# Presentation: 119281

## CHANGE OF HALF-LIFE OF ELECTRON CAPTURING NUCLEI IN DIFFERENT ENVIRONMENTS AND ITS IMPLICATIONS 

## Nuclear decay rate generally considered to be independent of environment

- Electron capture rate should be  susceptible to environment.
- 7Be most suitable candidate. 2s valence orbital influenced by the environment.
- Effect of 2s orbital on total electron capture rate  3.3%.
- Earlier studies found at most 0.2% level change of decay rate of different
- 7Be compounds.
- E. Segre, Phys. Rev** 71**, 274 (1947).
- J. J. Kraushaar, E. D. Wilson, K. T. Bainbridge, Phys. Rev **90**, 610 (1953).
- H. W. Johlighe, D. C. Aumann, H. J. Born, Phys. Rev C**2**, 1616(1970).
- Change of decay rate of 7Be due to pressure.
- 0.59% increase of decay rate found at 270 kilobar pressure.
- W. K. Hensley, W. A. Basset, J. R. Huizenga, Science **181**, 1164 (1973).

## Solar Neutrino Problem

- Discrepancy between observed and calculated solar neutrino fluxes

- High energy 8B neutrino flux

**Recent results on high energy ****8****B neutrino flux**

## Recent 8B solar neutrino flux result from SNO

- Recent 8B solar neutrino flux result from SNO

- SSM calculation

- Agreement implies neutrino oscillation

- Efforts going on to improve SSM calculation.

- A few percent level effects also being considered.

**Superkamiokande and Sudbury Neutrino Observatory**

- Measured all flavors of 8B solar neutrinos and found

- agreement with Standard Solar Model Calculations.

## Uncertainties in 8B solar neutrino flux calculations 

- Uncertainties in 8B solar neutrino flux calculations

- * Z/X is the heavy element to hydrogen mass ratio

- Considering dynamic equilibrium condition at the center
- of the sun, the flux of 8B solar neutrinos

- Here R(p), R(e) are proton and electron capture rates of 7Be

- at the solar core.

- Since R(p)10-3R(e), so

***(**8**B) ***

- R(e) at the solar core is calculated using nuclear matrix element

- extracted from terrestrial 7Be decay rate measurement.

## Calculation of R(e) at the solar core

- T,ne are  solar temperature, electron density at the solar core.

- ,Z fine structure constant, atomic number of 7Be.

*A* is atomic overlap factor for terrestrial 7Be.

- 1s(0) and 2s(0) are electronic wave functions at the nucleus.

*A* computed assuming 7Be has two full 1s and 2s electrons.

*This assumption questionable for all terrestrial measurements *
*done so far.*

## Change of 7Be decay rate in different environments

**Change of ****7****Be decay rate in different environments**

- Decay rate of implanted 7Be in Al, LiF, Au, Ta,
- Graphite(C) measured and 0.4% - 0.5% change in
- decay rate found.

- We measured change in decay rate of 7Be in Au and Al2O3
- and found 0.72% change in decay rate.

- Decay rate of 7Be in different beryllium compounds
- (7BeO, 7BeF2) measured and up to 0.2% change
- in decay rate found.

## 7Be  implanted in Au and Al2O3

- 7Be was produced by bombarding a 250 μg/cm2 thick lithium fluoride (LiF) target  with a 7 MeV proton beam obtained from Variable Energy Cyclotron Centre, Kolkata.
- Reaction *via* which 7Be was produced via

**Decay scheme of**
** ****7****Be electron capture**

## 	-ray spectra from decay of 7Be implanted in 

**	********-ray spectra from decay of ****7****Be implanted in **
**      ****(a) an Al****2****O****3**** pellet **
**      ****(b) an Au foil**

- 847 keV

- 847 keV

- Differential measurement

## Result

## Check of systematic error

**Check of systematic error**

- Plot of (AAu1-AAu2)exp(­Aut) **versus time**

- A. Ray et al., Phys. Lett. B**455**, 69 (1999).

## Recent Measurements of 7Be half-life 

**Implanted in different materials.**

- E. B. Norman et al., Phys. Lett. B **519**, 15 (2001).
- Z. Liu et al., Chinese Phys. Lett. **20**, 829 (2003).
- Norman et al., found
- Half-life of 7Be in Au longer than that in Ta by (0.22 0.13)%
- Half-life of 7Be in Au longer than that in graphite by (0.38  0.09)%
- Liu et al. found the decay rate of 7Be in Au and Be are equal
- within 0.06%.

- B. Wang, C. Rolfs et al., Eur. Phys. J. A **28**, 375 (2006)
- Half-life of 7Be in Pd, In increased by (0.5 0.2)% and (0.7 0.2)%
-  at 12 K compared to room temp value. No change for Li2O at 12 K.

## Qualitative understanding of decay rate results

- Decay rate of 7Be found to be slowest in Au.
- Electron Affinity of Au = 2.3 eV

- Decay rate faster in Al, graphite, Al2O3.

- Need to consider lattice structure also.

- Electron affinity of the host medium is primarily responsible
- for changing the number of valence 2s electrons of 7Be. As a
- result, the decay rate of implanted 7Be changes in different
- host media.

## Slide 15

## TB-LMTO calculations for 7Be in a medium or 

**forming compounds**

- Tight binding linear muffin-tin orbital method calculation is
- a first principle density functional calculation.

- Initial Ansatz: Charge distribution spherical around each atom.
- Kohn-Sham equation solved self-consistently
- while minimizing total energy.
- LMTO basis states used.

- Input: Lattice dimensions, symmetry group, atomic structures.

- Output:

- computed for 7Be.

- This represents average number (ns) of 2s electrons of 7Be in
- a host medium or compound.

## Measured terrestrial 7Be decay rate lower than neutral 7Be decay rate by 2% - 2.7%.

**between**
**7****Be(n****s****=2) and ****7****Be (n****s****=0)**
**is =3.4%.**
**Agrees with Hartree’s**
**calculation( 3.31%). **

- 1

- 8

- 7

- 6

- 5

- 4

- 3

- 2

**Measured terrestrial ****7****Be decay rate lower than neutral ****7****Be decay rate by 2% - 2.7%.**

- Plot measured 7Be decay rate (λBe) versus
- ns calculated from LMTO code.

- P. Das and A. Ray, Phys. Rev C**71**, 025801(2005).

## Slide 18

## Effect of medium on L/K electron capture ratio of 7Be

- If indeed ns is significantly different from 2, then
- unlike small effect on decay rate, large decrease of L/K
- electron capture ratio expected.

- Recently, L/K capture ratio of 7Be in HgTe measured
- P. Voytas et al., Phys. Rev. Lett 88, 012501 (2002).
**Expt L/K ratio = 0.040****±0.006**
- Theoretical L/K ratio = 0.09

- For 7Be in HgTe, ns=1.155
- Zeroth order correction factor =1.155/2.0 = 0.577
**Then theoretical L/K ratio = 0.052**

- A. Ray et al., Phys. Rev C**66**, 012501®(2002).

## 7Be in a medium loses significant fraction of its 2s electrons.

- Observed decay rate change of 7Be in different media
- &
- Measured L/K electron capture ratio

##  Endohedral (7Be@C60) fullerene

**Fullerene structure**
- C60 is made of 60 carbon atoms placed in a sphere of radius 3.54 Å. The C60 molecules are arranged in a face-centered cubic structure with lattice constant 14.17 Å.

-  Endohedral (7Be@C60) fullerene

- 7Be in C60 could be endohedral (7Be@C60)
- or exohedral 7Be-C60.

- Exohedral 7Be-C60 fullerene

## Motivation

- Should be possible to determine the geometrical positions
- of 7Be in endohedral 7Be@C60 and exohedral 7Be-C60
- complexes.
- Similar decay rate study might be useful to determine
- positions of radioactive atoms in a biomolecule such as DNA
- molecule.
- Abnormal change of DNA molecules in a living cell
- might be inferred from such studies.

## Change of 7Be decay rate in atomic clusters

**	****	****such as fullerene C****60**

- T. Ohtsuki et al., measured half-life of endohedral 7Be@C60 and
- 7Be in Be metal and found the decay rate of endohedral complex
- faster by 0.83%.
- T. Ohtsuki et al., Phys. Rev Lett. **93**, 112501(2004).
- We found that the half-lifes of exohedral 7Be-C60 and that of 7Be in Au
- Are equal within 0.2%.
- Formation probability of endohedral 7Be@C60 by nuclear implantation
- technique is about 5.6%. (chemical technique)
- Half-life of endohedral 7Be@C60 shorter by over 1% compared to that
- Of 7Be in Au, in agreement in Ohtsuki et al.’s result.
- A. Ray et al., Phys. Rev C**73**, 034323(2006).

## Inferences from half-life measurements

- Lu et al. (Chem. Phys. Lett. **352**, 8, 2002) obtained from
- density functional calculations of endohedral 7Be@C60 :
- Equilibrium geometrical position of 7Be is
- at the center of C60 cage.
- Our TB-LMTO calculation putting 7Be at the center of
- C60 cage shows half-life of 7Be@C60 1.1% shorter than
- that of 7Be in Au.  Good agreement with experimental results.
- Half-life of exohedral 7Be-C60 found to be equal to that of
- 7Be in Au within 0.2%.
- TB-LMTO calculations show agreement with experimental
- results if 7Be at one of the faces of FCC C60 lattice forming
- exohedral complex with C-Be bond length about 2 Angstrom.

## Possibility of observing change of electron capture rate heavier

**	****	****nuclei in different environments**

- E. B. Norman et al., searched for change of electron capture rate
- of 40K in different media. Did not find any observable change.
- E. B. Norman et al., Phys. Lett. B **519**, 15 (2001).
- Valence shell is s-orbital. Overlap at the nucleus negligible.
- However valence s-orbitals may screen inner shells significantly.
- Removal of s-orbitals change the screening seen by inner shells. So overlap of
- inner shells at the nucleus  should increase, changing electron
- Capture rate. Might be an observable effect.
- Mossbauer isomer shifts seen in compounds of Sn, Sb and Zn.
- Svane and E. Antoncik, Phys. Rev B**34**, 1944 (1986)
- A. Svane, Phys. Rev. Lett.** 60**, 2693 (1988).

## Search for change of decay rate of  110Sn,109In in 

**                          ****Au, Pb and Al**

- 110Sn, 109Sn produced by bombarding 150 MeV 20Ne on 93Nb.
- 20Ne beam obtained from Variable Energy Cyclotron Centre, Kolkata.
- 110Sn, 109Sn implanted on Au foil and Pb pellete and Al foil.
- 110Sn(0+)  110In(1+) (4.1 hrs) 280 keV -ray
- 109Sn109In (18 minutes); 109In(9/2+)  109Cd(7/2+) (4.1 hrs)
- Spectra recorded using segmented CLOVER detectors (4 crystals).
- 60Co used to provide reference lines (1172 keV, 1332 keV).
- Ratio of 280 keV line to 60Co lines monitored. Spectra recorded
- every 15 minutes. Similarly ratio of 203 keV line to 60Co lines monitored.

## Slide 27

## Slide 28

## Slide 29

## Slide 30

## Slide 31

## Slide 32

## Slide 33

## Change of decay rate of 110Sn,  109In, in Au and Pb

- Results

- Sn [Kr]4d105s25p2

- In [Kr]4d105s25p1

- Ionization potential  0.7 eV

- Ionization potential  0.5 eV

- Measured half-life of 110Sn in Au = (4.1454 0.0062)hours
- Measured half-life of 110Sn in Pb = (4.1653  0.0085) hours
-  = (0.48  0.25)% faster in Au compared to that in Pb.
- Measured half-life of 109In in AU = (4.1427  0.0041) hours
- Measured half-life of 109In in Pb = (4.1844  0.0056) hours
-  = (1.00  0.17)% faster in Au compared to that in Pb.

- Electron Affinity of Au = 2.3 eV; of Pb = 0.35 eV

## Qualitative Explanation 

- Valence s-orbital slightly reduces overlap of inner shell orbitals at
- the nucleus.
- In Au medium, more loss of valence s-orbital of indium
- compared to when indium is in lead.
- So more overlap of inner shell orbitals at the nucleus when
- Indium is in Au medium.

## Wang, Rolfs et al.'s results

**(Eur. Phys J A 28, 375 (2006)**

- At 12 K,
- Half-life of 7Be in Pd and In increases by (0.5 0.2)% and (0.7 0.2)%
- compared to room temp values . No observable change of decay rate seen
- for 7Be in Li2O, when cooled to 12 K.
- (Large correction 2% of geometrical efficiency due to thermal contraction
- was done for this experiment.)
- Observations qualitatively consistent with their Debye Plasma model.
- (1.1% increase expected)

**	****	****	**

## Change of nuclear electron capture rate in different media: 

*       **TB-LMTO calculation vs electron plasma model*

- In a metal, Coulomb energy of quasi-free electron cloud in the
- the presence of implanted nucleus Square root of (no. of
- Quasi-free electrons per unit volume/T). (Wong, Rolfs et al.)
- Effective Q value = Q - Coulomb energy
- So effective Q value of electron capturing implanted 7Be in a metal
- reduced slightly compared to its value in insulator.
- Hence decay rate of electron capturing nucleus in metal
- would be slower compared to that in an insulator.
- Decay rate in metal should decrease at low temperature.

**Electron plasma model**

## Comparison of TB-LMTO calculation with 

**               ****electron plasma model**

- TB-LMTO calculation is a first principle density functional
- calculation and so it includes the effect of quasi-free
- electrons in a metal.

*From comparison with experimental results*
- 1) Both TB-LMTO calculation and electron plasma model explain
- increase of half-life of 7Be in metal compared to that in
- insulator. However quantitatively speaking, TB-LMTO calculation
- does a better job for comparison of decay rate change of 7Be
- in Au vs C60, Au versus Be, Al vs Al2O3, Cu vs Al2O3 etc.

## Slide 39

## 2) Electron plasma model fails to explain observed 

- 2) Electron plasma model fails to explain observed
- Change of L/K ratio of 7Be in HgTe at 60 mK.
- Electron plasma model predicts no change of L/K
- ratio of 7Be in HgTe compared to theoretical value.
- TB-LMTO calculation can quantitatively explain the
- observations.
- 3) Electron plasma model fails to explain why for heavier
- implanted nuclei such as 109In, 110Sn, the decay rate faster
- in Au compared to Pb. TB-LMTO calculation qualitatively
- successful.

**Comparison of TB-LMTO calculation with **
**                ****electron plasma model**

## Comparison of TB-LMTO calculation with 

**           ****electron plasma model**

- 4) Wang et al.’s observation of increase of 7Be half-life
- At 12K in Pd and In. (0.5  0.2)% and (0.7  0.2)%
- Qualitatively in agreement with electron plasma model.
- TB-LMTO calculation predicts no observable change.
- However experiment involves large (~2%) correction
- of geometrical efficiency of HPGe detector due to thermal
- contraction at low temperature.
- Recent measurements by TRIUMF group do not report
- any observable change of 7Be decay rate around 10 K.

## Significant change of nuclear decay rate in metals at low 

- temperature not expected.
- We observe small effect ( >1% in some cases) on
- decay rate of electron capturing nuclei implanted
- in media of high and low electron affinities.
- The effect should be observable for a large number of
- nuclei covering a large half-life range.

**TB-LMTO calculation**

## Summary

- 1) Decay rate change of 7Be in different media observed and understood
- quantitatively. Calculated 8B solar neutrino flux should change by 2-2.7%.

- 2) Substantial change of decay rate of any other electron capturing nucleus
- in different media can also be seen, if valence shell electron screens inner
- shells. Then the removal of valence shell electron can cause substantial
- change of electronic wave function at the nucleus.
*Possible Astrophysical Applications:*
- 106Cd(,)110Sn, 106Cd(,)109In cross-section measurements
*Possible practical applications: *
- 1) Sensing chemical environment, electron affinity etc. on atomic scale.
- 2) Solution of nuclear waste disposal problem probably not possible by this
- method. (C. Rolfs' idea)

## Names of my Collaborators

- 1) P. Das (VECC)
- 2) S. K. Saha (Radiochemistry Division, VECC)
- 3) S. K. Das (Radiochemistry Division, VECC)
- 4) A. Mookerjee (S. N. Bose Centre, Kolkata)
- 5) B. Sethi (Saha Institute of Nuclear Physics, Kolkata)
- 6) A. Goswami (Saha Institute of Nuclear Physics, Kolkata)
- 7) J. J. Das (NSC, Delhi)
- 8) N. Madhavan (NSC, Delhi)
- 9) P. Sugathan (NSC, Delhi)

## Slide 45

## Slide 46

## (CC)

- (NC)

- (ES)

- CC

- ES

**SNO Experiment**

## Experimental result

**Experimental result**

## Electron density at 7Be nucleus should approximately depend linearly on the number of 2s electrons of 7Be. 

- Electron capture rate of 7Be proportional to
- electron density at the nucleus.

- Hence

| SNo. | Different media | Number of 2s electrons
ns | Half-life

in days | References on measured 7Be half-life |
| --- | --- | --- | --- | --- |
| 1 | Average of BeO, BeF2, Be(C5H5)2 | 0.220 | 53.5200.050 | Johlige+70 |
| 2 | 7Be in 9Be | 0.391 | 53.3760.016 | Liu+2003 |
| 3 | 7Be in Au | 0.416 | 53.3110.042 | Norman+
2001 |
| 4 | 7Be in Ta | 0.596 | 53.1950.052 | Norman+
2001 |
| 5 | 7Be in Al | 0.625 | 53.1700.070 | Lagoutine+
75 |
| 6 | 7Be in Graphite | 0.680 | 53.1070.022 | Norman+
2001 |
| 7 | 7Be in LiF | 0.725 | 53.1200.070 | Jaeger+96 |
| 8 | 7Be in Al2O3 | 0.786 | 52.9270.056 | This work &
Nor+2001 |

## Separated organic fraction dried up in a plastic crucible.

- Source of endohedral 7Be@C60 prepared.
- Two HPGe detectors (efficiency 30%) used to count
- 478 keV -rays from endohedral 7Be@C60 source and
- 7Be in Au source for 3 months.
- Result: Half-life of 7Be@C60 source shorter than that of
- 7Be in Au by (3.3 2.3)%.
- Comparing Ohtsuki et al. (PRL **93**,112501, 2004) and
- Norman et al.’s (Phys. Lett. **B519,**15,2001) results:
- Half-life of 7Be@C60 source shorter than that of
- 7Be in Au by (1.2 0.12)%.

**Half-life Measurement**

## Chemical separation of endohedral 7Be@C60

- Irradiated fullerene catcher dissolved in 5ml1,2,4 trichlorobenzene. Dissolved C60 and endohedral 7Be@C60 form purple color
- solution.

- Equal volume 6N HCl acid containing carriers added.
- Shaken for 5 minutes. Organic(purple color), aqueous
- (Colorless)fractions separated. Organic fraction
- contained endohedral 7Be@C60.
- Separated organic, aqueous fractions counted using
- HPGe detectors.

**Endohedral ****7****Be@C****60**** production = 5.6%.**
**Remaining 94.4% exohedral ****7****Be-C****60**** production.**

- Separated organic fraction dried up in a plastic crucible. 7Be@C60 source.