Lifetime measurements of nuclear levels with the charge plunger technique

NUCLEAR I N S T R U M E N T S

AND METHODS

148 ( 1 9 7 8 )

3 6 9 - 3 7 9 :. ©

NORTH-HOLLAND

P U B L I S H I N G CO.

LIFETIME MEASUREMENTS OF NUCLEAR LEVELS WITH THE CHARGE PLUNGER TECHNIQUE G. ULFERT, D. HABS, V. METAG and H. J. SPECHT

Physikalisches Institut der UniversitiJt Heidelberg and Max-Planck-lnstitut l~r Kernphysik, Heidelberg, 14/. Germany Received 29 June 1977 A new type of recoil distance method has been developed for in-beam measurements of nuclear lifetimes. States decaying by converted transitions lead to highly charged recoil ions as a result of fast Auger cascades in the atomic shells. The high charges are reset to the equilibrium value by traversing a thin carbon foil. The lifetimes are determined by measuring the intensity ratio of high and low charge recoil ions as a function of the target--carbon foil distance. An interesting application of this new technique is the lifetime measurement of rotational states in the second minimum of actinide nuclei.

1. Introduction The most widely used technique for measuring lifetimes of nuclear levels in the ps-ns range is the recoil distance methodl). For nuclei with Z>__ 82 the strong transitions are mostly low-energetic with small Doppler shifts and large conversion coefficients. In this mass region only a few lifetime measurements with conversion electrons have been published 2-5) using radioactive sources. A modified version of the recoil-distance method has been reported by Novakov et al.4). A very strong electrostatic potential gradient has been applied over the recoil distance, thus giving a net acceleration to the conversion electrons depending on the decay position. Similar techniques may also be applicable to inbeam measurements of sufficiently strong transitions. The purpose of this paper is, however, to describe a new type of recoil-distance method which is particularly suited for lifetime determinations of weak transitions in the heavy element region. Instead of observing the nuclear transitions directly their impact on the ionic charge distribution of the recoil nuclei is detected. The sensitivity of the method is so high that even lifetimes of rotational transitions populating fission isomeric states can be measured although these states are only populated with relative probabilities of the order of 10-4-10 -3. Section 2 describes the principle of the method. In section 3 details of the plunger set-up are given. The measurement of the charge distributions is described in section 4. Problems related to the data analysis and examples of the results obtained so far with this technique are discussed in

2. The principle of the "charge plunger" technique The basic idea of the charge plunger technique is illustrated in fig. 1. A recoil ion from a nuclear reaction leaves the thin target with a low equilibrium charge 6) (1 +, 2 + for v/c=0.2%) within 1 0 - 1 4 S - a time short compared to the nuclear lifetimes of interest. Following a converted transition outside the target an Auger cascade is initiated in the atomic shells which increases the ionic charge to a much higher value. For actinide nuclei average charge states of about 1"2+ are expected depending on the type of conversionT). The time scale of about 10-~4 s for the cascade is again short compared to the nuclear lifetime. In some distance from the target the recoil ion passes the "plunger" - a 3 #g/cm 2 carbon foil. Two possibilities now exist: the nuclear de-excitation occurs either before or beyond the plunger. In the first case - shown in the upper part of fig. 1 yield I PII

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370

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- the high charge states of the recoil ion are, in

traversing the plunger, reset to the equilibrium values and a low charge ion is observed; in the latter case - shown in the lower part - no change occurs and a highly charged ion is detected. Thus, the charge distribution of the recoil ions consists of two completely separate components with relative intensities depending on the time of the nuclear decay. By measuring the charge distribution behind the plunger foil as a function of the distance between the target and the plunger one can therefore determine the de-excitation time of the nuclear level decaying through a converted transition. Obviously, a certain analogy exists to the plunger technique for ),-transitions. In that case, a thick plunger is used to stop the recoil ions, and the intensities of Doppler shifted and unshifted ),-rays are compared, whereas in our case a thin plunger foil is used and the intensities of the high charge and low charge recoil ions passing the plunger arrangement are compared. If the nuclear reaction populates a sequence of levels like those, e.g., of a rotational band a cascade of several converted transitions may occur leading to even higher charge states up to 40* 8). The simple analysis just described then yields the overall time scale of the nuclear de-excitation. However, the high charge part of the distribution can also be unfolded into the individual contributions from 1, 2, 3 and more consecutive conversions using the known centre positions and widths of these components. Average charges of 14 ÷ , 21 ÷ and 26+ and widths of 8-10 charge units have been determined experimentally for 237Np ions undergoing 1, 2 and 3 consecutive converted transitions, respectivelyg). From this unfolding procedure more detailed information on the sidefeeding intensities as well as on the decay times of the individual levels may thus be extracted. It should be stressed once again that the application of the charge plunger technique is restricted to converted transitions. It is based solely on the measurement of the atomic charge distributions as a function of the target-plunger distance without ever observing the corresponding nuclear transitions directly.

with the charge plunger technique the distance of the carbon foil to the target then has to be varied between several /~m and ram. Consequently, target and carbon foil should be plane and parallel to each other within ~ 1 #m. This accuracy has been achieved with the set-up schematically shown in fig. 2. It consists of a target holder, a carbon-foil holder, and a stable frame of insulating material. The whole assembly is mounted on a stainless steel plate with a thickness of 15 mm for reasons of stability which also serves as a lid to the scattering chamber. The design of the arrangement is optimized for mounting in the small space available between the pole caps of.a magnet. Apart from the diameter of the stretched Nibacking foil, the target holder is identical to the type used for the measurement of fission isomer halflifes with the projection methodl°). The design is originally due to GallantrY). The 20/tg/cm 2 oxide-target layers of 3 mm in diameter are deposited either by heavy ion sputtering or vacuum evaporation. Target surfaces plane within 1/~m are easily obtained. The carbon foils are prepared by evaporation onto glass plates covered with a thin betain film. The mechanical stability of the carbon foil is improved by coating it with a ~ 6 ~g/cm 2 thick collodion layer. After floating off in water the foils are first mounted on standard-target frames and are then attached to the special carbon-foil holder shown in fig. 2 by gently pressing the foil in the standard-target frame against the central ring (2 mm high, 8 mm in diameter) of the carbon-foil holder which is covered with a small amount of vacuum grease outside the edge of the ring. The flatness of the C-foil is checked with a microscope Cgrbon

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LIFETIME

MEASUREMENTS

and usually found to be better than the focal depth of - 2 ~m. The collodion layer is immediately evaporated when the beam strikes the foil; thus a thin self-supporting carbon foil remains. The thickness of the C-foils is determined by measuring the energy loss of a~-particles in a stack of 20 foils. Typical values are (3+- 1)/~g/cm 2. The carbon foils are replaced after each run to avoid any additional carbon deposition although the vacuum is kept below 5× 104 torr in the target region. A serious source of systematical errors in the charge distribution measurement would result from pin holes in the carbon foils allowing a fraction of the recoil ions to pass through without changing the charge state. Consequently, the foils are carefully checked for pin holes before and after the run. The target holder is mounted on the frame with two screws. Four additional screws allow for fine adjustments of the target holder to position it parallel to the C-foil. The adjustment is checked with a stereo microscope. The distance between the C-foil and the target is changed by turning the screw cap (see fig. 2) so that the carbon-foil holder glides on a central cylinder made of stainless steel which is fixed to the frame. The distance is measured with a stereo microscope to an accuracy of +-3/~m. It is, in addition, controlled by measuring the capacity between the target and the carbon foil as described in ref. 12. This control is essential for monitoring the distance during the bombardment. The distance usually changes by less than 2/~m with a beam of 800 nA u-particles on the target. Taking into account all the effects mentioned

OF N U C L E A R

LEVELS

371

above the present overall accuracy of the distance determination is estimated to be +_4 ~m.

4. Measurement of charge distributions The charge distributions of recoil ions leaving the plunger arrangement may be measured by deflection in a magnetic field as illustrated in fig. 3. The recoil ions are confined by a tube to +-6° with respect to the beam direction allowing only -~3% of the ions to be detected. Thus, a sufficiently small angular and velocity dispersion is achieved. As shown in section 5 corrections for energy loss due to nuclear collisions in the target and the carbon foil are small in this configuration. Depending on their charge state the recoil ions are deflected onto different positions of a detector. In order to avoid a serious distortion of the charge distribution a vacuum of < 5 × 10 -6 torr is required to exclude charge-exchange reactions with the residual gas along the flight path of approximately 8 cm. In principle, direct detection of - 5 0 0 keV recoil ions with position-sensitive semiconductor detectors or open multipliers like channel plates, etc., may be possible. Work along these lines" is in preparation. It appears, however, to be extremely difficult to identify the particular final isotope using direct registration. Alternatively, a possible radioactive decay of the recoil nuclei stopped on a catcher foil may be detected. The charge distribution is then specifically measured for the recoil

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372

G. ULFERT et al.

ions of interest without interference from other reaction products with similar charge states. Such a procedure - although a singles experiment - is thus equivalent to a coincidence measurement. A sufficiently long-lived decay also allows the determination of the charge distribution off-line. Any decay with characteristic energies like a:-decay, ),-emission or even isomeric fission may be exploited. Our first application has been to investigate the charge distributions of 24°Cu recoil ions from the 239pu(a, 3n) reaction using the experimental arrangement of fig. 3. The distribution of the recoil ions along the cylindrical catcher foil is measured off-line by detecting the 6.29 MeV a-particles from the 26d activity of 2a°Cm with surface-barrier detectors. Fission isomeric recoil ions may be studied in an analogous manner with the experimental set-up shown in fig. 4. The photograph gives also details of the plunger arrangement. The detector consists of two oblique sections and a horizontal disc which is split into two parts at forward angles to provide an outlet for the beam. If the isomeric half-life is long compared to the flight time of ap-

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proximately 120 ns most of the isomeric decays occur after the recoil ions have been stopped on the detector. Using this set-up, the 8 # s fission isomer in 23~pu 13) has been studied in the 238U(a, 3n) reaction. No other fission isomers sufficiently longlived to reach the detector are produced in this irradiation. Therefore, a further identification of the recoil ions by a coincidence measurement becomes unnecessary, allowing the use of simple track detectors for the delayed fission fragments. All parts

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373

LIFETIME MEASUREMENTS OF NUCLEAR LEVELS

of the detector are covered with 15 # m thick Makmfol foils. In the usual way, the fragment tracks are then etched and made visible with the spark scanning techniquel4). Thus, despite the fast decay counting is done again off-line. To clarify the geometry, fig. 5 shows cuts through the detector set-up in forward and sideward direction. One of the fission fragments marks the position on the oblique section at which the recoiling fission isomer is stopped, the other one is registered in the horizontal foil. The oblique foils may be reached by fragments from isomers decaying in flight. In the forward direction - determined by the ___6° opening angle - they may also be reached by much more intense prompt fission fragments from the target which are only weakly deflected in the magnetic field. Although the small angles of incidence of these fragments reduce their detection efficiency tS) this suppression is not sufficient to completely avoid a possible contribution from prompt fission fragments to delayed fission tracks at forward angles. For this reason the horizontal detector foils - completely shielded from such events throughout the angular range - have been introduced. Thus, even the registration of only weakly deflected fission isomers with low equilibrium charge becomes possible without interference from prompt fission fragments. The foils on the other side of the beam provide a sensitive test for any background source since they are not reached by the recoiling isomers.

de-excitation time of a sequence of levels populated in the nuclear reaction is of interest, it is sufficient to compare in an "integral analysis" the yield of all high charge recoil ions (> 5 ÷) with the intensity of equilibrium charge recoil ions as a function of the carbon foil target distance. In the case of a rotational band, this overall time scale is controlled by the quadrupole moment. If, however, one is interested to deduce the individual lifetimes of a sequence of levels the charge distribution has to be unfolded into the contributions from several consecutive transitions, yielding decay curves for the corresponding parts of the charge distribution in a "differential analysis". In the final subsections, possible systematic errors in the determination of lifetimes inherent in =

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5. Data analysis and results Typical distributions of recoil ions along the catcher arrangement for several distances between the target and the carbon foil are shown in fig. 6. They have been obtained in the study of rotational lifetimes in 24°Cml6) using the 239pU(~, 3n) reaction at 33 MeV. The important aspects for the interpretation of these data are described in detail in the following subsections. First the distance along the detector and the distance between the target and the carbon foil have to be converted into the relevant physical quantities, i.e. charge states and flight time, respectively. In this connection it has to be verified that the charge resetting in the carbon foil - the essential feature of this method - is sufficiently effective. As already indicated in section 2, the final analysis may proceed in two ways. If only the overall

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374

G. ULFERT et al.

the method are considered. First results obtained for rotational levels in 24°Cm and 239mpu a r e also discussed. 5.1. DETERMINATIONOF FLIGHTTIMES AND CHARGESCALES The essential quantity influencing the conversion of distances into time and charge-state scales is the recoil velocity and its distribution. In a compound nuclear reaction like (~z, 3n) the momentum of the projectile is completely transferred to the recoil nucleus with an insignificant energy and direction spread by neutron evaporation. The recoil velocity is eventually determined by considering the energy loss in the target and the carbon foil. For typical recoil energies of 550 keV the nuclear stopping is generally dominant and the electronic stopping contributes only about 10%. However, since nuclear stopping is mainly due to large angle scattering its influence on recoil ions confined to _+6° is strongly reduced. Fig. 7 shows the calculated velocity distribution of 550 keV 24°Cm ions emerging, within the angular range of _+6°, (a) from a 10pg/cm 2 Pu-target and (b) from a 4 p g / c m 2 carbon foil. The dashed curves are ob-

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tained from the Monte Carlo code NELAS 17) taking only nuclear stopping into account. The full lines contain, in addition, the influence of electronic stopping taken from ref. 18. The average velocity of the recoil ions leaving the target corresponds to 9896 of the initial recoil velocity. On the basis of this value the distance between the target and the carbon foil is converted into a flight time. 24°Cm recoil ions produced in the 239pu(a',3n) reaction thus cover 6 . 5 p m in 10 ps. The average velocity of the recoil ions behind the carbon foil is reduced to 90°/6 of the initial velocity. The flight path of the recoil ions to the detector foil is then calculated for different charge states with a ray-tracing program using this recoil velocity and the precisely measured magnetic field distribution. A distance scale along the detector foil may thus be converted into a charge scale. According to fig. 7 the tails in the velocity distribution amount to less than 196 for velocities less than 80°/6 of the initial recoil velocity. This implies that the yield of recoil ions at a position on the detector foil corresponding to 1.25 times their charge state is less than 1%. Thus, a distortion of

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L I F E T I M E M E A S U R E M E N T S OF NUCLEAR LEVELS

375

should be de-excited to - 1 0 -4 after a distance of 1.5 mm (=-2.3 ns) assuming the quadrupole moment of 12.0 b for 24°Cm given in section 6. According to fig. 8, the yield of highly charged ( > 1 0 +) ions is, in fact, (3+__1.5)×10 -3. The effectiveness of the charge resetting is thus demonstrated to be >99%. This result can be understood on the basis of single electron capture cross sections, using - for lack of any experimental data for highly stripped ions calculated v a l u e s m) of 3 × 1 0 -t4 cm 2 and 5× 10-Is cm 2 for 20 + and 10 ÷ ions, respectively, in the velocity range of interest. Two electron capture cross sections are estimated tg) to be smaller by about a factor 10 - at least by more than a factor 2. Thus, consecutive single electron capture is the dominant mode during the charge-resetting process. The formulae used give reasonable agreement with experimental cross sections in the region where theory and experiment can be compared20). Based on these cross sections, a carbon

the high charge part of the distribution by a tail from the equilibrium part is negligible. In the differential analysis, however, the individual components within the high charge part are relatively closer together. Therefore, the proper asymmetric shape of the velocity distribution is taken into account in the unfolding procedure. 5.2. THE CHARGERESET MECHANSIM It is essential for a quantitative application of the charge plunger technique that the charge resetting (in the carbon foil) occurs with a sufficient efficiency. Fig. 8 shows the distribution of 24°Cm recoil ions along the catcher arrangement for a distance of 1.5 mm between the target and the carbon foil, using again the ;~39pu(~, 3n) reaction, but now at a bombarding energy of 27 MeV. This energy - 1.7 MeV above the reaction Q-value - suppresses any population of long-lived (>_ns) isomeric states above the pairing gap (see below). The ground-state rotational band, on the other hand,

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376

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foil thickness of 3 #g/cm 2 is more than sufficient to ensure a complete resetting of all charge states />40 + to equilibrium. 5.3• INTEGRAL ANALYSIS

Generally, a nuclear reaction populates several states which may then decay by converted transitions. In some cases the de-excitation of such a sequence of levels is controlled by a single parameter. In case of a rotational band the absolute scale of all halflifes is determined by the quadrupole moment; in case of a long-lived isomeric state feeding the band the overall de-exitation is governed by its half-life. It is then sufficient to measure the decay of all excited states together in order to obtain the physical quantities of interest. Fig. 9 shows such an "integral" decay curve, based on the raw data of fig. 6. The fraction of high charge states (>5 +, i.e. distance along the detector >20 mm) representing the percentage of all excited nuclear levels is plotted as a function of the target-carbon foil distance and the decay 239Pu(W.,3n) ZlOCm

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time, respectively. The data are dominated by the decay of the ground-state rotational band in 24°Cm. The full line represents a fit of a cascade calculation involving sidefeeding intensities obtained from a decomposition of the charge distribution measured without carbon foil. The only free fit parameter is the quadrupole moment of this nucleus (see section 6). Contrary to the data at 27 MeV, high charge states with a well defined maximum still occur for carbon foil distances > 1.0 mm (compare figs. 6 and 8). Since any possibility for tails has been ruled out above, they have to be attributed to converted transitions which still occur after passing the plunger foil and quite probably originate from the decay of an isomeric state in 24°Cm into the ground state rotational band with a halflife of 10 ns
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LIFETIME

MEASUREMENTS

OF N U C L E A R

Fig. 10 shows again the charge distributions from fig. 6, including now the decomposition into the contributions from several consecutive converted transitions. Up to 5 components are observed since the 10 ~ state of the ground-state rotational band in z4°Cm is still appreciably fed in the 239pu(at, 3n) reaction. The yield of the low charge recoil ions has also been fitted with a Gaussian curve centered at the equilibrium charge of 1 + If the transitions were fully converted, the partial distributions corresponding to 1, 2, 3... conversions would directly reflect the decay of the 2 +, 4 - , 6 + ... state, respectively. Otherwise - as for the higher states in this example - the analysis becomes slightly more involved. The resulting decay of the 2 + , 4 + , 6 + and higher rotational states as well as the increasing population of the 0 + state plotted in fig. 11 show good agreement with the corresponding time distributions which are calculated taking in-band feeding and side feeding into account. With a quadrupole moment of 12 b as found in the integral analysis (see below) half-lives of 154 ps, 71 ps and 41 ps are expected for the 2 ~, 4 + , and 6 + state, respectively, using the rotational model. For states with 1 > 8 + feeding times of 30 ps are required to reproduce the data. Lifetimes of rata-

far downstream that the magnetic field would be insufficient to deflect the high charge recoil ions as strongly as observed, Two quasi-particle states with similar half-lives and excitation energies of about 1.1 MeV have previously been identified in neighbouring even--even isotopes2t). The result demonstrates the high sensitivity of the charge plunger technique for the observation of weak transitions. 5.4.

DIFFERENTIAL ANALYS|S

If the halfiifes of individual levels in the band are of interest the charge distribution has to be decomposed into the corresponding contributions. The unfolding procedure uses the known centroids and widths of Gaussian curves representing l, 2, and 3 conversions which were already mentioned in section 2; the corresponding values for 4 and 5 conversions (centroids: 29 +, 33+; widths: 10 charge units) have been obtained by suitable extrapolation. After folding these Gaussian functions with the experimental resolution resulting from the acceptance angle of ___6°, the diameter of the beam spot and the asymmetric velocity-distribution function, they are fitted to the experimental data with their intensities as the only free parameters.

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G. ULFERT et al.

tional states in odd A nuclei may also be determined with the unfolding procedure, although in this case the analysis is more complicated because of the occurrence of cross-over transitions. 5.5. DISCUSSIONOF SYSTEMATICERRORS Most of the possible problems associated with the charge plunger method arise from nuclear physics aspects rather than from instrumental defects. They are therefore only shortly mentioned here and discussed more extensively in connection with the first experimental results on quadrupole moments in 24°Cm and 2y~mpul3'16). In the following, sources of systematic errors related to the m e a s u r e m e n t of lifetimes and the proper assignment to particular levels and those related to the interpretation of these lifetimes should be distinguished. The case of a single converted transition - easily recognized by the shape of the corresponding charge distribution - is completely equivalent to that of a single gamma transition in the conventional recoil distance method. Errors can then only be due to the recoil-velocity distribution as discussed in section 5.1. The case of a sequence of converted transitions is more complicated. Provided the unfolding procedure is done correctly, the assignment of the individual components of the charge distribution to particular transitions demands a corresponding knowledge about the level scheme, either from a separate experiment, or at least from a sufficiently well based model. For ground-state rotational bands in even-even nuclei in particular, converted transitions before reaching the band would be a way to perturb the unique assignment, leading thus to erroneous half-lives. Although no direct spectroscopic information is available for our first example 24°Cm, the observation of a 6% low charge component in the initial charge distribution (fig. 10) is consistent with the expected direct feeding into the ground state, placing a sufficiently low limit on such transitions. The interpretation of nuclear lifetimes usually involves a conversion into reduced transition probabilities. Therefore, internal conversion coefficients, transition energies and multipolarities have to be known. Fortunately, the dependence of the conversion coefficients 22) on the ionic charge states is less than 1% for charge states up to 23÷, making this influence on the half-lives observed negligible. If the energies and multipolarities of the individual transitions are not known from sep-

arate experiments, only especially favourable cases can still be dealt with. For rotational bands in heavy nuclei for example, exact knowledge about the level spacing is not required because of the nearly negligible energy depondence of the transition probability for fully converted E2 transitions. Further problems arising from the influence of side-feeding times or those specific to odd A nuclei are also discussed in detail in ref. 16. 5.6. RESULTS The charge plunger technique has thus far been applied to the determination of quadrupole moments for 24°Cm and 239mPU, deduced - within the framework of the rotational model - from reduced transition probabilities. The value of (12.0_0.5)b found for 24°Cm 16) is very close to those for 244Cm a n d 246Cm measured by Coulomb excitation23). The value of (36_+32) b obtained for the 239pu fission isomer 13) represents the largest quadrupole moment ever measured for atomic nuclei. It corresponds, for a prolate spheroid, to an axis ratio of 2.0_+0.1, thus providing quantitative proof for the interpretation of fission isomers as shape isomeric states24). 6. Conclusion A new technique for measuring lifetimes of nuclear states decaying by converted transitions has been described. It exploits the influence of the resulting Auger cascades on the atomic charge distribution of nuclei recoiling into vacuum as a function of the distance from the target. In its present version, the method may be applied to any level or band of levels provided two conditions are fulfilled for the band head state: it has to be sufficiently long-lived - with respect to further internal conversion - to survive deflection in a magnetic field, and it has to be identified in a unique and characteristic way by its decay.

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