Average charge states of heavy ions in rarefied hydrogen

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Abstract

We present the results of experiments on measuring the charges of heavy ions from Rn (Z=86) to Og (Z=118) in rarefied hydrogen performed at the DGFRS and DGFRS-2 separators. Two formulae are proposed that can be used to calculate the charges of ions in H2 and which take into account the influence of the shell structure of atoms on the charge value. The accuracy of estimating the charge of ions of superheavy atoms was measured to be 2%. The charges of Ra, Th, and No ions were measured at a hydrogen pressure from 0.5 to 3.3 mbar, which allowed us to evaluate the effect of H2 density on the charge value. A formula is proposed to account for the effect of gas density when performing experiments at different gas pressures. It is shown that the results of experiments performed at different separators DGFRS and DGFRS-2 are in good agreement with each other.

Introduction

The study of the heaviest nuclei is impossible without separation of the products of the complete-fusion reactions of target nuclei and beam particles from numerous background nuclei, mainly from beam particles, as well as scattered nuclei and products of incomplete fusion of interacting nuclei. For the synthesis of superheavy nuclei with Z112, except for one vacuum separator SHIP [1], the gas-filled separators DGFRS [2], TASCA [3], BGS [4], GARIS [5], and GARIS-2 [6], as well as the recently commissioned separator DGFRS-2 [7] were used.

In these gas-filled separators, synthesized atoms fly into a volume of the separator filled with rarefied gas at a pressure of about 1 mbar. After the passage of less than a few centimeters in this medium, with successive charge-exchange collisions with gas atoms, the distribution of charges of heavy ions reaches equilibrium which does not depend on their initial charge distribution before entering the gas. When passing the entire gas-filled volume of the separator, the average charge of heavy ions changes slightly due to the loss of energy in the gas. In the magnetic fields of the optical elements of the separator, heavy ions are bent with an approximately constant radius ρ in dipole magnets or are focused by quadrupole lenses. With the optimized fields of magnets, most of the synthesized heavy ions reach the surface of the detectors located at the separator focal plane. Precise knowledge of the average charge states of ions is crucial in order to maximize the observation efficiency of the ions.

Studies of heavy ion charges in a gas medium began immediately after the discovery of nuclear fission, since fission fragments are formed with high velocities and large charges. The results of the first experimental and theoretical studies of heavy-ion charges in gases were reviewed in [8]. Pioneering theoretical estimates of the average charge states have been proposed by Bohr [9] and Lamb [10]. Bohr assumed that a fast heavy ion moving through a rarefied gas retains all its electrons having orbital velocities larger than the velocity of the ion relative to the medium. For the average charge state q of a heavy ion with atomic number Z and velocity v this yielded the well known formula q=(v/v0)Z1/3,(1<(v/v0)<Z2/3).

Here v0 is the velocity (2.19 × 106m/s) of the electron in Bohr’s model of the hydrogen atom.

Independent of Bohr’s work, Lamb calculated the mean charge using energy considerations [10]. He assumed that an ion moving through a rarefied gas with a velocity v will be stripped of electrons until the ionization potential of the next stage of ionization is larger than the kinetic energy of electrons bombarding the ion with a velocity v. Later it was established that the equilibrium charge q is overestimated by Eq. (1), and that Lamb’s approach yields results which are in better agreement with experiment [8]. Moreover, these relatively simple considerations do not take into account the atomic number of the gas and the gas density. The atomic shell structure of the ion was also not considered in [9].

To obtain more realistic charge states, it is necessary to perform very detailed calculations of the probabilities for electron capture and electron loss by the heavy ions moving through a dilute gas. However, it has been realized that such calculations are too complex to be easily carried out in practice. A new attempt was made by Khuyagbaatar et al. [11] in 2013 to describe charge states by means of atomic calculations of the binding energies, electron-loss, and electron-capture cross sections, including the influence of the gas-density effect. The calculated charge states reproduce the experimental values for elements with Z = 80–114 within 20%.

The selection of an average ion charge state to be used for an experiment at gas-filled separators on the synthesis of heavy nuclei in fusion-evaporation reactions is based on a set of previously accumulated data on ion charges in gases and their empirical systematics [11], [12], [13], [14], [15], [16], [17], [18], [19]. The choice of charge is complicated by the fact that these measurements were performed at different facilities at slightly different gas pressures, which corresponded to the maximum transmission of the corresponding separators. Not all systematics took into account the influence of the atomic shell structure of the heavy ions. Most of the charges are measured in helium, while the use of hydrogen as a fill gas allows increasing the transmission of the separator and suppressing background particles to a greater extent, although it requires a higher magnetic field strength.

In agreement with Lamb’s theory, the shell effect is caused by different ionization potentials of heavy ions which reach maximum values for closed shells. Accordingly, this leads to oscillations in the average charge states of ions with different atomic numbers Z traversing a gas at a constant velocity. The ions that have to lose electrons from closed shells should have lower average charge states. Such a deviation from a linear dependence in charge states was first observed in [20] and was later studied in more detail in [12], [16], [19]. These observations were explained by the gradual filling of the 4f-5d and 5f-6d electron shells in lanthanides and actinides, respectively.

The influence of gas pressure on the average charge value (density effect) has been established in numerous experiments [8], [11], [12], [13], [15], [18], [19], [21], [22]. An explanation of this effect was suggested by Bohr and Lindhard [23]. The charge of ions fluctuates due to collisions with gas atoms which result in electron capture and electron loss. These collisions generally leave the ion in an excited state. It was assumed that at low pressures such excitation will be dissipated by radiation between successive collisions, and that the average charge of the ions simply depends on the cross sections for capture and loss by the ion in the ground state. In gases at higher pressures, the time between successive charge exchange collisions decreases, and the ions to a smaller or greater extent will remain in an excited state which changes the balance between electron capture and loss towards higher average charge of ions. If the pressure is high enough, no excitation energy is lost by radiation between two collisions, and charge reaches its maximum. For the heaviest ions moving in rarefied helium, the density effect was studied experimentally at TASCA in [11], [18] and theoretically in [11].

Recently, the experimental values of the electron capture and loss cross sections by ions moving in a rarefied gas were systematized and analyzed in [24]. These systematics were used to trace the evolution of the charge states of ions flying out of solid targets and moving in a gas depending on the distance from the target (the number of collisions). These systematics were also used in [25] to describe ion trajectories in DGFRS-2 depending on gas pressure (although without taking into account the density effect). The results were in good agreement with the experimentally measured widths of horizontal distributions of ions at DGFRS-2 [26].

In almost all separators where superheavy nuclei have been studied, helium is used as a fill gas. However, it is known that the use of hydrogen provides a larger transmission of nuclei through the separator and larger suppression factors of background particles [19], [27]. The replacement of hydrogen gas by helium is usually related to safety concerns, since hydrogen is a flammable gas, as well as by the need to increase the magnetic field strength in deflecting magnets and in focusing lenses. The charges of the heaviest synthesized ions in hydrogen are lower than the charges in helium by about 10%–15%; hence the selection of heavy ions requires higher fields.

All experiments at the separators DGFRS [2], [15], [17], [27], [28] and DGFRS-2 [7], [26] were carried out using hydrogen as a fill gas. In this paper, we present the results of experiments performed at DGFRS, in which average charges of ions from Ac (Z=89) to Og (Z=118) in H2 at a pressure of 1.25 mbar were measured. Some of these results were presented in [15], [17], and they have been fit with Eq. (18) in [19]. However, as it was concluded in [11], “this formula underestimates the experimental q of Fl (Z=114) by about 5%” in He. This fact does not allow us to fully rely on the reliability of the description of charges in H2 presented in [19]. It can be seen in Figs. 7 and 8 in [19], that the charges of heavy ions with Z=112 – 118 noticeably deviate from the systematics. In addition, not all of the data were used to obtain the systematics. In this regard, obtaining a more accurate formula for describing charges in H2 seems necessary.

Also, during the commissioning of the new separator DGFRS-2, we measured the charges of ions with Z=86 (Rn), 88 (Ra), 90 (Th), and 102 (No) at a hydrogen pressure of 1.15 mbar [26]. When choosing the optimal hydrogen pressure for this separator, we measured the charges of ions 88, 90, 102 at different gas pressures. Finally, charges of ions with Z=112 (Cn), 114 (Fl), and 115 (Mc) were measured in the experiments 238U+48Ca, 242Pu+48Ca, and 243Am+48Ca, respectively [7], [28], [29]. These data and their analysis may be of importance for the operation of gas separators, e.g., recently commissioned SHANS2 [30] built for experiments on superheavy nuclei.

Section snippets

Experiment

The experiments were performed at the Dubna gas-filled recoil separators DGFRS [17], [27], [31], [32] and DGFRS-2 [26]. The studied atoms were obtained as evaporation residues (ERs) of compound nuclei produced in complete-fusion nuclear reactions between beams of accelerated ions and heavy target atoms. At the DGFRS, the ERs recoiling from a thin stationary or rotating target (0.2–0.6 mg/cm2) were separated in flight from beam particles and other background nuclei in the separator’s dipole

Results and discussion

To describe the experimental data on the average charge of ions in dilute hydrogen, we used Eq. (1) in [16] or Eq. (18) in [19] as an initial version: q=L+csin[π/16(ZL+d)],where L = a x + b represents the linear part of the charge dependence on the relative ion velocity v/v0, x=v/v0 Z1/3, Z is atomic number of ion, and a, b, c, and d are free parameters which can be determined from the fit of experimental data.

However, in addition to Eq. (4), we have considered several other variants of this

Summary

Using the DGFRS and DGFRS-2 separators we measured the average charge states of heavy atoms with Z=88 (Rn) through 118 (Og), traversing hydrogen at about 1 mbar in the velocity range of 1.0 – 2.7 v/v0. In the first approximation, the charges follow linear dependence on the velocity. However, the shell structure of atoms clearly affects the charge value. From the viewpoint of an experimental application, the set of measured data allowed us to propose two expressions which can be used for

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

We express our thanks to N. S. Gustova, M. Voronyuk, and T. P. Drobina, for their help in preparing and carrying out the experiments. We thank the personnel operating the DC280 cyclotron and the associates of the ion-source group for obtaining 48Ca beams. These studies were supported by the Ministry of Science and Higher Education of the Russian Federation through Grant No. 075-10-2020-117 and by the JINR Directorate grant. Research at ORNL was supported by the U.S. DOE Office of Nuclear

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