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ISSN 0020-4412, Instruments and Experimental Techniques, 2008, Vol. 51, No. 1, pp. 44–58. © Pleiades Publishing, Ltd., 2008. Original Russian Text © E.M. Kozulin, A.A. Bogachev, M.G. Itkis, I.M. Itkis, G.N. Knyazheva, N.A. Kondratiev, Lˇ . Krupa, I.V. Pokrovsky, E.V. Prokhorova, 2008, published in Pribory i Tekhnika Eksperimenta, 2008, No. 1, pp. 51–66.

NUCLEAR EXPERIMENTAL TECHNIQUE

The CORSET Time-of-Flight Spectrometer for Measuring Binary Products of Nuclear Reactions E. M. Kozulin, A. A. Bogachev, M. G. Itkis, I. M. Itkis, G. N. Knyazheva, ˇ . Krupa, I. V. Pokrovsky, and E. V. Prokhorova N. A. Kondratiev, L Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research, ul. Joliot-Curie 6, Dubna, Moscow oblast, 141980 Russia Received May 21, 2007

Abstract—The CORSET time-of-flight spectrometer has been developed at the Flerov Laboratory of Nuclear Reactions of the Joint Institute for Nuclear Research (Dubna, Russia) for investigating binary products of nuclear reactions. The spectrometer has been used to study the dynamics of fusion–fission and quasi-fission of superheavy elements. The design and the main characteristics of the spectrometer, as well as the algorithms for deducing the mass–energy distributions of fragments and the cross sections of nuclear reactions, are presented. The spectrometer contains two time-of-flight arms based on microchannel-plate detectors and three telescopes, each of which is composed of two microchannel-plate detectors and one semiconductor detector. A system of four semiconductor detectors is used to obtain the absolute value of a cross section. The time resolution of the time-of-flight arms is 150 ps, which allows the time-of-flight distances to be set at 10–20 cm, thus providing a mass resolution of 3 amu and an angular resolution of 0.3°. Owing to these characteristics, the spectrometer can be used as a trigger in multidetector setups for measuring light charged particles, neutrons, and γ rays in coincidence with reaction fragments. PACS numbers: 25.85.-w, 29.30.-h, 29.40.Gx, 25.70.-z DOI: 10.1134/S0020441208010041

INTRODUCTION

ments (2V–2E). The last method provides the most exhaustive information on the binary products of a reaction; in this case, semiconductor detectors are conventionally used as stop detectors.

One of the problems of modern nuclear physics consists in determining the extreme conditions for existence of atomic nuclei. In recent years, increased interest has been expressed in carrying out multiparametric measurements and, as a consequence, in creating multidetector systems with the aim of investigating the properties of collective motion of nucleons inside a nucleus and the time characteristics of the nuclear interaction process. As is well known, the main channels for reactions with heavy ions are elastic and inelastic scatterings, deep inelastic reactions, fusion and deexcitation of a compound nucleus, fission, quasi-fission, and fast fission. In view of the variety of the output reaction channels, it is necessary that the contribution of each process to the reaction cross section be estimated in order to clarify the dynamics of interaction between two heavy nuclei. Measurements both of the binary fragments and of the evaporation residuals provide important information about interaction between two heavy nuclei.

The geometric efficiency of a setup based on smallarea semiconductor detectors is very low, while the use of large-area position-sensitive semiconductor detectors leads to a rise in the cost of the setup. In addition, the latter detectors have a low radiation hardness and require that corrections for the pulse height defect and the number of emitted neutrons be introduced. Ionization spark chambers having a much better energy resolution than semiconductor detectors are frequently used in measurements by the 2E method. However, these chambers are unsuitable for experiments on a charged particle beam due to a considerable increase in the background level and a high ionization of the working gas by bombarding particles. By contrast to the 2E method, the mass and energy values determined from the measured velocities in the 2V method refer to the primary fragments, since neutron emission is isotropic in the rest frame of the reaction fragment and the mean velocity of the fragment after neutron evaporation is virtually unaltered. The time resolution of the system is the main characteristic of experimental facilities based on the application of the 2V method. In addition, the start time mark detector

Binary products of nuclear reactions are detected using different methods that consist in (i) measuring the energies of two fragments (2E), (ii) measuring the velocities of two fragments (2V), (iii) measuring the velocity and energy of one fragment (V–E), and (iv) measuring the velocities and energies of two frag44

THE CORSET TIME-OF-FLIGHT SPECTROMETER

must be so thin that the velocity of a detected particle flying through it varies within the narrowest limits. Taking into account all these requirements, gas-filled counters [1] have been selected to perform these tasks. A drawback of gas-filled detector systems is that at least two thick foils are used in a start detector to isolate its gas volume from the vacuum volume of the reaction chamber [2], which leads to high energy losses and scattering of detected particles. To exclude effects of this type, it is possible to use detectors based on microchannel plates (MCPs) [3]. The time resolution of MCP-based start detectors with different designs may reach a value of 100 ps; however, when used in combination with gas-filled stop detectors, they fail to guarantee such a resolution for the entire setup. To attain the desired mass resolution, it is necessary that the flight paths of the spectrometers be increased, which leads to an increase in the dimensions of the setup. Nevertheless, to study emission of neutrons, γ rays, and light charged particles accompanying nuclear interaction process, a minimum volume of the material must be placed on the path of particles from the target to the detector to avoid possible rescattering of detected radiation. Therefore, the part of the experimental setup that detects binary reaction products must have the smallest possible size and a minimum amount of material must be used to manufacture it. At the same time, a decrease in the overall dimensions of the time-of-flight (TOF) spectrometer entails a decrease in its flight path, which causes its mass and energy resolutions to deteriorate. Thus, a position-sensitive detector based on large MCPs with a delay-line coordinate system is considered to be the best suited for use as a stop detector to perform this class of tasks [4]. To discriminate between different processes that may take place in reactions with heavy ions (such as fission, quasi-fission, etc.), it is necessary that, apart from the mass and energy distributions of fragments, their angular distributions, as well as the characteristics of light particles emitted in these processes, be measured. The angular distributions can be measured with the help of the 2V method, by placing the TOF arms at correlation angles. However, the transport velocity of a compound nucleus in reactions with heavy ions may reach very high values; therefore, the energies of fragments escaping at angles of >90° with respect to the beam axis in a laboratory system of coordinates are very low (of an order of a few MeV). All low-energy fragments slow down either in the target material or in the conversion foils of the start detectors. In this case, a single-arm V–E method can be used to measure the angular distribution of reaction products. Taking into account the aforesaid, the CORSET (Correlation Setup) spectrometer has been developed at the Flerov Laboratory of Nuclear Reactions (FLNR) of the Joint Institute for Nuclear Research (Dubna, RusINSTRUMENTS AND EXPERIMENTAL TECHNIQUES

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sia) to study the mechanisms of reactions with heavy ions. The spectrometer consists of two identical TOF arms, which measure the velocities of both fragments of reactions, and several V–E telescopes, which measure the mass and the energy of only one fragment of the binary process. Each TOF arm contains start and stop detectors based on MCPs, while each V–E telescope comprises two MCP detectors with an electrostatic mirror and a semiconductor detector. EXPERIMENTAL SETUP A double-arm TOF spectrometer forms the basis for the experimental setup (Fig. 1). This spectrometer includes compact start detectors St1 and St2 and position-sensitive stop detectors Sp1 and Sp2. Depending on the reaction under investigation, the arms can be positioned at different angles to the beam axis. The distance between the start and stop detectors of each arm (the flight path) ranges from 10 to 20 cm, and the distance from the start detector to the target is 3–5 cm. Additional V–E telescopes are installed to measure the mass–angular distributions of reaction products. Each of these telescopes contains start (V–E-St) and stop (V–E-Sp) time-mark detectors, by way of which MCP-based detectors with an electrostatic mirror and small-area (2 × 2 cm) surface-barrier detector SBD are used. The telescopes are set at angles of 5°–40° with respect to the beam axis. The flight path between the start and stop detectors is 10 cm. The surface-barrier detector is placed at a distance of 1–2 cm from the stop detector. A square collimator with dimensions of 1.8 × 1.8 cm is fastened in front of the surface-barrier detector to eliminate edge effects. An MCP-based position-sensitive detector (V–E-Sp) is used to detect fragments (corresponding to a 180° flyoff angle of fragments in the center-of-mass system) complementary to those detected by the telescopes. Thus, the 2V–E method (V–E telescopes + V–E-Sp) is used to study the reactions in which a fragment flying at a large angle has energy sufficient for its detection. In order to monitor the quality of the beam and its position at the target and to normalize the measured cross sections to the cross section for elastic scattering of the beam ions by the target nuclei, four surface-barrier detectors—the so-called beam monitors—are placed into the reaction chamber. An MCP-Based Detector with an Electrostatic Mirror The operating principle of the detector with an electrostatic mirror is based on secondary emission of electrons knocked out by the detected particle from the conversion foil of the detector. The schematic diagram of the detector is presented in Fig. 2. The detector is composed of a conversion foil, an accelerating grid, an electrostatic mirror, and a chevron MCP assembly [5]. Vol. 51

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V–E telescopes

Sp

2

St2

EV– p3 S EV– t3 S

V–E2 St

Target

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V–E2 Sp

SBD 2

V–ESp1

V–ESt1

SBD 1

Beam Time-of-flight arms E-

St1

V–

Sp

Beam monitors

Sp1

Fig. 1. Layout of the detectors in the CORSET spectrometer for measuring the mass, energy, and angular distributions of binary products of nuclear reactions: (St1, St2) and (Sp1, Sp2) start and position-sensitive stop detectors of the double-arm TOF spectrometer, respectively; (V–E-St1, V–E-St2, V–E-St3) and (V–E-Sp1, V–E-Sp2, V–E-Sp3) start and stop detectors of the V–E telescopes, respectively; (SBD) surface-barrier detectors; and (V–E-Sp) position-sensitive detector.

When passing through the conversion foil of the detector, a particle (from protons to heavy ions) knocks out electrons, which are accelerated in the electric field between the foil and the accelerating grid to an energy of ~3 keV. The grids of the electrostatic mirror deflect the electrons by 90°, and they hit the chevron MCP assembly. Wherever a particle hits the entrance foil, the electron ranges have equal lengths; therefore, the output timing signal of the detector is position-independent. Mylar films with a thickness of 70–150 µg/cm2 are used as the entrance foil. Gold or aluminum layers 20– 30 µg/cm2 thick are sputtered onto the films to raise the secondary yield of electrons. Carbon foils with a thickness of 20–40 µg/cm2 are used in precise measurements. A particle passes through all electrostatic fields generated by the grids without being deflected from its primary direction and practically without changing its initial velocity. Nevertheless, one must take into account the energy lost by a particle in its passage through the conversion foil. For fission fragments, these losses in the foils that we use are a few MeV (2–5% of the initial energy of a particle), and the change in the

particle direction due to collisions with atoms of the foil appears to be negligible. The detector design has been optimized in order to obtain the maximum active area at a minimum detector size. The accelerating grid and the internal grid of the electrostatic mirror lean against an assembly of two vertical triangular foil-clad glass–cloth laminate plates joined by three metal screws soldered in the corners of the triangular plates. The screws have a thread with a pitch of 0.5 mm, round which the internal grid (copper– beryllium wire 50 µm in diameter) of the electrostatic mirror is wound with a pitch of 1 mm. The external grid of the electrostatic mirror is fastened in the grooves of the support foil-clad glass–cloth laminate plates. A photograph of the manufactured detector is presented in Fig. 3. The MCPs are fixed in position in foil-clad glass– cloth laminate frames above the metallized anode. The output signal is read out of the anode and is further amplified in amplitude by a factor of ~10; in this case, the leading edge of the timing signal is 1.5 ns long. The voltages are supplied for the MCP, the conversion foil, and the grids of the electrostatic mirror through a highvoltage divider (see Fig. 2). The detectors used in the

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THE CORSET TIME-OF-FLIGHT SPECTROMETER Voltage applied to the conversion foil

47

Electrostatic mirror grids

Accelerating grid Particle

–3 kV 5.6 MΩ

Conversion foil

5.6 MΩ

Voltage applied to the conversion foil 5.6 MΩ

e 45°

5.6 MΩ 5.6 MΩ

Output signal

Anode

MCP

1 MΩ

Fig. 2. Schematic diagram of the detector with an electrostatic mirror.

experiments on the CORSET setup had the following dimensions of the entrance foil and the MCP active area: 10 × 10, 15 × 15, 20 × 30, and 30 × 40 mm. The time resolution of the detector was determined from the TOF spectrum of α particles from 226Ra, which was measured by two identical detectors of this type on different flight paths; its value was 130 ps. For heavier ions, the resolution of such a detector was 100 ps, which was verified on a heavy-ion beam. The transparency of the detector with the electrostatic mirror was 82%.

lium or tinned copper wire 0.1 mm in diameter. The wire is wound with a 0.5-mm pitch around kaprolon screws fastened on a steel reflecting plate. The diameters of the screws for the delay lines of the Y and X coordinates are 3 and 5 mm, respectively. Each “coordinate” is composed of two independent delay lines shifted by 0.5 mm with respect to each other. The potentials applied to the delay lines are selected so that electrons escaping from the MCP are collected on only one of them. The other delay line (which does not collect electrons) is used to compensate for the interference of the fast timing signal from the exit surface of the MCP.

Position-Sensitive Detector Based on an MCP The detector (Fig. 4) consists of a conversion entrance foil, a chevron assembly of two MCPs, a coordinate system, and a printed circuit board with fast amplifiers for one timing signal and two coordinate signals. The conversion foil is made of Mylar 70– 150 µg/cm2 thick with a sputtered aluminum or gold layer 30–40 µg/cm2 thick. The MCPs are fastened by means of foil-clad glass–cloth laminate frames with contact pads, through which the operating voltage is applied to the plates. A high-voltage divider is used to supply the high voltage (~1 kV) to the MCPs and deliver the necessary potentials for the coordinate system and the conversion foil. The design of the detector with dimensions of 80 × 100 × 20 mm for an MCP with an active area of 70 × 90 mm has been developed. The coordinate system consists of two mutually perpendicular delay lines produced from copper–beryl-

The coordinate of a particle’s hit point at the detector was determined from the difference in the arrival time of the timing signal and the signal from the relevant delay line. The circuit design of the preamplifiers for two coordinate signals was similar to that in [4]. An opaque plate with 1-mm-diameter holes drilled with a step of 2.54 mm was placed in front of the entrance foil to calibrate the coordinates and determine the nonlinearities. The coordinate spectra obtained while testing the detector with a 226Ra α source are shown in Fig. 5. In the figure, one can easily discern significant nonlinearities at the beginning and at the end of the coordinate scale, which are caused by the edge effects of the delay lines and the influence of the constructional materials of the frames on the path of electrons from the MCP to the delay lines. The detector resolution determined by analyzing the recorded spectrum was 0.4 mm for either coordinate.


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Beam Monitoring System

1 cm Fig. 3. Photograph of the detector.

The electrical properties of the delay lines made of different materials were estimated by measuring the coordinate dependence of the signal amplitude from the delay line at a fixed amplitude of the timing signal. For delay lines made of a Cu–Be alloy, the amplitude of the signal delayed for the maximum time decreased almost by 50%, which may be critical for particles with low ionization losses. As a result, though the Cu–Be alloy has better mechanical and oxidative properties, the use of delay lines from a tinned copper wire appears to be preferable.

The surface-barrier detectors register beam ions that are elastically scattered by target nuclei. The detectors are conventionally installed in the order “top–bottom– right–left”, at angles of 90° with respect to each other and 8°–17° with respect to the beam axis. Apertures with calibrated holes are fastened on these detectors. The diameter of these holes determines the counting rate of these detectors; as a rule, it is 1.0–1.5 mm. Owing to this arrangement of the semiconductor detectors, it is possible to monitor the beam transport quality. Knowing the counting rates of elastically scattered ions for each of the four detectors and comparing them to the values calculated from the Rutherford elastic scattering, one can find the point of incidence of the beam onto the target. Events from the monitoring detectors and binary products of reactions are recorded in parallel by a common data acquisition system. Measuring the counting rates and the energy spectra of scattered beam ions, it is possible to monitor both the beam position and energy. A SCHEMATIC DIAGRAM OF THE EXPERIMENT AND THE DATA ACQUISITION SYSTEM The circuit diagram of the double-arm TOF spectrometer is shown in Fig. 6. The timing and coordinate signals from the start and stop detectors (St1, St2, Sp1, Sp2, X1, Y1, X2, and Y2) are fed into constant-fraction discriminators (CFDs). Then, signals St1, St2, Sp1, and Sp2 arrive at the logic modules, which generate an output signal (a trigger) if there are two stop signals and at least one start signal. The start and stop signals come to time-to-amplitude converters (TACs, Ortec) and then to analog-todigital converters (ADCs) of the C420 type (CAEN).

Entrance foil

T

–3 kV

10 MΩ

MCP

100 kΩ

5.6 MΩ

100 kΩ

5.6 MΩ

100 kΩ

1.0 MΩ

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5.6 MΩ 1.0 MΩ

X

Y2

X1 Y1

270 Ω

270 Ω

Reflecting plate

X2 270 Ω

Y

360 kΩ

360 kΩ

360 kΩ

360 kΩ

100 pF

270 Ω 100 pF

Fig. 4. Schematic diagram of the MCP-based position-sensitive detector. INSTRUMENTS AND EXPERIMENTAL TECHNIQUES

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ToFL2 between the arrival of signals St1 and Sp2, ∆TSt between the arrival of signals St1 and St2, and ∆TSp between the arrival of signals Sp1 and Sp2. The start and stop signals, as well as the coordinate signals, are independently transmitted via delay lines to a time-to-digital converter (TDC) of the C414 type (CAEN). The trigger signal acts as the start signal for the TDC. The TDC is used to measure the following time intervals: TDC_St1 between signal St1 and the trigger, TDC_Sp1– between signal Sp1 and the trigger, TDC_X1 between signal X1 and the trigger, TDC_Y1 between signal Y1 and the trigger, TDC_St2 between signal St2 and the trigger, TDC_Sp2– between signal Sp2 and the trigger, TDC_X2 between signal X2 and the trigger, and TDC_Y2 between signal Y2 and the trigger. As noted above, for the coordinate signals to be obtained, the following relationships between the parameters measured with the TDC must be taken into account: X1 = TDC_X1 – TDC_Sp1;

Y, mm 60 50 40 30 20 10 0 0

10

20

30

40

50

60

49

70 80 X, mm

Fig. 5. Two-dimensional spectrum of coordinates X and Y obtained by calibration of the detector using an α source (226Ra). A mask with 1-mm-diameter holes was placed in front of the detector.

These converters are used to measure the following time intervals: ToF1 between the arrival of signals St1 and Sp1, ToF2 between the arrival of signals St2 and Sp2, ToFL1 between the arrival of signals St2 and Sp1,

Y1 = TDC_Y1 – TDC_Sp1; X2 = TDC_X2 – TDC_Sp2; Y2 = TDC_Y2 – TDC_Sp2.

Y2 X2 Sp2

X2

St2

CFD

∆TSp

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ADC ADC ADC ∆TSt

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1 St1

Trigger

&

TAC

CFD

Sp1

TAC

CFD X1 Y1

TAC

ToF1 ToFL1

ADC ADC

St1

CFD

Sp1 CFD

X1 Y1

Fig. 6. Block diagram of the double-arm TOF spectrometer. INSTRUMENTS AND EXPERIMENTAL TECHNIQUES

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Trigger CFD

E

St Sp St

Beam

CFD

TAC

TDC

CAMAC

ADC E Sp

ADC

CFD

Fig. 7. Schematic diagram of connection of the V–E telescope.

From the timing parameters measured using the TDC, it is also possible to derive the signals measured with the ADC: TOF1_TDC = TDC_Sp1 – TDC_St1; TOF2_TDC = TDC_Sp2 – TDC_St2; TOFL1_TDC = TDC_Sp1 – TDC_St2; TOFL2_TDC = TDC_Sp2 – TDC_St1; ∆TSt_TDC = TDC_St1 – TDC_St2; ∆TSp_TDC = TDC_Sp1 – TDC_Sp2. Duplication of the electronic channels via the TDC and ADC helps to significantly improve the accuracy of measurements, as it allows the electronic noise and the nonlinearities in the measured signals to be monitored. The schematic diagram of connection of one V–E telescope is presented in Fig. 7. The signals from the start and stop detectors of this telescope are fed into the CFDs, are divided between distinct paths, and arrive at the TACs and ADCs and, through a delay line, at the TDCs. The signal from the semiconductor detector is fed into the preamplifier. The signal from the fast output of the preamplifier arrives at the CFD and is divided between distinct paths. One of the divided signals is used as a trigger for the data acquisition system, while the other passes through the delay line to the TAC. The signal from the spectrometric output of the preamplifier is fed into the spectrometric amplifier and, further, into the ADC. The fact that only the semiconductor detector signal acts as a trigger signal for the telescope allows the efficiency of the start and stop detectors to be assessed, which is very important for determining nuclear reaction cross sections. The signals from the semiconductor detectors are fed into the preamplifier and then follow different paths. One of the divided signals is fed into the CFD and then used as a trigger signal, and the other is passed through the spectrometric amplifier to the ADC.

Since the CORSET setup consists of a few independent parts—the double-arm TOF spectrometer, the V–E telescopes, and the monitor detectors—the trigger signal for the data acquisition system is produced if there is at least one signal from the monitor detectors, or at least one signal from the semiconductor detector of the V–E telescopes, or two stop signals and at least one start signal from the double-arm spectrometer. The TDC and ADC electronic modules, along with an HYTEC-LP1342 list processor and an SCM-301 crate controller, are housed in a CAMAC crate. The crate controller communicates with the computer via the SCSI bus. The data acquisition system is based on the KMAX program [6]. As many as 300 parameters can be simultaneously obtained in experiments using the CORSET setup in the case where emission of light particles (protons, neutrons, γ rays, etc.) is measured in coincidence with binary products of nuclear reactions. In our experiments, the frequency of interruption is 3– 4 kHz. A graphics menu with which it is possible to rapidly change the format of an event word has been created for the electronic modules used in the setup. During the experiment, the computer with the data acquisition system is brought to a specially conditioned measuring room; it communicates with the crate controller via an SCSI extender. MAIN PARAMETERS OF THE CORSET SETUP The main parameters of the CORSET setup are presented in the table. The values obtained for the doublearm spectrometer refer to an 18-cm-long flight path between the target and the stop detector (i.e., the flight path that is usually selected in experiments). The mass resolution of the spectrometer was determined from the full width at half-maximum of the peak due to elastic scattering of 48Ca by 208Pb target nuclei. The high time and angular resolutions of the spectrometer permit the setting of minimum TOF distances (up to 10 cm) without significant deterioration of the


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mass resolution. This provides a means for reducing the overall dimensions of the reaction chamber and using the spectrometer as a convenient trigger of fission fragments in correlation measurements of neutrons and γ rays in 4π spectrometers, such as GASP, EUROBALL, GAMMA-SPHERE, and DEMON [7, 8]. An example of a compact (29 cm in diameter) reaction chamber used in experiments of this kind is shown in Fig. 8. The spectrometer arms are fixed in movable fasteners that can rotate with the aid of step motors without breaking a vacuum in the chamber. This type of the chamber design with minimum amount of materials used in it creates optimal conditions for spectrometric measurements of accompanying neutrons and γ rays in the 4π geometry. DATA ANALYSIS AND PROCESSING

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Characteristics of the CORSET setup Name of the characteristic

Double-arm V–E telescope spectrometer

Time resolution (full width 150 (of each at half-maximum), ps arm) Angular resolution, deg: in the plane of reaction ≈0.3 beyond the plane of reaction ≈0.3 Acceptance, deg: in the plane of reaction ±14 beyond the plane of reaction ±11 Geometric efficiency, % ~3 Detection efficiency, % ~67 Mass resolution (full width 3 at half-maximum), amu

180

±1.5 ±1.5 ±1.5 ±1.5 ~0.15 ~67 4

Measurements with the Double-Arm TOF Spectrometer Primary data processing. The presence of the electrostatic mirror’s grids on the path of a fragment is a drawback of the start detector design. After a fragment hits the grid, it can change its initial direction and velocity. By measuring the difference between the times of arrival of signals from the start and stop detectors (∆TSt, ∆TSp), it is possible to exclude such events from further processing. If a fragment does not hit the grids, the difference between the timing signals from the start detectors must be proportional to the difference between the timing signals from the stop detectors. The two-dimensional correlation between ∆TSt and ∆TSp of reaction products is shown in Fig. 9. From the

figure, it is apparent that most events actually fit the linear dependence (events inside a closed line). Nevertheless, some events lie beyond this contour; they are excluded from further processing. It should be noted that they account for ~5% of all events. Owing to the large dimensions of the stop detector, the time it takes for the timing signal to propagate over the MCP surface is 350 ps, which exceeds the intrinsic resolution of the detector. To take this time into account, the following calibration procedure is used. A TOF spectrum of α particles emitted by a 226Ra source is acquired. The surface of the stop detector is conventionally divided into squares with a side of 5 mm, and the flight time of 7.69-MeV α particles is calculated for each of these squares. The calculated values are compared to the measured flight time of αparti∆TSp

Start detectors

2800

Target assembly

2400

2000

Stop detectors

1600 Step motor

1200 100 Fig. 8. Outward appearance of the reaction chamber for the CORSET spectrometer, which is used as a trigger of fission fragments in correlation measurements of neutrons and γ rays. INSTRUMENTS AND EXPERIMENTAL TECHNIQUES

200

300

400

500

∆TSt

Fig. 9. Two-dimensional matrix (∆TSt, ∆TSp) obtained during measurements of 252Cf spontaneous fission on the CORSET setup. Vol. 51

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6 5 4 3 2 1 0 0

1

2

3

4

5

6

7

8

9 X, cm

Fig. 10. Example of the time correction for the signal propagation over the surface of a position-sensitive stop detector based on an MCP.

cles. As a result, we obtain a correction for the difference between the calculated and measured values for each square. An example of the correction obtained thereby is shown in Fig. 10. We see that the minimum correction corresponds to the region where the timing signal is picked off the MCP, while the maximum correction is introduced in the most distant MCP zone. Taking this correction into account during data processing helps improve the time resolution of the spectrometer. To increase the TOF distance of the spectrometer, the start detectors are set close to the target, at distances of ~3–5 cm. Therefore, their counting rates may be rather high and the dead time of each start detector increases. By using two starts and measuring times ToF1, ToF2, ToFL1, and ToFL2 for each event, it is possible to estimate the counting loss attributable to the dead time of the start detector and to introduce an appropriate correction to the number of detected reaction fragments. Let NSt1 be the number of events detected on condition that the first start detector is activated (the number of events in two-dimensional distribution ToF1, ToFL2), NSt2 be the number of events detected on condition that the second start detector operates (ToFL1, ToF2), and NSt12 be the number of events in which signals from both start detectors are observed (ToF1, ToF2). Hence, it follows that 2

N St12 -. eff = ------------------N St1 N St2

The correction for the counting losses in the start detectors depends on the quality of the beam and the arrangement of the detectors. In practice, this correction does not usually exceed 10%. Obtaining the mass–energy distributions of reaction products. Analysis of experimental data is based on measuring the velocity vectors of two reaction products. To determine the mass and the energy of fission fragments, the following conservation laws are used. 1. The momentum conservation law: M proj V proj = M 1 V 1 + M 2 V 2 ,

(1)

where Mproj is the mass of the projectile particle, V proj is the vector of its velocity, and M1, 2 and V 1, 2 are the masses and the velocity vectors of the fission fragments. The projections of vector equation (1) onto the beam axis and the axis perpendicular to the beam direction are M proj V proj = M 1 V 1 cos Θ 1lab + M 2 V 2 cos Θ 2lab ;

(2)

0 = M 1 V 1 sin Θ 1lab + M 2 V 2 sin Θ 2lab ,

(3)

where Θ1, 2 lab are the exit angles of the fission fragments with respect to the beam direction. Angles ΘX in the plane of reaction and ΘY beyond the plane of reaction are measured for each fragment in


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the course of the experiment. Therefore, the exit angle of the fission fragment with respect to the beam is (4) Θ lab = arccos { cos Θ X cos Θ Y }. 2. The nucleon conservation law: M proj + M tar = M 1 + M 2 + ν pre , (5) where Mtar is the target mass and νpre is the multiplicity of preequilibrium and prescission neutrons. Reaction products pass through the target material and the foil of the start detectors, where they lose a portion of their primary energy; therefore, the measured velocities of fragments must be corrected for the energy losses. The energy losses are calculated according to [9], in which the energy losses of fragments from 252Cf spontaneous fission in different media were measured and a semi-empirical formula for calculating them was proposed. To find the masses and energies of fragments using the iteration method, the system of Eqs. (3) and (5) in the unknowns M1, 2 and V1, 2 is solved: 0

(i) particle velocities V 1, 2 are calculated from the measured times and path lengths; (ii) these velocities are substituted in the system of equations (3) and (5) in order to determine the fragment masses: MV 2 sin Θ 2lab -; = ------------------------------------------------i i V 1 sin Θ 1lab + V 2 Θ 2lab i

i M1

(6)

M 2 = ( M proj + M tar ) – M 1 , where M = Mtar + Mproj – νpre; i

i

(iii) taking into account energy losses δ E 1, 2 ( M 1, 2 , i

i

i

V 1, 2 ) which were determined by the obtained masses and velocities, the fission fragment velocities at the reaction point are calculated (the reaction point is assumed to be located at the center of the target): V 1, 2 = V 1, 2 + δν 1, 2 ; i+1

0

i

(7)

(iv) the value of ε = M 1 – M 1 is calculated. This procedure is repeated from item (ii) until the value of ε satisfies the prescribed accuracy of determining the fragment mass. In our calculations, ε = 0.01. The number of iterations necessary to attain this accuracy is usually less than 10. Using these masses, the velocities of fragments in the center-of-mass system (CMS) were calculated and total kinetic energy TKE of reaction products was determined as the sum of the fragment energies in the CMS. Figure 11 presents the mass–energy distribution (MED) of fragments from 252Cf spontaneous fission that was measured on the CORSET setup. The yield and the mean kinetic energy of fragments as functions of their mass, which were measured on the CORSET setup (solid circles in Figs. 11b and 11c, respectively), i

i+1


53

are compared to the data in [10] (open circles in Figs. 11b and 11c), in which measurements were performed with an ionization chamber. Our results are in good agreement with these data. It should be noted that the peak-to-valley ratio in the mass distribution obtained in our measurements is P/V = 48, which is higher than in [10]. Apart from studying the characteristics of fragments of spontaneous nuclear fission, the CORSET setup can be used to investigate the mass–energy distributions of fragments in reactions with heavy ions without lowering the quality of experimental data. Extraction of the binary reaction channel. To determine the mass–energy characteristics of fusion– fission and quasi-fission processes, the binary reaction channel must be reliably separated from products of sequential fission after transfer and incomplete fission reactions or reactions on impurity atoms in the target. Extraction of the binary reaction channel was based on analysis of the kinematic diagram (the velocity vectors of two detected reaction products) in the CMS. For binary processes, the vectors of both products are coplanar and the folding angle in the CMS, as well as its projections in the plane of reaction and beyond it, is 180°. Neutron emission from the fragments, rescattering in the foils and by the grids of electrostatic mirrors in the start detectors, and the angular resolution of the spectrometer introduce variance to the angular distribution of the fragment velocities. Figure 12 illustrates extraction of events with a total momentum transfer in reaction 48Ca + 248Cm. This reaction is of interest in that the measured mass–energy distribution of fragments includes components due to fission and quasi-fission at the 248Cm target, reactions of incomplete momentum transfer, and fission of an excited 248Cm-like nucleus after a transfer (sequential fission) reaction, as well as fission products of a reaction 48Ca + natW on impurity tungsten atoms natW in a target. Figure 12a presents matrix (TKE, M), i.e., the yield of all detected reaction products versus their mass M and total kinetic energy TKE. It is apparent that the MED comprises elastically scattered events for two reactions (48Ca + 248Cm and 48Ca + natW). At the same time, the angular folding correlations point to the presence of three processes with different kinematics. The folding angle of projections Θcms = Θ1cms + Θ2cms in the plane of reaction in the CMS is laid off as abscissa in Figs. 12d–12f; on the ordinate axis, we plot TKE values (Fig. 12d), projection of the folding angle beyond the plane of reaction Ψcms = ψ1cms +ψ2cms (Fig. 12e), and atomic mass number M of reaction products (Fig. 12f). From this figure, it is apparent that the spectrometer detects three main groups of events in regions of 180°, 160°, and 140°. The percentage of events in these groups is 98.0 : 1.9 : 0.1%. For fissionlike fragments (events in the region of masses of 60– 120 amu, which are located between the elastic scattering peaks in Fig. 12a), the same relationship is Vol. 51

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220

(‡)

TKE, MeV

200

180

160

140 101 (b)

Yield, %

100 10–1 10–2 10–3

(c) 〈TKE〉, MeV

180

160

140

120

80

100

120 140 M, amu

160

180

Fig. 11. Mass–energy distribution of fragments of 252Cf spontaneous fission: (a) yield of fission fragments vs. their mass M and kinetic energy TKE, (b) yield of fragments vs. their mass M, and (c) average kinetic energy 〈TKE〉 of the fragment vs. its mass M. Open circles present data in [10], and solid circles correspond to the data obtained with the CORSET setup.

53.1 : 37.7 : 9.2%. The group of events for which the folding angle is 180° (contour K2 in Fig. 12e) corresponds to the binary products of reaction 48Ca(245 MeV) + 248Cm (Fig. 12c). Groups of events for which the folding angle is other than 180° were processed once more with the calibration factors equal to those of the main reaction 48Ca + 248Cm. In this case, the target mass was selected so that

the folding angle of reaction products in the CMS was 180°. It was determined thereby that impurity atoms 184–186W acted as the target nuclei for the second group of events associated with a folding angle of 160° (contour K1 in Fig. 12e). The outlined matrix (TKE, M) for these events is shown in Fig. 12b. For the third group of events corresponding to Θcms = 140°, the variance of the folding angle beyond the reaction plane is considerably


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THE CORSET TIME-OF-FLIGHT SPECTROMETER TKE, MeV

TKE, MeV

(‡)

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TKE, MeV

(b)

(c)

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250

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150

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100 Events inside contour K1

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50

Ψcms, deg

M, amu

210 (e)

250 (f)

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Events inside contour K2 100

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200

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170

100

K1

160

50 140

160

180

200

150

140

K2

160 180 Θcms, deg

50 200

140

160

180

200

Fig. 12. Mass–energy and angular folding distributions of products of reaction 48Ca + 248Cm at energy Elab = 245 MeV. The yields of reaction products vs. their mass å and total kinetic energy TKE are shown (a) for all recorded events, (b) for reaction 48Ca + natW (corresponds to contour K1 in Fig. 12e), (c) for the binary channel of reaction 48Ca + 248Cm (contour K2 in Fig. 12e), and angular folding distributions of (d) TKE, Θcms, (e) Ψcms, Θcms, and (f) M, Θcms.

greater than in the two previous cases. This group of events corresponds to sequential fission of a target nucleus excited by little-nucleon transfer reactions. This conclusion is corroborated by the analysis of velocities V|| and V⊥ (the projections of the sum angle of velocity onto the beam axis and the axis perpendicular to the reaction plane) of two detected reaction products, which was performed in [11]. Thus, the kinematic analysis of a reaction helps separate binary events of the primary reaction channel from reactions on impurity atoms and events of sequential fission. To discriminate events with incomplete momentum transfer, the shift of folding angle Θcms versus the momentum imparted is calculated. Calculations show that the selected contour of ΘcmsΨcms = 180° ± 5° corresponds to transfer of >90% of the momentum and allows reliably extract the binary reaction channel. This plays an important role in obtaining the mass–energy distributions of binary reaction products and determining the cross sections of different processes observed in reactions with heavy ions. Geometric efficiency of fission fragment detection. The spectrometer is capable of detecting reaction INSTRUMENTS AND EXPERIMENTAL TECHNIQUES

products with masses and energies ranging between the projectile ion mass and the target nuclear mass. However, in view of the angular acceptance of the spectrometer, each selected range of masses ∆Mi and energies ∆Ei is detected with its own probability; therefore, to reconstruct the true MED of reaction products, corrections for the geometric efficiency of the spectrometer must be taken into account. A program for calculating the geometric efficiency is used in design of experiments to position the spectrometer arms at optimal angles. This program is based on the method similar to that in [12]. For the prescribed ratio of fragment masses R = M1/M2 and projectile ion energy Elab, correlation curves Θ1lab(Θ2lab) are calculated for fission fragments, proceeding from the laws of conservation of mass, energy, and momentum. The total kinetic energy of fragments in the CMS both in the symmetrical and asymmetrical fragmentations is estimated using Viola’s systematization [13]. Using the known values of the fragment velocity vectors in the CMS for angles Θ1cms = 0°–180° (Θ2cms = 180°–Θ1cms), the fragment velocity vectors in the laboratory system are calculated and correlation Vol. 51

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Θ2lab, deg 100

TKE, MeV 40–60% 48Ca(240

MeV) + 208Pb

R = 2.0

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0.2 3.0

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40 208Pb

40

50

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90 100 Θ1lab, deg

Fig. 13. Correlation curves for reaction 48Ca + 208Pb at projectile ion energy Elab = 240 MeV. The square contour corresponds to the setting of the spectrometer arms. The angular correlations for elastically scattered 48Ca ions and 208Pb target ions are shown with dashed lines, and the correlations for fission fragments with different values of mass ratio R (designated by numbers) are shown with solid lines.

curves Θ1lab(Θ2lab) are determined. The correlation curves for reaction 48Ca + 208Pb at energy of the ion beam Elab = 240 MeV are shown in Fig. 13. The position of the spectrometer arms is indicated by square Θ1lab = Θ2lab = 63° ± 14°. For elastically scattered 48Ca ions and 208Pb target nuclei, the angular correlations are shown with dashed lines; for fission fragments with mass ratios R = 0.2, 0.33, 0.5, 1, 2, and 3, these correlations are shown with solid lines. From the figure, it is apparent that the detection efficiency is dependent on the mass ratio. The efficiency matrix is calculated in coordinates (TKE, M) in order to obtain true distribution (TKE, M) from the experimental distribution for binary fissionlike events. Correlation curve Θ1lab(Θ2lab) is calculated for each selected mass Mi and energy TKEi, and the number of detected events (see the square of the spectrometer acceptance in Fig. 13) is determined for a particular position of the spectrometer arms. As a result, two-dimensional matrix of the geometric efficiency (TKE, M) is calculated (Fig. 14). The experimental matrix is normalized with weighting factors that are inversely proportional to these values of the geometric efficiency.

60

80 100 120 140 160 180 200 220 M, amu

Fig. 14. Two-dimensional matrix of the geometric detection efficiency of the CORSET setup, calculated for reaction 48Ca + 208Pb at ion energy E lab = 240 MeV. The spectrometer arms are located at angles Θ1lab = Θ2lab = 63° ± 14°.

Measurements with the V–E Telescope The V–E telescope is used to measure the flight time and the fragment energy for each event. The fragment energies measured by the semiconductor detector must be corrected for the pulse height defects. According to Schmitt’s formula in [14], fragment energy E [MeV] with mass M [amu] and pulse height P is calculated as follows: E = ( aM + b )P + cM + d.

(8)

Coefficients a, b, c, and d are determined from elastic scattering of heavy ions (44,48Ca, 64Ni, 144,154Sm, 206Pb, and 186W). Fragment mass M [amu] is found using the relationship between particle energy E [MeV] and its velocity V [cm2/ns2]: 2

(9)

2

(10)

E = 0.5183MV ; M = 1.9294E/V .

However, it is necessary that calculation of the energy according to Eq. (8) include the energy lost by a fragment during its travel through the target material and the conversion foils of the start and stop detectors. Therefore, the iteration procedure is used to find the mass of a fragment; it is performed until the fragment mass is determined with a prescribed accuracy. The values obtained thereby are the masses after emission of pre- and post-fission neutrons. To find the masses of fragments before the emission of neutrons, it is neces-


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sary that these masses be corrected for the number of emitted neutrons. Determining the Differential Reaction Cross Section To determine the cross sections of different processes, it is required that the target thickness, the beam intensity, and other factors be known beforehand. Since these parameters are not necessarily known with an adequate accuracy, a method based on normalization of the measured cross section to the elastic scattering cross section can be used to obtain the absolute value of the cross section. The monitors described in the Beam Monitoring System subsection are used to perform this task. The cross section is determined according to the formula ∆N fis ∆Ω mon ⎛ dσ ⎞ eff mon - ---------------- -------------------- , σ ( Θ ) = --------------∆N mon ∆Ω fis ⎝ dΩ⎠ mon eff fis

(11)

where ∆Nfis is the number of fission fragments registered in the detector with solid angle ∆Ωfis and detection efficiency efffis, ∆Nmon is the number of elastic scattering events registered in the detector with solid angle ∆Ωmon and detection efficiency effmon, and (dσ/dΩ)mon is the Rutherford scattering cross section. EXPERIMENTS CONDUCTED ON THE CORSET SETUP Experiments using the CORSET setup were conducted at the U-400 cyclotron at the FLNR (Dubna, Russia), the K-130 cyclotron of the Department of Physics of the University of Jyväskylä (Finland), the ALPI + XTU tandem accelerator at LNL (Legnaro, Italy), the VIVITRON accelerator (Strasbourg, France), and the accelerator of the LNS laboratory (Catania, Italy). The binary fragments of reactions were measured in these experiments with the following beams: p, d, 6Li, 12C, 16,18O, 20,22Ne, 24,26Mg, 18Ar, 40, 44, 48Ca, 50Ti, 58Fe, 64Ni, and 86Kr. For the first time, these experiments provided information on the mass–energy characteristics of the fragments of reactions 48Ca + 238U, 244Pu, 248Cm, 58Fe + 238U, 244Pu, 248Cm, and 64Ni + 242Pu, which result in formation of superheavy systems with Z = 112, 114, 116, 118, 120, and 122 [15]. The asymmetry of fission of superheavy nuclei (which was determined by nucleon shells of a light fragment) was observed for the first time when studying the mechanism of fusion–fission of superheavy elements [16]. In addition, the shell effects occurring in quasi-fission process in superheavy systems were shown to play an important role in fragment formation. The most pronounced effect on the shape of the mass distribution was exhibited by the double-magic Pb shell in [15]. The double differential spectra of neutrons emitted during decays of heavy and superheavy systems were measured for the first time in [17]. Analysis INSTRUMENTS AND EXPERIMENTAL TECHNIQUES

57

showed that the neutron multiplicity in fusion–fission and quasi-fission processes demonstrated different dependences on the mass of the composite system formed in reactions with heavy ions. In addition, the multiplicities and mean energies of γ rays were measured in these reactions for the first time [17, 18]. These data allowed us to estimate the cross section for the formation of superheavy elements and to select optimum excitation energies and combinations “ion–target” for synthesis of new elements. Apart from measuring the MED of fission fragments of superheavy nuclei and the competition between the fusion–fission and quasi-fission processes, the CORSET setup has been used to investigate the characteristics of the true fission of heavy nuclei. A set of experiments with the aim of investigating the multimodality of fission in the region of Ra–Th nuclei was also performed. In particular, four independent fission modes for 226Th [19] and three independent fission modes for 220Ra [20] were discovered. Measurements of the neutron multiplicity on the CORSET + DEMON setup during the study of fission of 226Th compound nuclei produced in reaction 18é + 208Pb demonstrated for the first time that the number of prescission neutrons in asymmetric fission exceeds that in symmetric fission [21]. The objective of a series of experiments was the competition between the fusion–fission and quasi-fission processes for compound nuclei 192, 194, 202Pb and 216, 218Ra produced in the reactions 40, 48Ca + 144, 154Sm in [22] and 48Ca + 166, 168Er in [23]. The quasi-fission process is observed only in reactions where the target nucleus has a static deformation. In the case of a spherical nucleus (144Sm), quasi-fission has not been observed. The contribution of the quasi-fission process increases with a decrease in the energy of a projectile ion and becomes essential at energies near and below the Coulomb barrier. During collaboration of CORSET + DEMON + HENDES + BAF teams, the mass–energy characteristics of fission fragments and the multiplicity of neutrons and γ rays were measured in the reaction p + 232Th,238U,242Pu [24, 25]. CONCLUSIONS The CORSET setup composed of a double-arm TOF spectrometer and V–E telescopes has been developed at the FLNR to measure binary products of nuclear reactions. The use of the MCP-based start and stop detectors has made it possible to achieve high time and angular resolutions of the spectrometer. A data processing procedure has been developed that takes into account corrections for the time of signal propagation over the surface of the stop detectors. Events due to rescattering by the wires of the electrostatic mirrors are discriminated by the measured difference of times ∆TSt and ∆TSp. A new method for taking account of the ionization Vol. 51

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losses in the foils of the start detectors, the target, and its backing has been applied.

4. Sobotka, S.E. and Williams, M.B., IEEE Trans. Nucl. Sci., 1988, vol. 35, p. 348.

Binary events of the primary reaction channel are separated from events due to reactions on impurity atoms and events of sequential fission using the kinematic analysis method. The high time and coordinate resolutions of the spectrometer allow flight paths of ~10 cm to be used without significant deterioration of the mass resolution. This provides a means for reducing the overall dimensions of the reaction chamber and employing the spectrometer as a convenient trigger for binary products of nuclear reactions in correlation measurements of neutrons and γ rays in 4π spectrometers, such as GASP, EUROBALL, GAMMA-SPHERE, and DEMON.

5. Starzecki, W., Stefanini, A.M., Lunardi, S., and Signorini, S., Nucl. Instrum. Methods Phys. Res., 1982, vol. 193, p. 499. 6. http://www.sparrowcorp.com 7. Moszinsky, M., Costa, I.G.J., Guillaume, G., et al., Nucl. Instrum. Methods Phys. Res. A, 1994, vol. 350, p. 226. 8. Tilquin, I., Marsi, Y.El., Parlog, M., et al., Nucl. Instrum. Methods Phys. Res. A, 1995, vol. 365, p. 446. 9. Knyazheva, G.N., Khlebnikov, S.V., Kozulin, E.M., et al., Nucl. Instrum. Methods Phys. Res. B, 2006, vol. 248, p. 7. 10. Hambsch, F.J. and Oberstedt, S., Nucl. Phys. A, 1997, vol. 617, p. 347.

Owing to the supplementary V–E telescopes installed, it is possible to measure both the mass– energy and mass–angular correlations of reaction products. Mass–angular distributions are an important characteristic of processes that take place in reactions with heavy ions; they offer a chance to separate the fusion– fission channel from the other possible reaction channels.

11. Hinde, D.J., Dasgupta, M., Leigh, J.R., et al., Phys. Rev. C, 1996, vol. 53, p. 1290.

The use of surface-barrier monitor detectors allows the quality of beam tuning to be controlled and the cross sections of different processes measured with the spectrometer to be normalized to the cross section for elastic scattering of projectile ions. This provides a means for obtaining the cross section with a significantly higher accuracy, since it is now possible to eliminate errors in determining such parameters as the target thickness, the acquisition time, the beam current, etc.

15. Itkis, M.G., Aysto, J., Beghini, S., et al., Nucl. Phys. A, 2004, vol. 734, p. 136.

A set of measurements has been performed on the CORSET setup with the aim of determining the mass– energy distributions of fusion–fission and quasi-fission fragments of heavy and superheavy ions with Z = 88– 122 in reactions with light and heavy ions ranging from p to 86Kr. The effects of static deformations and excitation energies on the ratio of the quasi-fission and capture cross sections have been investigated. The phenomenon of multimodal fission in heavy and superheavy elements has been observed. The correlation measurements of accompanying neutrons and γ rays have been taken.

12. Schilling, K.D., Gippner, P., Seidel, W., et al., Nucl. Instrum. Methods Phys. Res. A, 1987, vol. 257, p. 197. 13. Viola, V.E., Kwiatkowski, K., and Walker, M., Phys. Rev. C, 1985, vol. 31, p. 1550. 14. Schmitt, H.W., Keker, W.E., and Williams, C.W., Phys. Rev., 1965, vol. 137, p. b837.

16. Itkis, M.G., Bogatchev, A.A., Itkis, I.M., et al., J. Nucl. Radiochem. Sci., 2002, vol. 3, p. 57. 17. Kozulin, E.M., Itkis, M.G., Oganessian, Yu.Cs., et al., Abstracts of Papers, Proc. of the Int. Conf. on Nuclear Physics at Border Lines, NPBL, (Lipary (Messina), Italy, 2001), Singapore: World Sci., 2002, p. 157. 18. Krupa, L., Bogatchev, A.A., Giardina, G., et al., Abstracts of Papers, Proc. of the 5th Int. Conf. on Dynamical Aspects of Nuclear Fission, DANF2001 (Casta-Papiernicka, Slovak Republik, 2001), Singapore: World Sci., 2002, p. 196. 19. Pokrovsky, I.V., Itkis, M.G., Itkis, J.M., et al., Phys. Rev., 2000, vol. 62, p. 014615. 20. Pokrovsky, I.V., Calabretta, L., Itkis, M.G., et al., Phys. Rev., 1999, vol. 60, p. 041304. 21. Kelic, A., Itkis, I.M., Pokrovski, I.V., et al., Euro Phys. Lett., 1999, vol. 47, p. 552. 22. Knyazheva, G.N., Kozulin, E.M., Sagaidak, R.N., et al., Phys. Rev., 2007, vol. 75, p. 064602. 23. Chizhov, A.Yu., Itkis, M.G., Itkis, I.M., et al., Phys. Rev. C, 2003, vol. 67, p. 011603.

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24. Rubchenya, V.A., Trzaska, W.H., Itkis, I.M., et al., Nucl. Phys. A, 2004, vol. 734, p. 253. 25. Kozulin, E.M., Aysto, J., Bogachev, A.A., et al., Abstracts of Papers, Proc. of the Int. Conf. on Reaction Mechanisms and Nuclear Structure at the Coulomb Barrier, (S. Servolo, Venezia, Italy, 2006), American Institute of Physics (AIP), Corradi, L. et al. Eds., 2006, vol. 853, p. 336.


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