научная статья по теме ELECTRON LOSS OF HEAVY MANY-ELECTRON IONS IN RELATIVISTIC COLLISIONS WITH NEUTRAL ATOMS Физика

Текст научной статьи на тему «ELECTRON LOSS OF HEAVY MANY-ELECTRON IONS IN RELATIVISTIC COLLISIONS WITH NEUTRAL ATOMS»

Pis'ma v ZhETF, vol. 94, iss. 2, pp. 157-165

© 2011 July 25

ПО ИТОГАМ ПРОЕКТОВ РОССИЙСКОГО ФОНДА ФУНДАМЕНТАЛЬНЫХ ИССЛЕДОВАНИЙ Проект РФФИ # 08-02-00005а

Electron loss of heavy many-electron ions in relativistic collisions with

neutral atoms

I. Yu. Tolstikhina, V. P. Shevelko^ P.N. Lebedev Physical Institute, 119991 Moscow, Russia Submitted 10 May 2011

Electron-loss processes arising in collisions of heavy many-electron ions (like U28+) with neutral atoms (H, N, Ar) are considered over a wide energy range including relativistic energies. Various computer codes (LOSS, LOSS-R, HERION and RICODE), created for calculation of the electron-loss cross sections, and their capability are described. Recommended data on the electron-loss cross sections of U28+ ions colliding with H, N, Ar targets and predicted lifetimes of U28+ ion beams in accelerator are given. Calculated electron-loss cross sections are compared with available experimental data and other calculations.

1. Charge-changing processes. Electron loss (EL), also called electron stripping or ionization of the projectile, occurs in collisions of ions with atoms or molecules

X«++A->-X(«+ro)+ + EA + roe-, m > 1, (1)

where Xq+ denotes the incident projectile ion with a charge q and A represents the target atom (or molecule), respectively. £A indicates that the outgoing target atom A can be excited or even ionized.

In general, for many-electron projectiles the reaction (1) involves multiple-electron losses (to > 1), a contribution of which to the total electron-loss cross sections can be more than 50%. With energy increasing multiple-electron losses become small and single-electron loss processes (to = 1) prevail, especially, in the relativistic energy range.

Electron loss together with electron capture (EC)

Xq+ + A ^ + Ak+, k> 1, (2)

constitute two main charge-changing processes playing a critical role in many fields of atomic, accelerator and plasma physics, such as heavy-ion fusion (HIF) program [1], particle tumor therapy [2], heavy-ion probe beam (HIPB) diagnostics in plasma devices [3] as well as the design of synchrotrons and beam transport structures. In particular, the International FAIR project (Facility

e-mail: shev8sci.lebedev.ru

for Antiproton and Ion Research) started recently at GSI, Darmstadt [4], where heavy many-electron ions (like U28+) are planned to be accelerated up to relativistic energies of a few tens of GeV/u, requires benchmarks for EL cross sections as EL-processes can dominate among other beam-loss processes. Single and multiple EL-processes are a subject of intensive experimental studies at GSI (Germany), ITEP and JINR (Russia), A&M Texas cyclotron (USA) and LIER (CERN).

A typical example of the cross sections for two competing charge-changing processes, loss and capture, is given in Fig. 1 for U42+ ions (50 electrons) colliding with Ar atoms as a function of collision energy. In general, cross sections for both EL- and EC-processes are rather large. At low energies, EC prevails and is characterized by a quasi-constant behavior whereas at high energies, EL is the main charge-changing process, which also has a quasi-constant cross section in the relativistic energy range. The position of the crossing point of both cross sections (E ~ 7MeV/u) strongly depends on the atomic structure of both colliding particles.

At present, experimental and theoretical data on relativistic ion-atom collisions are available mainly for a few-electron ions (H- and He-like) whereas for many-electron projectiles these data are practically absent. However, requirements for vacuum conditions and ion-beam lifetimes in accelerators are directly related with accurate knowledge of electron loss cross sections of heavy ions colliding with residual-gas atoms and molecules.

Письма в ЖЭТФ том 94 вып. 1-2 2011

157

10-

10

-16

10

-18

10

10 10 E (MeV/u)

10

Fig. 1. Charge-changing cross sections in U42+ + Ar collisions as a function of collision energy. Experimental data on single-electron capture and loss cross sections (open symbols) are given to show their contribution to the total cross sections (solid symbols). Solid curves: EC - calculations by the CAPTURE code, and EL - by DEPOSIT and RICODE codes (see [7] for description of the codes)

Relativistic ion-atom collisions involving H- and He-like like highly charged ions are considered in various books [8,9] and review articles [10,11]. Since the relativistic wave functions for H-like ions are known, the corresponding calculations can be used to check the applicability of the first-order perturbation theory and the influence of the so-called magnetic interactions arising between colliding particles at relativistic energies.

The aim of this work is to present a recent progress in theoretical calculations of electron-loss cross sections for heavy many-electron ions colliding with neutral atoms over a wide energy range including relativistic energies. A brief description of methods and recently created computer codes (LOSS, LOSS-R, HERION ¡nd RICODE) for calculations of electron-loss cross sections is given. Recommended data on EL cross sections for U28+ ions colliding with H, N and Ar targets (main residual-gas components) are presented.

Atomic units are used: m. = e = % = 1.

2. Non-relativistic approximation. The LOSScode. Over the last ten years, electron loss processes in the non-relativistic energy range, 1 MeV/u < E < < 100 MeV/u, were investigated experimentally and theoretically in more details. At present, two main different approaches are used in this range: a classical approximation (classical trajectory Monte Carlo (CTMC) method [12] and energy-deposition model [13]) and a quantum-mechanical non-relativistic Born approximation [14]. Classical approximation approaches are used to describe single-, multiple-electron loss and total loss

cross sections, and the Born approximation for a single-electron loss cross sections. It is important to note that in the case of many-electron projectile ions, a contribution of multiple-electron losses to the total loss cross sections can be very large and reach up to more than 50%, therefore, at low and intermediate energies, 1 MeV/u < E < 10 MeV/u, the classical models give more accurate results compared to the Born approximation which is applied for single-electron loss calculations. But at higher energies, E > 10 MeV/u, the Born approximation is preferable because the results in the classical approximation overestimate experimental data. As a result, two different approximations give different asymptotic behavior for the total loss cross sections: crtot ~ Ein the Born approximation and otot ~ in the classical approximation where the constant a varies approximately in the limits 0.3 < a < 0.9 depending on the target atomic number (e.g., a = 0.3 for Xe and a = 0.9 for H).

In the non-relativistic plane-wave Born approximation (PWBA), the single-electron loss cross section in the momentum-transfer Q-representation is given by [14]:

oo oo

^^IrE^E ld£l ^Z2T(Q)F2P(Q,nl,e, A),

ni A n

0 Qo

\FP(Q,nl,e,X)\2 = I (eA| exp(zQr)|nZ) I , Q0 =

(3)

Inl + £

?

v

(4)

\ZT{Q)? =

n

|exp(zQr)|i)

j=i

n

N-^2\(ex p(iQr)li)

i=i

(5)

Here v denotes a relative velocity, Fp(Q) - the projectile form-factor, Zt(Q) - the effective charge of the target atom, Z and N - the target nuclear charge and total number of electrons, e and A - the energy and orbital momentum of the ejected projectile electron to be ejected, Ini and Nni - the binding energy and number of equivalent electrons of the projectile shell nl. For neutral atoms one has Z = N and for protons Zt(Q) = 1- Qo in eq. (4) is the minimal momentum which can transferred to the projectile from the target after collision. |nl) and |eA) denote the wave functions of the projectile electron in the initial and final states and |j) denotes a wave function of outermost and inner-shell target electrons.

Equations (3)-(5) were realized in the LOSS computer code [7] where the wave functions of the bound

IlHCbMa b ?K3T<I) tom 94 bmu. 1-2 2011

|nl) and and continuum \e\) states of the projectile active electron are found by numerical solution of the non-relativistic Schrodinger equation, and those for the target | j) are calculated with the nodeless Slater functions. The atomic structure of the target is taken into account through the dependence of the effective charge Zt{Q), eq. (5) on the momentum trasfer Q.

The use of the non-relativistic wave functions for many-electron heavy projectiles is justified because the main contribution to the loss cross sections at high collision energies is given by the loss of outermost projectile electrons which can be treated as non-relativistic particles.

In the LOSS-code, the calculated cross sections decrease with the projectile energy increasing in accordance with the Born approximation:

E

oo, v —>■ OO, (J

In v

v

(6)

We note, that in the case of molecular targets, the Bragg's additive rule is usually used, i.e., the interaction with a molecule is presented as a sum of interactions with individual atoms composing the molecule, e.g., for C02 target one has <r(C02) = <r(C) + 2<r(0). A typical example of EL-cross sections for U28+ + N2 collisions is shown in Fig. 2 where experimental data are compared with LOSS-code and CTMC calculations.

a

o

io

a

o

io

E (MeV/u)

100

Fig. 2. Electron-loss cross sections in U28+ +N2 collisions as a function of collision energy. Experiment: ▲ [15], • [16], ■ [17]. Solid curve - LOSS-code, dashed curve -CTMC calculations [16]

3. Relativistic version of the LOSS-code: the LOSS-R code. Because the non-relativistic LOSS-code can not be used at relativistic energies E > 100 MeV/u, it was an attempt to extend the LOSS-code to the relativistic energy range and to create the LOSS-R-code (Relativistic LOSS). The LOSS-R code uses the same

equations (3)-(5) and non-relativistic wave functions but with the following changes [18]:

v 0c, Qo

¡

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