Radioactive beams by fragmentation and ISOL techniques - CERN

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RADIOACTIVE BEAMS BY FRAGMENTATION
AND ISOL TECHNIQUES!
W. Mittig
GANIL, B.P. 5027, 14021 CAEN, France
Invited contribution to the "lnteraational Workshop on Radioactive
Nuclear Beans produced by fragnent-separator techniquea", V
arna, Bulgaria, October 12-15, 1993.
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OCR OutputRADIOACTIVE BEAMS BY FRAGMENTATION
GANIL, B.P. 5027, 14021 CAEN, France
Abstract: The general behaviour of fragmentation cross—sections lead to simple
approximate analytical formulas. These formulas are used to compare the relative merits
of the fragmentation and the Isol method to obtain radioactive beams. lt is seen that for
beams with energies near the Coulomb barrier the Isol method gives much more intense
beams, whereas for high energy, the fragmentation method is more effective. The break
even is situated above or around 100 MeV/nucleon, the exact point depending on the
relative Isol and spectrometer efficiency. OCR Output
AND ISOL TECHNIQUES1)
W. Mittig

intensity.
During the last two decades, starting at LBL and continuing with high intensity
high energy heavy ion beams at GANH., RIKEN, MSU and more recently at GSI/SIS.
the fragmentation of the projectile was successfully used to produce secondary beams]
Simultaneously, the ISOL—method (isotope separation on line) was used to produce low
energy beams of 60 keV mainly for studies of decay and of ground state properties at
ISOLDE/CERN2). The combination of these methods corresponds to the fragmentation
of the beam or the target and the reacceleration of the reaction products to energies high
enough forstudies of nuclear reactions, this is of the order of 1-100 MeV/nucleon. The
first beams using this method were obtained at Louvain—la-Neuve3). Various projects all
over the world are very vigourously studied. A quite up-to—date compilation can be found
in the proceedings of the Dourdan workshop4). I-Iere we dont want to discuss the relative
merits of these projects but compare the fragmentation and the Isol methods for the
production of high energy secondary beams.
II. BEAM FRAGMENTATION
In this section we deduce a simple formula which allows to estimate the intensity
of a secondary beam produced by fragmentation and selected by a spectrometer. Three
main points will be discussedza) the influence of the primary beam energy on the yield
due to limited target thickness and spectrometer transmission, b) the choice of the primary
beam, c) the effect of degrading of the the energy of the secondary beam energy on the
a) Beam energy
The use of the fragmentation of the projectile produces nuclei over a broad range
of the nuclear chart. If the aim is the study of nuclei far from stability, a very selective
device is needed, in order to have a high rejection of beam particles and of nuclei near
stability, produced with several orders of magnitude higher yields. All recent studies have
made use of magnetic spectrometers for such a selection. These spectrometers have a
limited angular (A9, Arp) and momentum (Ap/p) acceptance.ln the following we will
estimate the losses due to such a device.
The variance ofthe distributions in the three dimensions (A0. Arp. Ap/phnay be
estimated using the Goldhaberjl rule :
é€f)
Gimg = Ofcrmi -%,%-j OCR Output

where ofmg is the variance of the momentum distribution of the fragment, ofcimi
is the fermi·momentum of about 100 MeV/c, and Af and AD the mass of the fragment and
the projectile respectively.
(2)
(4)
The variance 0 of the distributions in 0, tp, Ap/p for a given fragment is then
where Ei is the incident energy.
An other important factor is the limitation of the target thickness due to energyloss
differences between the incident and outgoing particle of atomic number Zi and Zi
respectively. The energy loss in the target is approximately AE = CA2!/E where c is zi
constant. The momentum spread introduced by the target of a thickness t is then
We used the fact that the energy per nucleon before and after fragmentation is
essentially the same. The maximum useful target thickness tom will be obtained if
(Ap/p)img€i ~ omg/p; for thicker targets the loss in transmission due to broadening of the
distributions will be stronger than the gain of yield due to a thicker target .
The final yield y we will obtain for a given fragment is proportional the target
thickness topi, and the angular and the momentum acceptance. If, as is the case very
often, the acceptance of the spectrometer is smaller as than the width of the distribution.
the yield ys at the exit of the spectrometer will be given by
Therefore the yield will increase with the incident energy in MeV/nucleon to the power
7/2. The validity of ths formula can be checked by comparison with codes as LISEO) and
Intensity’l. This is shown on fig. l). Deviations observed for energies above several
hundreds MeV/nucleon can be attributed to the fact that the distributions are no longer
very broad as compared to the acceptance of the spectrometer. Where this happens is
dependant on the reaction and the spectrometer acceptance considered. This can be seen
by writing explicitly the A-dependance of the yield. Using equation (1). we otain. for
example for G9 : OCR Output
Ofrag ] ($9i:($(p:()'A :——o

(5)
(4,)
A A -A B
69 = % = Gfumi IV ET`
Z _ Sym DE V A;(Ap—l) Ap’Af
Rewriting equation (4) gives
YOc E?/2/UXP-1
S (X)) P ‘ Af 3/2
A quantitative formula can be easily obtained from the considerations above with
of,ag=l()()MeV/c and Ei in units of MeV/nucleon
YS=opmd.tOp[.(l) 3/2 Q?—.&.
4,,) H G9 GQ? 6Ap/p
Z 4.08 (5,,,.,., . t.,,,,(§§
where SS, os, (Ap/p)S are the half acceptances of the spectrometer in units of
radians and percent respectively This formula is valid as long as the acceptance is small
as compared to the respective o—values of equation (5). Otherwise the gaussian
distribution should be integrated using the error function. The final intensities can be
obtained multiplying with the intensity of the incident beam.
b) Choice of the beam
A rough idea about the influence of the choice of the incident beam may be
obtained by the following considerations.
3/2 i*’l 30
9, (D, . Ei
The number of nuclei which will be produced can be approximated by the fact that
the width of the isotope chains is approximately proportional to the atomic number Zbcam.
Therefore for a constant total cross-section the cross-section will be devided by a number
of channels which increases as Zi. As the energy loss is AE/E = cAZbcami/(EE)
Zbeam for a given energy per nucleon we expect that the yield for a given channel in a
fragmentation process will decrease as l/Zjbcam. This simple prediction is once again
checked with respect to the codes LISE and Intensity on fig. 2.
Thus, the beam should be choosen as light as possible to produce a given final
product. However, one should not forget that more complicated processes than
fragmentation contribute. Pick—up reactions for example may give significant yields. as OCR Output
Q

1010
8 10
-A— —~ —Y‘ nd ES. 1 ) E? S
10°
104
106
105
104
1000
100
%
100
10 100 1000
E (MeV/nuclcon)
Fig 1: Prediction of secondary beam intensities by the programs LISE and
Intensity for a constant spectrometer acceptance compared tothe 7/2 E1aw,equ. (4).
Z beam
Fig 2: yield of 61-Ie as a function ofthe atomic number ofthe incident beum from
LISE and Intensity codes(open circles) compared to the Z ‘—‘ lawttriunglesl. OCR Output
10
\\
AV
/ _ .
/ c,
/ Z
\\
100

37
for example Si and 38 P observed with an 40Ar beam with sufficient yield to measure
their massgl.
product
(5)
c) Slowing down of energetic reaction products
For several domains of physics, it is necessary to have low energy products. For
example, interesting phenomena have been predicted in the fusion of neutron rich
nuclei9). Energies of 1-5 MeV/nucleon are therefore necessary. These may be obtained by
slowing down the beams before the reaction. For a study of fusion of Be isotopes with
an U target we measured the loss of intensity due to this slowing down]
Slowing down in a thick degrader increases the absolute width of the momentum
distribution. Writing a taylor serie to first order for Bpy as a fonction of Bp,
Bp{=Bp{()+(dBpf/dBpi)ABri, we see that the initial width GA;)/p will be multiplied by
(dBpf/dBpi
The transmission of the spectrometer is given by Ap/p, so even for a constant
width a loss of transmission of Bpi/Bpf will result. Thus the loss factor fi will be the
Fig. 3 shows that this relation holds experimentallyl
An achromatic degrader could in principle give better results than a thick target. In
practice, we found a yield 3 times lower than in the thick target case. The main reason is
the limitation of spectrometers : with a thick target the straggling will add to the finite
distribution of the nuclear reaction, and at least in the case studied here, the straggling is
small as compared to the width of the nuclear reaction in the (9,q>, Ap/p) space. With an
achromatic degrader, the Hrst part of the spectrometer already makes a severe cut in this
space. A very thick degader will enlarge this distribution once again due to straggling.
and it will be larger than the acceptance of the second part of the spectrometer, which is in
most existing devices identical to the one of the first part. The conclusion may be
different if the second part of the spectrometer has a very large acceptance. For the
spectrometer LISEwe U) concluded, that it is more easy, more efficient and gives lower
emittance beams if a thick target is used for simultaneous production and slowing down
instead of the use of an achromatic degrader.
For this case, we can use the analytical formulas of J.P. Dufour et allil. to
estimate the loss . We get OCR Output
f, 2 _
dBp{ Bpi
&Ea

(6)
and
(8)
(9)
III. ISOL PRODUCTION
incident beam can be used. This gives in a gain factor gl. Essentially all reaction products
from beam or target fragmentation will be collected in the target. This corresponds to a
gain gs with respect to a spectrometer, with gs = l/ts. Here, ts is the transmission of the
spectrometer. For a given acceptance of a spectrometer, this gain factor gs will depend on
energy as 1/Ei, 3/2as
seen in equation (4).
and reaccelerated. These different operations imply losses, which we will combine in the
factor fisoi. So the ratio of the yield between the two methods i.e. lsol and beam
fragemetation products, as a function of the incident energy and the final energy is
(10)
fl =
(dBpi/Epi) _ 1
(dBpr/Bpf) 1 - 4- `
where R is the range of the secondary particle considered and d the thickness of the target
between production and the end of the target. We have
(7) Ef E(d) E, (1 ) R
. f = E Y with Ei ~ 1.75 1 Y
Combining with equation (4), the yield is
3·5
¤ _¤ y(Er,E1)< E{- E, {
This equation will be used for the comparison with the ISOL-method.
a) General considerations and comparison with beam fragmentation
Using the lSOL—method, a very thick target corresponding to the range of the
However, in the lsol-method, the ions must be extracted from the target, ionized.
where we approximated Y = 2. OCR Output
R : Yisol = gigsfisol ,X {lsol fisol ·· (AKAI)-1 if/2
YM; fi E?/2.fi 12?’2 Et A¤·Ar

The absolute value of R depends on the acceptance of the spectrometer
12136
considered. For a reaction C(C, He) we find, for fiSOi=1, R :1800 for the LISEO
spectrometer and R :360 for SISSI13), for Ei = Ef and Ei : 50 MeV/nucleon. ln the
following we will use R :500.
MeV/nucleon.
We can now plot the behaviour of R as a function of incident energy, using
equation (10) on fig 4). In order to limit the number of parameters, we fixed Ef : 5
This figure 4) should be considered as qualitative, because as stated above, the
exact value or R depends on the spectrometer acceptance and on the reaction considered.
However, it allows us a general conclusion: if experiments with the secondary beam are
to be done at the energy of the primary beam (in units/nucleon), there is a break even
point of both methods at around 100 MeV/nucleon if the final yield is considered for a
given incident beam intensity The exact value of this energy depends on the ISOL
efficiency and the spectrometer characteristics considered.
lf low energy secondary beams are needed, the gain factor of the lsol method with
respect to slowed down products increase with the energy of the primary beam. So, for
low energies of the secondary beams the lsol method gives higher intensities and better
beam quality as long as the lsol efficiency is in a reasonable range (fisoi > 10*). For an
energy of the primary beam of about 100MeV/nucleon and of a final energy of
5MeV/nucleori the ratio R is about 1000 for fiSOi:0.0l as can be seen on figure 4)
b)Beams for ISOL-techniques
Up to now, we considered the same beam for the production of secondary beams
by fragmentation and ISOL techniques. In the lsol techniques the beam and the target
may be choosen more independantly than in the direct fragmentation technique, if target
residues are used. This means essentially that light ion beams of high intensity may be
used, such as high energy proton beams.
Here a delicate balance of production cross-section, range, and extraction
efficiency from the target will determine if light ion beams or heavy ion beams are more
efficient. As a general thumbrule, it turns out that heavy ion beams are. at same beam
power in units of Watt. are better for the production of ions below A ~100. whereas light
ion beams are more efficient for the production of secondary beams with A>l()0. Actual
limits for heavy ion beams in the 1 GeV region are 1-10 kW. Proton beams with about 1
GeV and more than 100 kW exist, and may be the most promising long range possibility
for the production of secondary beams. R+D programs for the use of these very intense
beams exist at Triumphm), PSIIS) and RAU6) and may show that the use of these very
intense beams for the present purpose is practical. A more detailed discussion may be
found in reference 17.18). OCR Output

5,, 1000
0.8
’·· 0.6
0.1
0.4
0.2 l—
105
10
I0
0 0.2 0.4 0.6 0.8 1 1 .2
before slowing down Ii (see equation 5)
&....=1
Q\`~
» - - ·i ’ "'
fl$0I=0·01
Fig 4: Ratio of Isol and beam—fragmentation secondary beam intensities as a function of
the primary beam intensity. In the last case it is supposed that the secondary beam is
selected by a spectrometer It is shown for two Isol efficiencies, and two cases of the
energy ofthe secondary beam, one is constant 5 MeV/nucleon, the other is equal to the
primary beam energy. Note that this graph is only qualitative, it depends on the reaction
and the spectrometer acceptance (see text). OCR Output
(dBm/dBpf>

emittance.
If a broad range of nuclei far from stability are to be produced, a total energy of
about l GeV in the composite system is needed. Lower total energies will give more
localised populations of the nuclear chart, thus giving higher cross—sections for nuclei
near the stability, however the cross-section far from stability will drop much faster. This
is, for example, the case for the Arenas device at Louvain la Neuvel9), where a 30 MeV
proton beam was used, and for the Oak Ridgem) project.
c) Special problems of the Isol techniques
The ISOL technique needs the extraction of the secondary ions out of the target
material, the ionisation and reacceleration of these ions. Due to different physico-chemical
behaviour each element has different problems. The 20 years of experience of
ISOLDE/CERN show simultaneously that these problems may be solved for most of the
elements, and however for each element a lot of R+D is required to get optimum results.
Besides the chemical behaviour, the diffusion—effusion time from the target to the
ion source is a difficultfproblems. The diffusion out of the target is determined mainly by
the mechanical structure of the target and the temperature, the effusion from the target to
the ion source by the sticking time of the atoms to the walls. Typical total delay times are
of the order of secondsm). This may be a serious handicap for very short lived ions.
The atoms must be ionised, and here other losses will occur. Three possibilities
are studied and/or used actually: production of negative ions for use in tandems.
production of singly charged positive ions, and multiple charged ions. With modern
ECR—sources the last possibility is promising, however a lot of R+D is still necessary to
make this possibility operational for a broad range of elements and of live—times together
with a high power (~lO kW) beam incident on the target near the plasma. Acceleration
will imply further losses, depending on the acceleration mode choosen, efficiency of
stripping if necessary in the acceleration mode chosen, and on the initial ion source
Following the preceeding considerations, it is clear that no general num ber exists
for the total ISOL efficiency. Best numbers which may be expected for a multi-charged
ion source followed by a cyclotron as at Louvain la Neuve and as in the Ganil—Spirale
project may be taken to be 2 x 10%, using 20 % for the total target + ionisation
efficiency, 20 % for the most probable charge state, and 50 % for the acceleration
efficiency. Actual best results are about l order of magnitude below this number.
These problems are avoided in direct use of fragmentation products. where short
life-times of down to l tts are available, and no chemical selectivity exists. OCR Output

Referen
The ISOL—method will give beams of good emittance, the same as the one of
primary beams. It will in most cases purify the beams by the specific selectivity of the ion
source and the accelerator. In the case of secondary beams by fragmentation, the
emittance is determined by the target thickness and the nuclear reaction, and will
correspond in most cases to the acceptance of the beam-lines. This may be a handicap for
the study of nuclear reactions induced by these ions. It may be overcome by tagging the
incoming particles, determining their characteristics event by event. This will limit the
intensity of the secondary beam below 106/s. Severe losses can occur by the purification
of the beam, due to increase of emittance and charge exchange in degraders and/or other
filters. Purification will often be necessary in order to separate the rare ions of interest
from much more frequent other ions, transmitted even after a magnetic rigidity selection.
These losses were not included in the numbers for figure 4) and in equation (l()).
V.C0nclusi0n
The ISOL—technique for the production of energetic secondary beams opens new
perspectives for the study of nuclear structure far from stability because it offers or will
offer several oders of mgnitude of increase in intensity of good quality, pure secondary
beams. With the actual techniques, the domain where this method is most advantageous
with respect to the direct use of fragmentation products of the beam is at energies around
the Coulomb-barrier. A breakeven of secondary beam intensities obtained from these two
methods occurs at an energy of the secondary beam above or around l()OMeV/nucleon if
the primary beam considered is the same.
The author thanks A.C.C.Villari for a careful reading of the manuscript.
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367, 375, 391
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