2. Internal Pair Production Following the 0+ – 0+ Transition of 90Zr
In the past there has been a great interest in so-called electric monopole transitions (E0) in certain nuclei. This may occur when there is no angular momentum change between initial and final nuclear states and no parity change (in particular, electromagnetic transition between states with J=0). For spin-zero to spin-zero transitions, single gamma emission is strictly forbidden, hence three alternative processes may occur: a) transitions give rise to transfer of radiation energy to an atomic electron in the orbital cloud by internal conversion b) if the energy of the process is greater than
![Atoms 01 00002 i001]()
(1.022 MeV, where m
e is the mass of the electron), transition can occur via electron-positron internal pair creation. c) two-photon emission, which is generally negligibly small.
The electric monopole transition takes place entirely in the nuclear volume, corresponding classically to a radially oscillating spherical charge distribution that does not give rise to a time-varying field outside the charged region. This may be visualized as a “breathing” mode without change of shape, that is only possible in a compressible nucleus. Past literature studies focused on a number of nuclei that undergo electric monopole transition. Among these,
16O,
40Ca,
72Ge,
90Zr have been studied. The importance behind these transitions lies in the fact that the analysis of the small branch ratio associated with two-photon decay provided useful information on the nuclear structure. A surprising result of these researches was that the angular correlation between the two gamma rays was asymmetric about 90
°. This was interpreted as arising from interference between the 2E1 and the 2M1 contributions to the transitions which were found to be of comparable strength [
1].
Figure 1.
a) Approximate level pattern for protons derived from the shell model. The spin-orbit coupling is adjusted in such a way that the empirical level sequence is represented. Round brackets (2), (4)
etc. and square brackets [
2], [
6],
etc. denote the level degeneracies and the total occupation number, respectively. b) Experimental energy levels of
90Zr (MeV). The total energies are reported.
Figure 1.
a) Approximate level pattern for protons derived from the shell model. The spin-orbit coupling is adjusted in such a way that the empirical level sequence is represented. Round brackets (2), (4)
etc. and square brackets [
2], [
6],
etc. denote the level degeneracies and the total occupation number, respectively. b) Experimental energy levels of
90Zr (MeV). The total energies are reported.
In particular, a number of past literature studies were dedicated to the analysis of the electric monopole transition (E0) occurring during the decay of
90Y nucleus to the fundamental level of
90Zr.
Figure 1a shows the approximate level pattern for protons derived from the shell model of
90Zr, while
Figure 1b) shows the associated low-lying excitations.
90Zr has 40 protons and 50 neutrons. 50 neutrons form a close shell, filling up to
![Atoms 01 00002 i002]()
. 28 of 40 protons fill first four shells, while the remaining 12 fill
![Atoms 01 00002 i003]()
,
![Atoms 01 00002 i004]()
and
![Atoms 01 00002 i005]()
. If one of the protons in
![Atoms 01 00002 i005]()
is excited to
![Atoms 01 00002 i002]()
, the remaining proton in
![Atoms 01 00002 i005]()
and the proton in
![Atoms 01 00002 i002]()
can form states with odd parity and
![Atoms 01 00002 i006]()
and 5. There are indeed 4
- and 5
- states.
- State 5 is lower presumably because two protons are closer in space by lining up the orbital angular momenta. If both protons are excited from
![Atoms 01 00002 i005]()
to
![Atoms 01 00002 i002]()
, it could give
![Atoms 01 00002 i007]()
Nevertheless, the anti-symmetry of the wave function allows only states with
![Atoms 01 00002 i008]()
.They should all have even parity. Indeed, 0
+, 2
+, 4
+, 6
+, 8
+ are observed in this order (
Figure 1b).
The radioactive decay of
90Y nucleus by beta emission to the fundamental level of
90Zr with a half-life of 64 hours has been widely studied in the past. However, in 1955 in a letter to the editor of the
Physical Review, Ford predicted an excited state (0
+ state) of
90Zr [
2]. For the aforementioned reasons, the evidence of the 0
+ state of
90Zr could be proved with the detection of positrons emitted from a
90Y source beta decaying to
90Zr. As a matter of fact, the predicted state was discovered by Johnson
et al. at the same laboratory in the same period and was described in a letter to the editor of the same journal issue [
3]. The authors discovered a transition at 1.76 MeV followed by positron emission by using a strong source of
90Y in a 40-cm radius of curvature magnetic spectrometer. Very precise measurements of the beta spectrum of
90Y gave no indication of any other group of beta rays between 0.5 MeV and the end point at 2.26 MeV. Further, the authors observed no gamma ray line in the region of 1.76 MeV and they concluded that this energetic transition was to be imputable to that of a monopole between two 0
+ states of the even-even nucleus of
90Zr. They observed an internal conversion line whose intensity relative to that of the 2.26 MeV beta spectrum was
![Atoms 01 00002 i009]()
. These authors also reported the probability of pair creation per beta decay as:
![Atoms 01 00002 i010]()
.
One year later Greenberg and Deutsch in a new experiment evaluated the entity of internal pair creation by assessing the number of positron emission relative to the main beta spectrum [
4]. They used a magnetic focus arrangement combined with coincidence counting of the annihilation radiation to allow the detection of very low positron intensities in the presence of other radiations. In their paper, the authors noted that in the assessment of the pair production probabilities three types of virtual intermediate states have to be considered. Indicating with
![Atoms 01 00002 i011]()
the nuclear wave function one has [
4]:
with the prime denoting the virtual intermediate state. They noted that the process (a) and (c) contribute about equally to pair creation, i.e. the pairs are formed by the field of the beta ray and of the residual nucleus.
In order to compare their findings with those obtained by other authors, Greenberg and Deutsch evaluated the internal pair production probability following the theoretical formulation proposed by Thomas [
5]. According to this formalism, the E0 transition strength from the initial excited state
![Atoms 01 00002 i013]()
to state
![Atoms 01 00002 i014]()
is defined by:
Where
![Atoms 01 00002 i016]()
represents a summation over all nuclear protons at positions
![Atoms 01 00002 i017]()
and the parameter
![Atoms 01 00002 i018]()
is the nuclear radius. Therefore the internal pair production probability,
![Atoms 01 00002 i019]()
, depends on the relevant matrix
![Atoms 01 00002 i020]()
[
4,
5]. Most notably, they observed that the evaluation of this matrix element could only be estimated from some nuclear models. On the other hand, the
relative probabilities for the emission of conversion electrons,
![Atoms 01 00002 i021]()
, or of a positron electron pair involve only an evaluation of the electron wave functions at the nuclear surface. Using the Thomas formulation for
![Atoms 01 00002 i019]()
and
![Atoms 01 00002 i021]()
no specific nuclear property, not even the nuclear radius, enter the ratio of internal conversion to internal pair creation.
According to Thomas’ formalism the internal pair production probability
![Atoms 01 00002 i019]()
is given by the following analytic formula [
5]:
with:
![Atoms 01 00002 i024]()
, α=1/137 fine structure constant,
R nuclear radius,
Z atomic number of the element and
![Atoms 01 00002 i025]()
denotes the gamma function. In Equation 3, units have been chosen such that
m,
c,
![Atoms 01 00002 i026]()
are equal to unity.
On the other hand, the probability for the emission of conversion electrons,
![Atoms 01 00002 i021]()
, is:
Where
![Atoms 01 00002 i028]()
is the energy of the outgoing electron, E is the transition energy and
![Atoms 01 00002 i029]()
is its momentum of the electron. For large
Z (>60), so that
![Atoms 01 00002 i030]()
, the following useful approximation may be inserted into Equation (5):
which also includes the expansion in power of
![Atoms 01 00002 i032]()
, good for all nuclei with
![Atoms 01 00002 i033]()
. Then one immediately obtains the relative probability of the emission of conversion electrons to that of a positron electron pair creation:
Following this formalism and resolving Equation (7) for the appropriate energy and atomic number, Greenberg and Deutsch obtained for the ratio of the K-conversion to pair creation:
On the other hand, one year before, Johnson and colleagues reported an internal conversion intensity relative to that beta spectrum
![Atoms 01 00002 i037]()
and a probability of pair creation per beta decay
![Atoms 01 00002 i038]()
. As a consequence, using the experimental data obtained by Johnson, one would obtain:
uncertain to about a factor of two. In view of this substantial discrepancy of the
![Atoms 01 00002 i040]()
ratio obtained by the two authors, Greenberg and Deutsch decided to measure the number of positrons per beta decay of
90Y with their apparatus.
The experimental problem Greenberg and Deutsch had to face consisted of the detection of a very small number of primary positrons in the presence of an overwhelmingly larger number of other radiations (beta rays, internal/external bremsstrahlung radiations and secondary positrons produced by the impact of photons and beta rays). The low relative intensity of the effect sought, made it imperative to use a very selective detection method. Such a method was allowed by the annihilation radiation produced when the positrons were stopped in a beryllium target (referred to as the “catcher”). The two annihilation gammas arising in the target were detected coincidently using two sodium iodide (NaI) detectors. To minimize the formation of positrons by energetic electrons or photons striking the catcher, the latter was located in a magnetic field in such a position that about one-half of all the positrons emitted by the source in the interesting energy interval would strike it while all trajectories of electrons with energy greater than 1 MeV either missed the catcher or were intercepted by the collimator (
Figure 2).
Figure 2.
Experimental apparatus used by Greenberg and Deutsch for the detection of positrons emitted from a
90Y source due to 1.75 MeV electric monopole transition to
90Zr. Image reproduced from reference [
4].
Figure 2.
Experimental apparatus used by Greenberg and Deutsch for the detection of positrons emitted from a
90Y source due to 1.75 MeV electric monopole transition to
90Zr. Image reproduced from reference [
4].
From their experiment, the positron branch ratio was determined to be
![Atoms 01 00002 i041]()
. Combined with the data for the intensity of the conversion line obtained by from Johnson and colleagues, they obtained an experimental value for the probability of pair creation per beta decay as
![Atoms 01 00002 i042]()
, in moderate agreement with the calculation of Thomas.
Later on, in 1961, in an attempt to quantify a predicted two gamma emission in the 0+/0+ transition of
90Zr by Ryde
et al. [
6], Langhoff and Hennies [
7] determined with a scintillation coincidence spectrometer the positron branch ratio to be
![Atoms 01 00002 i043]()
and a relative probability of the emission of conversion electrons to that of total beta decays to be
![Atoms 01 00002 i044]()
.
Figure 3.
Decay scheme of 90Y
Figure 3.
Decay scheme of 90Y
In recent years, Selwyn and colleagues [
8] used a high-purity germanium detector to determine the internal pair production branch ratio of the 0
+ – 0
+ transition of
90Zr. The basic measurement technique consisted in counting the gross number of gammas detected within a 511 keV (annihilation) peak and subtracting the bremsstrahlung continuum, environmental continuum, and environmental peak at 511 keV. The germanium detector was selected over other detectors (i.e., NaI and CdTe) based on its superior energy resolution. In the measurement, it is fundamental to quantify the extremely small 511 keV peak observed above the large bremsstrahlung spectrum and environmental 511 keV background. The authors found the branch ratio to be
![Atoms 01 00002 i045]()
.
Figure 3 shows the decay scheme of
90Y, while in
Table 1 the experimental values for the internal pair production branch ratio of the 0
+/0
+ transition of
90Zr are reported.
Table 1.
Probability of pair creation per beta decay measured in earlier and more recent literature studies.
Table 2,
Table 3 report the most updated properties of
90Y beta decay, from LNHB/CEA [
9].
Table 2.
Beta minus transitions of 90Y
Table 3.
Gamma transitions of 90Y, including conversion electron (ce)
Table 3.
Gamma transitions of 90Y, including conversion electron (ce)
| Energy (keV) | Probability γ+ce (x 100) | Multipolarity |
---|
![Atoms 01 00002 i054]() | 1760,7 (2) | 0.0000014 (3) | E0 |
![Atoms 01 00002 i055]() | 2186,282 (10) | 0,017 (6) | E2 |
3. Exploitation in Nuclear Medicine of the β+/β–Emission from the 0+ – 0+ Transition of 90Zr
90Y is one of the most widely used radionuclide for internal radiotherapy as the long range of the β particles allows more uniform irradiation in large tumours [
10]. Therefore,
90Y labelling is currently adopted for preparation of compounds belonging to various classes of therapeutic agents: peptides, antibodies, microspheres and citrate. In addition,
90Y is also used to label resin or glass microspheres for liver radioembolization, an interventional radiology procedure in which millions of
90Y microspheres are infused through a catheter into the hepatic artery. According to this procedure, the microspheres become embedded in the liver, and the therapeutic dose is delivered over a period of about two weeks allowing
90Y to irradiate the tumor while sparing healthy liver tissue.
Different authors have used the small positronic emission of
90Y to obtain high-resolution positron emission tomography (PET) images of
90Y-labelled radiopharmaceuticals. In 2004, Nickles
et al. assessed
90Y distribution on a Derenzo phantom using a micro-PET scanner provided with bismuth germanate (BGO) crystals showing the remarkable resolution and quantitative accuracy of positron tomography [
11]. In the same paper they concluded that
90Y provide a “clear picture of the regional dose delivered by the therapy”.
However, the issue associated with 90Y PET imaging is the extremely small emission probability of the β+ particles. In order to visualize (and properly measure) the activity taken up by a region of interest, a high 90Y concentration is required. In liver radioembolization the typically injected activity ranges from one to several GBq and the total amount of radioactivity is concentrated in the liver or in small regions inside it. Hence high 90Y concentration regions may be obtained with this technique and PET imaging of 90Y is possible.
Recently, accurate biodistribution assessment after microsphere administration by direct
90Y-PET scan after liver radioembolization was proven feasible by Lhommel
et al. [
12,
13] and Werner
et al. [
14] which used a TOF-PET equipped with lutetium-yttrium-oxyorthosilicate (LYSO) crystals and a non-TOF PET/CT with lutetium oxyorthosilicate (LSO) detectors, respectively. The results obtained by these authors pioneered further studies about the possibility of detecting the β
+ particles emitted by
90Y during internal radiotherapy treatments. In another work, Gates
et al. [
15] showed the feasibility of hepatic localization of microsphere using routine PET on three patients concluding that
90Y microspheres can be visualized with a simple 20-min PET/CT scan acquired using universally available technology. Bagni
et al. confirmed the feasibility of
90Y PET imaging for the assessment of microsphere biodistribution (
Figure 4) using a routine PET/CT scanner provided with BGO crystals [
16]. Recent studies performed by D’Arienzo
et al. [
17] and Willowson
et al. [
18] confirmed the feasibility of dosimetry and quantitative image reconstruction following
90Y PET, respectively.
Figure 4.
PET acquisition of β+ particles emitted in the 0+/0+ transition of 90Zr. The biodistribution of resin microspheres after liver radioembolization is shown (courtesy of Dr. Oreste Bagni).
Figure 4.
PET acquisition of β+ particles emitted in the 0+/0+ transition of 90Zr. The biodistribution of resin microspheres after liver radioembolization is shown (courtesy of Dr. Oreste Bagni).
Finally, it is worth mentioning that another study by Fabbri
et al. [
18] considered clinical applications of
90Y PET scans in locoregional therapies other than liver radioembolization.