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. 7 Be 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 7 Be 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 7 Be 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 8 B neutrino flux Recent results on high energy 8 B neutrino flux

Recent 8 B 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 8 B solar neutrinos and found agreement with Standard Solar Model Calculations.

Uncertainties in 8 B solar neutrino flux calculations * Z/X is the heavy element to hydrogen mass ratio Sources of uncertaintyUncertainty in 8 B neutrino flux pp He He 4 He Be+p0.038 Z/X * Luminosity0.028 Opacity0.052 Age0.006 Diffusivity0.040

Effect of 7 Be decay rate on 8 B solar neutrino flux Considering dynamic equilibrium condition at the center of the sun, the flux of 8 B solar neutrinos Here R(p), R(e) are proton and electron capture rates of 7 Be at the solar core. Since R(p)  R(e), so  ( 8 B)  R(e) at the solar core is calculated using nuclear matrix element extracted from terrestrial 7 Be decay rate measurement.

Calculation of R(e) at the solar core T,n e are solar temperature, electron density at the solar core. ,Z fine structure constant, atomic number of 7 Be. A is atomic overlap factor for terrestrial 7 Be.  1s (0) and  2s (0) are electronic wave functions at the nucleus. A computed assuming 7 Be has two full 1s and 2s electrons. This assumption questionable for all terrestrial measurements done so far.

Change of 7 Be decay rate in different environments Decay rate of implanted 7 Be 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 7 Be in Au and Al 2 O 3 and found 0.72% change in decay rate. Decay rate of 7 Be in different beryllium compounds ( 7 BeO, 7 BeF 2 ) measured and up to 0.2% change in decay rate found.

7 Be implanted in Au and Al 2 O 3 7 Be was produced by bombarding a 250 µg/cm 2 thick lithium fluoride (LiF) target with a 7 MeV proton beam obtained from Variable Energy Cyclotron Centre, Kolkata. Reaction via which 7 Be was produced via Decay scheme of 7 Be electron capture

 -ray spectra from decay of 7 Be implanted in (a) an Al 2 O 3 pellet (b) an Au foil 847 keV Differential measurement

Plot of versus time Result

Check of systematic error Plot of (A Au1 -A Au2 )exp( ­ Au t) versus time A. Ray et al., Phys. Lett. B455, 69 (1999).

Recent Measurements of 7 Be 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 7 Be in Au longer than that in Ta by (0.22  0.13)% Half-life of 7 Be 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 7 Be 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 Li 2 O at 12 K.

Qualitative understanding of decay rate results Decay rate of 7 Be found to be slowest in Au. Electron Affinity of Au = 2.3 eV Decay rate faster in Al, graphite, Al 2 O 3. Need to consider lattice structure also. Electron affinity of the host medium is primarily responsible for changing the number of valence 2s electrons of 7 Be. As a result, the decay rate of implanted 7 Be 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) 7 Be implanted in1 st medium2 nd medium Au and Al (0.27  0.15)% Norman+2001, Lagoutine+75 Au and Ta (0.22  0.13)% Norman+2001 Au and C(graphite) (0.38  0.09)% Norman+2001 Au and Cd/Zn negative (0.57  0.32)% This work Ta and C(graphite) (0.17  0.11)% Norman+2001 Au and LiF2.308~0 (0.36  0.15)% Norman+2001, Jaeger+96 Al and LiF0.441~0 (0.10  0.20)% Lagoutine+75, Jaeger+96 Au and Al 2 O ~0 (0.72  0.07)% This work Au and C (0.08  0.22)% This work Au and 9 Be2.308~0 (0.02  0.06)% Liu+2003 Ta and Al (0.05  0.13)% Norman+2001, Lagoutine+75 C 60 and C(graphite) (0.31  0.13)% This work, Norman+2001 (b) 7 Be compounds 7 BeF 2 and 7 BeO Fluorine Oxygen (  )% (  )% (  )% Leininger+49 Kraushaar+53 Johlige+70

TB-LMTO calculations for 7 Be 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 7 Be. This represents average number (n s ) of 2s electrons of 7 Be in a host medium or compound.

Decay rate difference between 7 Be(n s =2) and 7 Be (n s =0) is =3.4%. Agrees with Hartree’s calculation( 3.31%) Measured terrestrial 7 Be decay rate lower than neutral 7 Be decay rate by 2% - 2.7%. Plot measured 7 Be decay rate (λ Be ) versus n s calculated from LMTO code. P. Das and A. Ray, Phys. Rev C71, (2005).

Difference in Half-life of 7 Be in Percentage increase of half-life of 7 Be in1 st medium compared to that in 2 nd medium Method of 7 Be implantation in the hosts Experimental ValueCalculated value Au and Al 2 O 3 (0.72  0.07)% 0.61% Both using proton irradiation Al and LiF (0.1  0.2)% 0.17% Both using proton irradiation Au and 9 Be (0.02  0.06)% 0.04% Au and Ta (0.22  0.13)% 0.30% Both using heavy ion 7 Li irradiation Au and C(graphite) (0.38  0.09)% 0.44% Both using heavy ion 7 Li irradiation Ta and C(graphite) (0.17  0.11)% 0.14% Au and Al (0.27  0.15)% 0.35% Using 7 Li irradiation in 1st medium and proton irradiation in 2nd medium Au and LiF (0.36  0.15)% 0.51% Au and Cd/Zn (0.57  0.32)% 0.42% Both using 7 Be beam 7 BeO and 7 BeF 2 (hex) (  )% 0.124% The compounds were prepared following chemical processes (  )% 7 BeO and 7 BeF 2 (tetra) (  )% 0.115%

Effect of medium on L/K electron capture ratio of 7 Be If indeed n s 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 7 Be in HgTe measured P. Voytas et al., Phys. Rev. Lett 88, (2002). Expt L/K ratio = 0.040±0.006 Theoretical L/K ratio = 0.09 For 7 Be in HgTe, n s =1.155 Zeroth order correction factor =1.155/2.0 = Then theoretical L/K ratio = A. Ray et al., Phys. Rev C66, ®(2002).

7 Be in a medium loses significant fraction of its 2s electrons. Observed decay rate change of 7 Be 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%.  ( 8 B) , calculated  ( 8 B) decreases by 2 – 2.7%. Since

Fullerene structure C 60 is made of 60 carbon atoms placed in a sphere of radius 3.54 Å. The C 60 molecules are arranged in a face-centered cubic structure with lattice constant Å. Endohedral ( 7 60 ) fullerene Applications in cluster studies Properties of endohedral fullerene 60 and exohedral fullerene complexes. 7 Be in C 60 could be endohedral ( 7 60 ) or exohedral 7 Be-C 60. Exohedral 7 Be-C 60 fullerene

Motivation Should be possible to determine the geometrical positions of 7 Be in endohedral 7 60 and exohedral 7 Be-C 60 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 7 Be decay rate in atomic clusters such as fullerene C 60 T. Ohtsuki et al., measured half-life of endohedral 7 60 and 7 Be in Be metal and found the decay rate of endohedral complex faster by 0.83%. T. Ohtsuki et al., Phys. Rev Lett. 93, (2004). We found that the half-lifes of exohedral 7 Be-C 60 and that of 7 Be in Au Are equal within 0.2%. Formation probability of endohedral 7 60 by nuclear implantation technique is about 5.6%. (chemical technique) Half-life of endohedral 7 60 shorter by over 1% compared to that Of 7 Be in Au, in agreement in Ohtsuki et al.’s result. A. Ray et al., Phys. Rev C73, (2006).

Inferences from half-life measurements Lu et al. (Chem. Phys. Lett. 352, 8, 2002) obtained from density functional calculations of endohedral 7 60 : Equilibrium geometrical position of 7 Be is at the center of C 60 cage. Our TB-LMTO calculation putting 7 Be at the center of C 60 cage shows half-life of % shorter than that of 7 Be in Au. Good agreement with experimental results. Half-life of exohedral 7 Be-C 60 found to be equal to that of 7 Be in Au within 0.2%. TB-LMTO calculations show agreement with experimental results if 7 Be at one of the faces of FCC C 60 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 40 K 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 110 Sn, 109 In in Au, Pb and Al 110 Sn, 109 Sn produced by bombarding 150 MeV 20 Ne on 93 Nb. 20 Ne beam obtained from Variable Energy Cyclotron Centre, Kolkata. 110 Sn, 109 Sn implanted on Au foil and Pb pellete and Al foil. 110 Sn(0 + )  110 In(1 + ) (  4.1 hrs) 280 keV  -ray 109 Sn  109 In (18 minutes); 109 In(9/2 + )  109 Cd(7/2 + ) (  4.1 hrs) Spectra recorded using segmented CLOVER detectors (4 crystals). 60 Co used to provide reference lines (1172 keV, 1332 keV). Ratio of 280 keV line to 60 Co lines monitored. Spectra recorded every 15 minutes. Similarly ratio of 203 keV line to 60 Co lines monitored.

Change of decay rate of 110 Sn, 109 In, in Au and Pb Results Sn  [Kr]4d 10 5s 2 5p 2 In  [Kr]4d 10 5s 2 5p 1 Ionization potential  0.7 eV Ionization potential  0.5 eV Measured half-life of 110 Sn in Au = (  )hours Measured half-life of 110 Sn in Pb = (  ) hours  = (0.48  0.25)% faster in Au compared to that in Pb. Measured half-life of 109 In in AU = (  ) hours Measured half-life of 109 In in Pb = (  ) 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 7 Be 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 7 Be in Li 2 O, 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 7 Be 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 7 Be in metal compared to that in insulator. However quantitatively speaking, TB-LMTO calculation does a better job for comparison of decay rate change of 7 Be in Au vs C 60, Au versus Be, Al vs Al 2 O 3, Cu vs Al 2 O 3 etc.

2) Electron plasma model fails to explain observed Change of L/K ratio of 7 Be in HgTe at 60 mK. Electron plasma model predicts no change of L/K ratio of 7 Be 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 109 In, 110 Sn, 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 7 Be 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 7 Be in different media observed and understood quantitatively. Calculated 8 B 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: 106 Cd( ,  ) 110 Sn, 106 Cd( ,  ) 109 In 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)

(CC) (NC) (ES) CC ES SNO Experiment

Difference between the half-lives of 7 Be implanted in Percentage increase in Half-life of 7 Be in 1 st medium compared to that in 2 nd medium in column-1 Au and Al 2 O 3 (0.72  0.07)% Au and Zn/Cd (0.57  0.32)% Au and Fullerene (C 60 ) (0.08  0.22)% Experimental result

Electron density at 7 Be nucleus should approximately depend linearly on the number of 2s electrons of 7 Be. Electron capture rate of 7 Be proportional to electron density at the nucleus. Hence SNo.Different mediaNumber of 2s electrons n s Half-life   in days References on measured 7 Be half-life 1Average of BeO, BeF 2, Be(C 5 H 5 )  Johlige Be in 9 Be  Liu Be in Au  Norman Be in Ta  Norman Be in Al  Lagoutine Be in Graphite  Norman Be in LiF  Jaeger Be in Al 2 O  This work & Nor+2001

Separated organic fraction dried up in a plastic crucible. Source of endohedral 7 60 prepared. Two HPGe detectors (efficiency 30%) used to count 478 keV  -rays from endohedral 7 60 source and 7 Be in Au source for 3 months. Result: Half-life of 7 60 source shorter than that of 7 Be 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 7 60 source shorter than that of 7 Be in Au by (1.2  0.12)%. Half-life Measurement

Chemical separation of endohedral 7 60 Irradiated fullerene catcher dissolved in 5ml1,2,4 trichlorobenzene. Dissolved C 60 and endohedral 7 60 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 Separated organic, aqueous fractions counted using HPGe detectors. Endohedral 7 60 production = 5.6%. Remaining 94.4% exohedral 7 Be-C 60 production. Separated organic fraction dried up in a plastic crucible source.