Journal of Nuclear and Radiochemical Sciences,Vol. 3, No. 1, pp. 179–182, 2002

179

Structure and Spectroscopy of Transcurium Nuclei
I. Ahmad∗Physics Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA
Received: November 13, 2001; In Final Form: November 13, 2001
The stability of the superheavy elements depends on the shell corrections which are governed by the single-particle
spectra. Ideally one would like to experimentally determine the single-particle levels in the superheavy nuclei but
the production of only a few atoms of these nuclides precludes such measurements. One therefore has to identify
single-particle levels in the heaviest nuclei which are available in at least nanoCurie amounts. We have studied thestructure of such heavy nuclei in the Z = 98 region and identified many single-particle states. In particular, we havestudied the structure of 251 Cf and 249 Bk by measuring the radiations emitted in the α decay of 255 Fm and 253 Es. These
single-particle spectra can be used to test theoretical models for superheavy elements.

One of the fascinating areas of physics which is currently ofhigh interest to nuclear physicists is the production and stability of superheavy elements. Quite significant progress has been
made in recent years in the production of new elements. Element 112 was discovered at GSI in 19961 and the discoveriesof elements 114 and 116 were recently reported by the Dubnagroup.2–4 On the theoretical side, there is some controversy
about the location of the next proton shell after the Z = 82 shell.
The early calculations5–9 predicted 114 as the proton number and
184 as the neutron number for the maximum stability of superheavy elements which is confirmed by more recent Strutinsky10
type calculations.11–13 On the other hand, Relativistic Mean
Field calculations14 predict the next proton shell at Z = 120 andthe Hartree-Fock self-consistent calculations15 indicate the next
proton shell at Z = 126. Clearly experimental data are needed totest the validity of these calculations.
The best way to determine the single-particle spectra in transfermium nuclei is to measure radiations emitted in their decay.
These studies are, at present, not possible because of the production of only a few atoms of these nuclides. The states which areof interest in transfermium nuclei occur as excited states in thelower-Z nuclei. Because of high excitation energies, these levels
receive very little population in the α decay. Consequently large
amounts of activity is needed to investigate these levels. Transcurium nuclides are produced in the High Flux Isotope Reactor(HFIR) at Oak Ridge. The heaviest nuclides produced in milliCurie quantities at HFIR are the 20-d 253 Es and 20-h 255 Fm. We
obtained several samples of these isotopes from Oak Ridge andstudied the level structure of 249 Bk and 251 Cf.
The intensity of α decay to an excited state in the daughter
nucleus depends on the α-decay energy (Qα ) and the formation
factor which is determined by the wavefunctions of initial andfinal states. The dependence of 255 Fm α intensities on Qα isshown in Figure 1. For a 1-MeV level in 251 Cf, the intensity
drops by five orders of magnitude due to reduction in the barrier
penetration probability. The reduction due to formation factor
depends on the wavefunctions of the initial and final states andtypically it is in the range of 100. Thus for a 1-MeV level, an αintensity of 1.0 ×10−7 is expected. The decreased α intensities
to the high-lying levels produce fewer γ rays at the high energy
end of the γ-ray spectrum. This means lower background due toCompton scattered photons and higher sensitivity for observingvery low intensity γ rays. Thus milliCurie sources of actinide
nuclides can be used to study high-lying states in the daughter
nuclei.
The formation of α particle in the favored decay, where theodd nucleon occupies the same state in the parent and the daugh∗E-mail: ahmad@phy.anl.gov. FAX: +01-630-252-3612.

ter nucleus, and unfavored decay is shown in Figure 2. In thefavored decay, the α particle is formed from pairs of neutronsand protons in the same way as in the decay of an even-evennucleus. Thus favored transitions are fast and have hindrance
factors of ∼1. Hindrance factor is defined as the ratio of theexperimental partial half-life to the half-life calculated with thespin-independent theory of Preston.16 In the unfavored α decayof 255 Fm only one pair of neutrons participate. Here, the α particle is formed from the unpaired neutron and one neutron froma pair. In this case the probability depends on the wavefunctionsof initial and final states. The pair correlations have different
effects on α intensities to particle states (states above the Fermi
surface) and hole states (states below the Fermi surface). It has
been shown by Soloviev17, 18 that the α intensity to a level inthe daughter depends on the pair occupation probability, V 2 , ofthat level in the parent. This means that the hole states, whichhave higher values of V 2 , have higher intensities than the particle
states. For a 1-MeV state this difference corresponds to an orderof magnitude. One therefore expects that hole states will havemore α population than the particle states. In addition, phononstates exist at ∼1 MeV excitation. Phonon states, in particular,
β and octupole vibrational bands, have low hindrance factors.
2. Heavy Element Sources
The isotopes which were used in the present study were produced in the High Flux Isotope Reactor at Oak Ridge National
Laboratory as a part of the Heavy Element Production Program.
Curium targets were irradiated in the reactor for about a year.
The irradiated targets were processed to isolate Bk, Cf, Es, andα Particle Energy (MeV)
1

7.1

6.9

6.7

6.5

6.3

6.1

255 FmRelative α Intensity

1. Introduction

Effect of Q-Value

-2

10

-4

10

Effect of Q-Value+
Formation Factor

-6

10

0

200

400
600
800
Excitation Energy (keV)

1000

Figure 1. Dependence of 255 Fm α intensities on the excitation energy oflevels in 251 Cf. The solid line shows the effect of α-decay energy alone
and was calculated with the spin-independent theory of Preston.16 The
dashed line shows the combined effect of Qα and formation factor.

c 2002 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 6/30/2002

10 3

800

1000

1072.0Favored α Decay

10 4

971.3

n

1031.8 ( 250 Bk)

p

797.5

n

601.1

±Ω n1
p

519.2

±Ω n2

±Ω p1

C OUNTS / C HANNEL

±Ω n3

±Ω p2

255
Fm
100

437.6

10 5

α
±Ω p3

-4

10 6

366.3

251
Cf
98

204.2

255
Fm
100

Ahmad
2.4 x 10 / decay

180 J.Nucl.Radiochem.Sci.,Vol. 3, No. 1, 2002

α
±Ω p3

±Ω n3

±Ω p2

±Ω n2

±Ω p1

10 2

±Ω n1
p

200

n

p
Hindered α Decay

Figure 2. Effects of pair correlations on the probability of α-particle
formation. The top part shows the formation of α particle in favoreddecay, and the lower panel shows unfavored decay.

Fm. Californium and einsteinium fractions have the isotopic
composition shown in Figure 3. For an isotopically pure 253 Es
sample, Es was extracted from the Cf fraction in which 253 Es
grew as a daughter of 253 Cf. A chemically and isotopically pure255
Fm sample was isolated from the Es fraction in which 255 Es
decayed to 255 Fm. Three samples of 255 Fm, each ∼1 mCi, wereobtained from Oak Ridge National Laboratory in December
1998 and another three in November 2000. Two ∼50 mCi samples of 253 Es were acquired from Oak Ridge; one in early 1999
and the other early this year. The later samples had higher chemical and isotopic purity than the previous sources. Some samples
were counted while still in the glass bottle. One Fm sample wastransferred to a Pt disk in order to reduce the γ rays due to nuclear reactions of α particles with light elements. Similarly, one
Es sample was placed on a Ta disk to reduce background γ raysfrom nuclear reactions. For α-particle spectroscopy thin sourceswere prepared on glass and Pt disks.
3. Experimental Measurements
Except for the first 255 Fm sample, all samples had extremely
low radioactive impurities. The later Fm samples received in
November 2000 had about an order of magnitude less Es thanprevious samples. Gamma singles spectra of four samples were
measured with a 25% coaxial Ge detector and a high-resolution
2 cm2 × 7-mm planar Ge detector using different absorbers to
reduce the counting rates. In order to observe very weak transitions in the 255 Fm α decay, the spectra were measured in an
Californium
Fraction

249
250
251
252
253

Cf (351 y)

15%

Cf ( 13 y)

17%

Cf (900 y)

6%

Cf (2.6 y)

62%

Cf (17.8 d)

--

400

n

β

600
ENERGY (keV)

Figure 4. Gamma-ray spectrum of a 255 Fm sample measured with a
25% Ge spectrometer. The spectrum was measured in a very low background shield for 20 h. Most of the γ rays identified in the spectrum
have been placed in a level scheme for 251 Cf.

extremely low background shield. Because of high resolution,
the LEPS spectrum provided better information for γ rays up to∼300 keV. For higher energies, spectra measured with the 25%
detector were used. These spectra contained very weak lines
from Es–Bk isotopes and from reactions of α particles with lightelements in the sample and in glass. By comparing spectra of all
the four samples, we were able to identify transitions in 255 Fm
α decay. A γ-ray spectrum of a sample measured in November 2000 is displayed in Figure 4. As can be seen, there is very
low amount of 254 Es–250 Bk in the spectrum. For reference theintensity of the 971-keV γ ray is ∼3 ×10−7 photons per 255 Fm
α decay. Gamma rays with intensities of ∼1×10−8 photons per255
Fm α decay have been observed.
Gamma-gamma coincidence spectra of one 255 Fm sample
were measured with the Gammasphere19 in December 1998
when the Gammasphere was located at Argonne National Laboratory. Most of the levels populated in the α decay deexcite
directly to the ground state 1/2+ band or to the 7/2+ band at
106 keV which decays by highly-converted low-energy transitions. These transitions were not observed in γ-γ coincidence
spectrum. In some cases, high-lying levels were fed by K conEnergy(keV)

K π [ Nn z Λ ]

Iα

1078

7/2 + [613] x 0 +3.7 x 10 %

982

3/2

3.2 x 10 %974

9/2 + [604]

2.4 10 %510

626

9/2 + [615]
1/2 [750]370

11/2 [725]0.016%

530

178
106

+
3/2 [622]+
7/2 [613]

0.022%
93.4%

2600
1.2

+
1/2 [620]

0.07%

4400

H.F.
-5

-5

x

-5

100

350

253

Es (20.5 d) Isotopically pure
~10 µ g (~250 mCi)

Einsteinium
Fraction

253
254
255

Es (20.5 d)

99.6%

Es (276 d)~0.4%

Es (38.3 d)~0.004%~1 mg~20 Curieβ255

Fm (20.1 h) Isotopically pure
~ 2 mCi~ 4 ngFigure 3. Isotopic composition, in atom per cent, of the Cf and Es
fractions isolated from irradiated Cm targets at HFIR.

0

251
98 Cf

Figure 5. Intrinsic states in 251 Cf deduced from decay studies of 255 Fm
and 250 Cf(d, p) reaction. Right hand columns represent α intensity in% and hindrance factor calculated with the spin-independent theory of
Preston.16

J.Nucl.Radiochem.Sci.,Vol. 3, No. 1, 2002

708.0

π

Energy (keV)

7/2

1044.1

5/2
3/2

1009.1
981.6

408.2

632.0
625.7
600.8

[Nn z Λ ] K I

381.0

Nuclear levels can be characterized by measurements of α,
conversion electron, and γ-ray spectra of radioactive sources
and/or by charged-particle reaction spectroscopy. The former
provides definite spin-parity assignments whereas the latter
identifies the single-particle configuration. In an ideal case, levelstructure of a nucleus should be investigated by both techniques.
This has been done for 251 Cf which provides information on neutron single-particle states and for 251 Es which gives the proton
single-particle spectrum.
4.1. Neutron Single-particle States. The most detailed information on the neutron single-particle states of a heavy actinide nucleus has been obtained for 251 Cf. The level structureof this nucleus has been studied by measuring α, electron, andγ-ray spectra of 255 Fm, in singles and in coincidence,20, 21 high

520.0
578.0

632.0

683.3

553.0

632.0
625.7
600.8
479.0

[750] 1/2,1/2
7/2
3/2

607.4

708.0

660.2

5/2

601.0

4. Discussion

resolution α spectroscopy with a magnetic spectrometer,22 and250
Cf(d, p)251 Cf reaction.23 The intrinsic states of 251 Cf obtained
from these studies are shown in Figure 5. Rotational bands
1/2+ [620], 7/2+ [613], 3/2+ [622], 11/2− [725], 9/2− [734], and5/2+ [622] were first observed in decay studies. The singleparticle characters of the 1/2+ [620], 7/2+ [613], and 3/2+ [622]bands were confirmed by the (d, p) reaction data. In the proton
spectrum from the 250 Cf(d, p) reaction, peaks at 633, 600, 708,
and 626 keV were assigned to the members of the 1/2− [750]band. In our recent work, we observed γ rays from these levels
confirming their single-particle assignment. The (d, p) spectrum
containing the peaks from the 1/2− [750] band and the decay ofthese levels are shown in Figure 6. In our recent study, we also
performed a γ-γ coincidence measurement with the Gammasphere. The feeding of the members of the 1/2− [750] band fromhigher-lying levels is shown in Figure 7, providing further evidence for spins of these states. The 1/2− [750] level originatesfrom the h11/2 shell state. The location of this orbital provides
an estimate of the N = 184 spherical shell. The observed levels
in Figure 5 are fairly well reproduced21, 24 by a single-particle
model using Woods-Saxon potential.
4.2. Proton Single-particle States. Proton single-particle
states have been identified in 247 Bk (Ref. 25,26), 249 Bk (Ref. 27–29), 251 Bk (Ref. 28), and 251 Es (Ref. 25, 30, 31). In all these nuclei the ground state is either the 7/2+ [633] or the 3/2− [521]orbital. The next three orbitals, 7/2− [514], 1/2− [521], and9/2+ [624], have been identified in 247 Bk, 249 Bk, and 251 Es bydecay studies and (α, t) reactions. In 251 Bk, only the 1/2− [521]orbital, which was populated in the β− decay of 251 Cm, wasidentified. The best evidence for the assignments of these threeorbitals was found in 251 Es. The 7/2− [514] and the 9/2+ [624]states in 251 Es were identified in the EC decay studies of 251 Fm(Ref. 30) and the α decay of 255 Md (Ref. 31). The 1/2− [521]orbital was identified in the 250 Cf(α, t) reaction.30
The intrinsic states of 249 Bk have recently been studied bymeasurement of γ rays in the decay of 253 Es. The low-spin statesin 249 Bk were studied by measuring γ rays in the decay of 249 Cm(Ref. 28). Levels in 249 Bk were also studied by 248 Cm(α, t)249 Bk
reaction. However, because of poor resolution the data did notprovide as good information on proton states as was achieved

301.0

verted transitions which allowed the observation of γ rays deexciting to the ground band in the coincidence spectrum. Gammarays deexciting excited states to the 3/2+ band at 178 keV wereobserved in coincidence with Cf K X rays because the 3/2+ banddeexcites by M1 transitions with large K conversion coefficients.
The coincidence measurements allowed us to identify several
new bands.
Gamma singles spectra of the two 253 Es sources were measured by the same detectors used in 255 Fm measurements. The
decay of the spectra was followed for several months. Gammarays were assigned to 253 Es α decay on the basis of their estimated half-life and the fact that these γ rays are present in spectraof both Es samples. In addition, α-γ coincidence measurements
were also performed using a 2 cm2 Si detector and a 100% Ge
spectrometer. The source was ∼5 µCi in strength and the γ-ray
spectrum was counted for one week in coincidence with α particles with energies less than 6.2 MeV. The spectrum showed thepresence of several γ rays including 768- and 932-keV peaks.

181

349.6

Structure and Spectroscopy of Transcurium Nuclei[622] 3/2, 3/2 +
9/2 +
7/2 +

177.6
146.7

5/2 +
3/2 +
[620] 1/2, 1/2 +

47.8
24.8
0

105.7

251
Cf
98

Figure 6. A portion of the 250 Cf(d, p) spectrum measured with an Enge
split-pole magnetic spectrometer. Only peaks representing levels in the
1/2− [750] band are shaded. The γ-ray transitions were observed in a
γ-ray spectrum of 255 Fm measured with a 25% Ge spectrometer.

9/2+

146.71

7/2+

105.735/2+
3/2+[620] 1/2,1/2+

47.83
24.82
0
251
98Cf

Figure 7. A partial level scheme of 251 Cf showing the population anddecay of the 1/2− [750] band. The coincidence relationship was obtained in a Gammasphere run.

182 J.Nucl.Radiochem.Sci.,Vol. 3, No. 1, 2002
+

1040

+
+
7/2 [633] x 0932[624] 9/2, 9/2

7/2

768

[514] 7/2, 7/2~690[521] 1/2, 1/2643[530] 1/2, 1/2

569+[642] 5/2, 5/2 +[400] 1/2, 1/2

389
377

[521] 3/2, 3/2 +[633] 7/2, 7/2

249
Bk
97

9
0

Figure 8. Intrinsic states in 249 Bk deduced from decay studies of 249 Cm
and 253 Es and 248 Cm(α, t) reaction. The 768-keV level is most likely avibrational state.

in 251 Es. Proton intrinsic states identified in all these studies areshown in Figure 8. These levels are fairly well reproduced bysingle-particle model using Woods-Saxon potential. It should
be pointed out that the 1/2− [521] orbital originates from the f 7/2
shell state. Thus the location of this orbital gives an estimate of
the gap at Z = 114.
5. Summary
Nuclear structure of nuclei around A = 250 have been studied by a variety of techniques and many single-particle states
have been identified in these nuclei. In 251 Cf, all neutron singleparticle states between the N = 152 and N = 162 subshells havebeen identified by decay scheme studies and (d, p) reaction
spectroscopy. In Bk and Es nuclei, the 7/2− [514], 1/2− [521],
and 9/2+ [624] proton single-particle states, which occur above
the Z = 100, have been identified by decay scheme studies and(α, t) reactions. In addition, two-quasiparticle states in 250 Cf(Ref. 32) have also been studied. This well established nuclear
structure information on nuclei near A = 250, which are nearer
to the superheavy element region than any other experimentally
known region, can be used either to determine the parameters ofa single-particle potential or to test the nuclear models of superheavy elements.
Acknowledgement. The author would like to thank P.
Bhattacharyya, J. P. Greene, F. G. Kondev, and E. F. Moore forassistance in data analysis and R. R. Chasman for helpful discussions. This work was supported by the Department of Energy,
Nuclear Physics Division, under contract No. W-31-109-ENG38. The author is also indebted for the use of 255 Fm and 253 Es
to the Office of Basic Energy Sciences, U. S. Department of Energy, through the transplutonium element production facilities at
the Oak Ridge National Laboratory.
References(1) S. Hofmann, V. Ninov, F. P. Heßberger, P. Armbruster, H.
Folger, G. Münzenberg, H. J. Schött, A. G. Popeko, A. V.
Yeremin, S. Saro, R. Janik, and M. Leino, Z. Phys. A 354,
229 (1996).
(2) Yu. Ts. Oganessian, V. K. Utyonkov, Yu. V. Lubanov, F.
Sh. Abdullin, A. N. Polyakov, I. V. Shirokovski, Yu. S.

Ahmad
Tsyganov, G. G. Gulbekian, S. L. Bogomolov, B. N. Gikal,
A. N. Mezentsev, S. Iliev, V. G. Subbotin, A. M. Sukhov,
G. V. Buklanov, K. Subotic, M. G. Itkis, K. J. Moody, J.
F. Wild, N. J. Stoyer, M. A. Stoyer, and R. W. Lougheed,
Phys. Rev. Lett. 83, 3154 (1999).
(3) Yu. Ts. Oganessian, A. V. Yeremin, A. G. Popeko, S.
L. Bogomolov, G. V. Buklanov, M. L. Chelnokov, V. I.
Chepigin, B. N. Gikal, V. A. Gorshkov, G. G. Gulbekian,M. G. Itkis, A. P. Kabachenko, A. Yu. Lavrentev, O. N.
Malyshev, J. Rohac, R. N. Sagaidak, S. Hofmann, S. Saro,
G. Giardina, and K. Morita, Nature 400, 242 (1999).
(4) Yu. Ts. Oganessian, V. K. Utyonkov, Yu. V. Lobanov, F.
Sh. Abdullin, A. N. Polyakov, I. V. Shirokovsky, Yu. S.
Tsyganov, G. G. Gulbekian, S. L. Bogomolov, B. N. Gikal,
A. N. Mezentsev, S. Iliev, V. G. Subbotin, A. M. Sukhov,
O. V. Ivanov, G. V. Buklanov, K. Subotic, M. G. Itkis, K.
J. Moody, J. F. Wild, N. J. Stoyer, M. A. Stoyer, R. W.
Lougheed, C. A. Laue, Ye. A. Karelin, and A. N. Tatarinov,Phys. Rev. C 63, 011301(R) (2001).
(5) W. D. Myers and W. J. Swiatecki, Nucl. Phys. 81, 1 (1966).
(6) H. Meldner and H. Ryde, Ark. Fys. 36, 593 (1967).
(7) S. G. Nilsson, J. R. Nix, A. Sobiczewski, Z. Szymanski, S.
Wycech, C. Gustafson, and P. Möller, Nucl. Phys. A 115,545 (1968).
(8) U. Mosel and W. Greiner, Z. Phys. 221, 261 (1969).
(9) R. R. Chasman, Proceedings of the International Symposium on Superheavy Elements, Lubbok, Texas, March 1978.
(10) V. M. Strutinsky, Nucl. Phys. A 95, 420 (1967).
(11) P. Möller and J. R. Nix, J. Phys. G 20, 1681 (1994).
(12) A. Sobiczewski, Phys. Part. Nucl. 25, 295 (1994).
(13) R. Smolańczuk, J. Skalski, and A. Sobiczewski, Phys. Rev.
C 52, 1871 (1995).
(14) K. Rutz, M. Bender, T. Bürvenich, T. Schilling, P.-G.
Reinhard, J. A. Maruhn, and W. Greiner, Phys. Rev. C 56,
238 (1997).
(15) S. Ćwiok, S. Dobaczewski, P.-H. Heenen, P. Magierski, and
W. Nazarewicz, Nucl. Phys. A 611, 211 (1996).
(16) M. A. Preston, Phys. Rev. 71, 865 (1947).
(17) V. G. Soloviev, Phys. Lett. 1, 202 (1962).
(18) V. G. Soloviev, Theory of Complex Nuclei, translated by P.
Vogel (Pergamon Press, New York, 1976).
(19) I-Yang Lee, Nucl. Phys. A 520, 641c (1990).
(20) I. Ahmad, F. T. Porter, M. S. Freedman, R. F. Barnes, R. K.
Sjoblom, F. Wagner, Jr., J. Milsted, and P. R. Fields, Phys.
Rev. C 1, 390 (1971).
(21) I. Ahmad, M. P. Carpenter, R. R. Chasman, J. P. Greene, R.
V. F. Janssens, T. L. Khoo, F. G. Kondev, T. Lauritsen, C. J.
Lister, P. Reiter, D. Seweryniak, A. Sonzogni, J. Uusitalo,
and I. Wiedenhöver, Phys. Rev. C 62, 064302 (2000).
(22) I. Ahmad and J. Milsted, Nucl. Phys. A 239, 1 (1975).
(23) I. Ahmad, R. R. Chasman, A. M. Friedman, and S. W.
Yates, Phys. Lett. B 251, 338 (1990).
(24) R. R. Chasman, I. Ahmad, A. M. Friedman, and J. R.
Erskine, Rev. Mod. Phys. 49, 833 (1977).
(25) I. Ahmad, A. M. Friedman, R. R. Chasman, and S. W.
Yates, Phys. Rev. Lett. 39, 12 (1977).
(26) I. Ahmad, S. W. Yates, R. K. Sjoblom, and A. M. Friedman,
Phys. Rev. C 20, 290 (1979).
(27) J. R. Erskine, G. Kyle, R. R. Chasman, and A. M. Friedman,
Phys. Rev. C 11, 561 (1975).
(28) R. W. Lougheed, J. F. Wild, E. K. Hulet, R. W. Hoff, and J.
H. Landrum, J. Inorg. Nucl. Chem. 40, 1865 (1978).
(29) R. W. Hoff and I. Ahmad (to be published).
(30) I. Ahmad, R. K. Sjoblom, A. M. Friedman, and S. W. Yates,
Phys. Rev. C 17, 2163 (1978).
(31) I. Ahmad, R. R. Chasman, and P. R. Fields, Phys. Rev. C
61, 044301 (2000).
(32) K. Katori, A. M. Friedman, and I. Ahmad (to be published).