Introduction

Multi-nucleon transfer (MNT) is considered a promising method for the production of neutron-rich heavy or superheavy nuclei, and has been studied in the field of low-energy nuclear reactions for several decades [1, 2]. Despite significant theoretical [3-7] and experimental [8-12] efforts, the mechanism of MNT remains unclear because of complex phenomena involving the transfer and/or transport of numerous nucleons.

Owing to the intricacies of the reaction mechanisms involved, the measurement of MNT products requires improved precision, placing higher demands on the equipment: i) good mass (A) and charge (Z) identifications for validation of various reaction channels; ii) a large acceptance for the detection of rare products that are far from the projectile or target, considering the steep decrease in cross-sections with an increasing number of transferred nucleons; iii) a good energy resolution for the distinction of a large number of energy levels populated in a specific reaction channel.

Several detection techniques have been developed for particle identification, such as measurement of time-of-flight (ToF) with a known flight distance. The relative uncertainty was drastically reduced with a long flight distance. As a mature method, the E-ToF technique, which measures energy and ToF simultaneously, has been widely used in studies of transfer reactions at energies near the Coulomb barrier [13]. The mass resolution, determined by energy and ToF measurements, reached σ = 0.2 amu. For binary reactions, the kinematic coincidence technique is an effective method for enhancing the energy and mass resolution, such as simultaneous ToF measurements of projectile-like ions and correlated scattering angles [14].

To further investigate the MNT reaction mechanism, a ToF spectrometer for heavy-ion reactions, called HiToF, was constructed at the HI-13 tandem accelerator of the Beijing Tandem Accelerator National Laboratory. Its design resembles that of PISOLO [15] at Laboratori Nazionali di Legnaro, but with a focusing system that includes a quadrupole triplet lens. The maximum solid angle covered by HiToF reached 20 msr. The HiToF is equipped with two micro-channel-plate detectors dedicated to time-of-flight measurements and a specially designed ionization chamber for energy measurement and charge identification on the focal plane. A test experiment has recently been conducted successfully, laying a solid foundation for further investigation of multi-nucleon transfer reactions.

The remainder of this paper is organized as follows. Section 2 describes the detection system and ion optical elements. Section 3 presents the recent results of the ³²S + ^90,94Zr test experiment and Sect. 4 summarizes the results and our conclusions.

Spectrometer

The HiToF spectrometer consists mainly of an adjustable detection system and an ion-optical system. It was connected to a steal-tape sealed rotating chamber with a diameter of 40 cm. The spectrometer can rotate with the chamber as the center, covering an angular range from -40° to 160°. A schematic of the spectrometer is shown in Fig. 1.

Fig. 1Full-screen View

(Color online) Schematic view of the HiToF spectrometer

2.1

The detection system

The detection system includes a ToF measurement that mainly uses two microchannel plates (MCP1 and MCP2) and an energy measurement using a multisampling position-sensitive ionization chamber (IC) installed at the focal plane. A v-E detector, including an MCP and a double-sided silicon strip detector (DSSD) [16-18] is also installed at the complementary angle in the rotating chamber for the velocity and energy measurements of target-like ions.

ToF measurement consists of two transmission-type detectors that have good timing properties, such as timing detectors made of microchannel plates [19-21]. Two timing detectors, each using a pair of microchannel plates with a diameter of 45 mm, were installed to provide the start and stop signals along a flight path. The stop detector was placed at a distance of 40 cm from the focal plane. In the test experiment described in Section 3, the start detector was set 40 cm from the target. However, the start detector can be placed closer to the targets to reduce relative inaccuracy with a longer flight distance. Note that both MCP detectors, which define the geometric solid angle for the entire spectrometer, can be replaced with a position-sensitive MCP [22, 23] to provide position information such that the track of the projectile-like ions after magnetic focusing can be reconstructed. The energy resolution can be further improved by using the ToF information of a specific particle. Figure 2 shows the result of the offline test at a short flight distance of 5 mm using a standard α source consisting of the isotope ²⁴¹Am. The typical timing resolution was 120 ps.

Fig. 2Full-screen View

(Color online) ToF spectrum obtained by a ²⁴¹Am α source in a short flight distance of 5 mm

To improve the energy resolution for the experimental demands, a special IC with a transverse electric field was designed. The special design of the ionization chamber refers to conventional ionization chambers [24-27] and time projection chammbers [28-32]. The IC was constructed from printed circuit boards with dimensions of 300 mm × 200 mm × 200 mm, located at the focal plane. A length of 300 mm provided a broad energy range for Z identification. The circular entrance window of the IC, which is 100 mm in diameter, is positioned 18.3 cm away from MCP2 and is equipped with a 2-μm thick mylar foil. The large area of the entrance window provided a large acceptance for energy measurement. The grid consists of gold-plated tungsten wires with a radius of 0.08 mm, soldered 1 mm apart. The distance from the grid to the anode was 22 mm, and the spacing between the grid and the cathode was 136 mm. 67 equipotential rectangle shaped loop electrodes were evenly distributed along the plate with resistors of 1 MΩ to connect two adjacent electrodes.

This IC is designed with three-dimensional position resolution capabilities, allowing for precise ΔE-E and position detection. The energy resolution can be improved by the track reconstruction provided by the IC. Figure 3 shows the design details.

Fig. 3Full-screen View

(Color online) Schematic view of a) IC and b) its anode

The anode of the IC is divided into seven sections, which can provide not only the energy loss ΔE and residual energy E_R but also the trajectory (z-direction) of the entrance ion. Each section was divided into two wedge-shaped parts to determine the x-position using the charge-division method. The y-position is provided by the drift-time difference between the anode and cathode. The timing signal of MCP2 was also used as a reference for drift-time measurement. Typical x, y, and z position resolutions are approximately 1.0, 0.5 and 2.0 mm, respectively, primarily depending on the properties of the entrance ion, working gas, and high voltage supplied. A smart preamplifier (SPA) [33] was used for the signal readout of the IC. Figure 4 shows the results of the offline test using fission source ²⁵²Cf. The fission fragments of this source have a continuous energy spectrum mainly distributed around ¹⁰⁵Mo and ¹⁴⁰Xe. The energies of heavier fragments are typically lower than the Bragg peak energy; hence, the corresponding ΔE-E spectrum exhibits an upward trend. Lighter fragments with energies over the energy of the Bragg peak tend to be flatter in the spectrum. The working gas was 99.9% pure propane, at a pressure of 30 Torr. The operating voltages were 110 V for the anode and -308 V for the cathode.

Fig. 4Full-screen View

(Color online) ΔE-E spectrum obtained by a ²⁵²Cf fission source

Practical flight distances are constrained for many technical reasons, particularly solid angle considerations [34]. Because of optical focusing by the quadrupole triplet lens, the real flight distance of the projectile-like ions may deviate from the designated length between the start and stop detectors. For this reason, the x-y position information at the focal plane and the trajectory of the entrance ion provided by the IC can be used to correct the flight distance so that the relative inaccuracy of the ToF measurement is partly reduced.

2.2

The ion-optical system

The ion-optical system is designed to use a quadrupole triplet lens (Q1-Q2-Q3) to transport the entrance ions to the focal plane, which is approximately 2.70 m away from the target. Three quadrupole magnets Q1, Q2 and Q3 are equipped at 0.85, 1.35, 1.85 m from the target. The Q1 and Q3 quadrupoles have the same structure with an aperture of Φ_ape = 100 mm and a maximum magnetic flux density of B_max = 0.373 T. The Q2 quadrupole is located in the middle, with a reverse-phase current and an aperture Φ_ape = 130 mm and a maximum magnetic flux density of B_max = 0.636 T. Ions with a magnetic rigidity up to $B\rho \text{=}0.95$ T⋅m can be analyzed in terms of maximum angular acceptance $\text{Δ}\theta {=3.3}^{\circ }$ and $\text{Δ}\varphi {=7.3}^{\circ }$.

The HiToF spectrometer can be operated in three modes: a) both x and y focusing (double focusing), b) x focusing and y parallel, and c) x parallel and y focusing. The double-focusing operation mode, which provides the maximum solid angle, enhances the transmission efficiency, and mode c) offers a method for preserving the scattering angle information by focusing only perpendicular to the reaction plane [13, 34]. The solid angle of the spectrometer was confirmed by measuring the yield of all the quasi-elastic events on the focal plane as a function of the quadrupole field.

The corresponding ion trajectories calculated using GICOSY [35] are shown in Fig. 5. The setting of the quadrupole triplet lens is primarily determined by the mass, energy, and charge state of the entrance ion.

Fig. 5Full-screen View

Ion trajectories of the HiToF spectrometer in three operating modes: a) both x and y focusing (double focusing), b) x focusing and y parallel, and c) x parallel and y focusing

Performance of HiToF

An experiment on ³²S + ^90,94Zr at E_Lab = 135 MeV (approximately 15% above the Coulomb barrier) was conducted on the spectrometer to test its performance. The two targets consisted of ⁹⁰ZrO₂ and ⁹⁴ZrO₂ evaporated onto 25 μg/cm² carbon backings with thicknesses of 104 μg/cm² and 120 μg/cm², respectively. The focusing performance of the magnets, performance of the detection system, and particle identification capability were tested in the experiment.

The transmission efficiencies were determined by measuring the product ions on the focal plane with and without a magnetic field. The magnetic fields for maximum transmission efficiencies B0 were set based on GICOSY calculations. Several magnetic fields close to B0 are also tested. As shown in Fig. 6, the enhancement factors of the yield ratios with and without quadrupole fields for the charge states of 11⁺, 12⁺, and 13⁺ in the double-focusing operating mode are in good agreement with the GICOSY calculations. In this case, the magnetic field setting for the maximum transmission efficiency is B_Q2/B_Q1 = 1.678, with B_Q1 = B_Q3.

Fig. 6Full-screen View

(Color online) Enhancement factors provided by yield ratios varying with the Q2 field for different charge states. The solid line represents the GICOSY calculation

In the experiment, the ToF was measured between the two MCP detectors at a flight distance of 1.9 m. ToF measurement is influenced by a number of factors such as spectrometer isochronism, target thickness inhomogeneity, energy straggling in the target, imperfect software corrections, and finite resolutions of the ToF detectors [18]. As shown in Fig. 7, the FWHM of the main peak of particle ³²S without a magnetic field was 500 ps. The ToF of the focused ions was also affected by the uncertainty in the flight distance owing to the large solid angle.

Fig. 7Full-screen View

(Color online) ToF spectrum of ³²S elastic scattering from ⁹⁴Zr target

Different magnetic fields are required for particles of different energies, masses, and charge states. In addition, three operating modes of focus were tested. [Double-focusing mode]

For the test experiment, we redistributed the seven sections of the IC anode into three parts: two, two, and three sections. Propane was used as the working gas for ionization within the pressure range of 50–70 Torr. In Fig. 8, we show the tracking results provided by the IC, which are useful for more precise energy detection. Using the method described in Sect. 2, the images of the x-y distributions on the focal plane for the three focusing modes are shown in Fig. 9, which are consistent with the distribution results calculated by GICOSY. In this case, the magnetic field settings B_Q2/B_Q1 of different focusing modes (a), (b), and (c) are 1.678, 1.32, and 1.577, respectively, with B_Q1 = B_Q3. The results in Fig. 9 verify the position resolution capability of the IC and focusing performance of the quadrupole triplet lens.

Fig. 8Full-screen View

(Color online) Tracking results of IC in double-focusing mode for the reaction system ³²S + ⁹⁴Zr at θ_Lab = 55°. (a) trace on the xz plane; (b) trace on the yz plane

Fig. 9Full-screen View

(Color online) Comparison of x-y distributions for three focusing modes and GICOSY calculation results, for the reaction system ³²S + ⁹⁴Zr. (a) x-y distribution on focal plane for double-focusing mode at θ_Lab = 55° with IC pressure 60 Torr; (b) $x-y$ distribution on focal plane for y parallel - x focusing mode at θ_Lab = 50° with IC pressure 50 Torr; (c) $x-y$ distribution on focal plane for x parallel - y focusing mode for reaction system at θ_Lab = 50° with IC pressure 50 Torr. For different focusing mode, the left penal is position spectra on the focal plane, given by IC. The right panel is GICOSY calculation results under the corresponding condition

The large effective solid angle and good charge and mass resolution provide opportunities for measuring the cross sections of weak reaction channels. The ΔE-E measurement, shown in Fig. 10, precisely identifies different elements. The populated product isotopes at E_beam = 135 MeV extended from Z = 12 (4 proton stripping) to Z = 16. The lower-energy particles observed were elements C (Z = 6) and O (Z = 8) on the target backings.

Fig. 10Full-screen View

(Color online) ΔE-E matrix at θ_Lab = 55°. Different charges of projectile-like ions are clearly separated

The resolution of the HiToF spectrometer allowed for the unambiguous identification of numerous projectile-like reaction products. Two-dimensional mass-charge spectra were obtained for the reaction ³²S + ^90,94Zr at θ_Lab = 55° (close to the grazing angle), as shown in Fig. 11. Several reaction channels, including proton stripping, neutron stripping, and neutron pick-up reactions, were measured. The reaction products were clearly identified up to the pick-up of two neutrons and stripping of four protons. Rare events belonging to the -5p channels were also observed.

Fig. 11Full-screen View

(Color online) Z-A matrix at θ_Lab = 55°. The most intense spot at Z = 16 corresponds to A = 32. The resolving power of HiToF facilitates the clear and definitive identification of a diverse array of projectile-like reaction products

In the reaction system, the IC provides nuclear charge resolution $\text{Δ}Z/Z=\frac{1}{50}$. The mass resolution achieved was σ = 0.2 amu, which was mainly limited by the energy resolution of the IC.

Mass spectra for various Z selections are shown in Figs. 12 and 13. For Z = 16, an exponential decline in ion yield with an increase in the number of transferred neutrons was observed. In Fig. 13, reaction products from Z = 12 to Z = 15 were observed. The peaks with Z = 12 and A= 26 correspond to the -4p-2n channel.

Fig. 12Full-screen View

Mass spectrum for S isotopes populated in the reaction ³²S (beam) + ⁹⁴Zr at θ_Lab = 55°

Fig. 13Full-screen View

(Color online) Projections on the mass matrix in ³²S (beam) + ⁹⁴Zr shown in Fig. 11, for different Z selections. The mass resolution is σ = 0.2

Summary and outlook

According to the test experiment, the HiToF spectrometer, a simple and high-precision equipment that can provide a large solid angle of 20 msr and allow a good resolution for mass, energy, and position, was adequately prepared to study multi-nucleon transfer reactions. The resolutions of mass, charge, and position are σ = 0.2 amu, $\text{Δ}Z/Z=\frac{1}{50}$, and 1.0, 0.5 and 2.0 mm for the x, y, and z dimensions, respectively. The different focusing modes of the quadrupole triplet lens provide possibilities for further investigation. The energies and/or masses can be investigated mainly based on the resolving power of the detection system, which fundamentally determines the performance of the spectrometer.

In the near future, improved IC and track reconstruction via the timing detector of ToF measurement and IC will be combined to enhance the energy resolution with a more precise magnetic field. An angular distribution with higher precision is obtained via the coincidence of IC for the measurement of projectile-like ions and v-E detectors for the measurement of target-like ions.

In the field of low-energy nuclear reactions, HiToF provides good opportunities for the experimental study of reaction mechanisms. HiToF’s robust particle identification capability is crucial for identifying reaction products and channels in MNT processes. Owing to the broad detection range of the spectrometer, a large number of reaction channels can be observed. This facilitated a more profound understanding of the reaction mechanism. Superior performance of the device is required for frontiers; therefore, efforts will be made to improve the detection system, such as enhancement of energy and position resolution.