Flexible algorithms for background suppression in heavy ion induced nuclear reactions

A new algorithm for the analog spectrometer of the DGFRS-2 setup installed at DC-280 cyclotron is presented. The main goal of application of this algorithm is to search an optimal time correlation recoilalpha parameter directly during the acquisition C++ code execution. A new real-time flexible algorithm in addition to the conventional ER − α algorithm, which has been used for a several years at the DGFRS-1 setup installed at the U-400 FLNR cyclotron, is presented. The main parts of the spectrometer are a 48 × 128 strip DSSD detector (Double Side Strip Detector) and a low-pressure gaseous detector. They are presented schematically. Nuclear reactions for synthesis of element Z=119 at the DGFRS-2 are under consideration. Some attention is paid to computer simulation of the heavy recoil spectra, taking into account its pulse height defect in silicon. First beam test results are also presented. A new formula for half-life time using recent data for superheavy nuclei is obtained.


Introduction
With the discovery of uranium fission by Hann and Strassmann, the nuclei existence boundary was physically defined for the first time as a limit of nuclei stability with the spontaneous fission (SF) [1]. The fission barrier will promptly decrease with growing Z (Z > 92) [2]. In the macroscopic theory the situation with zero barrier occurs for the element with Z > 100. The situation is changed after observing the short spontaneous fission half-life of 242 Am (TSF ≈ 0.014 s), which has T SF > 3e+12 y in the ground state [3]. It means that nuclear structure does not disappear with increasing deformation but evolves an important role in nuclear fission process [4]. Elements with Z > 100 were produced in the reactions induced by charged particles.
In the beginning of present century, new Z = 114-118 elements were synthesized using the Dubna Gas-Filled Recoil Separator (DGFRS) [5][6][7][8][9][10]. That discovery confirmed the main role of shell effects in stability of superheavy nuclei. From the viewpoint of detecting procedure, the specifics of that experiment are in detection of ultra-rare α -decays or/and SF signals. A key issue is the probability P err that the observed sequence of event is due to a random correlation of unrelated events. The value of this probability allows readers and experimenters to judge the reliability of the interpretation. Present work aimed to a development of flexible real-time algorithms to decrease significantly P err parameter, and, therefore, to provide a higher interpretation validity.

Experimental technique
To synthesize new superheavy nuclei, the following technique should be in operation: • Ion source and accelerator to provide high projectile intensity because of extremely low cross-section values of the products under investigation formation; • Rotating actinide target: its design should provide long-term non-destructive operation under condition of high intensity of heavy ion beams; • Recoil separator: it should provide a high level of background products suppression and relatively high transmission factor for the products under investigation; • The detection system: High separation yield will increase background level, so the transmitted particles must be identified by detector system with high efficiency. During the last 30 years, these DGFRS-1 silicon detectors have been transformed from surface-barrier detectors based on n-Si(Au) into resistive layer PIPS position sensitive ones, and then into DSSD detectors. Namely, DSSD large area detectors are mostly efficient for ultra-rare α -decays detection.
The new detector system is composed of low-pressure (1.2 ± 0.0017 Torr pentane) proportional chamber detector and 48 × 128 strips DSSD focal plane detector, 8 strips 6 backward detectors, VETO-detector [11,12]. Figure 1 shows the schematic of the detector module. The thickness of the entrance Mylar foil is about 1.2 µ m. A silicon-veto detector to suppress the background particles passing through the DSSD focal plane completes the setup. The additional electrode, shown in Figure 1, located at a distance of 6 cm apart from ∆ E detector in the direction of DSSD one, is based by -200 V to reduce an influence of space charge to the parameter of detection efficiency under condition of high rate of highly ionized charged particles passing through ∆ E detector (up to ∼ 1e+4 s −1 ). Although a detailed description of the electronics is beyond the scope of the author, in order to help the reader understand the whole data taking process, Figure 2 shows general block schematics of the DGFRS-2 spectrometer. The main electronic modules with their functions are presented in the Table 1.  Splitter unit 3M 32-in unit to split signals from preamplifiers to digital and analog system(FLNR, JINR design). 12 1M unit 6OR 6-in logical TTL input signals to provide trigger TTL signal for gating of Pa3n unit. 13 1M unit PATS01 12 bit ADC to measure summary signal from all side detectors (FLNR, JINR design). 14 1M unit AM-208 8-in analog multiplexer(FLNR, JINR design).
The DGFRS-2 spectrometer consists of two independent branches. One is a digital spectrometer based on PIXIE-16 modules produced by XIA Corporation [13]. This subsystem allows detecting very short events with ∼ 120 ns dead time, whereas the second one based on ADP-16 CAMAC (manufacturer "ExTekh" firm, free economy zone "Dubna") units and allows detecting sequences of eight events with 2.8 µ s time interval between each two signals [14]. Regular dead time of analog branch is about 25 µs . Searching for the ERα correlation is performed with the second subsystem. Of course, it is assumed that 482 calibration parameters are ready for application before the starting the experiment. To obtain the calibration parameters, we usually use heavy ion induced complete fusion nuclear reaction nat Yb+ 48 Ca → 217 Th+3n and some others (xn) reactions of similar nature [11,12].

Method of active correlations
The heaviest element 118 (Og) was observed by a heavy ion induced complete fusion nuclear reaction, namely in 249 Cf+ 48 Ca → Og*. A first successful experiment to synthesize Z=118 element was made at DGFRS-1 in 2003, using a net irradiation time of 60 days and a beam dose of 4.3 · 10 18 [15]. The experiment was continued in 2006, reaching net irradiation time 4 months and beam dose of 4.1 · 10 19 [16]. As a result, four decay chains of 294 Og were observed. Note, that previous experiment to synthesize Z=118 element was strongly unsuccessful [16]. As to the synthesis of Z = 120 element, the experiment 244 Pu+ 58 Fe → 120* was unsuccessful too [17]. Only upper limit of cross-section value of 0.8 pb has been declared. With putting into operation both ultra-intense new FLNR cyclotron DC-280 and DGFRS-2 setup, we plan to synthesize new elements Z=119, 120. The most reasonable candidates to working reactions are: 243 Am + 54 Cr → 294 119 + 3n, 249 Bk + 50 Ti → 119 + 3n, 244,242 Pu + 58 Fe → 302,300 120 + 3n, 249 Cf + 50 Ti → 296 120 + 3n. The significant role in the discoveries of Z=113-118 elements played method of "active correlations". Namely, these techniques one can definitely consider as a "locomotive" which provides background free detection procedure for alpha decays of super heavy nuclei under investigation. Moreover, with an increasing of beam intensity, significance of this method will also increase. To apply this method correctly, one should predict energy-time property of nuclei under investigation with some accuracy. In the Table 2 (3 rd and 4 th column) Qα − Tα parameters of SHN measured in 48 Ca induced complete fusion reactions performed at the DGFRS-1 setup are presented basing on the Table 1 from the Ref. [5]. The column 5 with calculated values of T calc α corresponds to the formulae [18]: where a =1.78, b =-21.398, c =-0.25488 and d =-28.423 [19]. The K -parameter which was whown in Figures 3 is equal to K = T calc α /T α . In the Figure 3a, b dependence of LgK against Z value is shown. Figure 3b corresponds to an improved calculation with d =-28.0928 (last column). This d value is obtained via iteration process with condition | mean i | < 10 3 , where i -index of iteration process. For the sake of comparison, several T α values calculated using Royer's formulae are presented in the last column 6, lgK values are shown in Figure 3c. In contrast to formulae (1) containing two parameters ( Q α , Z ) Royer's formulae contain three parameters, namely Q α , Z and A [20]. Another required step for active correlations' method application is an exhaustive knowledge about registered amplitude values of implanted heavy nuclei. There are two approaches to that task, one of them is to use the empirical dependence of the registered energy on the incoming calculated energy using reactions leading to the complete fusion products close to Z =100 with relatively high cross-sections [20]. Another approach is related to computer simulation of heavy recoil registered energy spectra [21]. The code described in Ref.
[21] allows a simulation that considers the reasons for transformation of spectra originating in the target into that registered by a silicon detector. In the Fig.4 both measured in 242 Pu+ 48 Ca → Fl* reaction and simulated spectra are shown. The arrows show the registered recoil amplitudes measured in 238 U+ 48 Ca → 283 Cn+3n experiment. They demonstrate a perfect correspondence to each other.
The synthesis superheavy elements Z = 119, Z = 120 using the heaviest   available target materials 249 Bk, 251 Cf requires to switch to the higher-Z bombarding particles 50 Ti, 54 Cr except for double magic projectile 48 Ca. However, the cross-sections of fusion reactions with heavier projectiles are expected to be significantly lower than with 48 Ca. Therefore, it is necessary to increase noticeable the overall experiment efficiency. To solve this problem a new experimental complex is developed at FLNR (JINR) including the specialized high-current DC-280 cyclotron and new DGFRS-2 gas-filled recoil separator [22]. Of course, with higher beam intensity, requirement to suppress background products when detecting ultra-rare α -decays is of great significance. Below, in the Table 3, the predicted decay chains of 294 119 nuclei are shown [18,23]. T 1/2 and Q α of the isotopes 105-117 measured in the experiments on DGFRS-II [5].

Choice of initial parameters for "active correlations" technique application
Below, we shall consider different detection modes of an "active correlations" method, which are based on: • Standard algorithm; • Simple-flexible algorithm (trivial); • Flexible-probability algorithm; • High recoil signals rate algorithm; • Combined algorithm.

Standard algorithm
This approach is applied at both DGFRS-2 and DGFRS-1 during last year's (see e.g. [24]). The correlation time parameter is chosen from the upper presented T α = f (Q α ) systematic as T corr = n · T α , where n ≫ 1 . As usual, it uses a fixed ER − α correlation time interval, pre-setting by the experimentalist. In some cases, a functional dependence t = F(E α ) .
Here E α is the current value of the energy signal of alpha particle (or even imitating the alpha decay signal) and relation from [18] defines function F . In the Figure 5, such dependence is shown for different beam intensities for DGFRS-1 setup installed at U-400 cyclotron of FLNR.
Typical correlation time parameters are usually taken from1 to 5 s, with beam pause times of 1 to 2 minutes for those experiments. Note, that the background suppression factor for the DGFRS-2 is much greater than for the DGFRS-1 setup [23]. Thus, irradiation time losses are much smaller in the similar experiments ( 48 Ca + Actinide target → *SHN). For instance, in the reaction 242 Pu + 48 Ca → 287 Fl + 3n typical rate of random correlation beam stops value was about one-two per day at the DGFRS-2. It means when one takes into account the correlation time parameter 20 s and pause time 100 s, beam time loss will be about ∼ 400 s per day, or ∼ 0.5% from the whole irradiation time. An average 48 Ca +10 beam intensity was about 3 p µ A from DC-280 cyclotron. In the 238 U + 48 Ca → 283 Cn + 3n complete fusion reaction, the projectile beam intensity was up to ∼ 7 p µA for a few days.

Simple -flexible (trivial) algorithm
In this scenario, after the experimenter boots code, the first approximation for the ER − α correlation parameter Tcorr is read from the appropriate text file.
Each time interval (event onTimer C++ Builder) of 5-10 min, the code adds one T corr value until the iteration number is less than N max or the beam stop is already occur.
Here, N max -is a pre-set integer parameter (usually ∼ 10 or even more).

Flexible -probability algorithm (main)
The application of this algorithm was tested on the DC-280 48 Ca beam in various nuclear reactions. In our experiments, we apply a specific acquisition mode. Namely, when energy-time-position correlation like ER − α is detected, the system switches the beam off for a short time. Therefore, the forthcoming decay signals are detected in a background free mode. For example, if we start acquisition Builder C++ program with initial conditions as: -T corr is a first approximation of the correlation ER − α time value; -∆ t -beam stop pause time(fixed, usually 100-300 s ); -N b0 -random correlation expectation for one day acceptable by the experimentalists (float).
After booting, the new file system estimates each ten minutes an actual expectation value with the extrapolation to 24 hours using mean ER and α signals rate value and corrects T corr parameter. When T k corr corresponds to the where ε is a small positive value ( ε ≪ 1), system stops iteration process. In the Figure 6 an example of the mentioned algorithm application is shown for one decay chain of 288 Mc isotope that was registered in 243 Am + 48 Ca → Mc * complete fusion reaction. This experiment was carried out at the DGFRS-2 installation of the Superheavy Element Factory. During the experiment, 61 decay chains of two Mc isotopes were registered. Daughter nuclei which shown with shadows was registered after finding the ERα correlation, during beam off time. To a first approximation, τ 0 value was equal to 1 s and N b0 = 4 .
The iteration process flows in the form: , where k is a number of iteration. Additional successful test of the described algorithm application was performed in 242 Pu + 48 Ca → *Fl complete fusion nuclear reaction with up to 3 p µA projectile beam intensity for a few hours. Below, in the Figure 7 duration of the iteration process is shown as example. Note, that system stops iteration process for 70 minutes. Note, that during the calculation the probability of each ERα correlation chain to be a random, calculation operates with the parameter of effective area A e f f . The algorithm to calculate that parameter is presented below using coding in Python [25].The process of recalculation is usually performed for every 20-30 min.
The algorithm is designed to calculate the effective area of the focal plane detector -that is, the percentage of the detector area, which is 0.95 of the total dose (see Figure 8). Initially, the Levenberg-Marquardt gradient descent algorithm is used, but it showed low accuracy due to the complex relief of the dose distribution [26]. The algorithm entered the wrong local minimum and showed an incorrect estimation. The new algorithm can be illustrated as filling a vessel with an uneven bottom with water drops. As the filling is completed, the accumulated dose is calculated and checked for compliance with the factor.

High ER signal rate algorithm
The authors do not exclude the possibility that heavy-ion projectile intensity at the DC-280 FLNR cyclotron will reach such a high level, as the ER's rate will be high enough to start iteration process leading to a smaller parameter of T corr than the first approximation one. In this case, the acquisition program changes the trigger signal sequence. Namely, except for ERα sequence it will consider ERα − α energy-time-position correlation and, therefore, will use a more sophisticated algorithm. This approach was not tested at the DC-280 beam until now, but it was tested using a Monte Carlo PC-based simulation reported in [21]. The preliminary general conclusion of those simulations show that there is no need to switch the algorithms in the range from 1 to 10 p µA of the 48 Ca beam.
In the nearest future, we plan to extend similar conclusion for another projectiles, like 50 Ti and 54 Cr.

Combined algorithm
In principle, the same as flexible algorithm, but, additionally the range for the ER signal (left level) is varied by a small amount of ± 1 MeV with an iteration step of 0.2 MeV. In addition, the beam off pause time interval is varied for a small value, usually of ± 15 % with respect to a first assignment one too.

Conclusion
With the commissioning of the new super intense FLNR DC-280 heavy ion cyclotron and the new DGFRS-2 setup, new approach to the real-time algorithm for a radical suppression of background signals in heavy ion induced complete fusion reactions has been designed basing on a flexible scenario for a choice of the value of time correlation ERα interval. First tests were successfully carried out with an intense 48 Ca beam up to several pµA are successfully performed. The design of the DGFRS-2 setup allowed using those time intervals up to tens of seconds, even at a 48 Ca intensity up to 3-5 pµA . We plan to apply a similar algorithm in the forthcoming experiments with 54 Cr and 50 Ti projectiles aimed to the synthesis of Z=119 element in the nearest future. In addition, we will try to develop a similar algorithm and appropriate software for digital electronics manufactured by XIA Corporation. The first approximation of the time interval value following from the presented Log(T α ) = (aZ + b) · Q −1/2 + c · Z + d with d = -28.0928 formula, can be considered as a quite satisfactory. The spectrum of the ER registered energy for 54 Cr + 238 U → 289 Lv + 3n complete fusion nuclear reaction has been calculated. The estimated half-life value for 294 119 nuclei of about ∼ 110 µs will definitely allow applying the described analog spectrometer to detect such ERα correlated sequence.
One general extra conclusion can be drawn here, namely, development of the whole detection system (not only algorithms, software) including extensive beam tests is in progress now.