CHAPTER I
Introduction
There are 117 elements (Z=1-118) known at present, of which 94 occur naturally on
the earth. Eighty elements have stable isotopes, namely all elements with atomic numbers
1 to 82, except elements technetium (Z = 43) and promethium (Z = 61). Elements with
atomic numbers 83 or higher (bismuth and above) are inherently unstable and undergo
radioactive decay. The elements from atomic number 83 to 94 have no stable nuclei, but are
nevertheless found in nature, either surviving as remnants of the primordial stellar
nucleosynthesis which produced the elements in the solar system, or else produced as shortlived daughter-isotopes through the natural decay of uranium and thorium. The remaining
elements, not found on the earth or in astronomical spectra, have been derived artificially.
Element with Z = 117 has not yet been created or discovered, but its place in the periodic
table is pre-established. Recently an attempt is done by Oganessian et al [1] for the synthesis
of isotopes of element with Z =120 by the irradiation of 330-MeV 58Fe projectiles with 244Pu
target.
The stability of isotopes having magic numbers depends on the fact that their
nucleons (either protons or neutrons) are arranged into complete shells within the atomic
nucleus. The most widely recognised magic numbers are 2, 8, 20, 28, 50, 82 and 126. Magic
numbers are typically obtained by empirical studies. However, if the form of the nuclear
potential is known, then the Schrodinger equation can be solved from the motion of nucleons
and energy levels determined. Nuclear shells are said to occur when the separation between
energy levels is significantly greater than the local mean separation. In the shell model for the
nucleus, magic numbers are the numbers of nucleons at which a shell is filled. For instance
the magic number 8 occurs when 1s1/2, 1p3/2, 1p1/2 energy levels are filled as there is a large
1
energy gap between the 1p1/2 and the next highest 1d5/2 energy levels. The empirical values
can be reproduced using the classical shell model with a strong spin-orbit interaction.
Nuclei which have both neutron number and proton number equal to one of the magic
numbers are called "double magic" and are especially stable against decay. 4He,
48
Ca and
208
Pb are the examples of double magic isotopes.
100
Sn and
132
16
O,
40
Ca,
Sn are doubly magic
isotopes of tin that are unstable; however they represent endpoints beyond which stability
drops off rapidly. It is no accident that 4He is among the most abundant (and stable) nuclei in
the universe and that 208Pb is the heaviest stable nuclide. Both 48Ca and 48Ni are double magic
because 48Ca has 20 protons and 28 neutrons while 48Ni has 28 protons and 20 neutrons. 48Ca
is extremely neutron-rich for such a light element, but is made stable by being double magic.
Similarly 48Ni is the most proton-rich isotope known beyond 3He.
The theoretical description of the masses and fission barriers of the new nuclei in the
mid-1960s led to the prediction of "islands of stability" for the very heavy (super heavy)
nuclides in the vicinity of the closed proton and neutron shells. The hypothesis is that the
atomic nucleus is built up in shells in a manner similar to the electron shells in atoms. In both
cases shells are just groups of quantum energy levels that are relatively close to each other.
Energy levels from quantum states in two different shells will be separated by a relatively
large energy gap. So when the number of neutrons and protons completely fill the energy
levels of a given shell in the nucleus, the binding energy per nucleon will reach a local
maximum and thus that particular configuration will have a longer lifetime than nearby
isotopes that do not have filled shells. A filled shell would have magic numbers of neutrons
and protons. In super heavy region the possible magic number of neutrons for spherical
nuclei is 184 and some possible matching proton numbers are 114, 120 and 126 [2-9] which
would mean that the most stable spherical isotopes would be 298114, 304120 and 310126 which
are doubly magic and likely to have a very long half life. However, recent research indicates
2
that large nuclei are deformed, causing magic numbers to shift.
270
Hs is now believed to be
doubly magic nucleus with deformed magic numbers 108 and 162. Its half life may be as
high as 23 seconds [10].
The present thesis is a studies on the stability of heavy and super heavy elements
against cluster decay and it covers nine chapters. The first chapter is an introduction. This
includes the present status and development of cluster radioactivity research. The theoretical
description of cluster decay studies which includes the two approaches of decay mechanism
and some theoretical models are also mentioned in this chapter. A brief description of the
experimental techniques is also incorporated.
The second chapter is a review work on the synthesis and decay properties of all the
experimentally observed heavy and super heavy elements with atomic number Z = 93-118.
This chapter mainly concentrates on the methods of production, details of life time and all the
possible decay modes of heavy and super heavy elements with Z ranging from 93-118.
Based on the concept of cold valley the stability of heavy elements has been studied
against alpha and cluster decay and are given in chapter III. The stability of all the
and even-even
248-254
Cf
244-260
Fm isotopes are studied using Coulomb and proximity potential
model [11-15]. The detailed description of Coulomb and proximity potential model is given
in this chapter. The results obtained in this study with graphical representations for the
potential energy curves and decay half lives taking the Coulomb and proximity potential as
interacting barrier are also presented. The computed alpha decay half lives are compared with
the corresponding experimental data. The Geiger-Nuttal plots were studied for various
clusters emitting from these parents and the branching ratio with respect to alpha decay is
also studied.
Chapter IV presents the study on the stability of super heavy elements
294-326
116 and
122 against alpha and cluster decay with an aim to find the probable proton and neutron
3
280-314
shell closures in the super heavy region. The spontaneous fission of various Z = 122 isotopes
have also been studied. It has also been tried to find out those super heavy nuclei with
relatively small alpha decay half lives compared to spontaneous fission half lives. In such a
case these nuclei will survive fission and can be detected in the laboratory through alpha
decay. Isotopic and isobaric mass parabolas for various clusters emitted from various Z=116
parents are also studied in this chapter. The Geiger-Nuttal plots are also studied for various
clusters emitting from these parents.
The effect of deformations on half lives for the alpha and cluster emissions from
248-254
Cf and even-even
244-260
Fm isotopes are given in chapter V. The Coulomb and
proximity potential model is modified by incorporating the quadrupole and hexadecapole
deformations of the decaying parent nucleus along with that of emitted cluster and
corresponding daughter nucleus in the ground state. In fission and cluster decay the fragments
are strongly polarized due to nuclear force and accordingly their symmetry axes are aligned.
In the present calculations we consider only pole to pole configuration. The computed alpha
decay half lives (with including deformations) are also compared with the corresponding
experimental data.
Chapter VI aims to study the possibility of clustering in heavy nuclei by computing
the cluster formation probability for the entire experimentally observed cluster decays from
carbon to silicon taking the Coulomb and proximity potential as interacting barrier and
simple power law interpolation for overlap region. The cluster formation probability for
different C, O, Ne and Mg clusters from 112,114Ba,
116,118
Ce,
120,122
Nd and
124,126
Sm parents in
the trans-tin region are also computed.
A new semi-empirical model using minimum parameters and variables is proposed
for determining the half lives of radioactive nuclei exhibiting cluster radioactivity is
discussed in chapter VII. The semi-empirical formula is used to compute half lives of all the
4
experimentally observed cluster decays and is also applied to alpha decay of parents with
Z=85–102.
Chapter VIII aims to explore the possibility of finding long lived super heavy
elements by comparing the calculated alpha decay half-lives with the spontaneous fission
half-lives. The alpha decay half-lives of even-even elements with Z = 100-122 using the
Coulomb and proximity potential model and the spontaneous fission half-lives of even-even
isotopes with Z=100-138 is computed using the phenomenological formula. There has also
been an attempt to develop a semi-empirical formula for determining the spontaneous fission
half life time with minimum parameters. The predictions are compared with experimental
data and other empirical formulas.
Chapter IX is the summary of the present work which includes an over view of the
study.
1.1 Cluster radioactivity
Theoretical studies of the heavy cluster emission and the super-asymmetric fission
started at the end of seventies [16]. The phenomenon of spontaneous emission of particles
heavier than alpha particle by radioactive nuclei is known as cluster radioactivity. It is not an
isolated phenomenon and must be related to other processes like cold fission and cold
fusion [17]. This rare, cold neutron-less process is intermediate between α-decay and
spontaneous fission. This process can be treated as a case of strong asymmetric fission [18]
or a decay process of cluster formation and tunneling through the barrier making many
assaults on it similar to alpha decay [19].
Cluster radioactivity was first predicted in 1980 by Sandulescu et al [16] on the basis
of fission theory applied to very asymmetric processes (Quantum Mechanical Fragmentation
Theory [20], numerical and analytical super asymmetric fission models [18]) and by
extending the alpha-decay theory to heavier fragments. In literature there existed old fission
5
data of Jaffey et al [21] for
24
Ne decay of
232
U, which indicates that this phenomenon was
already observed in 1951, but the authors did not distinguish it from the spontaneous fission
process. In a very recent experiment, Bonetti et al [22] have confirmed that the emission of
24
Ne from 232U, seen in 1951 could not be due to spontaneous fission since the then-observed
cluster decay constant is larger by an order of magnitude 102 than their presently measured
upper limiting value of spontaneous fission decay constant. Experimentally, this phenomenon
as a new basic process was established by Rose and Jones [23] in 1984 by observing a
spontaneous
14
C decay of
223
Ra. A few months later, Alexandrov et al [24] confirmed this
phenomenon in the radioactive decay of
14
C from
223
Ra. After the observation of cluster
radioactivity, lots of efforts have been done on both experimental and theoretical fronts for
understanding the physics of cluster radioactivity. Altogether about 24 modes of cluster
decay from about 20 parent nuclei emitting clusters ranging from carbon to silicon are
confirmed so far. For e.g.
14
C from
221
230,232
Mg from
238
Th and
232, 234
U,
28,30
Fr,
Pu,
221-226
Ra and
226
32,34
Si from
238
Th,
20
O from
Pu and
228
Th,
24,26
Ne from
241
Am etc. are observed.
Upper limit for decay rate for 9 modes were measured and one case of fine structure in the
energy spectrum of 14C clusters from 223Ra was observed [25]. In cluster decay process the parent nucleus (A, Z) breaks into two fragments namely
the emitted cluster (A2, Z2) and the daughter nuclei (A1, Z1). Figure 1.1 shows an example of
cluster radioactivity. The emitted cluster is heavier than the alpha particle but lighter than the
lightest fission fragment observed so far. The energy released as Q value is completely
consumed as kinetic energy of the fragments.
6
223
Ra Parent nucleus
14
C
209
Pb
Cluster
Daughter nucleus
Figure 1.1 An example of Cluster radioactivity
The main physical interest to this investigation comes from the fact that cluster
radioactivity makes a bridge between the two extreme (α-decay and fission ) nuclear many
body phenomena which strongly differ by nucleon number, decay mechanism and properties
of the emitted fragments. For this reason the information obtained in the cluster radioactivity
goes beyond nuclear effects. The phenomenon of cluster radioactivity is a part of wider class
of cold decay process. Their distinctive feature is the formation of the decay products in the
ground state or in the lowest excited states. This is in contrast to normal hot fission which
leads to the production of highly excited fragments. Evidently α-radioactivity is the most
known member of the class of cold decays. The common feature of these studies is that the
spherical shell stabilization effects are found to be responsible for all the three phenomena.
The three regions of the cold decays are
1) “Traditional” cluster radioactivity leading to the formation of heavy clusters in the
vicinity of double magic 208Pb;
2) Cold fission;
3) New region of cluster decays leading to double magic 100Sn;
7
In these radioactive modes, almost all the residual nuclei resulting from cluster
emission have been found to be the doubly magic
208
Pb (lead radioactivity) or very close to
it [25]. The stability of deformed closed shell has also been observed [26], which suggests the
possibilities for similar phenomena with magic or nearly magic-deformed nuclei. In fact the
earlier calculations [27] based on QMFT suggested the use of one deformed reaction partner
for forming a cool compound system. Recently the “tin radioactivity” nuclei close to doubly
magic
100
Sn has been predicted theoretically and confirmed experimentally [28, 29]. In cold
fission the observed maximum yield is associated with the spherical closed or nearly
closed-shell nucleus; in particular [30] doubly magic spherical nucleus
132
Sn. Also the cold
fission process demands [31] scission configuration made up of deformed nuclei.
In cold fusion, all the successful experiments made for producing super heavy
elements with Z=104-114 used
208
Pb or
209
Bi as projectiles. The use of cold fusion for
complete fusion reactions and the existence of heavy cluster radioactivity prior to
experiments were suggested on the basis of quantum mechanical fragmentation theory. The
recent cluster decay calculations [22] also suggest an interesting new possibility of a
deformed daughter nucleus in the vicinity of deformed closed shell at N= 102 and Z = 76.
Also some cluster decay of some ‘stable’ nuclei are shown to correspond to daughter nuclei
with deformed magic shell at N = 108. Thus it seems that theoretically the existence of
deformed closed-shell effect in all the three phenomena such as cluster radioactivity, cold
fission and cold fusion is a reality.
1.1.1 Theoretical approach
To study the phenomenon of cluster radioactivity there are various theoretical models
with different realistic nuclear interaction potentials. Theoretical attempts in vogue are made
to understand the cluster decay of radioactive nuclei are assuming either a strongly
8
asymmetric fission or a two-step process of cluster formation followed by tunneling through
the barrier similar to alpha decay. Thus they fall under two categories, which are
1) Cluster Model
2) Fission Model
The cluster model [19, 32, 33] is considered to be a sudden non adiabatic (α-decay like)
process going in two steps; they are
™ Formation of the cluster in a parent nucleus;
™ Penetration through the potential barrier with given Q value;
In cluster model it is said that clusters of different sizes have different probabilities of
their being preformed in parent nucleus. Cluster formation probability is determined by the
overlap of the wave function of the parent nucleus with those of both fragments described by
so called spectroscopic factor S. Some examples of Cluster Model are,
¾ Microscopic Model of Blendowski et al [19], sum of coulomb potential, heavy ion
potential and centrifugal potential are used as interacting potential.
¾ Preformed Cluster Model (PCM) [22], interacting potential consists of Coulomb and
nuclear proximity potential.
¾ Cluster Model of Buck et al [34], the interaction between cluster and daughter is
obtained by a double folding integral involving their respective densities and effective
nucleon-nucleon potential.
The decay mechanism in the other case on the contrary is described as an adiabatic
(fission like) process. The fission process has two alternative approaches. In one approach,
Gamow’s idea of quantum mechanical barrier penetration is still used, but without worrying
about cluster being or not being preformed in the parent nucleus. From this point of view
cluster radioactivity is considered simply as a barrier penetration phenomenon, in between
fission and α-decay. In other words, Unified Fission Model (UFM) does distinguish between
9
three processes of α-decay, heavy cluster decay and fission. In the other fission approach,
Saddle Point Fission model (SPF) [35-37] the parent nucleus is considered to deform
continuously and reach the saddle scission shape, then penetrates the nuclear barrier after
running down the Coulomb barrier.
A new definition of the radioactive nuclei as suggested by Gupta et al [38] is,
“a radioactive nuclei is one which decays spontaneously to other stable nuclei not only by
fission but also by emitting a cluster (or clusters) heavier than α- particle, the α- particle
itself, the β-particle and the γ ray, or any combination of these”. The branching occurs more
often between α and β decays but also rarely between the α-particle and heavy cluster
(clusters). Some of the Fission Models are,
¾ Poenaru et al [39] have given an Analytical Super Asymmetric Fission Model
(ASAFM) which uses Coulomb and centrifugal potential for the post scission region
and uses a 2nd order polynomial for the overlap region.
¾ In Proximity Potential Model (PPM) of Shi and Swiatecki [40] the deformation
energy barrier for the separated configuration consists of Coulomb repulsion between
the fragments and nuclear proximity potential.
¾ Shanmugam et al [37] studied cluster decay using a cubic potential for the
overlapping region which is connected by Yukawa plus exponential potential
(CYEM) for the region after separation.
Recently Santhosh et al [11-15] put forward a fission model namely the Coulomb and
Proximity Potential Model (CPPM) which uses Coulomb and proximity potential for the post
scission region and the simple power law for the overlap region. Theoretical studies on
cluster radioactivity involve computation of half life time, branching ratio with respect to
alpha decay and other characteristics.
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1.1.2 Experimental techniques
The experiment on the search of the decay of radium isotopes with 14C emission was
proposed [41] as early as in 1970. It was based on the consideration that if three successive
α-decays are possible, the 12C emission is also allowed. The exotic decay modes were elusive
because of the earlier experimental inabilities to distinguish between the rare decay modes
and multiple pile-ups of α-particle pulses.
In the pioneering experiment of Rose and Jones [23], the events due to pile up were
rejected by separating the individual α-particle in the events by~100ns in time. The authors
used a solid state Si counter telescope that detected α-particle at the rate of ~4000/s in a solid
angle of
1
sr. The standard (∆E-E) method was used. After a run of 189 days, a group of
3
eleven events with a total energy of ~30MeV was observed. Although no mass determination
was possible. On examining the measured Q-value and branching ratio and with simple
theoretical estimates based on Gamow theory of α-decay, Rose and Jones concluded that
these eleven events were due to the new
was
227
14
C cluster radioactivity of
223
Ra.The source used
Ac (T1/2=21.7739y). Using the similar set up and technique Aleksandrov et al [24]
observed seven Carbon events in 30 days. This work was supported by the theoretical
suggestion of Sandulescu, Poenaru and Greiner [16]. This discovery was confirmed by
227
Gales et al [42] who used same but more intense
Ac source and magnetic spectrometer
(SOLENO) of Orsay MP Tandem accelerator with large solid angle
1
1
to
sr. Thus the
20
10
collection time for an observation of group of eleven events at the expected location of 14C in
a (∆E-E) telescope calibrated with 14C beam, was reduced to just 5 days. These authors [43]
then repeated their experiment for
222,226
222,226
Ra and
Am nuclei and established
Ra and set an upper limit for the emission of 34Si from
branching ratio relative to α-particle.
11
241
241
14
C decays of
Am, which is ~10-12 for the
Small decay constant and small branching ratios demand for a high efficiency and
high selectivity detecting apparatus. High selectivity means high rejection power of huge flux
of alpha particle accompanying the rare event searched for: so far, the most effective
technique for studying cluster radioactivity occurred to be the use of solid state nuclear track
detectors (SSNTD), because of their unique capacity of rejecting events due to low ionizing
particle such as α-particle and possibility to arrange geometrical efficiency approaching 2π.
They are generally plastic or glasses which are able to record latent tracks of heavy ions
whose reduced energy loss is above a given threshold, characteristic of a given detector itself.
Many other detectors are also used for the investigation of cluster decays which are
polycarbonate (PC), polyethylene terephtalate (PET) and special phosphate glass (PG).
Basically two different types of sources have been used in experiments on cluster
radioactivity: chemical sources (traditional sources) and ion implemented ones. Chemical
sources are obtained by chemical separation and generally by electro deposition of the active
material are allowed to perform experiments “off line”. On the other hand ion implanted
sources are mostly used for experiments, “on line” which is the only possibility when the
nuclide half life is too short. Common features of all sources are a rather strong activity (up to
few mCi), necessary for compensating the small branching ratios, a high purity or at least a
very well known isotopic and elemental composition, and are able to disentangle
contributions in cluster emission from competitive cases, and a relatively low thickness
(typically ≤ 1mg/cm2), to enable the clusters of ≈ 2-2.5 MeV/amu to escape from the source
with enough energy to be detected and identified.
12