Resonant versus nonresonant nuclear excitation of 115 In by positron annihilation

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An energetic positron may annihilate with an inner shell atomic electron into one, two, or possibly more photons.An additional radiationless annihilation channel was envisioned in 1951 by Present and Chen ͓1,2͔: a single virtual photon created in the annihilation process may be absorbed by the nucleus of the atom, giving rise to nuclear excitation, if the incident positron energy meets the nuclear resonance criteria.Many measurements ͓3-10͔ as well as numerous calculations ͓11-18͔ have followed.The experiments to measure the cross section n for radiationless ͑i.e., resonant͒ nuclear excitation via positron annihilation have relied on the irradiation of thick targets containing the nuclei of interest using the broad ␤ ϩ spectra from radioactive sources.The measurements have yielded unassailable evidence for nuclear excitation via positron annihilation, but the implied values of n are clouded by thick target complications and are generally much larger than the theoretical consensus.We report here the first direct measurement of n using a thin sample and a monoenergetic beam.Our result for n is a factor of 4 less than the cross section determined via radioactive sources, which suggests the existence of a hitherto unidentified and presumably nonresonant ͑i.e., inelastic͒ channel for nuclear excitation via positron annihilation.

115
In was chosen as the target material because it has been the main focus of study in nuclear excitation by positron annihilation experiments ͓3,4,7,8,10͔.This nucleus has also been extensively studied in nuclear resonance fluorescence experiments ͓19͔ on account of its very convenient level structure see ͑Fig.1͒.The 4.49 h half-life of the 336 keV isomer makes it possible to subject the nuclei to intense irradiation and then measure the effects of the irradiation in a low background environment.Although the multipolarity of this state renders it very difficult to populate directly, there are a number of accessible excited states that decay to the isomer.The state we seek to excite via resonant positron annihilation in this work is the 1078 keV level.
When a positron undergoes single quantum annihilation with a K-shell electron a photon of energy T is created, where TϭE e ϩϩ 2m 0 c 2 ϪB K . ͑1͒ tron shells since they are reduced from the K-shell contribution by at least an order of magnitude ͓9͔. Figure 1 shows a partial level scheme for 115 In, showing only the transitions relevant to this work.Once excited, the 1078 keV state will promptly decay to the 597 keV state ͑with a branching ratio of 19%͒ and thence fully to the isomer, which has a branching ratio to the ground state of 96.4% and decays via a highly converted M 4 transition (e/␥ϭ0.89).From Eq. ͑1͒, we see that a beam energy of 83.9 keV is required to excite this level by the resonant nuclear excitation process.Thus, following irradiation the sample may be removed to a low background environment where both conversion electrons ͑47%͒ and photons ͑53%͒ will be emitted as the isomer decays.Observation of this radiation constitutes, in the absence of competing processes, direct observation of nuclear excitation by positron annihilation.
The indium target foil used in our experiment was 5 m thick with an 18-m acrylic backing, which we were careful to align as the beam exit side.The foil was mounted in an Al holder that presented a 12.7 mm diameter exposed area.The manufacturer-specified purity of the foil was 99.8%.The target arrangement was mounted inside an accelerating section at the end of a magnetic slow positron beamline and could float at potentials up to 100 kV.
The positrons were created in a bremsstrahlung shower from the Lawrence Livermore National Laboratory 100-MeV electron linac ͓20͔.Positrons created by pair production in the vicinity of a tungsten foil arrangement were moderated and electrostatically focused into a beam, which was then magnetically guided to the target region.Before irradiating the foil, the beam intensity in the target region was measured using a NaI͑TI͒ scintillation detector.An intensity Iϭ(5 Ϯ1)ϫ10 8 e ϩ s Ϫ1 was measured, where the error assignment corresponds to two standard deviations or 95% confidence limit that includes the estimated uncertainties in the measurements of the solid angle and overall detector efficiency and estimated errors associated with corrections for scattered ␥ rays, pileup, and extrapolation to full beam intensity.During irradiation the beam was monitored for stability with the above detector as well as an integrating dosimeter placed near a constricted region of the transport system.The beam was found to be stable to within Ϯ10% during the 11 h irradiation.
Prior to the start of irradiation, a retractable microchannel plate ͑MCP͒ with a phosphor screen was extended into the beam path approximately 15 cm in front of the target to locate and focus the beam.The beam spot diameter measured at points of less than 25% of the central intensity was less than 1 cm.The target region layout is shown in Fig. 2. When the channel plate detector was retracted, the beam continued on to the indium and most of it passed through the thin foil.Using two highly collimated plastic scintillator detectors ͑labeled D1 and D2 in the figure͒ we were able to determine whether the beam was passing through the foil and annihilating on the end of the target chamber, or if it was annihilating on the Al sample holder.We optimized the beam location for maximum transmission by steering the beam first to hit the Al and then to pass through the In foil.All tests with the beam were performed at 83 keV, just below the resonance energy so as not to complicate the cross-section determination.
The irradiation was performed for 11 h at a ͑calibrated͒ beam impact energy of 89 keV in a vacuum of ϳ5 ϫ10 Ϫ7 torr.This beam energy was chosen in accordance with the positron stopping power of the foil.Positrons were expected to lose ϳ10 keV in passing through the foil ͓21͔, so by implanting the beam at 5 keV above the resonance energy the point of maximum 115 In activation was expected to be located close to the center of the In foil.After irradiation the foil was removed from the vacuum system and placed in close proximity to a well-shielded HPGe detector to detect the 336 keV photons from the decay of the isomeric state.The output from the detector was amplified and routed to a CAMAC controlled data acquisition system that downloaded and saved spectra from a memory buffer at regular intervals.
As a test of our system we photoactivated a thick indium sample in the linac bremsstrahlung shower.The 115 In decay fluorescence spectrum shown in Fig. 3͑a͒ identifies the expected peak location at 336 keV, the expected peak line shape, and the detector resolution.Spectra from the positronactivated foil and from background are shown in Fig. 3͑b͒.The data in Fig. 3͑b͒ were taken for the first 8 h of the decay of the 336 keV state, or approximately 1.26 mean lives, in order to optimize the signal-to-noise ratio.The background spectrum run lasted 100.5 h and is normalized to the 8 h run.To arrive at an upper limit on the 336 keV peak signal we compute 2 ϭ⌺(dϪb) 2 /b, where the sum is over the three channels around 336 keV; d is the measured positroninduced signal; and b is the expected number of counts ͓i.e., the average background of the signal ͑from 322-348 keV͒ plus a times the photoinduced signal from Fig. 3͑a͒, normalized to unity when summed over the three peak channels͔.We compute the likelihood function L(a)ϭexp͕Ϫ 2 (a)͖ for positive values of the fitting parameter a and normalize it to unit area.From the value of a for which ͐ 0 a L(aЈ)daЈ ϭ0.990, we find the upper limit on the amplitude of the peak signal over background in Fig. 3͑b͒ is 28.6 at a 99% confidence level.We would expect 113 counts if the resonance cross section were 1.7ϫ10 Ϫ25 cm 2 as determined by the positron source experiments ͓8,10͔ ͑see discussion below͒.
Since this experiment produced a null result it should be pointed out that the data presented here do not represent the only set collected.An earlier run, which also yielded no signal, alerted us to the fact that the expected count rate ͑see Fig. 3͒ might not be as large as expected.The data collected from this earlier run are not shown here for several reasons.The statistics present in that data set were not good due to a different experimental procedure that was adopted.In this case we attempted to measure both the emitted photons and conversion electrons from the decay of the isomer.This technique proved to be less efficient than optimizing for one type of signal or the other, and the experiment was considerably simplified by taking photon data only.There exist a number of other procedures that, ideally, we would liked to have undergone, such an additional runs at varying target thickness and beam energies, and perhaps even the investigation of other isotopes.However, both time and cost considerations prevented us.
The irradiation process creates isomeric states such that after an irradiation time t irrad ϭ11 h the total number of isomers present is

͑2͒
where we use N b (0)ϭ0 and the subscripts a and b refer to ground and excited states, respectively, and b ϭ0.154 h Ϫ1 is the decay rate of the 336 keV state.The time between the end of the irradiation and the beginning of the counting was 9 min and is neglected.ϭ0.19 is the branching ratio to the isomer from the 1078 state.The constant a is the rate at which nuclei are excited and is given by where I is the positron beam intensity, n is the resonance cross section, N a (0) is the number of available target atoms per unit area, and we use the fact that the typical rate at which any one nucleus becomes excited is negligible compared to b .
Since we are assuming in our analysis that this is a resonant process, we must be cautious when defining the number of available target atoms, N a (0).We include as the thickness of our foil only the effective thickness.d eff , which is simply that fraction of the foil through which the passing positrons are in the resonant energy range.This is clearly determined by the resonance width and the stopping power of the material.At the resonant positron energy of 83.9 keV the stopping power is (dE/dx) res ϭ18 980 keV cm Ϫ1 ͓21͔.As pointed out by Grechukhin and Soldatov ͓11͔, the resonance width is given by where the subscripts n and k refer to the nuclear and k levels, respectively.The nuclear width, ⌫ n ϭ6ϫ10 Ϫ4 eV ͓22͔, is orders of magnitude smaller than the electron shell width ⌫ k ϭ7.3 eV ͓23͔, which therefore dominates.The appropriate evaluation of d eff , is then, The effective number of target atoms presented to the beam is given by Here N A ϭ6.02ϫ10 23 is Avogadro's number, f ϭ0.9572 ͓24͔ is the natural abundance of 115 In, and ϭ7.29 g/cm 3 and A ϭ115 are the density and atomic weight of indium, respectively.We obtain our experimental value for N b (t irrad ) by using the 99% confidence level upper limit of 28.6 detected isomeric decays.Since we have used data integrated to t count ϭ8 h we have only counted a fraction 1Ϫexp ͕Ϫ b t count ͖ϭ0.708 of N b (t irrad ).The upper limit on the de- tected rate is corrected by dividing it by the product of 1 Ϫexp͕Ϫ b t count ͖, the measured detection efficiency, ϭ0.12Ϯ0.005, the branching ratio of the isomer to ground state ͑0.95͒ and the photon fraction ͑0.53͒ to yield N b (t irrad )Ͻ668.The upper limit for the resonant cross section is then Ͻ4.3ϫ10 Ϫ26 cm 2 ͓99% confidence level͔, ͑7͒ where we are using a 3 standard deviation or 99.7% confidence level positron flux lower limit FϾ3.5ϫ10 8 e ϩ s Ϫ1 in the evaluation, and ϭ0.15 is the fraction of the positrons that are transmitted or backscattered without being moderated to the resonance energy ͓25͔.
We are aware of five published experimental determinations of the ''resonant'' cross section of nuclear excitation of 115 In ͓3,4,7,8,10͔ by positron annihilation with a K-shell electron.Two of the results ͓8,10͔ are reevaluations of earlier works ͓7,4͔ that we believe represent the most accurate determinations of the rate for positron-induced excitation of 115 In using the continuous spectra of positrons emitted from a radioactive source.The reanalysis in Ref. ͓10͔ involved correcting for the effective thickness of their target foil, defined as in Eq. ͑5͒.The work of Vishnevskii et al. ͓7͔ was reevaluated ͓8͔ by considering a more accurate representation of the source distribution in the target material, leading to an increased cross section.These authors recognized the need to consider the K hole in the resonance width but did not take account of the effective thickness of their target material.Since both experiments used stopping targets of a similar thickness, we may apply the analysis of Saigusa and Shimizu ͓10͔ to the data of Vishnevskii et al. ͓8͔.The resulting deduced resonance cross sections from these two experiments are almost identical, both yielding ␤ ϭ1.7 ϫ10 Ϫ25 cm 2 , which is four times greater than our upper limit.
Various competing processes that might be present in the source-based experiments ͓8,10͔ do not seem to be responsible for this disparity.Barring an unusually large and unexpected error either in the present result or simultaneously in both source experiments ͓8,10͔, a remaining possibility is that the large energy distribution of the ␤ ϩ particles from a 64 Cu source (E max ϳ650 keV), allows some lower cross section inelastic processes to dominate in the radioactive source-based experiments.In these processes, the resonance constraint on the positron energy would be relaxed and the number of positrons that can take part in the excitation pro-cess would be greatly increased.The simple process of emitting a bremsstrahlung photon during the nuclear excitation ͓12͔ is too improbable to make any significant contribution to the rate ͓13͔.
Our measurement allows an unambiguous comparison with theoretical estimates of the resonant cross section for nuclear excitation.We make no comparison to the theoretical work of Present and Chen ͓1͔ and Watanabe, Mukoyama, and Shimizu ͓4͔ because they used the wrong nuclear transition (E1) and were based on a two-step approximation to the virtual annihilation.Of the remaining theories our upper limit is approximately consistent with the cross section calculated by Kolomietz and Fedotkin ͓16͔ and is consistent with the small cross section from the theory of Grechukhin and Soldatov ͓11͔.In view of our result it is not surprising that there has been a persistent disparity between the experimental and theoretical results, since they are evidently not describing the same process.
Although we are unable to shed light on the details of the excitation mechanism, our upper limit on the resonant cross section implies that some sort of nonresonant process is occurring in the source-based experiments.Indeed, the combination of our result with these experiments is a compelling indication of the existence of some as yet unidentified process.In order to investigate this further it would be of interest to scan a more intense beam over several hundred keV above the resonant energy in both a thin and a thick target.However, the experiment to resolve the nuclear excitation mechanism must probably await the implementation of a positron beam with an intensity of at least 10 10 e ϩ s Ϫ1 .

FIG. 2 .
FIG. 2. Target area for irradiating the In foil with monoenergetic positrons.Detectors D1 and D2 have restricted fields of view due to the presence of the lead collimators.The retractable microchannel plate ͑MCP͒ is used to image the beam before it hits the target.

FIG. 3 .
FIG. 3. ͑a͒ Photoactivated 115 In line shape.͑b͒ Measured positron-activated signal and background.The lines at ϳ320 and 350 keV are due to radioactivity from the lead detector shielding.