Cluster decay, also named heavy particle radioactivity or heavy ion radioactivity, is a rare type of nuclear decay in which an atomic nucleus emits a small "cluster" of
neutron
The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons beh ...
s and
proton
A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
s, more than in an
alpha particle
Alpha particles, also called alpha rays or alpha radiation, consist of two protons and two neutrons bound together into a particle identical to a helium-4 nucleus. They are generally produced in the process of alpha decay, but may also be produce ...
, but less than a typical binary
fission fragment
Nuclear fission products are the atomic fragments left after a large atomic nucleus undergoes nuclear fission. Typically, a large nucleus like that of uranium fissions by splitting into two smaller nuclei, along with a few neutrons, the releas ...
.
Ternary fission
Ternary fission is a comparatively rare (0.2 to 0.4% of events) type of nuclear fission in which three charged products are produced rather than two. As in other nuclear fission processes, other uncharged particles such as multiple neutrons and g ...
into three fragments also produces products in the cluster size. The loss of protons from the parent nucleus changes it to the nucleus of a different element, the daughter, with a
mass number
The mass number (symbol ''A'', from the German word ''Atomgewicht'' tomic weight, also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus. It is approxima ...
''A''
d = ''A'' − ''A''
e and
atomic number
The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every ...
''Z''
d = ''Z'' − ''Z''
e, where ''A''
e = ''N''
e + ''Z''
e.
For example:
: → +
This type of rare decay mode was observed in
radioisotope
A radionuclide (radioactive nuclide, radioisotope or radioactive isotope) is a nuclide that has excess nuclear energy, making it unstable. This excess energy can be used in one of three ways: emitted from the nucleus as gamma radiation; transferr ...
s that decay predominantly by
alpha emission
Alpha decay or α-decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle (helium nucleus) and thereby transforms or 'decays' into a different atomic nucleus, with a mass number that is reduced by four and an at ...
, and it occurs only in a small percentage of the decays for all such isotopes.
The
branching ratio
In particle physics and nuclear physics, the branching fraction (or branching ratio) for a decay is the fraction of particles which decay by an individual decay mode or with respect to the total number of particles which decay. It applies to eithe ...
with respect to alpha decay is rather small (see the Table below).
:
T
a and T
c are the half-lives of the parent nucleus relative to alpha decay and cluster radioactivity, respectively.
Cluster decay, like alpha decay, is a quantum tunneling process: in order to be emitted, the cluster must penetrate a potential barrier. This is a different process than the more random nuclear disintegration that precedes light fragment emission in
ternary fission
Ternary fission is a comparatively rare (0.2 to 0.4% of events) type of nuclear fission in which three charged products are produced rather than two. As in other nuclear fission processes, other uncharged particles such as multiple neutrons and g ...
, which may be a result of a
nuclear reaction
In nuclear physics and nuclear chemistry, a nuclear reaction is a process in which two atomic nucleus, nuclei, or a nucleus and an external subatomic particle, collide to produce one or more new nuclides. Thus, a nuclear reaction must cause a t ...
, but can also be a type of spontaneous
radioactive decay
Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is consid ...
in certain nuclides, demonstrating that input energy is not necessarily needed for fission, which remains a fundamentally different process mechanistically.
Theoretically, any nucleus with ''Z'' > 40 for which the released energy (Q value) is a positive quantity, can be a cluster-emitter. In practice, observations are severely restricted to limitations imposed by currently available experimental techniques which require a sufficiently short half-life, T
c < 10
32 s, and a sufficiently large branching ratio B > 10
−17.
In the absence of any energy loss for fragment deformation and excitation, as in
cold fission Cold fission or cold nuclear fission is defined as involving fission events for which fission fragments have such low excitation energy that no neutrons or gammas are emitted.
Cold fission events have so low a probability of occurrence that it is ...
phenomena or in alpha decay, the total kinetic energy is equal to the Q-value and is divided between the particles in inverse proportion with their masses, as required by conservation of linear momentum
:
where ''A''
d is the mass number of the daughter, ''A''
d = ''A'' − ''A''
e.
Cluster decay exists in an intermediate position between alpha decay (in which a nucleus spits out a
4He nucleus), and
spontaneous fission
Spontaneous fission (SF) is a form of radioactive decay that is found only in very heavy chemical elements. The nuclear binding energy of the elements reaches its maximum at an atomic mass number of about 56 (e.g., iron-56); spontaneous breakdo ...
, in which a heavy nucleus splits into two (or more) large fragments and an assorted number of neutrons. Spontaneous fission ends up with a probabilistic distribution of daughter products, which sets it apart from cluster decay. In cluster decay for a given radioisotope, the emitted particle is a light nucleus and the decay method always emits this same particle. For heavier emitted clusters, there is otherwise practically no qualitative difference between cluster decay and spontaneous cold fission.
History
The first information about the atomic nucleus was obtained at the beginning of the 20th century by studying radioactivity. For a long period of time only three kinds of nuclear decay modes (
alpha
Alpha (uppercase , lowercase ; grc, ἄλφα, ''álpha'', or ell, άλφα, álfa) is the first letter of the Greek alphabet. In the system of Greek numerals, it has a value of one. Alpha is derived from the Phoenician letter aleph , whic ...
,
beta
Beta (, ; uppercase , lowercase , or cursive ; grc, βῆτα, bē̂ta or ell, βήτα, víta) is the second letter of the Greek alphabet. In the system of Greek numerals, it has a value of 2. In Modern Greek, it represents the voiced labiod ...
, and
gamma
Gamma (uppercase , lowercase ; ''gámma'') is the third letter of the Greek alphabet. In the system of Greek numerals it has a value of 3. In Ancient Greek, the letter gamma represented a voiced velar stop . In Modern Greek, this letter re ...
) were known. They illustrate three of the fundamental interactions in nature:
strong,
weak, and
electromagnetic
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
.
Spontaneous fission
Spontaneous fission (SF) is a form of radioactive decay that is found only in very heavy chemical elements. The nuclear binding energy of the elements reaches its maximum at an atomic mass number of about 56 (e.g., iron-56); spontaneous breakdo ...
became better studied soon after its discovery in 1940 by
Konstantin Petrzhak
Konstantin Antonovich Petrzhak (alternatively Pietrzak; rus, Константи́н Анто́нович Пе́тржак, p=kənstɐnʲˈtʲin ɐnˈtonəvʲɪtɕ ˈpʲedʐək, ; 4 September 1907– 10 October 1998), , was a Russian physicist o ...
and
Georgy Flyorov
Georgii Nikolayevich Flyorov (also spelled Flerov, rus, Гео́ргий Никола́евич Флёров, p=gʲɪˈorgʲɪj nʲɪkɐˈlajɪvʲɪtɕ ˈflʲɵrəf; 2 March 1913 – 19 November 1990) was a Soviet physicist who is known for h ...
because of both the military and the peaceful applications of induced fission. This was discovered circa 1939 by
Otto Hahn
Otto Hahn (; 8 March 1879 – 28 July 1968) was a German chemist who was a pioneer in the fields of radioactivity and radiochemistry. He is referred to as the father of nuclear chemistry and father of nuclear fission. Hahn and Lise Meitner ...
,
Lise Meitner
Elise Meitner ( , ; 7 November 1878 – 27 October 1968) was an Austrian-Swedish physicist who was one of those responsible for the discovery of the element protactinium and nuclear fission. While working at the Kaiser Wilhelm Institute on rad ...
, and
Fritz Strassmann
Friedrich Wilhelm Strassmann (; 22 February 1902 – 22 April 1980) was a German chemist who, with Otto Hahn in December 1938, identified the element barium as a product of the bombardment of uranium with neutrons. Their observation was the ke ...
.
There are many other kinds of radioactivity, e.g. cluster decay,
proton emission
Proton emission (also known as proton radioactivity) is a rare type of radioactive decay in which a proton is ejected from a nucleus. Proton emission can occur from high-lying excited states in a nucleus following a beta decay, in which case t ...
, various beta-delayed decay modes (p, 2p, 3p, n, 2n, 3n, 4n, d, t, alpha, f),
fission isomers, particle accompanied (ternary) fission, etc. The height of the potential barrier, mainly of Coulomb nature, for emission of the charged particles is much higher than the observed kinetic energy of the emitted particles. The spontaneous decay can only be explained by
quantum tunneling
In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantizati ...
in a similar way to the first application of the Quantum Mechanics to Nuclei given by G. Gamow for alpha decay.
:''"In 1980 A. Sandulescu, D.N. Poenaru, and W. Greiner described calculations indicating the possibility of a new type of decay of heavy nuclei intermediate between alpha decay and spontaneous fission. The first observation of heavy-ion radioactivity was that of a 30-MeV, carbon-14 emission from radium-223 by H.J. Rose and G.A. Jones in 1984"''.
Usually the theory explains an already experimentally observed phenomenon. Cluster decay is one of the rare examples of phenomena predicted before experimental discovery. Theoretical predictions were made in 1980,
four years before experimental discovery.
Four theoretical approaches were used: fragmentation theory by solving a Schrödinger equation with mass asymmetry as a variable to obtain the mass distributions of fragments; penetrability calculations similar to those used in traditional theory of alpha decay, and superasymmetric fission models, numerical (NuSAF) and analytical (ASAF). Superasymmetric fission models are based on the macroscopic-microscopic approach
using the asymmetrical two-center shell model
level energies as input data for the shell and pairing corrections. Either the liquid drop model
or the Yukawa-plus-exponential model
extended to different charge-to-mass ratios
have been used to calculate the macroscopic deformation energy.
Penetrability theory predicted eight decay modes:
14C,
24Ne,
28Mg,
32,34Si,
46Ar, and
48,50Ca from the following parent nuclei:
222,224Ra,
230,232Th,
236,238U,
244,246Pu,
248,250Cm,
250,252Cf,
252,254Fm, and
252,254No.
The first experimental report was published in 1984, when physicists at Oxford University discovered that
223Ra emits one
14C nucleus among every billion (10
9) decays by alpha emission.
Theory
The quantum tunneling may be calculated either by extending
fission theory to a larger mass asymmetry or by heavier emitted particle from
alpha decay
Alpha decay or α-decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle (helium nucleus) and thereby transforms or 'decays' into a different atomic nucleus, with a mass number that is reduced by four and an atom ...
theory.
Both fission-like and alpha-like approaches are able to express the decay constant
= ln 2 / T
c, as a product of three model-dependent quantities
::
where
is the frequency of assaults on the barrier per second, S is the preformation probability of the cluster at the nuclear surface, and P
s is the penetrability of the external barrier. In alpha-like theories S is an overlap integral of the
wave function
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements mad ...
of the three partners (parent, daughter, and emitted cluster). In a fission theory the preformation probability is the penetrability of the internal part of the barrier from the initial turning point R
i to the touching point R
t.
Very frequently it is calculated by using the Wentzel-Kramers-Brillouin (WKB) approximation.
A very large number, of the order 10
5, of parent-emitted cluster combinations were considered in a systematic search for new
decay modes. The large amount of computations could be performed in a reasonable time by using the ASAF model developed by
Dorin N Poenaru,
Walter Greiner
Walter Greiner (29 October 1935 – 6 October 2016) was a German theoretical physicist. His research interests lay in atomic physics, heavy ion physics, nuclear physics, elementary particle physics (particularly in quantum electrodynamics and qu ...
, et al. The model was the first to be used to predict measurable quantities in cluster decay. More than 150 cluster decay modes have been predicted before any other kind of half-lives calculations have been reported. Comprehensive tables of
half-lives
Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable at ...
,
branching ratio
In particle physics and nuclear physics, the branching fraction (or branching ratio) for a decay is the fraction of particles which decay by an individual decay mode or with respect to the total number of particles which decay. It applies to eithe ...
s, and kinetic energies have been published, e.g.
.
Potential barrier shapes similar to that considered within the ASAF model have been calculated by using the macroscopic-microscopic method.
Previously
it was shown that even alpha decay may be considered a particular case of
cold fission Cold fission or cold nuclear fission is defined as involving fission events for which fission fragments have such low excitation energy that no neutrons or gammas are emitted.
Cold fission events have so low a probability of occurrence that it is ...
. The ASAF model may be used to describe in a unified manner cold alpha decay, cluster decay, and cold fission (see figure 6.7, p. 287 of the Ref.
.
One can obtain with good approximation one universal curve (UNIV) for any kind of cluster decay mode with a mass number Ae, including alpha decay
::
In a logarithmic scale the equation log T = f(log P
s) represents a single straight line which can be conveniently used to estimate the half-life. A single universal curve for alpha decay and cluster decay modes results by expressing log T + log S = f(log P
s).
The experimental data on cluster decay in three groups of even-even, even-odd, and odd-even parent nuclei are reproduced with comparable accuracy by both types of universal curves, fission-like UNIV and UDL
derived using alpha-like R-matrix theory.
In order to find the released energy
::
one can use the compilation of measured masses
M, M
d, and M
e of the parent, daughter, and emitted nuclei, c is the light velocity. The mass excess is transformed into energy according to the
Einstein's formula E = mc
2.
Experiments
The main experimental difficulty in observing cluster decay comes from the need to identify a few rare events against a background of alpha particles. The quantities experimentally determined are the partial half life, T
c, and the kinetic energy of the emitted cluster E
k. There is also a need to identify the emitted particle.
Detection of radiations is based on their interactions with matter, leading mainly to ionizations. Using a semiconductor telescope and conventional electronics to identify the
14C ions, the Rose and Jones's experiment was running for about six months in order to get 11 useful events.
With modern magnetic spectrometers (SOLENO and Enge-split pole), at Orsay and Argonne National Laboratory (see ch. 7 in Ref.
pp. 188–204), a very strong source could be used, so that results were obtained in a run of few hours.
Solid state nuclear track detectors (SSNTD) insensitive to alpha particles and magnetic spectrometers in which alpha particles are deflected by a strong magnetic field have been used to overcome this difficulty. SSNTD are cheap and handy but they need chemical etching and microscope scanning.
A key role in experiments on cluster decay modes performed in Berkeley, Orsay, Dubna, and Milano was played by P. Buford Price, Eid Hourany, Michel Hussonnois, Svetlana Tretyakova, A. A. Ogloblin, Roberto Bonetti, and their coworkers.
The main region of 20 emitters experimentally observed until 2010 is above Z=86:
221Fr,
221-224,226Ra,
223,225Ac,
228,230Th,
231Pa,
230,232-236U,
236,238Pu, and
242Cm. Only upper limits could be detected in the following cases:
12C decay of
114Ba,
15N decay of
223Ac,
18O decay of
226Th,
24,26Ne decays of
232Th and of
236U,
28Mg decays of
232,233,235U,
30Mg decay of
237Np, and
34Si decay of
240Pu and of
241Am.
Some of the cluster emitters are members of the three natural radioactive families. Others should be produced by nuclear reactions. Up to now no odd-odd emitter has been observed.
From many decay modes with half-lives and branching ratios relative to alpha decay predicted with the analytical superasymmetric fission (ASAF) model, the following 11 have been experimentally confirmed:
14C,
20O,
23F,
22,24-26Ne,
28,30Mg, and
32,34Si. The experimental data are in good agreement with predicted values. A strong shell effect can be seen: as a rule the shortest value of the half-life is obtained when the daughter nucleus has a magic number of neutrons (N
d = 126) and/or protons (Z
d = 82).
The known cluster emissions as of 2010 are as follows:
Fine structure
The fine structure in
14C radioactivity of
223Ra was discussed for the
first time by M. Greiner and W. Scheid in 1986.
The superconducting spectrometer SOLENO of IPN Orsay has been used since 1984 to identify
14C clusters emitted from
222-224,226Ra nuclei. Moreover, it was used to discover
the fine structure observing transitions to excited states of the daughter. A transition with an excited state of
14C predicted in Ref.
was not yet observed.
Surprisingly, the experimentalists had seen a transition to the first excited state of the daughter stronger than that to the ground state. The transition is favoured if the uncoupled nucleon is left in the same state in both parent and daughter nuclei. Otherwise the difference in nuclear structure leads to a large hindrance.
The interpretation
was confirmed: the main spherical component of the deformed parent wave function has an i
11/2 character, i.e. the main component is spherical.
References
External links
National Nuclear Data Center
{{Nuclear processes
Nuclear physics
Radioactivity