Decay properties of heavy mendelevium isotopes

NUCLEAR PHYSICS A

Nuclear Physics A563 (1993) 21-73 North-Holland

Decay properties

of heavy mendelevium

isotopes

K.J. Moody, R.W. Lougheed, J.F. Wild, R.J. Dougan, E.K. Hulet, R.W. Hoff, C.M. Henderson, R.J. Dupzyk, R.L. Hahn ‘, K. Siimmerer *, G.D. O’Kelley 3, G.R. Bethune + University of California, Lawrence Livermore National Laboratory, Livermore, CA 94551, USA Received 3 July 1992 (Revised 15 February 1993)

Abstract We investigated the nuclear properties of several mendelevium isotopes produced in the reactions of heavy ions with z54EsB.We measured the alpha particles, spontaneous fissions (SF), and photons emitted by counting samples resulting from chemical and/or mass separations. The 256Md half-life is (78.1 f 1.8) min; it decays primarily by electron capture (EC), but also by alpha emission (11 f 3)% of the time. The 256Md ground state has J < 2 (probably J” = l- ), and a mass excess of (87.611 f 0.053) MeV. The z57Md half-life is (5.523 f 0.050) h; it decays primarily by EC, but also by alpha emission (15.2*2.6)% of the time and by SF less than 1% of the time. The z7Md mass excess is (88.989 f 0.003) MeV. The zsMdg (J” = 8-j half-life is (51.50*0.29) d. It decays by alpha emission; the sum of SF, EC, and p - decay branches is less than 3 x 10e3 %. The alpha decay of =sMdg populates 254Esm (0.60*0.08)% of the time. The *‘*Mds mass excess is (91.691 f 0.007) MeV. The half-life of J” = 1- VsMdm is (57.0 f 0.9) min. It decays by EC, the branch for decay by alpha emission is less than 1.2%. The sum of SF and p- decay branches is less than 30%. The half-life of 25gMd is (1.60 f 0.06) h; it decays primarily by SF. The alpha decay branch of =‘Md is less than 1.3%. From the “‘Md half-life we calculated a SF hindrance factor associated with the s-[514] proton configuration of 3.6~ 106. From our data we proposed partial level schemes for “‘Es, z3Es, and 254Es.

1. Introduction The production of heavy actinide nuclides in transfer reactions of heavy ions with 254Esg targets has been measured [l-41. These transfer reactions lead to broad isotope distributions of above-target nuclides, extending upwards in neutron number to nuclei that are not accessible by heavy-ion fusion reactions [2,5-71.

’ 2 3 +

Present address, Chemistry Department, Brookhaven National Laboratory, Upton, NY, USA. Gesellschaft fiir Schwerionenforschung, Darmstadt, Germany. Oak Ridge National Laboratory, Oak Ridge, TN, USA. Bethune-Cookman College, Daytona Beach, FL, USA, deceased.

037.5-9474/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved

22

KJ. Moody et al. / Decay properties

Table 1 The production of mendelevium isotopes in the reactions of 105 MeV “0 ions and 126 MeV **Ne ions with 254Es8 Product

Cross section (cm*)

nuclide

105 MeV 180

126 MeV ‘* Ne

5.8 x 4.5 x 1.3 x 3.6 x 5.0 x 3.9 x

6.5 x 1.6 x 6.4 x 1.5 x 3.7 x 4.7 x 2.8 x

10Fzs 10-28 10-2s 1O-29 10-30 10-31

1O-28 lo-*’ lo-= 10-28 10-29 10-30 10-31

Extrapolations of the systematic trends of the cross-section distributions inspired experiments leading to the discoveries of new neutron-rich mendelevium, nobelium, and lawrencium isotopes [8,9]. The cross sections for nuclides near the limits of the known nuclei are large enough that we have been able to study their spontaneous fission (SF) properties with unprecedented numbers of events [8,10131. We accomplished many of these SF measurements by performing off-line mass separations, then following the decays of the nuclides in the mass fractions of interest. In other experiments, we chemically separated adjacent actinide elements from one another and counted the appropriate chemical fractions. As a by-product of these experiments, we accumulated a vast amount of spectral data by counting nearby mass fractions or chemical fractions obtained from sample processing. In this paper, we describe the results of the analysis of some of these data. Table 1 shows the cross sections for production of mendelevium (element 101) isotopes from 254E~g with 105 MeV 180 ions and with 126 MeV 22Ne ions. We produced counting samples containing unprecedented amounts of many of these isotopes and improved on the accepted values of their half-lives and decay properties. In the cases of 256Md, 257Md, and 258Mdg, we extracted the partial nuclear level schemes of their decay daughters. We will discuss the discovery and decay properties of 260Md in a separate publication [ 141.

2. Experimental 2.1. Irradiations and sample preparation

We bombarded targets containing approximately 10” atoms/cm2 of 254Esg with 180 and 22Ne ions at the Lawrence Berkeley Laboratory 88-inch cyclotron. We prepared the targets by electrodepositing 254Esg from isopropanol solutions of the

KJ. Moody et

al.

/ Decay properties

23

chloride onto 4.5 mg/cm2 molybdenum substrates. The resulting uniform layer contained from 3 to 6 pg of 254Esg (half-life 276 d); we performed irradiations as late as 250 d following the production of the target. We overplated the deposits with 20 pg/cm2 of palladium to reduce sputtering and thermal-evaporation losses. The beams were collimated to the 3 mm diameter of the target and passed through a molybdenum window, a volume of nitrogen cooling gas, and the molybdenum target substrate before encountering the einsteinium target material. Mid-target projectile energies were 105 MeV for “0 and 126 MeV for 22Ne, which correspond to energies a few percent above the respective interaction barriers. Typical beam intensities were about 1.2 x 1012 particles per second. Reaction products recoiled from the target and passed through a 50 pg/cm2 aluminum cover foil and approximately 1 cm of 10 torr helium cooling gas before they were collected with 3.6 mg/cm2 tantalum or 4.6 mg/cm2 molybdenum foils. These foils subtended laboratory angles out to 55” from the beam axis, covering all angles at which transfer-reaction products were likely to be emitted [15]. Irradiations varied in length between 2 h and 2 d, depending upon the particular mendelevium isotopes to be studied. After each bombardment, the recoil catcher foil was processed by electromagnetic separation and/or chemical purification. In experiments using tantalum recoil foils, the foils were transported by helicopter to the Lawrence Livermore National Laboratory, where they were inserted into the ion source of an electromagnetic mass separator [12]. The ion source emitted the actinide reaction products as singly-charged ions, which were accelerated by a 47 kV potential through the separator. We collected masses 252 through 263 on a strip of aluminum foil, which was cut into separate mass fractions that constituted our counting samples. The horizontal separation between each mass unit was 1.3 cm. The mass separator yield was typically on the order of 20% for the mendelevium isotopes, determined by comparing end-of-irradiation activities with the yields of the same nuclides obtained in previous experiments [1,2]. Decontamination factors of a given mass fraction from nuclides at adjacent masses were usually on the order of 3 x 10P3. Samples were ready for counting in as few as 60 min following the ends of the irradiations. In experiments using molybdenum recoil foils, we treated the foils with a chemical procedure to isolate the isotopes of mendelevium [93. Aluminum foils containing mass-separated samples were similarly processed when purification from other elements was desired. The collecting foil was dissolved and the actinide reaction products were chemically isolated from the bulk of the collecting medium. We separated the mendelevium isotopes from the other actinide reaction products by differential elution from cation-exchange resin with buffered alpha-hydroxyisobutyrate solutions. Often, more than one of these ion-exchange columns were run to obtain the necessary purification from the interfering activities of the fermium and einsteinium isotopes. The resultant mendelevium fractions were electroplated onto platinum disks and heated in the flame of a Bunsen burner prior to counting.

24

KJ. Moody et al, / ~cay~ro~rt~s

2.2. Alpha-particle and gamma-ray spectrometry and SF counting

Alpha-particle spectrometry was performed with either surface-barrier or gasionization [16] detectors. Counting geometry was determined from the solid angle subtended by the detector, typically about 25-33%. Alpha-particle spectra were taken on 1024-channel analyzers, covering the energy region between 4 and 9 MeV. Events occurring in the alpha detectors with more than 20 MeV of kinetic energy were often stored in the uppermost channel of the pulse-height alpha spectra, and were treated as SF events in subsequent data analyses. We determined energy calibrations with standard sources and from the energies of the alpha particles emitted by the known impurities in the samples themselves. Table 2 lists the nuclides and alpha energies used in these calibrations; data are taken from ref. [17], except for that given for 254Fm El81 and 255Fm [19]. When spectral peaks were well-resolved, peak centroids were obtained from gaussian fits to the channels near the peak m~imum. For complicated spectra, peak centroids were obtained from the FITEK code [20], which iteratively establishes a peak shape consisting of the sum of a gaussian and two exponential tails using the data in a defined spectral region. We assumed that the peak shape did not change with energy. Alpha-particle intensities used in decay-curve analyses were obtained by summing the histogra~ed data in the energy region of interest in each spectrum. The mass-256 fraction from one experiment and mass-257 fractions from two other experiments were counted for gamma rays by placing them near the end windows of large-volume germanium detectors. Counting efficiency as a function of energy was determined using a set of mixed radionuclide standards, as was the energy calibration of the counting system. Gamma-ray spectra were taken on 4096-channel analyzers, over the energy interval from 40 to 1200 keV. Integrals and centroids of peaks in the gamma-ray spectra were obtained with the GAMANAL code [21] or by histogram analysis [22] in the event of low statistics. X-ray peaks were always analyzed as histograms. In the histogram-analysis procedures, the background under each interesting photon peak was established graphically and subtracted from the sum of the data in a region whose width was taken to be the same as those of nearby peaks with higher statistics.

Table 2 AIpha energies used in detector ~librat~ons Nuclide

Energy (MeV)

241/,,,,

5.4857 f 5.8050 f 6.0308 f 6.4288 + 7.022 i 7.192 f

244Cm 25OCf 254%

“*Frn 254Fm

0.0001 0.0001 0.0006 0.0015 0.002 0.002

KJ. Moody et al. / Decay properties

25

The mass-257 and mass-258 fractions from one experiment were counted for gamma rays coincident with alpha particles of over 6.60 MeV. Samples were mounted facing a 450 mm* surface-barrier detector in a brass cup, which slid over the end of an intrinsic-germanium photon detector with a beryllium end-window. An O-ring near the edge of the brass cup made a vacuum seal with the cryostat housing of the photon detector. We maintained the resulting counting chamber at a pressure of approximately lo-* torr during the several months of data acquisition. We determined efficiencies and energy calibrations of the alpha-particle and gamma-ray detectors by counting 249Cf sources prepared on the same backings as the experimental samples and mounted between the detectors in the same fashion. Gamma rays emitted in the alpha decay of 249Cf were also used in setting the timing of the coincidence circuit. 2.3. Spectrum handling Individual spectra were accumulated over counting times less than the half-lives of the nuclides of interest; we made corrections to the decay curve data for the effects of finite counting intervals. Decay-curve analyses were performed with an iterative least-squares code. In addition to half-life determinations, we searched for previously undiscovered low-intensity alpha-particle and gamma-ray transitions. To do this, we constructed sum spectra from the data mentioned above. After each experiment we segregated the spectral data into “early” and “late” counts, breaking at a time determined by the half-life of the nuclide(s) of interest. We summed all the early and late data taken from each sample on a channel-by-channel basis. The resulting sum spectra were mathematically gain-shifted to make them comparable with sum spectra taken from similar samples generated in other experiments. We determined gain-shifting parameters from the positions of the most intense peaks in the sum spectra. After the conclusion of our experimental series, sum spectra derived from the equivalent counting of similar samples were added together to give early and late pulse-height spectra for each mass fraction.

3. Mendelevium-256 3.1. Historical background, 256A4d

Mendelevium-256 was the first isotope of this element to be observed 1231, produced in the bombardment of 253Es with 4He ions. The initial identification was via the growth of a 3 h SF activity following the 1 h EC/P+ decay of the chemically separated mendelevium activity. In later work, the z6Md half-life obtained from the growth and decay of the SF activity of the z6Fm daughter was

26

LJ. Moody et al. / Decay properties

modified to 1.5 h 1241.A complex alpha activity with the most intense peak at 7.17 MeV was observed with a half-life of 1.5 f 0.2 h and with a decay branch of roughly 3% [251. More recent work has established that the half-life of 256Md is 76 + 4 min [26-B] and the most intense group in the complex alpha spectrum is at an energy of 7.210 f 0.007 MeV [27-301. The branch for alpha decay is (9.3 f 0.51% [301, based on the observation of the growth of the SF activity coming from the fermium daughter [27,28] and on the intensities of the fermium K X-rays relative to the intensities of the alpha groups [27]. The mass number obtained from the genetic relationship to 256Fm was confirmed with mass separation [28]. An initial attempt to link the alpha decay of 260Lr to its daughter 256Md was unsuccessful due to background [31]; more recent attempts involving the rapid chemical separation of 260Lr have been successful [32]. The upper limit on the branching ratio for the direct SF decay of 256Md is 2.8% [28]. A gamma ray, coincident with the alpha particles, was observed at an energy of 400 + 20 keV with a NaI(T1) detector; its intensity relative to the einsteinium K X-rays, assuming that they arise primarily from the internal conversion of this transition, indicates that it is of pure Ml multipolarity [27]. 3.2. Experimental results, mass 2.54 The alpha-particle and gamma-ray spectra of the mass-256 fractions are dominated by =‘jEsrn (half-life = 7.6 h) [33] and by 256Fm (half-life = 2.627 h) [34], both of which are produced in higher yield than is 256Md. The gamma rays emitted in the beta decay of 256Esm have been measured [35] and have been used to determine the partial nuclear level structure of 256Fm, which is also the electroncapture daughter of 256Md. SF is the major decay mode of 2$6Fm, and its alpha-decay branch is 8.1% [361. 3.2.1. Half-life of 256Md We measured the half-life of 256Md from samples generated following six 22Ne irradiations. In three of these experiments, mendelevium fractions were chemically isolated and the 2s6Md half-life was determined from the growth and decay of the 256Fm SF activity, holding the daughter half-life fiied in the calculation. The only other SF activities present in the sample were 258Mdm, 259Md, and 260Md, which were overwhelmed by the 256Fm activity. Using the half-lives that we measured for 258Mdm (see sect. 6.2.1) and 259Md (see sect. 7.2.1) and using the initial activities that we calculated from their known cross sections and the bombardment parameters, we subtracted the SF contributions of these nuclides from the data prior to fitting the growth and decay function. The 260Md activity was negligible. In the three other experiments, we counted the mass-256 fractions for alpha particles and determined the 256Md half-life from the decay of the intensity

K J. Moody et al. / Decay properties

27

between 7.15 and 7.70 MeV (see sect. 3.2.3). The only interfering activity in this energy window was 254Fm (half-life = 3.24 h, alpha energy 7.19 MeV) 1371,which is produced both directly and as the daughter of 254E~m(half-life = 39.3 h) [38]. The decay curves were fitted with a single free component in addition to the 254Fm growth and decay with fixed parent and daughter half-lives. The weighted-average result of the six half-life determinations is (78.1 f 1.8) min. This is in good agreement with the literature. 3.2.2. Relative decay modes of 256Md In experiments where we measured both alpha particles and SF fragments, we never chemically removed the 256Es or 256Fm from the mass-256 fraction. As a result, we could only try to resolve the component of the growth of the 256Fm fissions arising from 256Md decay from those arising from the decays of 256E~mand 256Esg (half-life = 22 m) [33]. We obtained an alpha branch of (11 f 3)%, which is in agreement with the more precise literature value of (9.3 f 0.51% [30]. 3.2.3. Alpha-particle spectra, mass 256 Mass-256 fractions generated after six 22Ne irradiations and three IgO irradiations were followed for several days with alpha pulse-height analysis using surfacebarrier detectors. The spectra obtained during the first 4.5 h of counting of each sample were used in the construction of the sum of early counts (sect. 2.4), shown as the top spectrum in Fig. 1, scaled upward by a factor of 10. The bottom spectrum in Fig. 1 shows the sum of spectra taken after 4.5 h of counting. The peak caused by the 8.1% alpha-decay branch of 256Fm dominates both the early and late alpha spectra. A peak arising from decays of 255Fm is also readily visible. The alpha spectrum above 7.1 MeV is due to 254Fm and z6Md decays. The energy resolutions of the detectors used to take the data shown in Fig. 1 were degraded by the high beta background caused by 256E~m and by the fission products arising from the 92% SF branch of 256Fm. There is also a flat background of spurious events in all channels caused by scattered fission fragments. Using the known level scheme of 252Cf [39], we calculated the energies of the 256Fm alpha transitions to the 2+ and 4+ members of the ground-state rotational band, relative to the energy of the O+-to-O+ transition. Fig. 2 shows the fraction of the decay to the ground-state band arriving at the 2+ state versus the alpha-particle energy of the O+-to-O+ transition for even-even nuclides with neutron numbers greater than 140 [30,40-421. From Fig. 2, we estimate that 11.5% of the alpha decay of 256Fm populates the lowest 2+ state in z2Cf. From a similar treatment, we estimate that 0.2% of the decay populates the 4+ state. We resolved both the early and late alpha spectra into component alpha groups using the FITEK code. The peak shape was defined primarily by the 256Fm activity. We gave the code the relative energies and intensities that we calculated for the alpha decay of 256Fm and the absolute energies and relative intensities of

KJ

28

Moody et al. / Decay properties

‘.&

10

.

.**s.

2.

l

.

:.t'.,

. .

.

. .

.

l-

. .**.*

”

. .

. .

.

.

. ..”

i

11 6.0 I

/

6.5

I

7.0

I

7.5

f

8.0

.

.

*_

_-

.

I

Alpha energy (MeV) Fig. 1. Alpha spectra taken with surface-barrier detectors of mass-256 samples. The top spectrum is the sum of the first 4.5 h of counting of each sample, scaled upwards by a factor of 10. The lower spectrum is the sum of later counts. Several important activities are indicated, many arising from contamination with nuclides from nearby masses. The resolution of the high-energy portion of the upper spectrum into discrete alpha groups is the result of a FITEK calculation (see text>.

254Fm [18], 255Fm [19], and 257Md (see sect. 4.2.3), and held them fixed. Though used for energy-calibration purposes, we excluded the “‘Cf and 254E~g peaks from the fitting procedure because some of these decays occurred on the detector faces rather than in the samples. We subtracted a constant value from each channel of a given spectrum prior to the FITEK analysis, shown by the horizontal lines on the right of Fig. 1, to remove the effect of scattered fission fragments. We had to include a second gaussian component in the peak shape to accurately reproduce the shape of the spectrum on the high-energy side of each peak. The energy resolution derived from the peak shape of the early spectrum was about 70 keV full-width-at-half-maximum (FWHM); the energy resolution of the late spectrum was better due to the decrease in the beta activity. From the late alpha spectrum, we obtained a principal alpha-particle energy for the decay of 256Fm of (6.918 f 0.002) MeV, comparable to the literature value of (6.917 rt 0.005) MeV [30,431. A 400-keV Ml gamma ray is emitted in the alpha decay of 256Md (see sect. 3.1) following the most intense alpha transition. The transition is highly converted,

KJ. Moody et al.

0.101

4

/ Decay properties

29

I

1

I

5

6

7

a

Principal alpha energy (MeV) Fig. 2. The fraction of the alpha-decay intensity of even-even actinides that populates the 2+ member of the ground-state rotational band, as a function of principal alpha-particle energy.

primarily in the K-shell [44], and some fraction of the energy of the resultant electrons can sum with the energy of the alpha particle when both strike the detector simultaneously [16,45]. In the spectrum, this produces a high energy “tail” of uncertain shape with an endpoint at the sum of the alpha particle and photon energies, less the binding energies of the electrons. In our case, this means that some unknown fraction of the events between the main alpha energy and a point approximately 260 keV above it [42,46] belongs to the main alpha peak. We assume that the summing of alpha particles with conversion electrons from higher shells is of negligible intensity. From the early alpha spectrum, we obtained the data given in Table 3 for the resolved alpha groups due to the decay of 256Md. We plot some of these groups as the smooth curves in Fig. 1. Because of poor detector resolution and conversionelectron summing (discussed above), FITEK was unable to settle on a single solution for the number of alpha components in the 7.25 to 7.40 MeV region of the spectrum. Relative intensities of alpha groups arise both from FITEK peak areas and from decay curve analyses of lOO-keV-wide regions of the original alpha spectra. Table 3 presents the results from previous studies of the alpha decay of 256Md

30

KJ. Moody et al. / Decayproperties

Tabte 3 A comparison of the results of previous dete~inatio~s of 256Md with that of the present work

of the alpha-particle spectrum from the decay

Fields et al. (271

Hoff et al. [28]

This work

7.136 + 0.005 (21 f 31% 7.202 f 0.005 (69 f 51%

7.16 + 7.23 + 7.33 * 7.46 f 7.49 +

7.155 f 0.005 (21* 2)% 7.221 + 0.003 (47 f 3)% more groups (19 f 2)% 7.455 f 0.006 (4.5 f 0.51% 7.532 f 0.010 (2.5 f 0.5)% 7.611 f 0.010 (1.5 + 0.51% 7.678 i 0.006 (4.0 f 0.41% 7.773 f 0.016 (0.5 + 0.31%

7.44 + 0.01 * 2% 7.58 + 0.01 y 2% 7.64 f 0.01 _ 4% 7.67 + 0.01 * 2%

0.015 (16 f 21% 0.01 (63 + 41% 0.03 (4 + 0% 0.03 (5 rt l)% 0.02 (6 f 11%

7.67 + 0.03 (2 + 11% 7.72 + 0.02 (4 f 11%

[27,28]. The largest difference between our results and those determined in earlier work relates to the intensity of the strongest transition; we found that much of our “missing” intensity was in the energy region near 7.28 MeV (included in ‘“more groups” in the Table). We would like to be able to attribute part of the discrepancy to a closely spaced doublet that was not resolved in the earlier work, but we cannot exclude the effects of conversion-electron summing. Table 4 lists the excitation energies of the states in 252E~ populated by “‘Md decay and the alpha-decay hindrance factors for those transitions. We assume that the highest-energy alpha transition we observed is to the ground state. We calculated rates for unhindered decay from the data in refs. [30] and 1421. 3.2.4. Gumrna-ray specfra, mass 256 We counted a single mass-256 fraction for gamma rays. The start of the first data accumulation was 110 min after the end of the “0 irradiation. The decay of the sample was followed for 30 h. We observed not only gamma-ray peaks associated with the decay of 256E~m[33,35], but also many gamma rays emitted by the 256Fm SF fragments [34,47]. Using known gamma-ray intensities [48] and decay-curve analysis, we reproduced the mass-yield curve of the SF decay of

Table 4 States in “‘Es populated by “‘Md alpha decay and alpha hindrance factors for the transitions Alpha energy (MeV)

Excitation energy CkeV)

Partial halflife (s)

Hindrance factor

7.155 7.221

628+ 561 f (other 323 f 245 + 165 + 96i O+

2.25 x 105 Q 1.01 x 10s

7.0 d 5.9

7.455 7.532 7.611 7.678 7.773

6 3 states) 7 10 10 7 16

1.05 x 1.89 x 3.16 x 1.18 x 9.47 x

106 106 106 lo6 106

520 1.9 x 6.3 x 4.2 x 7.6 x

103 lo-’ lo3 lo4

K.J. Moody et al. / Decay properties

31

O.loc

'II 5 'S 5 O.OlC ._ 8 ._ IL

A = 256

/

0.001 1

100

110

1

1

120

130

140

150

1 0

Mass number Fig. 3. Mass-yield cmve of the spontaneous fission of 256Fm, from gamma counts of a mass-256 sample. The smooth curve is taken from ref. [34].

256Fm. Fig. 3 shows our data along with a smooth curve describing the results of previous work [34]. We performed decay-curve analysis, using fixed half-lives and known 256E~m relative intensities [351, on the gamma-ray lines arising from known transitions in 256Fm. Only in the case of the fermium K X-rays [461 were we able to resolve a 78 min component in the data, attributable to 256Md EC decay. We established upper limits on the intensities of the 256Md component of each gamma-ray line associated with transitions within the z6Fm ground-s tate band and on several transitions from low-spin states above the pairing gap to the ground-state band. Table 5 lists some of these data. 3.3. Dimmion,

mass 256

3.3.1. Ground state of 256Md The X-ray intensities in Table 5 correspond to a total K X-ray intensity [49,50] of (560 f 80) in the same arbitrary units. Assuming that 256Md decays by EC with

32

KJ. Moody et al. / Decay properties

Table 5 Intensities of the fermium K X-rays due to the decay of 256Md and upper limits (2~) on the intensities of photons emitted in several gamma transitions in 256Fm Photon energy (keV)

Identity a

Intensity (arbitrary units)

111.6 172.8 634.2 833.7 115.3 121.1 136

4+ (g.s.) + 2+ (g.s.) 6 + (g.s.> + 4 + (g.s.1 2+ (b.h.)+ 2+ (g.s.1 2- (b.h.1 -+ 2+ (p.s.1 K 02 K al Kg1 + K53

< 30 ,130 Q 160 < 110 213 f 43 238 f 56 81 f30

’ (p.s.) labels states in the ground-state band; (b.h.1 labels band heads above the pairing gap.

an energy of about 2 MeV (see sect. 3.3.3) and assuming that there is no internal conversion of gamma transitions, we calculate [51] a K-vacancy per EC-decay ratio of about 0.76. Given a fluorescence yield [52] of 98%, we estimate a t&al EC rate of about 750 units. We also calculate a 256Md EC rate of 740 units from the observed 256E~mactivity, the 256Md decay branches, the relative cross sections for 256E~m and 256Md production [1,2,53], and the parameters of the “0 irradiation. Our measurement supports the argument that most of the 256Md decay directly populates the ground-state rotational band of 256Fm. The gamma transitions depopulating the ground-state band of 256Fm are of E2 multipolari~. From the internal conversion coefficients [44,54] and the limits on the intensities of the 173 and 112 keV photons (Table 5>, we estimate that the fraction of the 256Md EC/p+ decay that passes through the 6+ state corresponds to 6 190 units (20) and the fraction passing through the 4+ state to be < 480 units. Since the EC decay of 256Md to states above the pairing gap will decay through the ground-state rotational band via low-multipolari~ electromagnetic transitions, we can exclude the possibility that “‘Md has a ground-state spin greater than 4. From the known level structure of 2s6Fm, the data in Table 5, and the arguments above, we conclude that less than half of the EC decay of a J & 4 25bMd isotope passes through the states in 256Fm above the pairing gap. This conclusion leads to a value of log ft for decays to the ground-state band of less than 6.8, consistent with an allowed or first-forbidden transition [551, and’s 256Md ground state of J < 2. It has been postulated [56,57] that the ground state of 256Md is J” = O- from the antiparallel coupling of the proton $-[514] and neutron i *[6131 Nilsson states according to the Gallagher-Moszkowski rule [58]. The low spin of the 256Md ground state is supported by its partial EC half-life [28] and the log ft for decays to the ground-state band that we present above. The parallel coupling of the proton and neutron states is expected to give a low-lying 7- isomeric state. This state should have a longer partial EC/P+ half-life than does the ground state,

KJ. Moody et al. / &cay properties

33

since EC decays to levels below the pairing gap in 256Fm should be highly forbidden. We have never observed the alpha decay of a 256Md isomer, though it should have been readily apparent in any experiment in which Md isotopes were produced in transfer reactions (e.g. ref. [25]), since the members of isomer pairs are typically produced with about the same yield [7,59]. Also, we did not observe

Calculation Eneigy

““r 509 l

400

K”

Observed r , .Energy G

\ Proton Neutron

Ezzzz2 7.0 1-A

7/2+ [%33]

9/2- [734]

1-p

l/2- [521]

1/2+ [620]

O-A

7/2- [514]

7/2+ [613]

2- A 0- A

712’ [533]

lln-f725]

l/2- 15211

ll2+ [%20]

L

ms5.9

V77F7J

200-

[521]

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3/2- [521]

3/2+ [%22]

3!2- f521]

l/2+ [%20]

2- A 0- A

3s

1-A lOO-

0

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Y

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3/2- [521]

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7!2+ [633]

l/2+ [%2%1

t6201-

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520

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1,900

pzz?j

8,300

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4,200

7%,%0%

Fig. 4. Comparison of the results of a caicuiation of the quasiparticle excitation energies of 252Es, on the left, with the level scheme determined from the alpha decay of 256Md, on the right. Only odd-parity states with K < 2 are shown, except for the ground state. The labels “P” and “A” refer to parallel and antiparallel couplings of single-particle configurations, respectively. The thickness of the experimental levels defines their energy uncertainty. Tentative correspondence between the calculated and measured level schemes is made on the basis of the odd-nucleon configurations and the observed hindrance factors for alpha decay (far right). The state anaIogous to the “6Md ground state is marked with an asterisk. H values are the observed hindrance factors for alpha decay to the indicated states.

KJ. Moody et al. / Decay properties

34

any unexplained components in the growth and decay of the 256Fm SF activity. From the systematics of odd-neutron levels [60], we expect that both the a+[6201 and 5’[622] Nilsson states could couple with the proton G-l5141 state to yield low-lying 3- and 5 states, respectively, some combination of which may provide a bridge for the rapid internal-transition decay of the 7- state. Similarly, the $-[521] proton state is predicted to lie close to the G-[514] state [61] and could couple with the :+[613] neutron state to provide a similar bridge. Though the 256Md ground state is probably K = 0, there is some question 1301as to whether the spin and parity are O- or l- due to the Newby shift [62]. The following empirical rule was proposed [63] to predict the lowest spin state in a K = 0 band in an odd-odd rotational nucleus: I, =

(j, +j,) mod 2,

(1)

where j, and j, are the single-particle quantum numbers and I, is the favored lowest spin. The favored spin predicted by this rule is correct more often than not; most failures occur when one or both of the single-particle states are poorly described by the Nilsson quantum numbers because of configuration mixing [63]. Eq. (1) predicts a ground-state spin for 256Md of J” = l-. This is supported by the population of states in 252E~ fed by the alpha decay of 256Md (described in sect. 3.3.2). 3.3.2. Level structure of 2s2Es We calculated the quasiparticle excitation energies of 252E~ using the model of Hoff et al. [64]. The model takes as input the experimental Nilsson levels and rotational parameters of nearby deformed odd-A nuclei. It assumes that the pn residual interaction energy is small compared with the energy that binds the odd nucleons to the nucleus and treats it as a perturbation. The model has been very successful in reproducing the excited states of odd-odd light actinides [64,651. For the 252E~ calculation, we gave the code the odd-proton levels of 251E~ [42] and 253E~ (see sect. 41, and the odd-neutron levels of 251Cf [42] Fig. 4 presents the results of the calculation, indicating the energies of odd-parity band heads with J G 2 and their Nilsson assignments. The state with the same configuration as the 256Md ground state is indicated with an asterisk. We also show the level structure determined from our alpha-particle spectra, taken from Table 4. The ground state of the experimental level scheme has been shifted downwards 75 keV relative to the calculated level scheme for ease of comparison. The thicknesses of the experimental levels are defined by the uncertainties of the alpha-particle energies. We suggest a possible correspondence between calculation and experiment in Fig. 4 based on the values of the hindrance factors and the energy spacings. Hindrance factors for the alpha decay of odd-A actinide nuclides have been calculated in the shell model [66,67]. In these calculations, alpha-particle preformation is calculated

KJ. Moody et al. / Decay properties

35

Table 6 Calculated shell-model reciprocal formation factors for alpha decay between the indicated Nilsson states. Data from ref. 1661for =‘Md, z5Fm, and z7Fm decays Reciprocal formation factor

Transition proton

f[514]$-

+ $5141 3+

9f+

+ $6331 ; + 3[5211 f 5T_ -+ 7 + 5 neutron :[613] G+ + $6131 ?+ G+ + i+ + $6201 + 3+ + T 5+ + 2 7+ -+ i+ + $6221 ; 5+ + 2 +

7+ i

neutron $6151 ;+ + 416151 e’ II + + T+ + ;[613] ; 9+ --f 5, + $6221 f 5+ + i 7+ -+ i

2.6 17 7700 42000 520 430 3.1 18 1600 990 230 380 46000 6900 4300 2.4 15 1600 2600 7500 3400 2400

with pairing-force wave functions from superconductivity theory [68] under a delta-force approximation. This results in a reciprocal formation factor that is analogous to the experimentally derived reduced hindrance factor. Table 6 lists some relevant reciprocal formation factors. We expect alpha decays to states with antiparallel np coupling, like the 256Md ground state, to be favored over decays to states with parallel coupling. In Fig. 4, a P after the K assignment of the state indicates parallel coupling, and an A indicates antiparallel coupling. From the calculated reciprocal formation factors, we expect decays from 256Md involving a change in neutron configuration from 3+[6131 to +‘[620] to be highly favored over transitions involving the change from neutron ; ‘[613] to + ‘[622]. We expect decays involving no change in neutron configuration to be even more highly favored. This accounts for our assignments of the lowest four excited states in the experimental 252Es scheme, all of which have a proton configuration of $-[521].

36

LL Moody et al. / Decuy propertks

The low hindrance factors for decays to the states at 561 and 628 keV imply that both are associated with favored alpha decay to the state indicated by the asterisk in Fig. 4. The (67 f 7) keV difference in energy between the levels compares with the calculated rotational spacings between the O- and 2- states of 34 keV, and between the l- and 3- states of 57 keV. This is evidence for a negative Newby term for the pairing of the proton 5 -[514] and the neutron g +[613] states, and a l- ground state for 256Md. The hindrance factor for the apparent decay to the 4+ ground state is consistent with that expected from an 1 = 5 alpha emission from a negative-Paris band [42]. Hypothetically, much of the de-excitation of the state produced by the favored alpha decay should be by a (396 f 11) keV gamma transition of Ml multipolarity to the K” = O- band head at 165 keV; this would be consistent with the previous observation [27] of a (400 rf: 20) keV Ml photon in coincidence with the main alpha transition. 3.3.3. Mass excess of 256Md If we assume that the 7.773 MeV alpha transition is to the ground state, we calculate a Q-value for alpha decay of (7.896 k 0.016) MeV. Using the mass excess for =‘Es [69] of (77.29 + 0.05) MeV, we obtain an atomic mass excess for 256Md (no screening correction [70]) of (87.611 & 0.053) MeV. This compares with other e~erimentally justified values of 87.42 MeV [71] and (87.55 + 0.05) MeV 1691. From the known 256Fm mass excess [69], we obtain a value of Qnc for 256Md decay of (2.129 f 0.054) MeV.

4. Mendelevium-257 4.1. Historical background, 257Md Mendelevium-257 was first observed in one of the original experiments where actinide activities were produced in transfer reactions 1251.A 3 h activity with an alpha energy of 7.07 MeV was observed in a chemically separated mendelevium fraction following the irradiation of 252Cf with ‘iB, 12C and 13C ions. Its mass number was assigned on the basis of cross-section systematics and by the fact that the activity could not be made in 4He irradiations of 253E~.A weak alpha group at 7.24 MeV, which was initially assigned to 257Md, was later assigned to 254Fm, produced from the EC decay of 254Md 1291.The partial half-life for SF was greater than 30 h, and the branch for alpha decay was roughly 8%, based on the “estimated yield” for its production. Mendelevium-257 was later made in irradiations of mixed einsteinium isotopes with 4He ions. It was determined that its half-life is 5.2 j, 0.5 h [26-281, the energy of the only observed alpha group is 7.064 & 0.005 MeV [27,28], and the branch for alpha decay is (IO f 3>% determined from the ingrowth of 257Fm 12’71.The upper

MT. Moody et al. / Decuyproperties

37

limit on the branch for SF is 3.6%, and the mass number was confirmed by isotope separation [28]. From mass systematics, the analog state for alpha decay in the 253Es daughter is at an excitation energy of several hundred keV [25,72]; from Nilsson systematics, this level is probably the $ -[514] proton state [25,29,57,72]. 4.2. Experimental results, nzass257 Shortly after mass separation, the decay of =‘Md dominates the alpha-particle and gamma-ray spectra of the mass-257 fractions. At later times, =‘Frn (half-life = 100.5 d) [73] and 253Es (half-life = 20,47 d) [42] dominate the alpha spectra. Most of the SF events observed at early times are due to contamination from the mass-256 decay chain (see sect. 3.2); at later times, the SF events decay away with the =‘Frn half-life at an intensity relative to the 257Fm alphas [42] consistent with the known 0.21% SF decay branch 1731. 4.2.1. Hatf-life of 257Md We measured the half-life of 257Md from mass-257 samples generated following six **Ne irradiations and five “0 irradiations. We determined nine values of the half-life from the decay of the 7.07 MeV peak in the alpha spectra. In some of the decay-curve analyses, we included an extra component with the fixed half-life of 255Fm (half-life = 20.07 h) [74] to bring the reduced x2 of the fit to unity. We also determined four values of the half-life from the decay of the fermium Km2 and Km1 X-ray peaks in photon spectra that we obtained following two of the irradiations. The weighted-average result of the thirteen half-life determinations is (5.523 f 0.050) h, consistent with the literature value of (5.2 f 0.5) h [26-281. 4.2.2. Relatiue decay modes of 257iMd We used mass-257 samples generated following four of the shortest irradiations to determine the alpha branch of 257Md. The =‘Md alpha-decay intensity was determined using the data given in sect. 4.2.3. The 257Md EC-decay intensity was determined from the ingrowth of the main alpha-group of 257Fm [751 during the first day following the mass separations. We performed the decay-curve analyses using fixed half-lives (given above). The alpha-decay branch that we determined for 257Md was (15.2 + 2.6)%, in marginal agreement with the literature value [27] of (10 + 31%. This earlier value was obtained by assuming that any %‘Frn present after several days in a chemically separated mendelevium fraction must have arisen from 257Md decay. Any 257Fm left in the sample at the separation time would have resulted in a reduced alpha branch. To generate our value of the alpha branch, we had only to assume that no significant amount of 257Es (an unknown nuclide) decayed to =‘Frn during the times that data were collected. This assumption is reasonable, based on both the expected formation cross sections and half-life of 257E~. ~though a recent calculation [76] arrived at an estimated 257Es beta

K.J. Moody et al. / Decay properties

38

half-life of about three days, we believe that more reasonable values were obtained by others: 1.5 h 1771, 1 h [78], and 40 min [79]. The saturation factor during the bombardments and decay after the bombardments both serve to reduce the amount of 257Es relative to 257Fm and 257Md in the mass-separated samples arriving at the detectors. In addition, by extrapolating the known cross sections for heavy-ion transfer reactions with 254E~g [2,3], we expect the cross sections for the production of 257Es to be much lower than those for 257Fm and 257Md production. Not only is the pick-up of three neutrons by the target an unlikely exchange, but the binary reactions at the projectile energies we used provided barely enough energy to produce 257E~ even assuming deformation in the exit channel to lower the minimum recession ;elocity [3]. We also established a limit on the branch for the SF decay of 257Md. Spill-over from mass 256 introduced a fission activity in all the mass-257 fractions with an t t 10’

I

I

E

i

/

: :

*. -.

;‘.

’

6.0

‘. .

.

I

: t

. .. -2%. . .22 l; . .

10’ -

4

i

I

.

lo* :

I

A = 257

*

i

l--

I

I

I

6.5

:

,. a!

. . . . . ..... 2. .*. ..... . ... . I

7.0

. *. *.

. . * .’ .. t

. . . .. . . . _. Wm. .. _ . . . .. m_. ,“._ m. M. . ..I. _“_._. 7.5

6.0

Alpha energy (MeV) Fig. 5. Alpha spectra taken with surface-barrier and gas-ionization detectors of mass-257 samples. The top spectrum is the sum of the early counts of each sample, scaled upwards by a factor of 103. The lower spectrum is the sum of later counts. Several important activities are indicated, many arising from contamination with nuclides from nearby masses. The resolution of the 257Md activity in the upper spectrum into discrete alpha groups is the result of a FITEK calculation (see text).

KJ. Moody et al. / Decay properties

39

apparent half-life of 8 to 9 h, from the decay of 256E~m to 256Fm (see sect. 3.2). With the low counting statistics, it was impossible to resolve a 5.5 h component from the SF decay curves. We picked the data from the mass-257 sample with the lowest amount of mass-256 contamination and forced a 5.5 h half-life to the data to arrive at an upper limit (2~) of G 1.0% for the SF decay of 257Md, using the alpha-decay branch given above. This branch corresponds to a partial SF half-life of 3 23 d and an SF hindrance factor, based on the SF half-lives of neighboring even-even nuclides [42,80], of 2 6 x lo5 (see sects. 5.3.3 and 7.3.1). 4.2.3. Alpha-particle spectra, mass 257 Mass-257 fractions generated after five 22Ne irradiations and four “0 irradiations were followed for several months with alpha pulse-height analysis using surface-barrier and Frisch-grid ionization detectors. The spectra obtained during the first three hours of counting of each sample were discarded to avoid including significant amounts of 256Md activity in the sum spectrum. We summed the spectra obtained during the next 16 h to yield a final sum of early counts, shown as the top spectrum in Fig. 5, scaled upward by a factor of 103. The spectra taken after the first 19 h of counting were similarIy treated, and the resultant sum of late counts is shown as the bottom spectrum in Fig. 5. The peak due to the alpha decay of 257Md dominates the early alpha spectrum. At late times the peaks arising from decays of 253E~and “‘Frn dominate. Besides being =‘Md decay daughters, both are produced directly, and 253Es is the granddaughter of 257Fm decay 2421. Events above 7.0 MeV in both spectra are due to 257Md, 255Fm, and 254Fm; both fermium isotopes are produced directly and are the daughters of longer-lived 255Es (half-life = 38.3 d) [421 and 254E~m,respectively. We resolved both the early and late alpha spectra into component alpha groups. The 257Md, =‘Frn, and 253Es activities defined the peak shape. We gave the code the relative energies and intensities of the 257Fm alpha groups [75] and the absolute energies and relative intensities of both 255Fm and 253Es 1191.Although we used the 250Cf and 254Esg peaks for energy calibration purposes, we excluded them from the fitting procedure. We included two gaussian components to the peak shape as before to simulate the effect of conversion electrons and of the slightly different peak shapes arising from different detectors. Since the derived intensity of the satelhte gaussian was a factor of 15 less than that of the main, lower-energy gaussian, its presence or absence did not significantly affect the fit to the alpha spectrum above 7.2 MeV. The energy resolutions of the peak shapes of both early and late spectra were appro~mately 26 keV FWHM. From the late alpha spectrum, we obtained a principal alpha-particle energy for the decay of =‘Frn of (6.519 f 0.002) MeV, comparable to the literature value of (6.520 it 0.002) MeV [75]. From the early alpha spectrum, we obtained the data given in Table 7 for the energies and relative intensities of the resolved alpha groups arising from the

40

K J. Moody et al. / Decay properties

Table 7 Energies and intensities of alpha-particle groups from the decay of 257Md, hindrance factors a for those decays, and derived energy levels in z53Es Alpha energy (MeV)

Relative intensity

Hindrance factor

Excitation energy in Es-253 (keV)

7.014 f 7.074 f 7.260 f 7.303 + 7.336 f 7.361 f 7.403 f 7.440 f

- 350 10000 21* 5 26* 5 14 f 10 10 f 10 26 f 20 38+ 6

- 35 2.1 5500 6600 17000 30 000 17000 15 000

433 f 372 f 183 f 139 f 106 f 80 f 38 f 0

0.006 0.001 0.002 0.002 0.003 0.007 0.006 0.002

7 3 3 3 4 8 7

a Hindrance factors use alpha-decay branch from sect. 4.2.2

decay of 257Md. We plot these groups as smooth curves in Fig. 5. For this analysis we assumed that the effect of summing alpha particles and conversion electrons was negligible because of the multipolarity of the gamma transitions (see sect. 4.3.1) and the response of our Frisch grid counters to electrons [16]. The 254Fm activity obscured any low-intensity peaks caused by 257Md in the region between 7.1 and 7.2 MeV. Alpha events in the original spectra between 7.2 and 7.5 MeV were treated with decay-curve analysis and were found to decay with the 257Md half-life. Our value of (7.074 f 0.001) MeV for the energy of the main alpha peak can be compared with previously determined alpha-particle energies of (7.064 * 0.005) MeV [27] and (7.075 + 0.020) MeV [28]. Energy and intensity data given for the 7.014 MeV alpha transition are very uncertain because they are strongly affected by the energy uncertainties of the 255Fm alpha peaks (Table 2). Table 7 also lists the hindrance factors for the alpha decay of the different groups and the excitation energies of the levels in the 253Es daughter, assuming that the highest-energy transition we observed is to the ground state. We calculated hindrance factors from the unhindered rates (see sect. 3.2.3), the half-life (see sect. 4.2.11, and the branch for alpha decay (see sect. 4.2.2). 4.2.4. Gamma-ray spectra, mass 257 We counted two mass-257 fractions for gamma rays. The start of the first data accumulation was about 80 min after the end of each irradiation. The spectra taken during the first 14 h of counting were summed and are shown as the upper spectrum in Fig. 6. We counted a third mass-257 sample for gamma rays in coincidence with alpha particles of over 6.6 MeV energy (see sect. 2.3). The start of the first data accumulation was 65 min after the end of the irradiation. The spectra taken during the first 23 hours of counting were summed; this sum is shown as the lower spectrum in Fig. 6. In Fig. 6, we labeled peaks in the gross (upper) gamma-ray spectrum due to background activities with a “B”. We labeled gamma-ray peaks that appear in both

41

RJ. Moody et al. / Decayproperties IQ4 L

I

I

A= 257

Fm_Ka

. ..__. 0

100

I

I

I

200

300

1

_

.

400

500

Photon energy (keV) Fig. 6. Gamma-ray spectra of mass-257 samples. The upper spectrum is gross gamma activity. The lower spectrum is coincident with alpha particles of more than 6.6 MeV energy. Background peaks in the gross spectrum are labeled with a “B”.

the gross and alpha-coincident spectra with their energies. We accounted for all the major gamma-ray peaks in both spectra, implying that the EC branch of =‘Md, which is much larger than the alpha branch, produces many K X-rays but very few gamma rays. The coincidence counting filtered out almost all of the fermium K X-rays and the detector background, allowing us to observe the einsteinium K X-rays. The fermium K X-rays and the gamma-ray lines at 325.1 and 371.4 keV decay with the 257Md half-life. Above 372 keV in the coincidence spectrum, we observed only one event in 23 h of counting, and it occurred during the first two 257Md half-lives. Since the energy of this event (388.5 keV) corresponds to a difference between two of the energy levels in 253Es determined from the alpha spectra (Table 71, we tentatively identified it as being caused by a true transition in 253Es. We include this transition in Table 8, where we summarize the results of the photon counting. The X-rays occurred at energies consistent with those predicted in ref. [46]. The observed relative intensities of the fermium K X-rays are somewhat closer to those calculated in ref. [.50]than to those calculated in ref. [49], though both significantly overpredict the intensity of the K,, line relative to the other X-rays. We determined the intensity of the 7.074 MeV alpha-particle transition relative to the photon intensities during the coincidence experiment; most of the quoted uncertainty is due to the poorly determined source size. 4.3. Discussion, mass 257 4.3.1. Level structure of 253Es The ground state of 253Es has an odd-proton configuration of i +[633] [421. The reciprocal formation factors [66,67] given in Table 6 indicate that the observed

K3. l&miy

42

Table 8 Photon energies and intensities alpha-particle transition

from the decay of “‘Md,

K nz K ul %a+:,

Kw einsteinium

K,, K Czl %a+3

photon

relative to the intensity of the main

Relative intensity

Observed decav 7.074 MeV fermium

et al. / Decay proper&s

181.3 + 0.5 keV 325.1 10.2 keV 371.410.1 keV 388.5 f 1.5 keV

1.00

f 0.05

0.908 1.255 0.500 0.143

f f f f

0.035 0.031 0.030 0.023

0.0337 f 0.0050 0.0548 f 0.0065 0.0264 f 0.0057 0.0291 + 0.0075

0.175 + 0.021 0.820 + 0.037 _ 0.005

hindrance factor (Table 7) for the 7.44 MeV alpha transition is consistent with a f-[514] to :‘[633] alpha transition from the ground state of 257Md. The hindrance factor for the alpha decays of 7.074 MeV energy, populating a state about 372 keV above that populated by the 7.44 MeV alpha decay, indicates that it is the analog state, of confi~ration $-[514]. From Tables 7 and 8, we state that the intensity of the 371.4 keV photon relative to that of the different alpha-particle groups requires both that the photon arise from depopulation of the level populated by the 7.074 MeV alpha transition and that the transition be of El or E2 multipolarity. An El transition is consistent with the population of the 253Es ground state by the 7.44 MeV alpha decay. By analogy to the rotational spacings observed for the 2 +[633] band in z47Bk [42,61] and 249Bk [19,81], we expect the %* member of that band to occur near 42 keV and the G + member to occur near 94 keV. The two lowest excited states shown in Table 7 have similar energies, with hindrance factors for alpha decay to those states consistent with their assignment to the ;+[633] band, The intensity of the alpha-coincident 325.1 keV gamma ray relative to the intensities of the alpha transitions requires that it also arise following population of the analog state, terminating in a state at 46.3 keV, consistent with the first excited state of 38 t_ 7 keV (Table 7). Therefore, the 325.1 keV gamma transition should also be of El multipolari~. The Bohr-Mottelson gamma transition rates for gamma decays of multipolarity L to the different members of a rotational band [821 are related by: R(L)

aEZL’1[(JfKf/JiLKiAK)]2,

(21

where Jf and K, describe the finaI states, Ji and Ki describe the initial state, and AK = K, -K,. Using eq. (2), we calculate the ratio of the rate of depopulation of

KJ. Moody

et al. /

Decay

properties

43

the $-[514] state by 325.1 keV transition to that of depopulation by 371.4 keV transition to be 0.192. The ratio of the observed intensities of the photons, corrected for internal conversion [44,54], is 0.21 f 0.03, in good agreement with the calculation. Assuming that the only modes of depopulation of the 372 keV excited state are by these two gamma transitions, we obtain a total depopulation rate of (1.03 rf: O.OS>,in the units of Table 8, in good agreement with the rate of population by the 7.074 MeV alpha particle. Table 7 lists several more alpha-particle transitions than we have yet identified. In the level schemes of odd-mass berkelium isotopes, the $-[521] state lies close to the q+[633] state [42]; therefore, we conclude that some of the lowest excited states in 253Es are the members of this band. The reciprocal formation factors given in Table 6 indicate that alpha decays from the ~-[!I141 state to some members of the $-[521] state are less hindered than are decays to the ;+I6331 band. This is similar to what we observe. By analogy to the rotational spacings observed for the z$-[521] band in 247Bk and 249Bk, as before, we expect the $ - level to be about 35 keV above the $ band head, and the $- level to be about 85 keV above the band head. This corresponds to the spacings between the 106 + 4 keV, 139 I~I3 keV, and 183 f 3 keV states listed in Table 7. The hindrance factors for decays to these states do not exactly mimic the data in Table 6, but the tendency of the hindrance factors to decrease with increasing spin is reproduced. The hindrance factor for decays to the state at 433 keV is consistent with decays to the second member of the z -[514] analog band. By analogy with *‘*Es [28,42,61], we expect the z- state to be about 62 keV above the $ - band head, which is what we observe. Based on the data in Tables 7 and 8 and the discussion above, we construct the level scheme of 253E~, shown in Fig. 7. We place the gamma rays in the level scheme based on the difference in level energies. The intensity of the weak 181.3 keV gamma ray is considerably higher than can be explained by the population of the state by the 7.26 MeV alpha transition; some of the population of the 371.4 keV state must deexcite by an Ml/E2 transition to the g- state at 181.3 keV. This increases the total depopulation rate of the 371.4 keV state to 1.06 k 0.06, which is still in agreement with the 7.074 MeV alpha-transition intensity. Only photons of El multipolarity were observed; given the internal conversion fractions and the poor response of the detectors to electrons [16], we expect no si~ificant contribution to the interesting portions of the alpha spectra from summing with conversion electrons. 4.3.2. Mass excess of *j7Md From the energy of the alpha transition to the 371.4 keV state, we obtain a Q-value for the alpha decay of X7Md of (7.557 f 0.001) MeV. Using the atomic mass excess for z53Es [69J of (79.007 & 0.002) MeV, we obtain an atomic mass

LJ. Moody et al. / Decay properties

44

a -15%

E*(keV)

7l2-

7t2[514]

4

~

7l2-

2/2[5211 *

11/2+

253

h=5500

h~l7ow h=30000 h=17000

9l2’ 7/2+

95%

h=6600

s/2w2-

h 12.1

7/2[633]

M-

h=15000

ES

Fig ‘ 7 . The alpha decay of 257Md and the level scheme of 253Es. Observed gamma transitions are placed in the level scheme. Values of h are observed hindrance factors for alpha decay to the indicated states.

excess for 2s7Md of (88.989 f 0.003) MeV. This compares with the experimentally justified values of 89.04 MeV [71] and (89.01 f 0.20) MeV [69]. From the known 257Fm mass excess [69], we obtain a value of Qnc for 257Md decay of (404 j, 8) keV. 4.3.3. Alpha-decay branch and 257Fm levels from photon intensities In the units of Table 8, the tota fermium K X-ray intensity is (2.81 f 0.06) units. The total depopulation intensity of the 371.4 keV state is (1.06 f 0.06) units (see sect. 4.3.1). From Table 7, the fraction of alpha decays arriving at the 371.4 keV state is about 95%, leading to a total alpha-decay rate of 1.12 units. If 100% of the EC decay directly populates the ground state of 257Fm, we apply the total K fluorescence yield for fermium [42] of 0.98 and the fraction of EC decays producing a K vacancy [51] of 0.64 to the total fermium K X-ray intensity to yield an EC rate of 4.50 units and an alpha-decay branch of 20%, which is significantly higher than our measured value (see sect. 4.2.2). If we assume that the EC decay of 257Md populates only the ;+[615] ground state of 257Fm, we obtain a value of log fr = 5.4, somewhat low for a first-forbidden decay. The absence of gamma rays in the gross gamma spectrum (Fig. 6) does

KJ. Moody et al. / Decay properties

45

not preclude some of the decay passing through the low-lying ;+I6131 band (by analogy to the level schemes of 253Cf [42,75] and 255Fm [42]), which would decay to the ground state by highly converted Ml transitions. If we assume that the 9+[613] band in 257Fm is at an excitation energy low enough to be significantly populated by the EC decay of 257Md, we also require that it is at an energy below the 142 keV binding energy of the fermium K electrons [46], since the log ft value for decays to this state is probably similar to that for decays to the ground state. The presence of the 3+[6131 state lowers the number of K X-rays per EC event by lowering the effective decay energy in the calculation of K vacancies per EC [51] without introducing any extra K X-rays through internal conversion of the depopulating gamma transition. This lowers the calculated alpha branch of 257Md somewhat, bringing it closer to the observed value. We use this argument and the low value of log ft calculated above to propose that the $+[613] excited state of 257Fm probably lies within 140 keV of the ground state.

5. Mendelevium-25gg 5.1. Historical background, 2s8Md g

Mendelevium-258g was first produced in the irradiation of mixed einsteinium isotopes with 4He ions [831. The accepted value of its half-life is 55 & 4 d [27,831. It has prominent alpha groups at 6.716 * 0.005 MeV and 6.79 f 0.01 MeV, with intensities of (72 f lo>% and (28 f 6)%, respectively [271, and the partial half-life for the sum of EC, p-, and SF decays is greater than 140 yr [84,851. The mass number has been confirmed by watching the growth and decay of the alpha-decay daughter [27,83]. Mass systematics indicate that the analog of the =‘Md ground state in z4Es is at an excitation energy of approximately 500 keV [29,561. The ground state of 258Md must be of very high spin, since the /3- and EC half-lives are so long [27], and it seems likely that it is formed from the coupling of the proton a-[5141 and neutron ;+I6151 Nilsson states to J” = 8- [30,56,57]. 5.2. Experimental results, 2s8A4dg 5.2.1. Half-life of 258Mdg

We measured the half-life of z8Mdg from mass-258 samples generated following two “Ne irradiations and two “0 irradiations. In three of these experiments, we followed the decay of the alpha activity between 6.68 and 6.85 MeV for 40 to 60 d following mass separation. We excluded data taken during the first three days of counting to eliminate short-lived contaminants. The only interfering activity in the samples was 257Fm, which has approximately 4% of its alpha intensity [75] in

RI. Moody et al. / Decay properties

46

t,,

=

51 .O f 0.4 days

Growth and decay of 254Esg,x l/10, = 53.1 * 2.3 days

,044

0

100

200

300

Time after chemical separation (days) Fig. 8. Decay of zssMd8 and growth and decay of zs4Es8 from alpha counts of a mass-258 sample which was chemically purified from other actinide activities. The 254Es8 data has been scaled downwards by a factor of 10.

the defined energy window. We established the magnitude of the correction from the intensity of the main 257Fm alpha peak and found it to be negligibly small in each case. After one 22Ne irradiation, we chemically separated mendelevium from the mass-258 sample, according to the procedure outlined in sect. 2. We counted this sample for 270 d and determined the half-life of 258Mdg not only from the decay of the alpha activity in the 6.68 to 6.85 MeV window, but also from the growth and decay of the 254Esg daughter, whose half-life we held fixed at 275.7 d [%I. Fig. 8 shows the two decay curves generated from this sample. The weighted-average result of the five half-life determinations is (51.50 rfr0.29) d. This compares favorably with values of (56 r%:7) d [27], (54 f 5) d [83], and (53.3 + 1.2) d 1841 determined previously from sources produced from 4He-ion irradiations of mixed einsteinium isotopes. X2.2. ~~rnrna rays in ~5~ncide~ce with 258Mdg alpha particles A single mass-258 sample, generated following a 22Ne bombardment, was counted for gamma rays in coincidence with alpha particles of over 6.6 MeV

RJ. Moody et al. / Decayproperties

47

Photon energy (keV) Fig. 9. Gamma-ray spectrum from =sMdg decay, coincident with alpha-particles of over 6.6 MeV energy. The most intense peaks are labeled with their energies in keV.

energy. We chose this cut-off energy because none of the long-lived contaminant activities in the mass-258 fractions emits gamma rays following alpha decays with this energy, yet the defined energy region encompasses virtually all of the =*Mdg alpha decay (see sect. 5.1). The start of counting was 3.1 d after the end of the irradiation. We summed the gamma-ray spectra taken during the next 55 d to obtain the spectrum shown in Fig. 9. The largest gamma-ray peaks are labeled with their energies in keV, and the einsteinium K X-rays are also indicated. Table 9 gives the energies and intensities of the alpha-coincident photons. The measured energies of the einsteinium K X-rays compare favorably with those given in the literature [461. Table 9 also gives the approximate intensity of the 258Mdg alpha decay, from the number of alpha particles with energies greater than the cut-off value detected by the surface-barrier detector during the coincidence measurement. Most of the uncertainty in this number is due to the poorly defined source size and the estimated fraction of the activity caused by the decays of contaminants (see sect. 5.2.3). The intensities of the 277-, 368- and 448 keV gamma rays relative to the alpha intensity, and the weakness of the K X-rays, imply that all three gamma rays are of El multipolarity and arise in the depopulation of the state which receives most of the alpha intensity (see sect. 5.3.1). With this information, we construct a partial level scheme for 254Es shown in Fig. 10, which we use in the analysis of the alpha sum spectrum in the ‘next subsection. The low intensity of the 80 keV

48

LJ. Moody et al. / Decay properties

Table 9 Photons emitted in the alpha decay of 258Mds

Es Es Es Es

Kcrz, K,,, KgI+3, Kgz,

“‘Mdg

Energy

Intensity

56.7 71.1 80.1 86.9 91.0 171.1 189.1 205.7 214.7 276.8 296.7 298.1 367.8 376.8

rt 0.2 rt 0.1 rt:0.2 f 0.2 p 0.3 * 0.2 + 0.2 i 0.2 f 0.2 f 0.1 + 0.2 k 0.3 k 0.1 f 0.4

5.4 f 1.3 80 * 5 24.3 f 2.3 5.6 f 1.5 3 i1.8 11.4* 3.7 9.9 * 3.9 12.1 f 4.3 11.6& 4.6 202 + 19 54 f 9 18.9 f 5.6 1000 f 69 17.2i6.7

389.1 447.9 112.4 117.9 133.4 136.8

f 0.2 f 0.1 & 0.2 rt 0.2 f 0.4 rt 0.3

alpha intensity

40* 366 22 36 13 7+ 2800

9 f 38 + 3 & 4 + 3 3 * 400

transition following the 368 keV transition is due to internal conversion (see sect. 5.3.1). 5.2.3. Alpha particles from 258Mdg decay Mass-258 fractions generated after one 22Ne and three ‘*O irradiations were followed for several months with alpha pulse-height anaIysis using gas-ionization detectors. The spectra obtained during the first 3.5 d of counting of each sample were discarded to reduce the amounts of 254Fm (daughter of 39 h 254Esm) and 255Fm brought into the sum spectrum. We summed the remaining spectra to yield a final sum of late counts, shown as the top spectrum in Fig. 11, scaled upward by a factor of 100. The chemically purified mass-separated sample mentioned in sect. 5.2.1 was counted with a surface-barrier detector. The spectra obtained during the first 200 d of counting were added together to yieid the bottom spectrum in Fig. 11. The alpha activities of “‘Mdg and its daughter, 254Esg, dominate the two alpha sum spectra. In the upper spectrum, we also see 2s3E~ (from the decay of 257Md spihed-over from the adjacent mass), small amounts of 254Fm, and lighter actinides coming primarily from detector contamination. Although we removed contaminant activities from the sample giving the lower spectrum, the data are of limited use for

KJ. Moody et al. / Decayproperties

49

Fig. 10. Partial level scheme of 254Es from the gamma rays emitted in the decay of *“Mds. Used in the analysis of the alpha spectra, discussid in sect. 5.2.3. Arrow widths are proportional to the intensities of the gamma rays placed in the level scheme.

spectral analysis because of the summing of alpha particles with conversion electrons (see sect. 3.2.3 and ref. [16]). We resolved both spectra shown in Fig. 11 into component alpha groups. The peak shapes were defined primarily by the 254E~g and 258Mdg activities. We provided the absolute energies and relative intensities of the z3Es, 254E~g, 254Fm, and z5Fm alpha groups (see sect. 4.2.3). Although we used them for energycalibration purposes, we excluded peaks arising from decays of 242Cm and =‘Cf from the fitting procedure. The energy resolution of the peaks in the top spectrum is about 23 keV FWHM and in the bottom spectrum it is about 29 keV FWHM. The energy of the main =*Mde alpha peak is (6.718 f 0.002) MeV, compared with the literature value of (6.716 f 0.005) MeV [27]. From the data in Fig. 10 and the energy of the alpha transition to the analog state, given above, we know there are states in 254Es corresponding to alpha energies from =‘Mdg decay of 6.697, 6.788, 7.080 and 7.159 MeV. Since these states are accessible to low-multipolarity electromagnetic transitions from the alpha-decay analog state, we expected alpha decay to proceed directly to these states with observable rates. Therefore, we held variable-intensity alpha components at these fixed energies during the fits to the data.

50

KJ. Moody et al. / Decay proper&s

A = 258

. . .

102-

: l

_. *

,o

f .*

. .

‘Z l: * . . l:* . . .t . l f l

5 _. . *.- .-.

l

.

.

. . .

1

I

I

I

6.0

6.6

7.0

..* .“.

. “.

“..

* *.(I 7” 7.5

Alpha energy (MeV) Fig. 11. Alpha spectra of mass-258 samples. The upper spectrum is the sum of all counting with gas-jonization detectors, scaled upwards by a factor of 100. The lower spectrum is the sum of counting of a chemically purified mendelevium fraction with a solid-state detector. Contaminant and detectorbackground activities are labeled. Note the severe conversion-electron summing in the lower spectrum.

Table 10 shows the results of this anaIysis. The energies and intensities of the alpha transitions with less than 7 MeV of energy come primariIy from the analysis of the top spectrum; the complex alpha structure between 6.65 and 6.80 MeV was reproduced in the analysis of the bottom spectrum. The peak structure on the high-energy shoulder of the strongest transition comes from requiring an aipha transition at an energy of 6.788 MeV, from the level structure in Fig. 10. The strongest transition of the group comprising the shoulder is not at that energy and must deexcite without the emission of strong gamma rays. The energy of this alpha transition corresponds to an excitation energy of 402 _45 keV in 2J4Es. We give

KJ. Moody et al. / Decay properties

51

Table 10 Analysis of z8Mds alpha-decay data. Energies of asterisked transitions held fixed relative to the 6.718 MeV transition during fitting procedure. The value given for 254Fm is for decays resulting from 258Mdg decays (see text) Alpha energy (MeV)

Relative intensity

* 6.697 + 0.002 6.718 + 0.002 6.763 f 0.004 * 6.788 + 0.002 6.80 to 6.98 * 6.990 f 0.002 7.00 to 7.07 * 7.080 + 0.002 7.09 to 7.14 * 7.159 + 0.002

0.052 f 1.000 f 0.316 + 0.151 f Q 0.082 < 0.003 Q 0.015 < 0.003 < 0.003 d 0.003

254Fm

Hindrance factor 0.021 0.019 0.018 0.015

- 50 3.0 15 37 2 11000 > 24000 > 49000

0.010 f 0.002 [ = (0.60 f O.OS)%l

limits for the intensities of alpha decays with more than 6.80 MeV energy, since we are unable to estimate the contributions from conversion-electron summing in either spectrum. The data above 7.00 MeV arise primarily from the analysis of the lower spectrum, from the chemically processed sample. The alpha group with the highest energy in either sample is at 7.19 MeV. Since we specifically removed einsteinium and fermium from the chemically processed sample, and since the start of the first accumulation period was 14 d after the end of the irradiation, we believe this peak cannot be due to 39 h 254Esm left in the sample. Furthermore, while statistics are poor, the events seem distributed in time proportional to the “‘Mdg activity. Therefore, this alpha group is caused either by 25*Mdg decay directly or by some fraction of the 25sMdg decaying to 254Esm,which then decays to the observed 3.2 h 254Fm activity. We believe that the latter explanation is the correct one, partially because the breadth of the 7.19 MeV peak indicates that some fraction of the activity has recoiled from the source onto the detector face. We will present other arguments in sect. 5.3. 5.2.4. Limits on relative decay modes of 2’8A4dg We generated a mass-258 fraction from a long irradiation followed by an unusually good mass separation. We characterized the alpha-decay rate of Z8Mdg and any contaminant activities from several days of alpha counting with a surfacebarrier detector. We then transferred the sample to a high-efficiency, low-background argon-ionization counter to determine the SF rate of the sample. In the course of 157 d of counting, we observed 12 SF events. Detector background and contaminants in the sample (primarily decays of 242Cm and “‘Cf) [42] account for a large fraction of these events. The expected number of SF decays from the 254Esg

52

KJ. Moody et aL / Decay properties

daughter of “‘Mdg alpha decay is insignificant [37]. About 0.6% of the =‘Mdg decay results in W4E~m (sect. 5.3.1), which in turn decays to 254Fm 99.6% of the time [87] and to 60 d 254Cf [87,88]0.08% of the time [87]. SF decays of both these nuclides [37,88] contribute about three events to the total. After correcting for the inte~erences listed above, we established an upper limit on the fraction of =‘Mdg decays resulting in SF: Q 3 X 10w3%, or a partial half-life > 4700 y. A preliminary result which was presented in a prior publication [8] was in error, and should have been given as 1.5 X 10’ days, rather than years. The systematics of mass excesses [42,69,71] indicate that 258Mdg is probably unstable to both EC and p- decays to the SF nuclides 258Fm (tip = 0.4 ms) [10,89,901 and =*No (t,,, = 1.2 ms) [12,91], respectively. Therefore, our observed upper limit for SF is really the upper limit for the sum of the SF, EC, and pdecays of “*Mdg. The Q-value for the EC decay of 258Mdg has been estimated [79,92] to be about 1.3 MeV. Using the lower limit for the half-life given above, we calculate that log ft for decays to states just over the pairing gap is 2 12.9. 5.3. LXscussion, 2J8iktdg 53.1. Level structure of 254Es The ground state of =*Md is probably K”’ = 8-, from the parallel coupling of the proton G-[514] and neutron :+[6fS] states, extrapolated from the ground-state configurations of 2$7Md and *s’Fm (see sect. 4.3). We calculated the quasiparticle excitation energies of 2s4E~ using the model of Hoff et al. (see sect. 3.2.2). As input, we gave the code the odd-proton levels of “‘Es from Fig. 7 and the odd-neutron levels of 253Cf [42,75]. We assumed that the ;‘[624] state in 2s3E~ is at an excitation energy sufficiently high relative to the other states that it would not couple with odd-neutron states to produce low-lying levels in 254Es; we base this argument on the e~rapolation of the level structures of 2s1Es and the odd-mass berkelium isotopes [42,60,61,93]. We ignored the odd-proton 3 -f521 J and 4 ‘[400] states because of their expected excitation energies and because they are unlikely to couple with any odd-neutron states to produce 254E~ levels populated by alpha decay of the “*Md ground state. We assumed that the odd-neutron $‘[622] and +‘[620] states in =‘Frn lie at excitation energies between 100 and 200 keV, and that the y-[725] and ;-[734] states are at such high excitation energies that they will not couple to yield levels near the 254E~ ground state; we base these arguments on the extrapolation of the level structures of 247Cm [94], 24gCm [94,95], 249Cf [96,97], and =lCf [98,99]. The left side of Fig. 12 shows the partial results of the calculation of the level structure of 2$4E~.Other than the 2’ isomeric state [l~,lOll, we show only those intrinsic states with J 2 6, most of which share either a proton or neutron single-particle configuration with the 258Md ground state. The calculation correctly

RJ. Moody et al. /

Decay

properties

53

Calculation EFergy (keV)

Observed

K” Proton Neutron

Energy

H

700

l

El-

7/2- [514] 9/2+[615 469

600

448

500

#?&mm 377

7-

7/2- [614] 7/2+[613]

6-

3/2- [521] 9/2+ [616]

6+

7/2+ [633] 9/2+ [616]

2+

7/2+ [633] 3/2+ [622]

60 3.0

16 37

400

300

200

0

>49,ooo

100

0

7+

Fig. 12. Comparison of the results of a calculation of the quasiparticle excitation energies of z4Es, on the left, with the partial level scheme determined from the gamma rays emitted in the decay of 25sMd8, on the right. Most states with J G 5 are omitted from the calculation results. Tentative correspondence between the calculated and measured and the observed hindrance factors (far right). The state analogous to the “‘Md ground state is marked with an asterisk. H values are the observed hindrance factors for alpha decay to the indicated states.

reproduces the 254E~ground state [42] and predicts rotational states at 76 and 162 keV, similar to the lowest excited states in Fig. 10. The assignment of these states to the ground-state rotational band is supported by the decay of the 448 keV 8analog state to these levels by El gamma transitions and by the absence of other high-spin even-parity states at low excitation energies in the model calculation. The limits on the hindrance factors for alpha decay to these states (Table 10) are consistent with what we expect from the single-particle hindrance factors given in

54

KJ. Moody et al. / Decay properties

Table 6 for decays from 25*MdB to the ground state of 254E~ (approximately 107). We therefore contend that the highest-energy alpha transition observed in the chemically separated sample (Fig. 11) is due to 254Fm, since the energy of this peak is beyond that calculated from Fig. 10 for alpha decay to the ground state. The right side of Fig. 12 shows our experimental level scheme, shifted upwards in energy for ease of comparison. The known 2+ isomeric state at 78 keV [loll is not shown. The cluster of levels near the analog state populated by the decay of 258Mdg and the low hindrance factors for the alpha transitions to these levels show that there may be considerable configuration mixing among them, This is borne out by the relative intensities of the 277, 368 and 448 keV gamma rays, which should be reproduced by using eq. (2). Correcting for the internal conversion of these El-multipolarity transitions, Table 9 yields relative intensities of 0.132, 0.637, and 0.231, respectively. Eq. (2) yields relative rates of 0.002, 0.065, and 0.993, respectively. Clearly the analog state shares a lot of character with higher-order members of another rotational band. Examination of the reciprocal formation factors in Table 6 suggests that alpha transitions where the neutron configuration does not change but where the proton configuration changes from z -[514] to 3 -[521] would not be highly hindered, particularly for higher rotational states. All transitions involving the conservation of the proton configuration but involving a change in neutron configuration from q+[615] might be expected to be more highly hindered (see below). Therefore, we expect alpha decays to members of the rotational band based on the 6- state at 457 keV in the calculated level scheme to be less hindered than most transitions and to lie close to the analog state. Based on the relative intensities of the gamma rays depopulating the 377 keV state and on their similarity to the relative intensities depopulating the analog state, we assume that the 377 keV state is the 8- member of the 6- rotational band. Our calculation indicates that the 9- rotational member should be about 100 keV higher in energy than the 8- member, so we assume that the 469 keV state is the 9- member. This yields a preliminary rotational constant of A2/26 = 5.13 keV (compared with 5.9 keV predicted by the code), which places the 7- state at about 295 keV and the 6- band head at about 220 keV. Table 9 gives an as-yet unassigned 214.7 keV gamma ray, which could correspond to the El electromagnetic transition between the 6- band head and the 7+ ground state. Similarly, we list an as-yet unassigned 86.9 keV gamma ray, which could correspond to the Ml (E2) transition between the 8- rotational member at 377 keV and a postulated 7rotational member at 290 keV. The difference in energy between these 6- and 7states yields a rotational constant of 5.37 keV and calculated 8- and 9- energies of 376 and 473 keV, respectively, in surprisingly good agreement with Fig. 10, given the configuration mixing. Except for the 189.1 keV photon, we have tentatively placed all of the gamma

KJ. Moody et al. / Decay properties

5.5

rays listed in Table 9 with energies higher than the einsteinium K edge in the 254Es level scheme. All of these photons are of El multipolarity except the 171.1 keV transition, which is of E2 multipolarity. From the conversion coefficients for electromagnetic transitions in einsteinium nuclei [44,54], there is a total K X-ray production of 47 units from the placed transitions. This comprises more than half of the observed production of einsteinium K X-rays of (80 f 7) units, from Table 9, corrected for fluorescence yield [42]. If the 189.1 keV photon were of Ml multipolarity, the transition would be responsible for the production of about 58 units of K X-ray intensity. Even assuming that there are no other processes producing K X-rays than the ones we observe, the possibility of the 189.1 keV transition having significant Ml character is excluded. We cannot exclude the possibility of either El or E2 multipolarity. Although the alpha transition populating the 254Es state at (402 f 5) keV is second in intensity only to that populating the analog state, we have not yet identified any gamma rays arising from the decay of this level. Since most of the K X-ray intensity is accounted for, and only the weak 189.1 keV photon is unassigned, the 402 keV state must decay primarily by electromagnetic transitions with energies below the einsteinium K edge. If the 189.1 keV photon is emitted in the decay of this state, the receiving state is probably the 6- state at 215 keV. Given the intensity of the alpha transition and the absence of Ml intensity, the 404 keV state is probably J” = 7- or 8-. A positive-parity state is precluded by the alpha-decay hindrance factor. The absence of intense El-multipolarity transitions from this state to the ground-state rotational band and the weakness of the 189 keV transition imply that the 404 keV state is a high-spin member of a low-K rotational band. The odd-neutron t +[615] state derives from the g9/* spherical state. The odd-neutron +‘[620] state derives from the g’/* spherical state. The reciprocal formation factors for decays between these states were not tabulated in the work which is quoted in Table 6; however, we can assume that decays from the :+[615] state to the high-spin members of the +‘[620] band would be favored, because of the similarity in principal quantum numbers. The antiparallel coupling of the proton G-[5141 and neutron 3’ [620] states produces a K” = 3- band at a low excitation energy in 254Es. The excitation energy resulting from our calculation has little meaning because we estimated the energy of the i +[620] state in 253Cf from systematics, but we expect the K” = 3- band head to lie only slightly higher in energy than the 2+ isomeric state. If the 404 keV state is the 7- or 8- member of the 3- band, we expect a significant fraction of the depopulation of this state to proceed through low-energy transitions down the rotational band. We observe the ingrowth of a small amount of 254Fm from the decay of the 2+ isomeric state that results from these transitions. The antiparallel coupling of the proton $-[521] and neutron ;+[615] configurations also produces a low-lying 3- band in 254Es that could participate in the alpha decay of 258Mdg

KJ. Moody et al. / Decay properties

56

E* (keV)

376.6

214.7 .-tjjjj-

Fig. 13. The alpha decay of =‘Mdp and the level scheme of 254Es. Observed gamma transitions are placed in the level scheme.

Fig. 13 shows the partial level scheme of 2s4E~, based on the arguments presented above. The relative intensities of the gamma rays are consistent with the intensities of the alpha transitions. 53.2. Mass excess of 258Mdg From the energy of the alpha transition to the 447.9 keV state, we obtain a Q-value for the alpha decay of 256Mdg of (7.272 & 0.002) MeV. Using the atomic mass excess for 254E~g [69] of (81.994 _t 0.006) MeV, we obtain an atomic mass

KJ. Moody et al. / Decay properties

57

excess for =‘MdK of (91.691+ 0.007) MeV. This compares with the experimentally justified values of 91.82 MeV [71] and (91.84 + 0.30) MeV [69]. 5.3.3. Hindrance factor for SF decay of 2s8Mdg The SF half-lives of even-even actinide nuclides change in a regular way when plotted against neutron number at constant Z (e.g. refs. [88,89,102,103]). The systematics of these SF half-lives are characterized by broad peaks of relatively long half-lives centered near neutron number 152. The extra stabilization against SF caused by the 152neutron subshell dies away with increasing neutron number and increasing proton number. The gradual disappearance of the second minimum in the double-humped fission barrier causes this decrease in stability [104,105]. With the disappearance of the second hump, the systematics of SF half-lives change abruptly, showing a gradual increase with increasing neutron number [102,103]. Alpha-decay half-lives of odd-mass and odd-odd nuclides are often treated in terms of hindrance factors, which are the ratios of the observed half-lives to those expected based on the systematics of the decays of even-even nuclides. The size of the hindrance factor is dependent not only on the effect that the odd nucleons have on the preformation of the alpha particle, but also on the effect of changing quantum numbers in the transitions. We will treat the SF half-lives in the same way. In the case of SF, the hindrance factors caused by odd nucleons can be thought to arise from changes in the ordering of the excited states in the fissioning nucleus as it elongates toward the scission point (specialization energy) [106,107]. Strict conservation of quantum numbers requires that the SF of nuclei with unpaired nucleons proceeds along paths other than those with the minimum potential energies. In contrast, the lowest-energy state in even-even nuclei is J” = O+ at all deformations. In Fig. 14 we plot the SF half-lives [80] of even-even actinides with given neutron numbers as a function of proton number (element). We do not include the tentative half-life of 260No [103j because the evidence for the assignment of a 106 ms SF activity to this nuclide is not compelling, and the half-life does not fit in with the systematics of the SF of other even-even nuclides. As expected, the half-lives drop with increasing Z until the second barrier vanishes, when the trend abruptly changes. Using Fig. 14, we extract hypothetical “even-even” SF half-lives for the mendelevium isotopes to serve as the basis for our hindrance ~lculations; these are plotted in Fig. 15. From Fig. 15, we obtain a value of about 2 ms for the unhindered SF half-life of “‘Mdg. From our experimental lower limit on the half-life of 4700 yr (sect. 5.2.41, we obtain a hindrance factor of > 7 x 1013. By analogy to alpha decay, we can assume that both the odd-neutron and odd-proton configurations tend to be conserved in the SF of an odd-odd nucleus. Therefore, we expect the SF hindrance factor for =‘M1dg to be the product of

KJ. Moody et al. / Decay properties

58

-51

’

I

Cm Bk

I

I

Cf

Es

I

1

I

Fm Md No

1

I

I

I

I

Lr 104 105 106

Element Fig. 14. Half-lives for the spontaneous fission of even-even heavy actinide nuclides at constant neutron number as a function of proton number (element). These data are used to extract the unhindered mendelevium SF half-lives, to be used as the basis for hindrance-factor calculations.

characteristic hindrance factors for odd-mass nuclides with proton 3 -[514] or neutron :+[615] configurations. This assumes that the effect of the pn residual interaction is roughly constant at all deformations. From the SF half-life of 257Fm [73] and the data in Fig. 14, we obtain a hindrance factor for the odd-neutron configuration of 1.8 x log. From the SF half-life of 259Md (see sect. 7.3.1) and the data in Fig. 15, we obtain a hindrance factor for the odd-proton configuration of 3.6 X 106. The product of these hindrance factors is 6.5 X 1014, only slightly larger than our lower limit. The only other odd-odd nuclides where meaningful data exist for the SF half-life are 242Am, 254E~g, and 260Md, This “product rule” for hindrance factors does not apply to 242Amm;since the isomeric state starts out with some excitation energy, the configuration can move downwards with respect to the ground state as well as upwards with increasing deformation, and therefore will not be as highly hindered as predicted. This, in fact, is what has been observed [108,109] (see sect. 6.3.2). The hindrance factor for the SF decay of 254E~g is greater than 2.5 X lo7 [37,80]. From 253E~ [110,1111 and 255E~ [37], the hindrance factor associated with the ;‘[633] proton is about 105. From 255Fm [87], the hindrance factor associated

RJ. Moody et al. / 9,

-3

I

I

I

I

252

254

properties

Decay

59

I

1

256

260

I

I

256

Md mass number Fig. 15. Unhindered

SF half-lives for the mendelevium isotopes, extracted from Fig. 14, to be used as the basis for hindrance-factor calculations.

with the 3+[613] neutron is about 3 x 105. Therefore, the expected 254Esg hindrance factor is 3 X lOlo, much larger than the lower limit. We will discuss 260Md, where we measured the SF half-life, in a separate publication [14].

6. Mendelevium-258m 6.1. Htitorical background, 2s8Mdm

For several years before its discovery, the existence of a l- isomeric state in “‘Md was postulated [27,561 from the antiparallel coupling of the proton :-[514] and neutron :+[6151 Nilsson states according to the Gallagher-Moszkowski rule [SS]. This short-lived isomer was first observed following the bombardment of a mass-separated 255Es target with 4He ions [85,112]. The half-life determined in these experiments was (43 &-4) min, obtained from 177 SF events in which both fragments had kinetic energies over 101 MeV. There was a large 256Md-256Fm background. Based on the expected cross section, on predicted Q-values for /3and EC decays, and on expected SF hindrance factors, the experimenters con-

60

Kf. Moody et al. / Decay properties

eluded that the observed SF events were probably due to the decay of 370~ps 25EFm [90] following the EC decay of 258Mdm. In previous publications [8,10-12,901, we discussed how we used this genetic relationship to confirm the 2 and A assignments of both 258Fm and =‘Mdm by observing fermium K X-rays associated with the SF events in a mass-separated A = 258 fraction. In those experiments, we remeasured the half-life of 258Mdm and obtained a value of (60 k 2) min [8,90]. 6.2. E~~e~menial results,

2s8Mdm

6.2.1. Half-life of 258Mdm We measured the half-life of 258Mdm from mass-258 samples generated following six 22Ne irradiations and five ‘*O irradiations. A subset of these data was used to determine the half-life mentioned above. The start of the first data-acquisition period for a given sample was usually about 90 min after the end of irradiation, and we usually observed about 2000 SF events in the next 24 h. About 15% of the observed events were due to the nuclides in the mass-256 decay chain because of incomplete mass separation. The SF decay curve generated from each mass-258 fraction was analyzed with a multistep procedure. First, from the SF decay curve obtained from the mass-256 fraction produced in the same experiment, we deduced the relative amounts of 256Fm, 256Md, and 256E~min the mass-258 fraction (see sect. 3.2). We assumed that no further chemical fractionation occurred in the mass spill-over. Next, using the 7.07 MeV alpha-particle decay curves from the mass-256 and mass-257 fractions (caused by decays of 257Md) we determined the amount of 259Md spilled over into the mass-258 fraction, relative to the amount collected at mass 259. Finally, we determined the amount of 259Md in the mass-259 fraction (see sect. 7.2). The correction for 25gMd decays in the mass-258 fractions was always very small. We fixed the initial activity of 259Md, the relative activities of 256Fm, 2s6Md, and 256E~m, and the half-lives of all four nuclides for all eleven decay curves. We estimate that neglecting the uncertainties on the fixed quantities had little effect on the uncetrainty of the calculation. From our least-squares decay-curve code, we obtained eleven values for the half-life of 258Mdm. The weighted-average result is (57.0 + 0.9) min. We cannot account for the disagreement between our value and the earlier value of (43 t 4) min [85,112]. 6.2.2. Search for other decay modes of 258Mdm We counted mass-258 fractions produced following two 22Ne irradiations and four “0 irradiations for alpha particles with pulse-height analysis using Frisch-grid ionization detectors. In each case the first alpha count was started within 90 min of the end of irradiation. The spectra obtained during the first five hours of counting of each sample were added together to yield a final sum of early counts, shown in

RI. Moody et al. /

Decay

61

properties

242Clbl

I

214PCI

.i

.. -

“.

.

.

.”

17

.

. ._.-

6.0

.

.” . .

.”

..”

.

.

.

... - . .._ 6.5

.

.

.

.

.

.

. ”

. 7.0

.

. . .

-

.

“.”

.“.“”

.

.

.

.

.

.

-I..-._-_. 7.5

.

.

.

“-

. .. ..- ..- ._. 8.0

Alpha energy (MeV) Fig. 16. The sum of the first five hours of counting of six mass-258 fractions, with gas-ionization alpha-particle detectors. Several important activities are indicated, mostly arising from contaminant nuclides with nearby masses. We see no unexplained alpha groups.

Fig. 16. We see no unexplained peaks in this alpha spectrum that could be attributed to the decay of =‘Mdm. During the data accumulations resulting in the spectrum shown in Fig. 16, SF events were stored as overflows in the top channel of the multichannel analyzer. A total of 11563 SF events were observed, associated with the alpha spectrum shown. From the alpha peak at 6.92 MeV, we calculate that (1840 + 220) of these SF events are due to decays of 256Fm leaving a net of (9723 f 245) 258Mdm events. From the calculated unhindered alpha rates for mendelevium isotopes (see sect. 3.2.31, we expect no alpha-decay branch from =‘Mdrn with an intensity of more than 1% to have an energy of less than 7.0 MeV. We performed decay-curve analysis of the 256Fm, Z7Md(255Fm), 254Fm, and *14Po peaks, looking for unexplained short-lived components. We also examined individual spectra taken from samples produced in experiments in which the mass separation was unusually clean. In the alpha-energy region between 6.8 and 8.0 MeV, we establish a 2a upper limit on the alpha-decay branch of 258Mdm of 1.2%. We searched for growth of the 258Mdg activity in alpha spectra taken after short **Ne and “0 irradiations to establish an upper limit on the internal transition (IT) decay of 258Mdm. Assuming the limiting case, that 258Mdg was not produced directly, we establish an upper limit of 6 60% on the IT branch. This limit is considerably larger than we would expect [421 for a low-energy M7(E8) transition

62

ICI. Moody ei al. / Decayproperties

(see sect. 6.3.1). We assume in the Discussion section (6.3) that IT and alpha emission do not contribute to the decay of 258Mdm. 62.3. Fermium K X-rays associated with 2s8Mdmdecay We counted mass-258 samples generated following three 22Ne irradiations in the apparatus described in ref. [90]. With this apparatus, a clock that was started upon detection of photons having energies near those of the fermium K X-rays (112 to 145 keV) was stopped upon detection of an SF event. The energies and detection times for the last several photons preceding each SF event were stored. Along with establishing the genetic relationship between 258Mdm and 258Fm, we determined the fraction of SF events preceded by fermium K X-rays. We observed a total of 2502 SF events, of which (2407 + 88) were due to 25sMdm (from decay-curve analysis). A total of 459 of these events were preceded by fermium K X-rays in the time window between 1 gs and 3.7 ms. We estimate that approximately 23 of these events were due to random detector background in the energy region of interest [903. Correcting for the relative efficiencies of the SF and photon detectors (see below), we observed (0.528 ~fr0.032) fermium K X-rays per SF event. This number has not been corrected for the effect of summing in the photon detector. Given the close-in mounting geometry, the s~ming of gamma rays and L X-rays with the K X-rays, producing events outside the narrow energy region we examined, could seriously reduce the number of observed K X-rays. 6.3. Discussion, 258Mdm 6.3.1. The EC decay of 2581vfd” Although it has been proposed that 258Mdm is formed from the antiparallel coupling of the same states that form the ground state in their parallel configuration (see sect. 6.11, there are other possibilities. In particular, we argue that the antiparallel coupling of the neutron f+[613] and proton $-15141 states produces a low-lying I(‘” = O- band analogous to the 256Md ground state (see sect. 4.3.31, or that the neutron 4 +[622] state could couple with either the proton 5 -15211 or $-[521] states to produce K” = O- or 2- bands, respectively (see sect. 53.1). We calculate negative Newby terms 162,631 for both K = 0 bands, implying that the lowest state in each band may be J = 1. We expect a significant fraction of the EC decay of 258Mdm to populate directly the ground-state band in 258Fm. The Q-value for the EC of 258Mdm is probably about 1.5 MeV [79,92,113-1151. If we assume that the decay exclusively populates the ground-state band of 258Fm, we obtain a log ft of about 6.0; this is somewhat less than we would expect from the decay of a low-spin negative-parity isomeric state, based on similar EC decays from other odd-odd actinides (e.g. 236Np, 242Am,248Bk, and 250E~)[42]. Regardless of the spin and parity we assign to 258Mdm, with this decay energy we expect

KJ. Moody et al. / Decay properties

63

substantial population of states above the pairing gap in =‘Frn. This gap is approximately 600 keV in excitation energy [42,1161. We would like to use our measured value of (0.528 f 0.032) fermium K X-rays per SF event to establish a limit on the fraction of 258Mdm decays that proceed directly by SF or by p- decay followed by the SF of *58No. Unfortunately, the actual EC branch of 258Mdm decay cannot be related to the measured quantity without knowing summing losses, which cannot be estimated without knowing the relevant decay scheme. We can, however, obtain a lower limit on the EC branch by assuming that 258Mdm decay directly populates only the ground-state rotational band in 258Fm, which causes the production of the lowest number of extraneous photons. Since the fraction of mendelevium EC events that proceed via K capture [51] is only slowly changing with energy for decays with energies between 700 keV (71%) and 2000 keV (76%), the uncertainty in the predicted Qnc is not terribly important. Assuming that Qnc is approximately 1.5 MeV, we expect 0.756 K vacancies per EC [51]; given the fluorescence yield of 0.98 1421,we expect 0.741 K X-rays per EC. Even with this simplified decay scheme, the effect of summing K X-rays with L X-rays is hard to quantify, not only because of the number of sources of L vacancies [50,117], but also because of the rapidly changing detector efficiencies (photopeak-plus-Compton) in the L X-ray energy region [118]. Another complication is that summing involving K, X-rays with lowest-energy L X-rays results in photon events in the detected energy region [901. We estimate that the losses from summing with L X-rays are at least 5%, based only on the production of L X-rays in the EC process itself, including those from the filling of K vacancies and on the production of L X-rays from the IT decay of the 2+ rotational state in the ground-state band of 258Fm. It follows that the EC branch of =*Mdm decay is > 70%. 6.3.2. Limits on other decay modes of 258Mdm The Q-value for the decay of 258Mdm has been estimated [69,79,92,113-1151 to be approximately 0.5 MeV. We cannot exclude the possibility that some of the SF events we observe are due to the decay of the 1.2 ms 258N~ daughter [12,911 of any p - decays. Our upper limit for the sum of the p--decay and SF-decay intensities of 258Mdm is 30%. Assuming that the Q-value for p- decay is about 0.5 MeV, this results in a log ft for decays to the 258N~ ground-state rotational band of > 5.6. From /3decays of other odd-odd actinides [42], we expect a log ft for decays to the ground-state band of about 6.4, corresponding to a p--decay branch of about 5%. It may seem somewhat facetious to apply the upper limit given above to the direct SF decay of an odd-odd actinide; however, consider the case of 242Amm. The hindrance factor associated with the s-[5231 proton is about 105.‘, from the SF half-lives of “‘Am 11091and 243Am[119]. There are no SF half-life determina-

64

KJ. Moody et al. / Decay properties

tions for odd-neutron nuclei with 2 +[622] ground-state configurations; we expect the hindrance factor to be about 105, based on the similarity in quantum numbers with the f +[613] configuration of the 255Fm ground state 1871.From our discussion in sect. 53.3, we expect a 242AmmSF hindrance factor of about lOlo, if it were not an isomer. What is actually observed is a hindrance of 102.3, or a rate augmentation of 1O7.7over what is expected for the ground state, which is formed from the antiparallel coupling of the same single-particle states. The =‘MMdisomeric state may be composed of the same single-particle states as is the ground state. A rate enhancement similar in magnitude to that found in 242Ammwould result in an expected SF half-life of 258Mdm of about 200 min, or an SF-decay branch of about 30%.

7. MendeIevium-259 7.1. Historical background, 2’gMd The SF decay of 25gMd was first observed (though not assigned) in chemically purified nobelium fractions, produced following “0 irradiations of 248Cm [120]. In these experiments, a few SF events were observed in excess of a substantial background. These events seemed to decay with roughly the same half-life as (58 f 5) min 25gN~. It was later determined, in radiochemic~ milking experiments [121,122], that the SF events were due to (95 + 25) min 25gMd, which grows into the nobelium fraction from a 22% EC branching by 25gNo. These experiments also showed that 25gMd has no more than a 5% alpha-decay branch. There is a substantial difference between the mass and kinetic-ener~ distributions from the SF decay of 259Md and those of 1.5 s 25gFm [123,124], proving that 259Md does not decay primarily by EC [122,125,126], though a substantial EC branch cannot be ruled out. It is unknown whether 25gMd is stable to EC decays [79,92,113-1151. The accepted values for the half-life of 259Md are (103 + 12) min [126] and 95 min (no error given) 181.The alpha-decay branch is less than 3% for emission of alpha particles with energies between 6.5 and 7.0 MeV [126]. 7.2. Experimental results, mass 259 7.2.1. Half-life of 259Md

We measured the half-life of 25gMd from mass-259 samples produced following six “Ne irradiations and four 180 irradiations. In each case, we followed the decay of the SF activity for at least 24 h after each mass separation. The start of the first data acquisition period for a given sample was between 1 and 3 h after the end of

KJ. Moody et al. / Decay properties

65

irradiation. We usually observed about 500 SF events before the end of counting. About 25% of the observed SF events were caused by nuclides in the mass-256 decay chain, and about 1% of the events were due to =sMdm. The SF decay curve resulting from each mass-259 fraction was analyzed similarly to the 25*Mdm decay curves (see sect. 6.2.1). We deduced the relative amounts of 256Fm, 256Md, and 256Esm in the mass-259 fraction as before. We assumed that the spill-over of mass-258 nuclides into the mass-259 fraction was similar in relative magnitude to the spill-over of mass-256 nuclides into the mass-257 fraction, deduced from the SF activity in the appropriate samples. Finally, we determined the amount of Z9No in each sample from the alpha-particle spectra collected during the SF measurements. From the decay of the alpha intensity between 7.43 and 7.73 MeV [120], we determined the initial activity of 259N~ in each sample. We fixed the initial activities of =*Md” and 259No and the relative activities of 256Fm, 256Md, and 256Esm. We also fixed the half-lives of all five nuclides. The large uncertainties in the half-life and initial activities of 259No had little effect on the Z9Md half-life since the initial quantities of 259N~ were relatively small. From least-squares analysis, we obtained ten values for the half-life of 259Md. The weighted-average result is (1.60 If: 0.06) hours, in good agreement with the literature [8,126]. 7.2.2. Alpha decay in the mass-259 fractions Mass-259 fractions generated following five **Ne irradiations and four i*O irradiations were counted for alpha particles with pulse-height analysis using Frisch-grid ionization detectors. In each case the first alpha count was started within 100 min of the end of the irradiation. The spectra obtained during the first six hours of counting of each sample were added together to yield a final sum of early counts, shown as the top spectrum in Fig. 17, scaled upwards by 103. The spectra obtained during the times between six hours and approximately two days following the start of data acquisition were added together to yield a final sum of late counts, shown as the lower spectrum in Fig. 17. During the data accumulations resulting in the sum of early counts, we observed a total of 3896 SF events with the alpha data shown. From the alpha peak at 6.92 MeV, we calculated that (703 f 131) of these SF events were due to decays of 256Fm. We estimated that about 25 of the SF events were due to decays of *‘*Md”; this leaves a net of (3168 f 145) SF events from decays of 259Md. We performed decay-curve analyses of the alpha-particle peaks caused by decays of 253E~, 258Mdg, Z6Fm, and *“Frn (257Md), looking for unexplained short-lived components. We also searched individual spectra taken from samples produced in experiments in which the mass separation was unusually clean. In the alpha-energy region between 6.5 and 6.95 MeV, we established a 2a upper limit of 1.3% for an alpha-decay branch of 259Md. In the alpha-energy region between 6.95 and 7.10 MeV, our sensitivity was lower because of the growth of the zs5Fm activity

K.J. Moody et ai. /

66

Lkcayproperties

I

I

I

A

2%

2:

254Fm 254Es

I

25sNo + “‘PO i

--

*.

.

t

1

11’

6.0

-I

.... .

... .. .

*

”

.

”

*

I

.

.

I

6.6

7.0

.

.

.

.

.

.

.

.

.

.

.

.

.

,

I*..

7.5

.

.I.

._...

4 .

8.0

Alpha energy (MeV) Fig. 17. Alpha spectra taken with gas-ionization detectors of mass-259 samples. The top spectrum is the sum of the first six hours of counting of each sample, scaled upwards by a factor of 103. The lower spectrum is the sum of later counts. Several important activities are indicated, mostly arising from contamination with nuclides of lower mass following incomplete mass separation.

from the decay of z5gNoBhowever, we still estabhshed a 2a upper limit on alpha decays of 2.3% in this energy region. The Q-vaiue for the alpha decay of 259Md is probably about 7.0 MeV [79,92,113-11.51 and is almost certainly less than 7.3 MeV. From the odd-proton level structure of 251Es [28,42,61] and 253Es (see Fig. 71, it is unlikely that the f -[514] state in 255E~ lies at an excitation energy below 300 keV. Therefore, the hypothetical analog alpha decay from the 3 -[X4] 259Md ground state would result in an alpha particle with an energy of less than 6.9 MeV. From this argument and given the unhindered alpha-decay rates [42], we exclude the possibility of a 259Md component with alpha energies between 6.95 and 7.10 MeV and place a 2u upper limit of 1.3% on the alpha-decay branch of 259Md.

RJ. Mwdy et al. / Decay properties

61

Table 11 Comparison of the energies and relative intensities of the alpha groups arising from the decay of zgNo with the literature [120] Literature

This work Alpha energy (MeV)

Relative intensity

1.472 f 7.520 f 7.551 + 7.581 f 7.619 f 7.651 f * 7.689 f

6.0 f 27.5 f 24.4 f 19.2 f 11.3 + 11.6 + < 22

0.006 0.004 0.004 0.004 0.005 0.005 0.004

1.8 3.9 3.9 3.3 2.6 2.7

Alpha energy (MeV)

Relative intensity

7.455 f 0.010 7.500 f 0.010 7.533 f 0.010

13+ 4 39 f 12 23* 7

7.605 f 0.010

14*

4

7.685 f 0.010

11+

3

* At least some of the intensity of this peak is caused by decays of *14Po.

We resolved the top spectrum shown in Fig. 17 into component alpha groups. The 2s4E~g and 254Fm activities defined the peak shapes. We provided the absolute energies and relative intensities of the 253E~, 254E~g, 254Fm, 255Fm, 256Fm, and 257Md alpha groups (see sect. 4.2.3). The energy resolution of the peak shapes in the spectrum is about 22 keV FWHM. We give the results of the FITEK analysis of the alpha spectrum above 7.4 MeV in Table 11 and compare them with the data from the literature [120] for the decay of z9No. In the literature data given in Table 11, we see an excess of 7.45 MeV alpha particles, probably caused by decays of 0.52 s *llPo (7.450 MeV alpha particles [127,128]), which is a daughter of 7.2 h *ilAt [1271; the literature values were obtained by counting unprocessed recoil-collection foils, in which other activities produced from lead impurities in the targets were also present [120]. With the exception of the highest-energy alpha group, the distribution of intensity between our data and the literature data is about the same. It is quite likely that most of the intensity we observe at 7.69 MeV arises from the decay of *14Po [43,129], whose precursors [1301 were introduced into many of our samples by the mass separator (see Fig. 16). 7.3. Discussion, mass 259 7.3.1. The SF hindrance factor for the decay of 259Md

As mentioned above (sect. 7.11, the total-kinetic-energy distribution of the SF of 259Md is somewhat different than that of the SF of 259Fm [122,125,126]. Although we cannot eliminate the possibility of an EC-decay branch, most Q-value calculations [79,92,113-1151 indicate that even if 259Md is not stable to such decays, the Q-value for EC must be very small. From the systematics of the odd-neutron Nilsson configurations [42,75,94-991, the lowest two states in 259Fm are $‘[6221 and ; +[615]; only first-forbidden EC decays could take place from the g -[514]

RJ. Moody

68

et al. / Decay properties

259Md ground state. Even if Qnc were as much as 300 keV [42,113], we would expect an EC-decay branch of no more than a few percent. From Fig. 15 we obtain an unhindered half-life for the SF decay of Z9Md of 1.6 ms. From our observed half-life of 1.60 h, we obtain an SF hindrance factor of 3.6 x 106, associated with the mendelevium odd-proton configuration. This factor is compatible with the limit we set on the SF hindrance factor in Z7Md decay of > 6 X 10’ (see sect. 4.2.2).

8. Summary In Table 12, we summarize the results of our experiments and subsequent interpretation of the data. We investigated the nuclear properties of several mendelevium isotopes, produced in reactions of 180 and 22Ne with 254E~g.We measured the alpha particles, spontaneous fission fragments, and photons emitted by counting samples resulting from chemical and/or mass separations. We measured the half-lives and the relative intensities of the different decay modes of 256Md, 257Md, =‘Md9, 258Mdm, and 259Md. We established partial level schemes for 252E~, 253Es, and 254E~,populated by the alpha decay of the appropriate mendelevium isotopes. We demonstrated that the ground-state spins of the heavy mendelevium isotopes are all consistent with a proton i -[514] Nilsson assignment. The SF hindrance factor associated with this configuration is about 4 x 106. The ground states of “6Md, “‘MdB and 258Mdm are probably J” = l-, 8and l-, respectively. The derived mass excesses of 256Md, 257Md, and 258Mdg closely match literature values based on systematics.

Table 12 Summary of experimental results and interpreted

decay properties of heavy mendelevium isotopes

‘s6Md

257Md

2ssMdB

258Mdm

‘s9Md

r1/2

(78.1 + 1.8)min

(1.60 + 0.06) h

(11 f 3)% (7.221 + 0.003) MeV (87.611 + 0.053) MeV (89 + 3)%

d 1.2%

4 1.3%

1-

7I

(51.50 f 0.29) d 100% (6.718 f 0.002) MeV (91.691 f 0.007) MeV d 3 x 10_3% < 3 x 10_3% Q 3 x lo-“% 8-

(57.0 + 0.9) min

branch print. (YE

(5.523 f 0.050) h (15.2 f 2.6)% (7.074 f 0.001) MeV (88.989 f 0.003) MeV (84.8 f 2.6)%

3 70% $30% < 30% 1-

- 100% 7i

a

mass excess EC/P ’ branch p- branch SF branch probable J”

Q

1%

RJ. Moody et al. / Lkay properties

69

We thank the staff and crew of the Lawrence Berkeley Laboratory 88-inch cyclotron for supplying the “0 and “Ne beams used in the irradiations. We are grateful to H.L. Hall for making the level scheme of 256Fm available to us prior to its publication and to K.E. Gregorich for informative discussions. Thanks are also due to Ruth Anderson and L. Maynard who helped with the photon counting, and Bonnie McGurn who helped prepare the manuscript. One of us (KS.) thanks the members of the Heavy Element Group for their kind hospitality during his stay at the Lawrence Livermore National Laboratory. We are indebted for the use of the 2$4Esg target material to the Office of Basic Energy Sciences, U.S. Department of Energy, through the transplutonium-element production facilities of the Oak Ridge National Laboratory. This work was performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under Contract No. W-7405-ENG-48.

References [I] M. SchPdel, W. Briichle, M. Briigger, H. Giiggeler, K.J. Moody, D. Schardt. K. Siimmerer, E.K. Hulet, A.D. Dougan, R.J. Dougan, J.H. Landrum, R.W. Lougheed, J.F. Wild, G.D. O’KelIey and R.L. Hahn, J. Less-Common Metals 122 (1986) 411 [2] M. Schiidel, W. Briichle, M. Briigger, H. Giiggeler, K.J. Moody, D. Schardt, K. Siimmerer, E.K. Hulet, A.D. Dougan, R.J. Dougan, J.H. Landrum, R.W. Lougheed, J.F. Wild and G.D. G’Kelley, Phys. Rev. C33 (1986) 1547 [3] K.J. Moody, R.W. Lougheed, R.J. Dougan, E.K. Hulet, J.F. Wild, K. Siimmerer, R.L. Hahn, J. van Aarle and G.R. Bethune, PhysRev. C41(1990) 152 [4] J.F. Wild, E.K. Hulet, R.W. Lougheed, J.H. Landrum, R.J. Dougan, A.D. Dougan, H. GHggeler, M. Schiidel, K.J. Moody and G.T. Seaborg, “LLNL Nuclear Chemistry Division Annual Report FY83,” Lawrence Livermore National Laboratory Report UCAR 10062-83/l, p. 144 (1983) [S] D. Lee, H.R. von Gunten, B. Jacak, M. Nurmia, Y.-F. Liu, C. Luo, G.T. Seaborg and D.C. Hoffman, Phys.Rev. C25 (1982) 286 [6] D. Lee, KJ. Moody, M.J. Nurmia, G.T. Seaborg, H.R. von Gunten and D.C. Hoffman, Phys.Rev. C27 (1983) 2656 [fl K.J. Moody, D. Lee, R.B. Welch, K.E. Gregorich, G.T. Seaborg, R.W. Lougheed and E.K. Hulet, Phys. Rev. C33 (1986) 1315 [8] R.W. Lougheed, E.K. Hulet, R.J. Dougan, J.F. Wild, R.J. Dupzyk, C.M. Henderson, K.J. Moody, R.L. Hahn, K. Siimmerer and G. Bethune, J. Less-Common Metals 122 (1986) 461 191 R.W. Lougheed, KJ. Moody, R.J. Dougan, J.F. Wild, E.K Huiet, R.J. Dupzyk, C.M. Henderson, C.M. Gannett, R.A. Henderson, D.C. Hoffman, D.M. Lee, K. Siimmerer and R.L. Hahn, “LLNL Nuclear Chemistry Division FY87 Annual Report,” Lawrence Livermore National Laboratory Report UCAR 10062/87, p. 4-2 (1987) [lo] E.K. Hulet, J.F. Wild, R.J. Dougan, R.W. Lougheed, J.H. Landrum, A.D. Dougan, M. Schldel, R.L. Hahn, P.A. Baisden, C.M. Henderson, R.J. Dupzyk, K. Siimmerer and G.R. Bethune, Phys. Rev. Lett. 56 (1986) 313 [HI E.K. Hulet, J.F. Wild, R.J. Dougan, R.W. Lougheed, J.H. Landrum, A.D. Dougan, M. Sch;idel, R.L. Hahn, P.A. Baisden, C.M. Henderson, R.J. Dupzyk, K. Siimmerer and G. Bethune, J. Less-Common Metals 122 (1986) 469 [12] E.K. Hulet, J.F. Wild, R.J. Dougan, R.W. Lougheed, J.H. Landrum, A.D. Dougan, P.A. Baisden, CM. Henderson, R.J. Dupayk, R.L. Hahn, M. SchZdel, K. Siimmerer and G.R. Bethune, Phys. Rev. C40 (1989) 770

70

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