Journals published by the American Physical Society can be found at http://publish.aps.org/We report a clear demonstration of the effect of hyperfine quenching of a forbidden transition by direct comparison of the lifetimes of the 2 3P0 level in the heliumlike isotopes Ni-61(26+) and Ni-58(26+). We find the quenched lifetime of the 2 3P0 level in Ni-61(26+) to be 470(50) ps. From this we deduce the 2 3P0-2 3P1 energy splitting to be 2.33(15) eV. We also report a measurement of the lifetime of the 2 3P2 level in Ni-58(26+), which is found to be 70(3) ps

Berrahmansour, N.

Church, David A.

Curtis, L. J.

Dunford, R. W.

Last, J.

Liu, C. J.

Vondrasek, R.

English

Texas A&amp;M Repository

PHYSICAL REVIEW A VOLUME 44, NUMBER 1 I JULY 1991Direct observation of hyperfine quenching of the 2 I'o level in heliumlike nickelR. W. Dunford, C. J. Liu, J. Last, N. Berrah-Mansour, and R. VondrasekPhysics Division, Argonne National Laboratory, Argonne, Illinois 60439D. A. ChurchDepartment ofPhysics, Texas A d'cM University, College Station, Texas 77843L. J. CurtisDepartment of Physics and Astronomy, University of Toledo, Toledo, Ohio 43606(Received 11 February 1991)We report a clear demonstration of the eft'ect of hyperfine quenching of a forbidden transition bydirect comparison of the lifetimes of the 2'Po level in the heliumlike isotopes 'Ni + and ' Ni . Wefind the quenched lifetime of the 2'Po level in 'Ni + to be 470(50) ps. From this we deduce the2 Po—2 P& energy splitting to be 2.33(15) eV. We also report a measurement of the lifetime of the 2 'P2level in Ni +, which is found to be 70(3) ps.One of the most interesting phenomena in the theory ofhighly forbidden transitions is the effect of hyperfinequenching, whereby mixing by the hyperfine interactioncan significantly alter the lifetimes of the levels. Thephenomenon was first discussed by Bowen [1] in 1930,who pointed out that the substantial strength that wasobserved in the 6S21SD-6S6p 3p2 line at 2270 A in thespectrum of Hg I was primarily due to E1 radiationcaused by coupling with the nuclear spin and not to pos-sible higher-order multipole radiation as had been sug-gested [2]. Thus both the S and J labels are only nominalhere. Bowen's conclusion was confirmed in 1937 by Mro-zowski [3], who experimentally observed the6s 'So —6s6p Po line at 2656 A in Hg I. This transitionwould be rigorously forbidden to all multipole orders ofsingle-photon decay in an atom with a spinless nucleus bythe J=0~J=0 selection rule of angular-momentumconservation. Mrozowski [3] attributed the appearanceof this line to coupling between the magnetic moments ofthe spin and orbit of the electron and the spin of the nu-cleus. A discussion of these transitions in Mg, Zn, Cd,and Hg has been given by Garstang [4].In the two-electron case of the helium isoelectronic se-quence, the existence of the 1s2s S& —1s2p Po E1 transi-tion provides a decay channel not available to thealkaline-earth sequences. Thus the presence or absenceof the hyperfine quenched 1s 'So —1s2p Po channel canbe detected in the triplet-to-triplet channel because thePo level has a lifetime that is sensitive to the nuclearspin.Hyperfine quenching in the helium isoelectronic se-quence was first observed by Gould, Marrus, and Mohr[5] who found that hyperfine effects contributed appreci-ably to the lifetime of the 2 P2 level in V ' . Calcula-tions of decay rates for the 2 Po level in odd-Z nucleiZ =9 through Z =29 have been made by Mohr [6]. Re-cently, Marrus et al. [7] exploited the effect of hyperfinemixing to provide a determination of the 2 P& —2 Pofine-structure splitting in heliumlike Ag +, based on ex-tensive calculations presented by Indelicato, Parente, andMarrus [8]. This experiment is significant because themixed levels are nearly degenerate, and the method pro-vides a sensitive means for measuring this energy split-ting.In this paper we report a direct observation of theeffect of hyperfine quenching by comparing the lifetimesof n =2 decays in the two isotopes 'Ni and Ni. Theisotope Ni has nuclear spin I =0 and so will not beaffected by hyperfine quenching, whereas 'Ni has I =—,',and hyperfine effects are important to understanding thelifetimes of the excited states. By using theoretical valuesfor the lifetimes of the unperturbed levels and the matrixelements of the perturbation, our measurement of thequenched lifetime can be used to determine the2 Po —2 P, level splitting. Alternatively, since the nickelmeasurement is not as sensitive to the fine-structure split-tings as is the Ag + measurement of Marrus et al. [7],our results can be used to confirm the theory of the un-quenched lifetimes and hyperfine-mixing matrix elementsassuming the energy splittings are known. In this way,our work complements the Ag + work.Figure 1 shows the low-lying atomic energy levels [9]of heliumlike Ni + and their theoretical lifetimes. The2 'P, and 2 P, levels are mixed by the spin-orbit interac-tion and decay primarily to the ground state by allowedEl transitions [10]. All other levels in the spinless Niisotope decay by higher multipole radiation or by two-photon emission and so are relatively long lived.Hyperfine quenching in the isotope 'Ni mixes the meta-stable levels 2 P2 and 2 Po with the short-lived 2 P, and2 'P, states. Munger [11] has calculated the quenchedlifetimes for the 2 P2 hyperfine levels. The I' =—', level isunperturbed and so has the same lifetime (71.0 ps) as the2 P2 level in Ni +. The I'= —,', —„'—,' levels have life-times of 69.7, 70.0, and 70.7 ps, respectively, and are onlyslightly affected by hyperfine quenching. Our experiment764 1991 The American Physical SocietyBRIEF REPORTS 7657.85— IOC3~ 7.75—12 S012 P7.SO—E11.65 fs154 s M2+E1(h f s )71 ps213fs i2.5 ns(0.45 ns)5IO—1061N1lF 1r 32.3 ns~ IOO7.70— 2E1 (hfs) IOO —1 S, ~' (61) 58 . 26+IOFIG. 1. Electronic energy-level diagram for the low-lyinglevels of heliumlike Ni + showing decay modes and lifetimes.E&(hfs) refers to transitions in 'Ni + induced by the hyperfineinteraction. The 2'Po level has a lifetime of 2.5 ns in ' Niand 0.45 ns in 'Ni4 6 8ENERGY (keV)IO l2FIG. 2. Si(Li) detector spectra for three different foil-detectordistances corresponding to times since excitation of 0.27, 0.84,and 2.8 ns.is not sensitive to these small changes. Qn the otherhand, there is a substantial effect on the lifetime of the2 Po level. The theoretical lifetime [5] for this state is 2.5ns in Ni, while in 'Ni values of 0.443 ns [11],0.450 ns[12], and 0.464 ns [13] have been obtained. Thedifference between Ni and 'Ni is readily observed inour experiment.The highly ionized nickel beams were obtained fromthe Argonne Tandem Linac (ATLAS). The ion sourcewas charged with enriched isotopes of 'Ni (42 at. %%uo )an dNi (58 at. %). First the Linac was tuned with the Niisotope for a beam energy of 340 MeV. The ions wereprestripped with a 200-pg/cm carbon foil, and the 26+charge state (15% of the beam) was magnetically ana-lyzed and directed to the experimental area. The switchto the 'Ni isotope was accomplished by increasing theTandem energy so the velocity of the ions delivered to thelinac was the same as it was for Ni. In this way, thelinac parameters remained substantially the same, and inparticular, the final velocity of the ions was the same forboth isotopes. The velocity of the ions was determinedwith an uncertainty of 0.1%%uo by a time-of-Aight velocityanalyzer. Since this analyzer was between the linac andthe 200-pg/cm foil, a correction had to be made for theenergy loss in the foils. The final uncertainty in the ve-locity determination was 0.5%%uo. The time-of-fiight mea-surements verified that the velocity was the same for thetwo isotopes within this error.In the experimental area a thin (42 pg/cm ) carbon foilwas moved relative to two fixed Si(Li) x-ray detectors,which were collimated so as to observe a region of 5 mmalong the beam. The foil was mounted to a precisiontranslation stage which measured the position to an accu-racy of 10 pm. Decay curves were obtained by recordingspectra as a function of foil-detector distance. A lowerresolution silicon x-ray detector was attached to the tar-get holder and used for normalization. It was collimatedso as to observe a region along the beam axis from 5 to 15mm from the target.Spectra from one of the Si(Li) detectors are shown inFig. 2 for three different foil-detector distances corre-sponding to delay times after excitation of 0.27, 0.84, and2.8 ns. Prominent features include peaks at 7.8 and 1.4keV and a broad continuum in between. There are alsosmaller peaks to the high-energy side of the intensepeaks. The 1.4-keV peak corresponds to transitions fromn =3 to 2 in lithiumlike and heliumlike ions. The broadcontinuum is largely due to the two-photon decays of the2 So level in heliumlike ions [14]. This component has alifetime of 154 ps and is absent in the 2.8-ns spectrum.Of most interest for the present work is the 7.8-keV line.Apart from a small contribution due to cascade repopula-tion of the short-lived 2 P, and 2 'P, levels, this line con-sists of a blend of transitions from the 2 P2 2 Pp and2 S& levels. The linewidth, which is dominated by the in-trinsic resolution of the Si(Li) detectors (about 220 eV), isinsufficient to resolve the individual transitions. At laterdelay times, the line narrows slightly and shifts to lowerenergy. This is due to depletion of the somewhat fasterdecaying 2 Pz level, which lies 55 eV higher in energythan the 2 S& level.The number of counts in the 7.8-keV line for the twoSi(Li) detectors and the normalization detector are deter-mined at each foil-detector distance by fitting them to aGaussian plus a linear background. The width and posi-tion are taken as free parameters in order to allow for thefact that the line is a blend of transitions from states withdifferent lifetimes. We then multiply the Si(Li) detectorcounts at each foil position by a factor that is the averagenormalization count divided by the normalization countat that position. The resulting normalized decay curvesfor one of the two Si(Li) detectors are shown in Fig. 3.The upper plot is the decay curve for the case of the spin-less Ni. These data are fitted we11 by two exponentialsand a constant background. The short-lived componentis identified with the M2 decay of the 2 P2 state. From766 BRIEF REPORTSIO I I l I I I l I I I IfO5lO I ~I.2'lo—p X 20lTlME SlNCE EXClTATiON (ns)IO I 1 I I & s s c c I t s e s2the fits to the data from the two detectors, we obtain alifetime of 70(3) ps for this state in agreement with thetheoretical values of Munger [11] (71 ps) and Gould,Marrus, and Mohr [5] (72 ps). The other component inthe Ni decay curve has contributions from both the2 S& and the 2 Po states. The lifetimes of these statesare 2.3 and 2.5 ns, respectively, and they are too close tobe resolved as separate components. Although a good fitis obtained and the resulting lifetime for this componentis consistent with the theoretical lifetimes, the ambiguityof the two contributions makes it difficult to make an ac-curate determination of either the unquenched 2 Po life-tiIne or the 2 S, lifetime.The decay curve for the 'Ni isotope, which was takenunder identical conditions, shows a significant differencein shape compared to that of the Ni data and does notfit to two exponentials (the reduced y for a two-exponential fit is 9.8). In order to fit these data, three ex-FIG. 3. Decay curves showing normalized count rate vs timesince excitaiton for Ni + (upper) and 'Ni + (lower). Thesolid lines are the fits to the data. The dashed lines show contri-butions to the fit from the 2 'I'o level and the 2 'P&+2 'S& levels.ponentials are needed. Since our Ni data confirm thetheoretical value for the lifetime of the 2 Pz level and re-cent data have confirmed agreement with theoreticalvalues for the 2 Si lifetime [15,16], we base our deter-mination of the lifetime of the 2 Po state in 'Ni on afive-parameter fit. The five parameters are the ampli-tudes for the three exponentials, the lifetime of the 2 Pplevel and a constant background. The lifetimes of the2 Pz and 2 S, levels are fixed at the theoretical values.This fit is shown as the solid line in the lower plot of Fig.3, and it is in excellent agreement with the data. Alsoshown in the lower part of Fig. 3 is the fitted curve withthe 2 Po component left out. The shape of this curve isclose to that of the Ni data. The values for the 2 Polifetime in 'Ni obtained from these fits agree for the twodetectors and so we simply average the two values to ob-tain 470(50) ps. We also tried fitting the data with otherfitting procedures, including repeating the fit to three ex-ponentials but allowing the 2 Pz and 2 S& lifetimes to befree parameters. All of the fits are consistent with the re-sults of the five-parameter fits which we chose for ourfinal results. The quoted error in the determination ofthe 2 Po lifetime has been increased in order to accountfor the uncertainty inherent in using a many-componentfitting function. Errors from cascade contributions areestimated to be less than 1%.Our results for the quenched lifetime of the 2 Po levelin 'Ni + are in agreement with the various purelytheoretical calculations [11,12,13] and provideconfirmation of the theory for the unquenched lifetimes,mixing matrix elements, and energy levels. Another wayto interpret the data, suggested by the work of Marruset al. [7], is to use theoretical values for the matrix ele-ments and unquenched lifetimes and use the experimentaldata to determine the 2 Po —2 P, fine-structure splittingb.Eo, ~. Using the matrix elements and level widths cal-culated by Indelicato [13] and the procedure described inRef. 7, we find that our value for the quenched lifetime470(50) ps corresponds to a fine-structure splitting of~b,Eo, ~=2.33(15) eV. This is in good agreement withthe calculation of Drake [9] which yields 2.3090 eV.We wish to acknowledge the excellent technical sup-port provided by the ATLAS staff and by B.J. Zabranskyduring this experiment. This work was supported by theU.S. Department of Energy, Office of Basic Energy Sci-ences, under Contract Nos. %-31-109-ENG-38 and DE-FG05-88ER-13958 (University of Toledo) and by the Na-tional Science Foundation (Texas A&M University).[1]I. S. Bowen (unpublished). See Ref. [2].[2) D. Huff'and W. V. Houston, Phys. Rev. 36, 842 (1930).[3] S. Mrozowski, Z. Phys. 108, 204 {1938).[4] R. H. Garstang, J. Opt. Soc. Am. 52, 845 (1962).[5] H. Cxould, R. Marrus, and P. J. Mohr, Phys. Rev. Lett. 33,676 (1974).[6] P. J. Mohr, in Beam Foil Spectroscopy, edited by-I. A. Sel-lin and D. J. Pegg (Plenum, New York, 1976), Vol. 1, p.97.[7] R. Marrus, A. Simionovici, P. Indelicato, D. D. Dietrich,P. Charles, J.-P. Briand, K. Finlay son, F. Bosch, D.Liesen, and F. Parente, Phys. Rev. Lett. 63, 502 (1989).[8] P. Indelicato, F. Parente, and R. Marrus, Phys. Rev. A 40,3505 (1989).[9] Cx. W. F. Drake, Can. J. Phys. 66, 586 {1988).[10]C. D. Lin, W. R. Johnson, and A. Dalgarno, Phys. Rev. ABRIEF REPORTS 76715, 154 (1977).[11]C. T. Munger iprivate communication).[12] Our own calculation, based on the formulation of Ref. [6]and the energy-level calculations given in Ref. [9].[13]P. Indelicato, private communication. In the notation ofRef. [7], the matrix elements and level widths for 'Ni2~+are given by 8'» = —0.0109 eV, W&0 = —0.0057 eV,I 0=2.640X 10 eV I ) =0.0518 eV.[14] R. W. Dunford, M. Hass, E. Bakke, H. G. Berry, C. J. Liu,M. L. A. Raphaelian, and L. J. Curtis, Phys. Rev. Lett.62, 2809 (1989).[15]R. Marrus, P. Charles, P. Indelicato, L. de Billy, C. Tazi,J.-P. Briand, A. Simionovici, D. D. Dietrich, F. Bosch,and D. Liesen, Phys. Rev. A 39, 3725 (1989).[16]R. W. Dunford, D. A. Church, C. J. Liu, H. G. Berry, M.L. A. Raphaelian, M. Hass, and L. J. Curtis, Phys. Rev. A41, 4109 (1990).

Direct Observation of Hyperfine Quenching of the (2)3p0 Level in Helium-Like Nickel

Texas A&M University

PHYSICAL REVIEW A VOLUME 44, NUMBER 1 I JULY 1991
Direct observation of hyperfine quenching of the 2 I'o level in heliumlike nickel
R. W. Dunford, C. J. Liu, J. Last, N. Berrah-Mansour, and R. Vondrasek
Physics Division, Argonne National Laboratory, Argonne, Illinois 60439
D. A. Church
Department ofPhysics, Texas A d'cM University, College Station, Texas 77843
L. J. Curtis
Department of Physics and Astronomy, University of Toledo, Toledo, Ohio 43606
(Received 11 February 1991)
We report a clear demonstration of the eft'ect of hyperfine quenching of a forbidden transition by
direct comparison of the lifetimes of the 2'Po level in the heliumlike isotopes 'Ni + and ' Ni . We
find the quenched lifetime of the 2'Po level in 'Ni + to be 470(50) ps. From this we deduce the
2 Po—2 P& energy splitting to be 2.33(15) eV. We also report a measurement of the lifetime of the 2 'P2
level in Ni +, which is found to be 70(3) ps.
One of the most interesting phenomena in the theory of
highly forbidden transitions is the effect of hyperfine
quenching, whereby mixing by the hyperfine interaction
can significantly alter the lifetimes of the levels. The
phenomenon was first discussed by Bowen [1] in 1930,
who pointed out that the substantial strength that was
observed in the 6S21SD-6S6p 3p2 line at 2270 A in the
spectrum of Hg I was primarily due to E1 radiation
caused by coupling with the nuclear spin and not to pos-
sible higher-order multipole radiation as had been sug-
gested [2]. Thus both the S and J labels are only nominal
here. Bowen's conclusion was confirmed in 1937 by Mro-
zowski [3], who experimentally observed the
6s 'So —6s6p Po line at 2656 A in Hg I. This transition
would be rigorously forbidden to all multipole orders of
single-photon decay in an atom with a spinless nucleus by
the J=0~J=0 selection rule of angular-momentum
conservation. Mrozowski [3] attributed the appearance
of this line to coupling between the magnetic moments of
the spin and orbit of the electron and the spin of the nu-
cleus. A discussion of these transitions in Mg, Zn, Cd,
and Hg has been given by Garstang [4].
In the two-electron case of the helium isoelectronic se-
quence, the existence of the 1s2s S& —1s2p Po E1 transi-
tion provides a decay channel not available to the
alkaline-earth sequences. Thus the presence or absence
of the hyperfine quenched 1s 'So —1s2p Po channel can
be detected in the triplet-to-triplet channel because the
Po level has a lifetime that is sensitive to the nuclear
spin.
Hyperfine quenching in the helium isoelectronic se-
quence was first observed by Gould, Marrus, and Mohr
[5] who found that hyperfine effects contributed appreci-
ably to the lifetime of the 2 P2 level in V ' . Calcula-
tions of decay rates for the 2 Po level in odd-Z nuclei
Z =9 through Z =29 have been made by Mohr [6]. Re-
cently, Marrus et al. [7] exploited the effect of hyperfine
mixing to provide a determination of the 2 P& —2 Po
fine-structure splitting in heliumlike Ag +, based on ex-
tensive calculations presented by Indelicato, Parente, and
Marrus [8]. This experiment is significant because the
mixed levels are nearly degenerate, and the method pro-
vides a sensitive means for measuring this energy split-
ting.
In this paper we report a direct observation of the
effect of hyperfine quenching by comparing the lifetimes
of n =2 decays in the two isotopes 'Ni and Ni. The
isotope Ni has nuclear spin I =0 and so will not be
affected by hyperfine quenching, whereas 'Ni has I =
—,
',
and hyperfine effects are important to understanding the
lifetimes of the excited states. By using theoretical values
for the lifetimes of the unperturbed levels and the matrix
elements of the perturbation, our measurement of the
quenched lifetime can be used to determine the
2 Po —2 P, level splitting. Alternatively, since the nickel
measurement is not as sensitive to the fine-structure split-
tings as is the Ag + measurement of Marrus et al. [7],
our results can be used to confirm the theory of the un-
quenched lifetimes and hyperfine-mixing matrix elements
assuming the energy splittings are known. In this way,
our work complements the Ag + work.
Figure 1 shows the low-lying atomic energy levels [9]
of heliumlike Ni + and their theoretical lifetimes. The
2 'P, and 2 P, levels are mixed by the spin-orbit interac-
tion and decay primarily to the ground state by allowed
El transitions [10]. All other levels in the spinless Ni
isotope decay by higher multipole radiation or by two-
photon emission and so are relatively long lived.
Hyperfine quenching in the isotope 'Ni mixes the meta-
stable levels 2 P2 and 2 Po with the short-lived 2 P, and
2 'P, states. Munger [11] has calculated the quenched
lifetimes for the 2 P2 hyperfine levels. The I' =—', level is
unperturbed and so has the same lifetime (71.0 ps) as the
2 P2 level in Ni +. The I'= —,', —„'—,' levels have life-
times of 69.7, 70.0, and 70.7 ps, respectively, and are only
slightly affected by hyperfine quenching. Our experiment
764 1991 The American Physical Society
BRIEF REPORTS 765
7.85— IO
C3
~ 7.75—
1
2 S
0
1
2 P
7.SO—
E1
1.65 fs
154 s M2+E1(h f s )
71 ps
2
13fs i
2.5 ns
(0.45 ns)
5IO—
10
61
N1
lF 1r 3
2.3 ns
~ IOO
7.70— 2E1 (hfs) IO
O —1 S, ~' (61) 58 . 26+
IO
FIG. 1. Electronic energy-level diagram for the low-lying
levels of heliumlike Ni + showing decay modes and lifetimes.
E&(hfs) refers to transitions in 'Ni + induced by the hyperfine
interaction. The 2'Po level has a lifetime of 2.5 ns in ' Ni
and 0.45 ns in 'Ni
4 6 8
ENERGY (keV)
IO l2
FIG. 2. Si(Li) detector spectra for three different foil-detector
distances corresponding to times since excitation of 0.27, 0.84,
and 2.8 ns.
is not sensitive to these small changes. Qn the other
hand, there is a substantial effect on the lifetime of the
2 Po level. The theoretical lifetime [5] for this state is 2.5
ns in Ni, while in 'Ni values of 0.443 ns [11],0.450 ns
[12], and 0.464 ns [13] have been obtained. The
difference between Ni and 'Ni is readily observed in
our experiment.
The highly ionized nickel beams were obtained from
the Argonne Tandem Linac (ATLAS). The ion source
was charged with enriched isotopes of 'Ni (42 at. %%uo )an d
Ni (58 at. %). First the Linac was tuned with the Ni
isotope for a beam energy of 340 MeV. The ions were
prestripped with a 200-pg/cm carbon foil, and the 26+
charge state (15% of the beam) was magnetically ana-
lyzed and directed to the experimental area. The switch
to the 'Ni isotope was accomplished by increasing the
Tandem energy so the velocity of the ions delivered to the
linac was the same as it was for Ni. In this way, the
linac parameters remained substantially the same, and in
particular, the final velocity of the ions was the same for
both isotopes. The velocity of the ions was determined
with an uncertainty of 0.1%%uo by a time-of-Aight velocity
analyzer. Since this analyzer was between the linac and
the 200-pg/cm foil, a correction had to be made for the
energy loss in the foils. The final uncertainty in the ve-
locity determination was 0.5%%uo. The time-of-fiight mea-
surements verified that the velocity was the same for the
two isotopes within this error.
In the experimental area a thin (42 pg/cm ) carbon foil
was moved relative to two fixed Si(Li) x-ray detectors,
which were collimated so as to observe a region of 5 mm
along the beam. The foil was mounted to a precision
translation stage which measured the position to an accu-
racy of 10 pm. Decay curves were obtained by recording
spectra as a function of foil-detector distance. A lower
resolution silicon x-ray detector was attached to the tar-
get holder and used for normalization. It was collimated
so as to observe a region along the beam axis from 5 to 15
mm from the target.
Spectra from one of the Si(Li) detectors are shown in
Fig. 2 for three different foil-detector distances corre-
sponding to delay times after excitation of 0.27, 0.84, and
2.8 ns. Prominent features include peaks at 7.8 and 1.4
keV and a broad continuum in between. There are also
smaller peaks to the high-energy side of the intense
peaks. The 1.4-keV peak corresponds to transitions from
n =3 to 2 in lithiumlike and heliumlike ions. The broad
continuum is largely due to the two-photon decays of the
2 So level in heliumlike ions [14]. This component has a
lifetime of 154 ps and is absent in the 2.8-ns spectrum.
Of most interest for the present work is the 7.8-keV line.
Apart from a small contribution due to cascade repopula-
tion of the short-lived 2 P, and 2 'P, levels, this line con-
sists of a blend of transitions from the 2 P2 2 Pp and
2 S& levels. The linewidth, which is dominated by the in-
trinsic resolution of the Si(Li) detectors (about 220 eV), is
insufficient to resolve the individual transitions. At later
delay times, the line narrows slightly and shifts to lower
energy. This is due to depletion of the somewhat faster
decaying 2 Pz level, which lies 55 eV higher in energy
than the 2 S& level.
The number of counts in the 7.8-keV line for the two
Si(Li) detectors and the normalization detector are deter-
mined at each foil-detector distance by fitting them to a
Gaussian plus a linear background. The width and posi-
tion are taken as free parameters in order to allow for the
fact that the line is a blend of transitions from states with
different lifetimes. We then multiply the Si(Li) detector
counts at each foil position by a factor that is the average
normalization count divided by the normalization count
at that position. The resulting normalized decay curves
for one of the two Si(Li) detectors are shown in Fig. 3.
The upper plot is the decay curve for the case of the spin-
less Ni. These data are fitted we11 by two exponentials
and a constant background. The short-lived component
is identified with the M2 decay of the 2 P2 state. From
766 BRIEF REPORTS
IO I I l I I I l I I I I
fO
5
lO I ~I
.
2'lo—
p X 20
l
TlME SlNCE EXClTATiON (ns)
IO I 1 I I & s s c c I t s e s2
the fits to the data from the two detectors, we obtain a
lifetime of 70(3) ps for this state in agreement with the
theoretical values of Munger [11] (71 ps) and Gould,
Marrus, and Mohr [5] (72 ps). The other component in
the Ni decay curve has contributions from both the
2 S& and the 2 Po states. The lifetimes of these states
are 2.3 and 2.5 ns, respectively, and they are too close to
be resolved as separate components. Although a good fit
is obtained and the resulting lifetime for this component
is consistent with the theoretical lifetimes, the ambiguity
of the two contributions makes it difficult to make an ac-
curate determination of either the unquenched 2 Po life-
tiIne or the 2 S, lifetime.
The decay curve for the 'Ni isotope, which was taken
under identical conditions, shows a significant difference
in shape compared to that of the Ni data and does not
fit to two exponentials (the reduced y for a two-
exponential fit is 9.8). In order to fit these data, three ex-
FIG. 3. Decay curves showing normalized count rate vs time
since excitaiton for Ni + (upper) and 'Ni + (lower). The
solid lines are the fits to the data. The dashed lines show contri-
butions to the fit from the 2 'I'o level and the 2 'P&+2 'S& levels.
ponentials are needed. Since our Ni data confirm the
theoretical value for the lifetime of the 2 Pz level and re-
cent data have confirmed agreement with theoretical
values for the 2 Si lifetime [15,16], we base our deter-
mination of the lifetime of the 2 Po state in 'Ni on a
five-parameter fit. The five parameters are the ampli-
tudes for the three exponentials, the lifetime of the 2 Pp
level and a constant background. The lifetimes of the
2 Pz and 2 S, levels are fixed at the theoretical values.
This fit is shown as the solid line in the lower plot of Fig.
3, and it is in excellent agreement with the data. Also
shown in the lower part of Fig. 3 is the fitted curve with
the 2 Po component left out. The shape of this curve is
close to that of the Ni data. The values for the 2 Po
lifetime in 'Ni obtained from these fits agree for the two
detectors and so we simply average the two values to ob-
tain 470(50) ps. We also tried fitting the data with other
fitting procedures, including repeating the fit to three ex-
ponentials but allowing the 2 Pz and 2 S& lifetimes to be
free parameters. All of the fits are consistent with the re-
sults of the five-parameter fits which we chose for our
final results. The quoted error in the determination of
the 2 Po lifetime has been increased in order to account
for the uncertainty inherent in using a many-component
fitting function. Errors from cascade contributions are
estimated to be less than 1%.
Our results for the quenched lifetime of the 2 Po level
in 'Ni + are in agreement with the various purely
theoretical calculations [11,12,13] and provide
confirmation of the theory for the unquenched lifetimes,
mixing matrix elements, and energy levels. Another way
to interpret the data, suggested by the work of Marrus
et al. [7], is to use theoretical values for the matrix ele-
ments and unquenched lifetimes and use the experimental
data to determine the 2 Po —2 P, fine-structure splitting
b.Eo, ~. Using the matrix elements and level widths cal-
culated by Indelicato [13] and the procedure described in
Ref. 7, we find that our value for the quenched lifetime
470(50) ps corresponds to a fine-structure splitting of
~b,Eo, ~=2.33(15) eV. This is in good agreement with
the calculation of Drake [9] which yields 2.3090 eV.
We wish to acknowledge the excellent technical sup-
port provided by the ATLAS staff and by B.J. Zabransky
during this experiment. This work was supported by the
U.S. Department of Energy, Office of Basic Energy Sci-
ences, under Contract Nos. %-31-109-ENG-38 and DE-
FG05-88ER-13958 (University of Toledo) and by the Na-
tional Science Foundation (Texas A&M University).
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BRIEF REPORTS 767
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[11]C. T. Munger iprivate communication).
[12] Our own calculation, based on the formulation of Ref. [6]
and the energy-level calculations given in Ref. [9].
[13]P. Indelicato, private communication. In the notation of
Ref. [7], the matrix elements and level widths for 'Ni2~+
are given by 8'» = —0.0109 eV, W&0 = —0.0057 eV,
I 0=2.640X 10 eV I ) =0.0518 eV.
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Direct Observation of Hyperfine Quenching of the (2)3p0 Level in Helium-Like Nickel

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Direct Observation of Hyperfine Quenching of the (2)3p0 Level in Helium-Like Nickel

Abstract

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