Forty seven years ago Marinov et al.    reported evidence for possible synthesis of a super heavy (SH) element (Z = 112) in the irradiation of tungsten target with 24 GeV protons.
They irradiated three W-targets, each with mass of 33 g and thickness 120 g∙cm−2 using the CERN PS accelerator. These targets are referred to as W1, W2 and W3. Table 1 gives some information on irradiation of the targets  . The W1 target was available for analysis 3 - 4 month after the end of the irradiation.
Table 1. Irradiation data for three tungsten targets from  .
For reasons given in  most of the reported experimental results and findings are for W2-target and we will focus on this target as well.
The synthesis of isotope of element 112 via reaction was reported in 1999   . Prior to that in 1996  , production of 277Cn in 208Pb (70Zn, n) reaction has been reported. The half-life of 283Cn is 4 s and 277Cn has a half-life of 0.69 ms.
Discovery of the short-lived isotopes of element 112 does not rule out the existence of long-lived isotopes of this element.
Marinov et al.    suggest that neutron deficient long lived isotopes of element 112 can exist and may be produced with higher cross-sections.
Their claim is based on the following assumptions and observations:
1) Element 112 would be a chemical homologue of mercury (Eka-Hg).
2) Detection of spontaneous fission events in Eka-Hg sources separated from proton irradiated W-targets, which could not be attributed to actinides or to any other known isotope.
Heavy ion fusion experiments such as   obviously will not be able to detect the long-lived SH isotopes because very few atoms of these are produced. On the other side, experiments like that of the Marinov et al. will not be able to detect the short-lived SH isotopes because of the required long chemical separation times.
Several attempts to reproduce the experimental findings of Marinov et al. were inconclusive, see e.g.     . The rejection by Barber et al.  of the claim of Marinov et al. was recently addressed by Brandt et al.  who point out that presently unexplained findings may indicate novel reaction paths leading to unexpected results.
In this paper we use the experimental results given in the publications of Marinov et al. to investigate the feasibility of reproducing their findings in possible future experiments.
2. Calculation of Spontaneous Fission Half-Life of Eka-Hg
Table 2 gives a timeline of the experiments and measurements on W2 target after the end of the proton irradiation, taken mainly from  . For those periods where no information was available in the literature, reasonable times have been assigned by us. The timeline given in the last column of Table 2 is used in this report.
The most unambiguous experimental results reported  are the fission
Table 2. Timeline of experiments and measurements after the end of the irradiation.
events recorded after attempts to reduce the thickness of the Eka-Hg source prepared from W2 target, (Table 2, rows 15 - 17). The spontaneous fission half-life of Eka-Hg can be calculated using these data.
The fission events in the source were recorded as tracks in Makrofol KG polycarbonate foils (hereafter referred to as Makrofol) that were placed in close contact with the surface of the source.
First of all one need to convert the observed fission tracks in the Makrofol foils to the number of fission events in the source.
Fission track density ρ (tracks cm−2) in a foil in contact with a fission source is related to the number of fission events per unit volume of the source, Nv by the following relationship  
n is number of fragments per fission event (we use n = 2);
ε is fission track detection efficiency of Makrofol foil which is ~1;
μ is a parameter that depends on fission source thickness d and range of the fission fragments in the source material, R.
For a thin source (d < R) equation 1 can be written as
where Nc is total number of fission tracks detected in the Makrofol foil, Nf is number of fission events in the source and η is
For a thin source, μ is given by  
Determination of μ requires knowledge of source thickness, and range of fission fragments. The authors of  mention that the thickness of the Eka-Hg source was 2 mg∙cm−2, but the density of the source material is not given. If we assume that source material has a density equivalent to the density of HgO (11.14 g∙cm−3), thickness of the source and range of fission fragments in the source material may be calculated as 1.8 µm and 8 µm, respectively.
Using the Equation (4) and values of n and ε we obtain η = 0.89.
The first Makrofol foil was in contact with W2 source for 8 days and showed 28 tracks (row 15 of Table 2). Thus
where N1 is the number of Eka-Hg nuclei in the source at the start of the 1st Makrofol exposure (row 15 of Table 2) and λ is the spontaneousfission decay constant.
The second Makrofol exposure (row 16 of Table 2) started 13 days after the end of the first one and the number of tracks in this foil after 8 days of exposure was 23. The number of Eka-Hg nuclei at the start of the second exposure is
Thus for the second Makrofol exposure we get
From Equations (5) and (6) we obtain: λ = 9.37 × 10−3 d−1 and t1/2 » 74 d.
The number N1 of Eka-Hg at the start of the fission track measurements can be calculated using Equation (5) or Equation (6);
Taking into account that fission track recording (row 15 of Table 2) started 105 days after the end of the irradiation, the number of Eka-Hg at the end of the irradiation was:
This number must be corrected for the number of the produced Eka-Hg nuclei that have decayed in the course of the 4 month irradiation period.
The total number of 24 GeV protons that was delivered to W2 target from the PS accelerator of CERN in late 1960s was 7 × 1017. With a pulse repetition time of 2.4 s and number of protons per pulse of 1012   total actual target exposure time has been ~1.68 × 106 s (~19 days). This implies that ~84% of the irradiation time (~4 month) the target did not receive any proton while the produced Eka-Hg nuclei were decaying. Therefore a large number of the nuclei of interest have been lost prior to the start of chemical separation. An accurate calculation of this lost activity requires knowledge of the exact timeline of the irradiation and pulse intensity distribution during the irradiation period. In absence of such data and taking into account the calculated half-life, we estimate that at least 60% of the activity survived to the end of the irradiation. Thus the corrected number of the produced Eka-Hg is
3. Production of Spallation Residues in Interaction of 24 GeV Protons with Tungsten Target
It is assumed that the production of element 112 in a W-target irradiated with 24 GeV protons is possible via fusion of Sr isotopes (spallation products) with W nuclei of the target. Marinov et al.  and Kolb et al.  suggest and reactions.
We used HTAPE card in the MCNPX 2.7 code  to calculate the types and numbers of residual nuclei produced in the interaction of 24 GeV protons with a natW-target. The target specifications were same as given by  , i.e. cylindrical natW targets of thickness (length) 120 g∙cm−2 and mass of 33 g, which translates to a cylinder of diameter 0.6 cm and length 6.2 cm. In the calculations the direction of the proton beam coincided with the target axis.
Figure 1(a) shows the charge distribution of all isotopes (spallation products) and Figure 1(b) illustrates the yield of Sr isotopes (Z = 38) produced in the interactions. All together sixteen isotopes of Sr with (A = 77 to 92) with total yield of 8.32 × 10−3 per proton are produced. The spallation residue yield is strongly dependent on the target length (along the beam line); for a shorter target length it will be less than the above given figure.
From Figure 1(b) it is evident that most abundantly produced isotopes of Sr (62%) are those with mass numbers of 82, 83 and 84. Fusion of these isotopes with 184W and 186W will result in
Figure 1. Spallation residues produced in 24 GeV p + natW interactions. (a) Yield of all spallation products (b) Yield of Sr isotopes. Lines connecting data points are to guide the eye.
The mass numbers of Eka-Hg in the above given interactions are less than 272 given by Marinov et al.  and the products are neutron deficient isotopes.
Combined production rate of these three Sr isotopes (82-84Sr) is 5.15 × 10−3 per proton which is 7 times higher than the combined production rates of 88Sr and 86Sr (7.25 × 10−4), considered by Marinov et al. to be the principal participants in the fusion reaction with W nuclei  .
4. Estimation of the Eka-Hg Production Cross-Section
An accurate estimation of the production cross-section of Eka-Hg with the available data is not possible for the following reasons:
1) The exact number of protons that hit the target is not known. From the publications it is not clear how the targets were irradiated? What was the proton direction with respect to the target axis? How was the beam fluence measured? Do the given proton numbers refer to those that hit the target or are they the numbers of the protons that were extracted from the accelerator?
Lack of this information in the publications implies that measurement of the production cross-section of Eka-Hg was not part of the experimental plan of Marinov et al.
2) As already mentioned, 16 isotopes of Sr are produced with different production rates. Out of these 88Sr and 86Sr have been nominated to produce 272Cn via fusion with W nuclei. Each Sr isotope has its own fusion reaction cross-section with a given W-isotope of natW.
However a rough estimation of the production cross-section of 272Cn is possible with the following assumptions:
1) The given proton numbers are actually those that hit the target.
2) The beam direction was along the target axis.
3) Cross-sections for and reactions are similar to each other.
Then, using the calculated yields of the Sr isotopes of the interest, isotope fractions of the W-isotopes in natW and a beam dose of 7 × 1017 protons, one obtains a production cross-section of 1.6 nb.
5. Case of Uranium Target
Production of element 112 is possible via fusion of 238U with Ca. Similar to the case of the W-target, we calculated the spallation residue yields in the interaction of 24 GeV protons with a U-target, of the same shape and dimensions as the W-target. The mass of U-target will be slightly less (~1.5%) than that of the W because of the difference in densities.
Figure 2(a) shows the charge distribution of all spallation residues produced in the interactions. Obviously the hump in the middle of the distribution is populated mainly with the 238U-fission products.
Figure 2. Spallation residues produced in 24 GeV p + 238U interactions. (a) Yield of all spallation products; (b) Yield of Ca isotopes. Lines connecting data points are to guide the eye.
All together 22 isotopes of Ca with A = 40 - 62 are produced, with a total yield of 3.14 × 10−3 per proton. This is about 2.7 times less than the yield of Sr-isotopes produced in the W-target. Isotopes 42,43,44Ca make about 63% of the total Ca yield. The yield of 48Ca relevant to the experiments of Oganessian et al.  is less than 2% of the total Ca yield.
If isotopes 286Cn and 283Cn were produced in the proton irradiated U-target, they would not be detectable by chemical separation method because of their very short half-lives. If fusion of Ca isotopes (from the spallation residues) with 238U nuclei in the target was possible then in order to produce the isotope 272Cn, the post fusion compound nuclei must evaporate between 6 and 28 neutrons which is highly improbable for energetic reasons.
Boos et al.  irradiated a uranium target of mass 65 g with (4 ± 1) × 1017 protons of 24 GeV using the CERN PS accelerator. The irradiation period was 20 days and chemical separation process of the target started three weeks after the end of the irradiation. They prepared two thin sources of HgS as carrier for Eka-Hg. For detection of the possible spontaneous fission activity in the HgS sources mica foils were placed in close contact with source 1 and 2 for periods of 2.6 y and 0.6 y, respectively. The mica foil placements on source 1 and 2 started 2.4 month and 1.4 month after the end of the irradiation, respectively. After exposure the mica foils were etched and scanned under an optical microscope; not a single fission track was detected.
The theoretical calculations given in this section confirm the experimental observations of Boos et al.  .
6. Energy Distribution of the Spallation Products
Figure 3 shows the energy distribution of the all residual nuclei in the target volume, produced in interaction of the 24 GeV protons with natW-target. As can be seen, almost all of the residual nuclei, regardless of their charge and mass have energies less than 100 MeV, well below (about one third of) the coulomb barrier
Figure 3. Energy distribution of the spallation residues produced in the interaction of 24 GeV protons with tungsten target of thickness 120 g∙cm−2 and total mass of 33 g.
height of the (Sr + W) system. Therefore, if fusion of these nuclei in proton irradiated W-target were possible, then it had to be deeply sub-barrier fusion.
7. Effects of Proton Beam Energy on the Energy Distribution of Spallation Residues
Figure 4 shows the spectra of the neutrons and protons in interaction of 24 GeV protons with a tungsten target of thickness 120 g∙cm−2 and mass 33 g. On average for every incident proton, there are 0.71 protons with energy greater than 23.7 GeV in the exit channel. Neutrons carry 5.2% and protons 80.6% of the beam energy. With energy and target size  used in the calculations majority of the beam protons leave the target without being engaged in an inelastic nuclear interactions and only lose small fraction of their energy via electronic interactions.
To increase the production rate of Sr nuclei in the W-target one need to:
1) Increase the target length to reduce number of the non-interacting beam protons.
2) Increase the beam dose at optimum proton energy.
Figure 5 shows the energy distribution of the heavy spallation residue (Z > 2) at different incident proton energies in interaction with a tungsten target of length 20 cm and diameter 0.6 cm. The energies of the spallation residue correspond to those at the moment of their production (i.e. maximum possible energy) and the energy degradation in the target environment is not taken into account. We chose a target with small diameter to reduce the amount of the unnecessary and disruptive radioactivity production. Obviously for a target of diameter 0.6 cm one prefers to have a proton beam of diameter less than 0.6 cm.
Spectra of the heavy ion residue at beam energies in the range of 3 GeV < Ep £ 24 GeV do not change significantly. For clarity of the figure in Figure 5 only the spectra at Ep > 5 GeV are shown. Most important, the total number of the produced ions per incident proton at different beam energies remains almost constant (Table 3). This is expected because; the heavy spallation residue mainly result from the proton induced fission of the target tungsten nuclei, a process that takes place after the cascade, pre-equilibrium and evaporation stages of the spallation reaction.
Table 3. Total number of heavy spallation residues produced on irradiation of a 20 cm long W target with protons of different energies.
Figure 4. Spectra of the neutrons and protons escape the W-target (diameter 0.6 and length 6.2 cm) on its irradiation with 24 GeV protons.
Figure 5. Energy distribution of the heavy nuclei (Z > 2) in irradiation of a W-target of diameter 0.6 cm and length 20 cm with protons of different energies.
Thus we conclude that if one intends to search for the interaction of any heavy spallation residue with the target nuclei, very high energy proton beam is not required.
From the available published data  the half-life of the spontaneous fission events detected in the source from W2 target was estimated to be ~74 days.
Monte Carlo calculations show that, in the irradiation of a tungsten target with 24 GeV protons 16 isotopes of Sr are produced. The yields of these isotopes are sufficiently high to justify the assumption of the fusion reaction of Sr + W in the target. However, because of low energies of the spallation residues, if fusion of Sr and W nuclei in proton irradiated W-target were possible, then it had to be deeply sub-barrier fusion.
If sub-barrier fusion of (U + Ca) system is possible, auranium target irradiated with 24 GeV protons is not expected to showany isotopes of element 112. Most abundantly produced Ca isotopes are 42,43,44,45Ca where the product mass range goes from 40Ca to 62Ca. The post fusion compound nuclei need to evaporate 6 to 28 neutrons to reach mass 272 which is very unlikely. Short lived isotopes of element 112 produced via irradiation of 238U with Ca ions will not be detectable because of the required long chemical separation and sample preparation times.
The proton dose of the W1 target was 2 × 1018 over an irradiation period of about one year. Similar to the case of the W2 target, it is estimated that the actual irradiation period during which the W1 target was receiving protons, was about 58 days. The estimated half-life and duration of the proton irradiation of the W1 target and considering that fission track recording started ~200 days after the end of the irradiation, failure to detect any spontaneous fission activity in source prepared from W1-target may therefore be justified.
Monte Carlo calculations using the MCNPX code show that energy distribution of the heavy ion spallation residue do not change for a very wide range of the incident proton energies. Therefore, if Sr + W fusion in proton irradiated W-target is possible, then one does not need to have very high energy proton beam. A relatively long target at a proton energy of ≥3 GeV will be sufficient to produce the desired number of Sr nuclei in the tungsten target.
Findings of Marinov et al. imply the following possibilities:
1) Production of super-heavy element in proton irradiated tungsten target.
2) Production of very long-lived isotope of SHE which are not known so far.
3) Production of SHE in deep sub-barrier fusion reactions.
4) Production of SHE with much higher cross-sections than those known so far.
We believe that new experiments with today’s knowledge, experimental facilities and techniques are required to examine and test the reproducibility or otherwise disprove the Marinov et al. claims.
As strontium isotopes in the proton irradiated W-target will not have energies greater than 100 MeV (fission fragment energy), the most straightforward method for examining the Z = 112 production in a W-target is to irradiate a thin foil of W with a very heavy dose of 100 MeV Sr ions and look for fission events.