Extending ATIMA to transuranium elements for mass
measurements at SHIPTRAP
Björn Riese
Justus Liebig Universität Giessen, Heinrich-Buff-Ring 16, 35392 Giessen
[email protected]
The ion-trap facility SHIPTRAP enables precision mass measurement with a Penningtrap mass spectrometer on heavy elements produced in fusion-evaporation reactions at
the velocity filter SHIP at the UNILAC. For the analysis it is necessary to slow down
the superheavy elements (SHEs) i.e. to calculate the stopping power in a stopping
cell. Presently the simulation software ATIMA is not applicable for the energy loss
calculation of transuranium elements but is extended to this field of these elements in
the present work.
1
Introduction
dE/dx = (dE/dx)n + (dE/dx)e
(1)
Only for high velocities (E≥ 100M eV /u) relativistic
effects become important. For further introduction
see [1].
2
The majority of masses in the region of the elements
heavier than uranium is only known from extrapolations and therefore most attractive because from the
measured mass values the nuclear binding energy can
be deduced. For these SHEs the production rates are
very low in magnitude of a few ions per week. These
reaction products from SHIP with energies in the order of af few 100 keV/u have to be stopped for further measurements in a buffer-gas filled stopping cell
with smallest possible loss of ions. Consequently, the
energy loss must be well known. At these kinetic energies the stopping is due to nuclear and electronic
stopping (fig. 1).
Stopping Power dE/( dx) [MeV/(mg/cm )]
90
80
70
Projectile:
238
U
60
Target:
63
50
Cu
ATIMA:
sum
40
elec. stop.
elast. stop.
30
20
10
0
1E-5
1E-4
1E-3
0,01
0,1
1
10
100
Kin. energy E [MeV/u]
Fig. 1: Electronic and nuclear stopping calculated with
ATIMA
where N is the atomic density of the target. The elastic energy transferred to the stationary atom (target)
1.1 Nuclear stopping - Elastic energy loss
depends of interatomic potentials which are described
The elastic energy loss by the ion per unit path length by several solid state atomic models. In ATIMA a
dE/dx in the target matter is related to the nuclear universal formular for nuclear stopping is used ([2] p.
50-53).
stopping cross section
Z bmax
T (b)dσ(b)
(2)
Sn (E0 ) =
bmin
by the relation
(dE/dx)n = N Sn (E)
(3)
39
1.2 Electronic Stopping - Inelastic energy
loss
loss. Heavy ions have in agreement with experimental data of p-stopping powers an energy loss
roughly proportional to velocity. Experimental
data show the following dependence:
Possible origins of electronic energy loss are direct
momentum transfers to target electrons, excitation
or ionization of target atoms, excitation of band- or
conduction-electrons, excitation, ionization or electron capture of the projectile itself.
The energy loss of heavy ions to the electrons of a
solid depends on their velocity v1 . Heavy ions with
lower velocity v1 can’t excite the target inner shells
electrons, so the energy loss is mostly due to the conduction electrons with velocity vF , which can be described as a free electron gas in the ground state.
The stopping power can be calculated by
Z Tmax
T dσ
(4)
(dE/dx)e = N Z2
S(Z1 = 1, Z2 , v) ∝ v 0,9
• v1 > 3vF (≈ 200keV /u):
The heavy ion scaling rule
SHI (v1 , Z1 )
SH (v1 , Z2 )
=
SH (v2 , Z2 )
SHI (v2 , Z2 )
∗
2
SHI = SH (ZHI
)2 = SH ZHI
γ2
where
(5)
where S(1, Z2 , v1 ) are experimental stopping powers
of protons (Z1 = 1) and S(Z1 , Z2 , v1 ) is the calculated
stopping power for an ion with atomic number Z1
penetrating at a speed v1 through a medium with
atomic number Z2 . Fitting all available experimental
H and He stopping powers with
i=0
ai ln E i
(6)
and using equation 5 the stopping power for He-atoms
follows by
2
S(Z1 = 2, Z2 , v) = 4S(1, Z2 , v)γHe
(11)
• vF < v1 < 3vF (≈ 25 − 200keV /u):
Ions in this energy range are transmitting an
electronic plasma, which is described by the
Brandt Kitagawa model (BK theory). The physical assumptions for this purpose are:
The determination of the charge state of the ion
depends on the relative velocity between the ion
and Fermi velocity of the electrons in the solid.
This effective charge is used to calculate the stopping power for distant collisions. For close collisions there is less shielding of the nucleus and
the stopping power increases.
The effective charge fraction is defined by
P5
)
(10)
takes into account that the heavy ion is stripped
of all electrons whose classical orbital velocities
v0 are less than the ion velocity v1 .
1.3 Evaluation of stopping powers by
ATIMA
2
= 1 − e−
γHe
2/3
γ 2 = 1 − e−0,92v1 /(v0 Z1
Hence the degree of ionization ζ of the ion depends
on the ion velocity v1 and target Fermi velocity vF
based on the electrons density.
S(Z1 , Z2 , v1 )
Z12 S(1, Z2 , v1 )
(9)
leads analog to the previous discussion to
Tmin
γ2 =
(8)
(7)
A frequently used approximation, consistent with experimental observations, is that γ 2 does not depend
on the target atomic number Z2 .
For the evaluation for heavy ions with Z1 > 2 [2]
distinguishs 3 different cases depending on the ion’s
velocity:
• v1 < vF (≈ 25keV /u):
If the ion’s velocity is low, the majority of targets electrons moves faster than the ion so collisions are mostly adiabatic without direct energy
40
2
Investigation of ATIMA’s capabiltiy
for transuranium elements
2.1 Simulation of energy loss in matter
For the study of heavy ion transition through matter
in the energy range from 1 keV/u up to 100 MeV/u
the following programs are available and allow to extend/improve ATIMA for the transuranium elements:
• ATIMA:
The specific kinetic energies ranging from 1
keV/u to 500 GeV/u and various physical quantities can be calculated like stopping power, angular straggling, range, beam parameters [3].
For energies E ≤ 10M eV /u ATIMA bases on [2].
For the range of 10 MeV/u - 30MeV/u a combination of the Bethe formula and the Ziegler approach is used. For energies above 30 MeV/u the
stopping is described by the Bethe- and correction formulas and ATIMA is very accurate for
projectiles with any atomic number in this energy range.
Presently ATIMA processes atomic numbers
Z1 , Z2 ≤ 92 therefore this work depicts the problems and possibilites to extend it.
2.2 Stopping power for ions and targets
with Z1 > 92
Calculating plots like fig. 2 in the energy range of
(0.01-1)MeV/u the stopping power for all ions with
Z1 ≥ 92 was noticable reduced compared to Z1 ≤ 92
projectiles. Obviously these results originated from
the calculation of the degree of ionization ζ (fig. 3 )
i.e. the missing λ values:
The diameter of the charge distribution of the penetrating ion depends on it’s degree of ionization ζ and
• SRIM:
is used for separating the distant or close collisions.
The most accurate and semi-empiric program for In the case of a distant collision the target electrons
energies around the stopping power maximum just see a charge
[4]. SRIM calculates the energy loss for ions in
qef f = γZ1
(12)
targets within the energy range 1,1 eV - 2 GeV
and with atomic number Z1,2 ≤ 92 [5]. Calcu- in the close collision the electrons of the medium
lations are based on [2] but code and data has feel an increased nuclear interaction because they
been continously updated.
penetrate the ion’s diameter.
1,1
Energy:
1,0
[MeV/u]
0,9
Target:
208
(v,Z1)
0,8
Zeta
• CasP:
The program CasP makes use of the convolution
approximation PCA (P=perturbative) or UCA
(U=unitary) and calculates the electronic energy
loss for all impact parameters from the mean
electronic energy transfer Qe for any ion with
Z1 ≤ 118 and any target with atomic number
Z2 ≤ 92 [6]. Therefore it is used for comparison here. CasP allows the user to increase the
accuracy with expert options.
Pb
0,001
0,7
0,063
0,398
0,6
2,512
0,5
15,85
100
0,4
0,3
0,2
0,1
0,0
2
Stopping Power dE/( dx) [MeV/(mg/cm )]
160
140
0
10
20
30
40
50
60
70
80
90
100
110
Atomic number Z1
Projectile:
238
U
120
Target:
9
Be,
63
Cu,
Fig. 3: Degree of ionization ζ for
Pb
ATIMA
100
SRIM
CasP
80
60
The atomic density distribution
40
ρ(r) ∝
20
0
1E-3
208
P b-Target and different kinetic energies. For low energies (≤ 2M eV /u) the
graphs had remarkable deviation for Z1 > 92.
208
0,01
0,1
1
10
100
Kin. energy E [MeV/u]
Fig. 2: Stopping power for 238 U in different targets calculated with ATIMA, SRIM and CasP.
41
e−r/λ
r
(13)
depends on the ion’s screening length λ. The λ values
are tabulated in ATIMA up to the atomic number of
Z1 = 92. For transuranium targets ATIMA is inapplicable because atomic data like Fermi velocity, ionisation potential and density are not available from
literature. The measurement of stopping power with
protons in these elements is difficult though a condition to calculate the stopping power with equation
9.
Improvement of ATIMA code
before.
For the stripping of ions in the experiments often carbon is used. Therefore in fig. 5 the stopping power
of 277 112 in 12 C is shown in comparison to CasP.
2
Stopping Power dE/( dx) [MeV/(mg/cm )]
To make ATIMA applicable for ions with atomic
number Z1 > 92 the missing lambda values were
appended. For this purpose guess values have been
used and are confirmed to be reasonable since the
ζ-values in fig. 3 show a smooth behaviour for
Z1 > 92 and thus follow the trend for Z1 < 92.
70
60
Target:
208
Pb
Projectile:
200
Projectile:
2
3.1 Projectiles with atomic number
Z1 > 92:
Stopping Power dE/( dx) [MeV/(mg/cm )]
3
180
160
277
(112)
Target:
12
C
140
120
ATIMA
CasP
100
80
60
40
20
244
50
Pu
1E-3
260
Lr
0,01
0,1
1
10
100
Kin. energy E [MeV/u]
277
112
40
Fig. 5: comparison of stopping powers for
30
277
112 in
12
C
calculated by ATIMA and CasP.
20
10
0
1E-3
0,01
0,1
1
10
100
References
Kin. energy E [MeV/u]
Fig. 4: Stopping power for transuranium elements in a
208
P b-target with ATIMA after improvement.
Updating ATIMA with the recent atomic data of
SRIM 2006 failed because the code seemingly has
changed. As a result the implementation of the latest code/data of SRIM in ATIMA is necessary to obtain more accurate stopping powers. This would be
reasonable in the course of transfering ATIMA from
FORTRAN77 to C++ and making the program available on WINDOWS platforms.
The extrapolation of ATIMA for SHEs without λvalues is possible if one consider the degree of ionisation shown in fig. 3. By determination the slope of
the curve for elements with higher atomic number one
is able to extrapolate the Zeta values by a straight
line. Depending on the used numerical methods a
good accuracy should be achievable. In [7] a approximation formula is used to calculate the screening for
heavy ions.
Fig. 4 shows the stopping power graphs for the projectiles 244 P u,260 Lr and 277 112. The underlying data
is calculated with the appreciated λ-values mentioned
42
[1] H. Geissel, H. Weick, C. Scheidenberger, Experimental studies of heavy-ion slowing down in
matter, 2002
[2] J. F. Ziegler, J. P. Biersack, The stopping and
range of ions in solids, Volume 1, 1985
[3] H. Geissel, C. Scheidenberger, ATIMA - ATomic
Interaction with MAtter (Software)
[4] H. Paul, A. Schinner, Nuclear Instruments and
Methods - Judging the reliability of stopping
power tables and programs for heavy ions, Volume 209, Pages 252-258, August 2003
[5] J. F. Ziegler, SRIM - The Stopping an Range
of Ions in Matter (Software), SRIM-2006.01,
2006
[6] P. L. Grande, G. Schiwietz, CasP - Convolution
Approximation for Swift Particles (Software),
CasP3.1, 2004
[7] P. Sigmund, A. Schinner, Nuclear Instruments
and Methods - Letter to the Editor: Effective
charge and related/unrelated quantities in heavy
ion stopping, B174, Pages 535-540, 2001