure =26.5 million GPa.
Density Functional Calculation performed putting 7Be in dense solar plasma.
Electron density at 7Benucleus and decay rate calculated.
No direct experimental check of the calculation possible.
Calculated 7Be decay rate at solar core determines 8B solar neutrino flux.
Important to measure the increase of 7Be decay rate under compression in terrestrial condition
&
Compare with density functional calculation.
A good understanding of the effect of compression in terrestrial condition
would provide higher confidence in 7Be decay rate calculation at solar core.

6. 7Be Electron capture Decay
10.4% probability of populating 7Li*(478 keV) state.
Decays by emitting a 478 keV g-ray photon.
Monitor 7Be electron capture decay by observing 478 keV
g-ray line.

7. Compression of 7Be atom by applying external pressure
on 7BeO lattice
W. K. Hensley et al., Science 181, 1164 (1973)
∆𝜆 𝜆 =(2.2±0.1)× 10 −4 𝑃 ,
where P is the applied pressure in GPa.
Density functional calculations underpredict experimental result by a factor of 5.

8. Compression of 7Be atom by confining in a small lattice
7Be ion compressed when implanted in a small lattice such as Palladium (Pd).
Lattice constant = 3.9Å
Compared to
When implanted in a large lattice such as lead (Pb).
Lattice constant = 5Å
Both Pd and Pb have low and similar electron affinity.
Observed increase of decay rate of 7Be in Pd could be attributed to compression.
Measure change of decay rate of 7Be in Pd versus Pb.

9. Implantation work Counting using a 80% efficiency HPGe detector.
7Be in Pd and Pb foils counted alternately every week for five months.
A 60Co source used as standard for dead time correction.
Ratio of 478keV/60Co lines monitored with time.
7Be
(1-3) MeV
7 MeV, 500 nA proton beam
from RTC at VECC, Kolkata
LiF target
Pd/Pb catcher foil

10. Implantation work Range of 7Be in Pd and Pb = 1 mm to 3.3 mm
7 MeV proton beam produces negligible damage where 7Be ions implanted.
10-5 vacancies/Angstrom/ion
7Be ions implanted in essentially undamaged Pb and Pd lattices.
Locally deforms lattice site where 7Be ion is implanted.

11. Fig. Typical g-ray spectra of sources implanted in Pd and Pb foil.

12. Fig. Superposition of exponential fits of ratio of (478 keV/ sum of 60Co peak area)
in Pd and Pb with time.

13. Dl/l=(0.84± 0.16)% Gaussian fits of residual data points shown below
Exponential fits (upper panel) and residual plots (lower panel) of data points for 7Be in Pd and Pb media.

14. Results
Increase of decay rate (0.84±0.16)% of 7Be in Pd compared to Pb somewhat higher than
the increase of decay rate(0.6%) observed by compressing 7BeO with 27GPa pressure.
Using Hensley et al.’s results,
Lattice Compression in Pd equivalent to applying 40 GPa pressure on 7BeO lattice.
Electron affinity of Pb=0.36 eV and that of Pd=0.56 eV.
Small decrease of 7Be decay rate in Pd expected due to electron affinity
Density Functional calculations (WIEN2k) performed putting 7Be in octahedral and tetrahedral interstitial sites of Pd and Pb.
Host Lattice deformed in calculation to minimize energy and forces on lattice atoms.
Average calculated increase of electron density and corresponding
increase of decay rate= 0.15%.

15. Conclusions Increase in decay rate in Pd w.r.t Pb is Dl/l=(0.84±0.16)%
WIEN2K predicts 0.15% shorter half-life of 7Be in Pd.
Effect of finite nuclear size and quantum anti-Zeno effect
expected to be negligible.
Large discrepancy between DFT calculations and observed increase of
7Be decay rate under compression found.
Our understanding of the results in terrestrial
condition would provide confidence in the calculation of 7Be decay rate
at the solar core which is
not directly accessible by experiment.

17. Quantum Anti-Zeno effect
In quantum mechanics, any decay is non-exponential at initial time
Non-exponential decay time for electron capture process
tneℏ/ER 10-22 s for ER ~ 1 MeV
Minimum response time of valence shell ~ s
Change in decay rate ~ (10-22/10-16)×100%=10-4 %
For Non-exponential decay time ~ s
Change in decay rate ~ (10-18/10-16)×100% ~ 1%