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 C2, 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 ProblemDiscrepancy between observed and calculated solar neutrino fluxes

High energy 8B neutrino flux

Recent results on high energy 8B neutrino flux

12610.)(38.0.)(27.021.5 scmsyststatSNONC

Recent 8B solar neutrino flux result from SNO

12601.181.0 1005.5

scmSSMSSM 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

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

Sources of uncertainty Uncertainty in 8B neutrino flux

pp 0.0403He3He 0.0213He4He 0.0757Be+p 0.038

Z/X* 0.200

Luminosity 0.028

Opacity 0.052

Age 0.006

Diffusivity 0.040

Effect of 7Be decay rate on 8B solar neutrino flux

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

)()(

)()(8

pReR

pRB

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

)(

1

eR

at the solar core.

Since R(p)10-3R(e), so (8B)

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

elabsun ZnkT

AeReR

2/1

1 2)()(

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.

2

2

2

1200

41

ssA

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

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 vianBeLip 77

Decay scheme of 7Be electron capture

-ray spectra from decay of 7Be implanted in

(a) an Al2O3 pellet

(b) an Au foil

847 keV

847 keV

Differential measurement

tAlOAu

AueAA )(

)()( 000AlOAuAlO AAtA

AuAlO

( A

Au -

AA

lO )

exp

(A

u t

)

Time (days)

(2b)

(2a)

0 20 40 60 80 100-140000

-120000

-100000

-80000

-60000

150000

200000

250000

300000

350000

400000

)00072.000705.0(

Au

)0016.00078.0(

Au

)0007.00072.0(

Au

A(

tAlOAu

AueAA )( Plot of versus time

Result

(AA

u1-

AA

u2)e

xp(

Aut)

Time (days)

0 10 20 30 4080000

84000

88000

92000

96000

100000

104000

Check of systematic error

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

A. Ray et al., Phys. Lett. B455, 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 aresult, the decay rate of implanted 7Be changes in different

host media.

Difference between the half-lives of

Electron affinity* in (eV)

Observed half- life difference

100%

References on e half-life

measured (a) 7Be implanted in 1st medium 2nd medium

Au and Al 2.308 0.441 (0.270.15)% Norman+2001, Lagoutine+75

Au and Ta 2.308 0.322 (0.220.13)% Norman+2001

Au and C(graphite) 2.308 1.25 (0.380.09)% Norman+2001

Au and Cd/Zn 2.308 0-negative (0.570.32)% This work

Ta and C(graphite) 0.322 1.25 (0.170.11)% Norman+2001

Au and LiF 2.308 ~0 (0.360.15)% Norman+2001, Jaeger+96

Al and LiF 0.441 ~0 (0.100.20)% Lagoutine+75, Jaeger+96

Au and Al2O3 2.308 ~0 (0.720.07)% This work

Au and C60 2.308 2.6 (0.080.22)% This work

Au and 9Be 2.308 ~0 (0.020.06)% Liu+2003

Ta and Al 0.322 0.441 (0.050.13)% Norman+2001, Lagoutine+75

C60 and C(graphite) 2.6 1.25 (0.310.13)% This work, Norman+2001

(b) 7Be compounds7BeF2 and 7BeO

 

Fluorine-3.40

Oxygen-1.46

(0.13750.0053)%(0.06090.0055)%(0.11300.0058)%

Leininger+49Kraushaar+53

Johlige+70

TB-LMTO calculations for 7Be in a medium or forming compounds

Tight binding linear muffin-tin orbital method calculation isa 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: 2

2sBetotal computed for 7Be.

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

Decay rate differencebetween

7Be(ns=2) and 7Be (ns=0)is =3.4%.

Agrees with Hartree’scalculation( 3.31%).

ns

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Be(

day

-1)

0.01292

0.01296

0.01300

0.01304

0.01308

0.01312

1

8

7

6

54

3

2

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

Plot measured 7Be decay rate (λBe) versusns calculated from LMTO code.

P. Das and A. Ray, Phys. Rev C71, 025801(2005).

Difference inHalf-life of

7Be in

Percentage increase of half-life of 7Be in1st medium compared

to that in 2nd medium

Method of 7Be implantation in the hosts

Experimental Value Calculated value

Au and Al2O3 (0.720.07)% 0.61% Both using proton irradiation

Al and LiF (0.10.2)% 0.17% Both using proton irradiation

Au and 9Be (0.020.06)% 0.04%Au and Ta (0.220.13)% 0.30% Both using heavy

ion 7Li irradiation

Au and C(graphite) (0.380.09)% 0.44% Both using heavy ion 7Li irradiation

Ta and C(graphite) (0.170.11)% 0.14%Au and Al (0.270.15)% 0.35% Using 7Li irradiation in

1st medium and proton irradiation in 2nd medium

Au and LiF (0.360.15)% 0.51%Au and Cd/Zn (0.570.32)% 0.42% Both using 7Be

beam7BeO and 7BeF2 (hex) (0.13750.0053)% 0.124% The compounds were

prepared following chemical processes(0.06090.0053)%

7BeO and 7BeF2 (tetra) (0.11300.0058)% 0.115%

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 measuredP. Voytas et al., Phys. Rev. Lett 88, 012501 (2002).

Expt L/K ratio = 0.040±0.006Theoretical L/K ratio = 0.09

For 7Be in HgTe, ns=1.155Zeroth order correction factor =1.155/2.0 = 0.577

Then theoretical L/K ratio = 0.052A. Ray et al., Phys. Rev C66, 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

Overlap factor A decreases by 2% to 2.7% in different media.

R(e) increases by 2 – 2.7% .

elabsun ZnkT

AeReR

2/1

1 2)()(

)(

1

eR(8B) , calculated (8B) decreases by

2 – 2.7%. Since

Fullerene structureFullerene 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

Applications in cluster studies

Properties of endohedral fullerene Be@C60 and exohedral fullerene complexes.

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

Exohedral 7Be-C60 fullerene

Motivation

Should be possible to determine the geometrical positionsof 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 DNAmolecule.Abnormal change of DNA molecules in a living cell might be inferred from such studies.

Change of 7Be decay rate in atomic clusterssuch as fullerene C60

T. Ohtsuki et al., measured half-life of endohedral 7Be@C60 and 7Be in Be metal and found the decay rate of endohedral complexfaster 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 AuAre equal within 0.2%.

Formation probability of endohedral 7Be@C60 by nuclear implantationtechnique is about 5.6%. (chemical technique)

Half-life of endohedral 7Be@C60 shorter by over 1% compared to thatOf 7Be in Au, in agreement in Ohtsuki et al.’s result.

A. Ray et al., Phys. Rev C73, 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 isat 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 thanthat 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 heaviernuclei 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.A. Svane and E. Antoncik, Phys. Rev B34, 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

109Sn109In (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 recordedevery 15 minutes. Similarly ratio of 203 keV line to 60Co lines monitored.

Au Host

Energy (keV)0 300 600 900 1200 1500

CO

UN

TS

100

1000

10000

100000

1000000203 keV

280 keV

1172

keV

1332

keV

Al Host

Energy (keV)

0 300 600 900 1200 1500

CO

UN

TS

100

1000

10000

100000 203 keV

280 keV

1172

keV

1332

keV

109In in Au

Time (min)

0 100 200 300 400 500 600 700

N(

203)

/N(

1172

+13

32)

0

1

2

Time(min)

0 100 200 300 400 500 600

% a

ge

de

via

tio

n f

rom

be

st f

it

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

data

Time(min)

0 100 200 300 400 500 600 700

N(203)/N

(1172

+1332)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Time(min)

400 450 500 550 600

N(203

)/N

(11

72+13

32)

0.20

0.25

0.30

0.35

Time(min)

0 50 100 150 200

N(203

)/N

(11

72+13

32)

0.6

0.7

0.8

0.9

1.0

109In in Au

109In in Pb

Time(min)

0 50 100 150 200

N(20

3)/N

(11

72+13

32)

0.6

0.7

0.8

0.9

1.0

Time(min)

400 450 500 550 600

N(203)/N

(1172+1332)

0.20

0.25

0.30

0.35

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)hoursMeasured 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) hoursMeasured 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 atthe nucleus.

In Au medium, more loss of valence s-orbital of indiumcompared 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 seenfor 7Be in Li2O, when cooled to 12 K.

(Large correction 2% of geometrical efficiency due to thermal contractionwas 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 thethe 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 energySo effective Q value of electron capturing implanted 7Be in a metalreduced 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 explainincrease of half-life of 7Be in metal compared to that in insulator. However quantitatively speaking, TB-LMTO calculationdoes 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.

Comparison of TB-LMTO vs Electron Plasma model

0

0.2

0.4

0.6

0.8

-0.5 0 0.5 1

% change (Experiment)

% c

ha

ng

e (

Th

eo

ry)

Expt vs TB-LMTO

Expt vs Electronplasma model

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/Kratio of 7Be in HgTe compared to theoretical value.

TB-LMTO calculation can quantitatively explain theobservations.

3) Electron plasma model fails to explain why for heavier implanted nuclei such as 109In, 110Sn, the decay rate fasterin Au compared to Pb. TB-LMTO calculation qualitativelysuccessful.

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-lifeAt 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 thermalcontraction at low temperature.

Recent measurements by TRIUMF group do not reportany 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 implantedin media of high and low electron affinities.

The effect should be observable for a large number ofnuclei covering a large half-life range.

TB-LMTO calculation

Summary

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

2) Substantial change of decay rate of any other electron capturing nucleusin different media can also be seen, if valence shell electron screens innershells. 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 thismethod. (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)

eppde

xx npd

ee xx

(CC)

(NC)

(ES)

CC

ES

SNO Experiment

Difference between the half-lives of 7Be implanted in

Percentage increase in Half-life of 7Be in 1st medium compared to that in 2nd medium in column-1

Au and Al2O3 (0.720.07)%

Au and Zn/Cd (0.570.32)%

Au and Fullerene (C60)

(0.080.22)%

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 toelectron density at the nucleus.

Hence sdecay nSNo. Different media Number of 2s

electronsns

Half-life

in days

References on measured 7Be half-life

1 Average of BeO, BeF2,

Be(C5H5)2

0.220 53.5200.050 Johlige+70

2 7Be in 9Be 0.391 53.3760.016 Liu+2003

3 7Be in Au 0.416 53.3110.042 Norman+2001

4 7Be in Ta 0.596 53.1950.052 Norman+2001

5 7Be in Al 0.625 53.1700.070 Lagoutine+75

6 7Be in Graphite 0.680 53.1070.022 Norman+2001

7 7Be in LiF 0.725 53.1200.070 Jaeger+96

8 7Be in Al2O3 0.786 52.9270.056 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) andNorman 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 7Be@C60 production = 5.6%.Remaining 94.4% exohedral 7Be-C60 production.

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