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MICROCOPY RESOLUTION TEST CHART
NATIONAL QUREAU OF STANDARDS – 1963
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MASTER
2262
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To be submitted for publication in the August issue of the IEEE's Transactions on Nuclear Science,
Proceedings of the International Conference on Isochronous Cyclotrons, Gatlinburg, Tennessee,
May 2-5, 1966.
CISO RICO
Cort-660510-9
HC: 1:00: *. ,50
RESEARCH WITH AVF CYCLOTRONS IN THE USA*
Invited Paper
JUN 27 1966
R. H. Bassel**
Oak Ridge National Laboratory, Oak Ridge, Tennessee
In the past several years many interesting well defined. Fundamental theory gives, at best,
experiments have been performed with AVF
only a hint. One can turn the problem around and
cyclotrons. In the brief period of time allotted study the scattering in terms of a phenomenological
to me it is only possible to discuss a small
potential with parameters dictated by fitting to
fraction of them.
experiment. Careful perusal of these parameters
then give some idea of the physical processes,
of the broad range of experiments performed
I thought it might be of interest to review some
It is useful to extend these studies to the
oſ the applications to nuclear reaction mechanisms particles and energies spanned by the AVF cyclo-
and nuclear spectroscopy.
..................trons for many reasons. Several of these are:
1) The optical potential is energy dependent, in
An important class of experiments are the part because of the energy dependence of the non-
scattering of various projectiles from nuclei.
elastic processes; ?) The scattering at low
These experiments are interesting for a variety energies is insensitive to details of the poten-
of reasons: 1) The elastic scattering, especially tial. This is easily understood if one realizes
of nucleons, gives some measure of the gross
that the wave length of, say, a 10-MeV proton is
properties of the nucleus, for example its size larger than most nuclei bombarded; and, 3) In
and its shape; 2) Another aspect of the elastic
connection with various reaction studies carried
scattering is that it gives information about
out at the same energy.
the average interaction of the projectile with
the nucleus; and 3) Modern reaction theories, in
In this vein a group at Oak Ridge consisting
one sense or another, require knowledge of the
of L. 1. Blumberg, E. E. Gross, A. Van der Woude,
elastic scattering.
and A. Zucker have measured polarizations and
differential cross sections of elastically
The problem is exceedingly complicated - scattered protons at a bombarding energy at 40
the nucleus is made up of a collection of protons MeV. The targets considered ranged from 12C to
and neutrons and, in principle, one should
208 Pb so that the mass dependence of the optical
consider the interaction of the projectile with potential could be studied.
each of these target nucleons.
The first slide shows the differential cross
Fortunately, to a good approximation, it section data and the optical model attempt to
is possible to reduce this many body problem to
describe it. The fits shown in this slide are
a two body problem in which the complicuted sum the resulüs of forcing the model parameters to
of interactions is replaced by an effective two vary smoothly with target mass. In general, the
body potential between target and projectile.
agreement is good though not perfect. r: the
Since the nucleus, and sometimes the projectile, next slide are shown the measured polarizations
is not an inert object this potential has an
and the optical model fits to the data. A
imaginary part to account for the various
striking feature of the measurements is the fact
excitations and reactions which the system can
that back angle polarizations are predominantly
undergo. Thus particles are removed from the
positive for the light nuclei. As you go to
incident beam and this has a profound effect on heavier targets this feature gradually goes away
the elastic scattering.
until at Pb the polarization pattern oscillates
about a zero mean.
The model to which I am referring is, of
course, the optical model. It has proven to be
These features place severe and rather
quite a good approximation for the elastic scat interesting restrictions on the optical model
tering of almost every projectile used in nuclear parameters which fit the data.
physics, and in a different but related form it
has been applied to the projectiles of high
The shape of the real potential follows, in
energy physics, the pions and kaons, and at "he some sense, the density distribution of the
other end of the energy scale, to the scattering nucleus. That is, at small distances, there is a
of slow electrons from neutral atoms.
great deal of nuclear matter while at large
distances the potential falls smoothly to zero -
The model is difficult to justify, from
reflecting the fact that there is some probability
first principles, except for the scattering of
for nucleons to exist far from the center of the
fairly high energy nucleons. For the same
nucleus.
reasons the form of the optical potential is not

RELEASED FOR ANNOUNCEMENT
IN NUCLEAR SCIENCE ABSTRACTS

RELEASED FOR ANNOUNCEMENT
IN NUCLEAR SCIENCE ABSTRACTS
The shape of the imaginary potential is
not as simply described. It is proportional to
the nuclear density distribution but also depends
on the probability that a reaction can take place.
Deep within nuclear matter nucleons are tightly
bound and it takes a great deal of energy to
initiate a reaction. For low proton (1.0-17 MeV)
energies, this is improbable and the imaginary
potential is peaked at the nuclear surface. At
the energy of the Oak Ridge experiments this
situation has changed and it is necessary that
there be some absorption in the body of the
nucleus as well as in the nuclear surface.
for 43.7-MeV He ions scattered from 19 Y and Z r.
The data is from the University of Colorado and
was taken by Gibson, Kraushaar, Rickey, and
Ridley. The smooth fall off of the differential
cross section with angle is a characteristic of
strongly absorbed projectiles even though the
energy is well above the classical Coulomb
barrier.
That the model works well over a range of
energy is illustrated on the next slide which
shows data and fits to the scattering of 3He ions
from 58Ni at energies from 22 → 44 MeV. These
fits were achieved by allowing only the depths
of the real and imaginary wells to vary with
energy as shown on the next slide.
Another feature of the potential is that
the spin-dependent interaction is centered
somewhat within the body of the nucleus. Its pre-
cise position and shape, however, are not known.
The reasons for this are not clearly understood
although more fundamental considerations at high
energy indicate that it is plausible.
The potentials found thus far have not
included a spin-dependent interaction although
the SHe ion has an intrinsic spir. The spin-
dependence must await detailed measurements of
polarization and consistent analyses in connection
with the differential cross section. Such
measurements are planned at a number of labora-
tories, Oak Ridge and Colorado, and some
experiments have already been carried out at
Birmingham.
There are other, esoteric, features of
this potential which distinguish it from the
potentials found for protons at lower energies.
Among these are the fact that the central real
well radius parameter is smaller while the fall
off distance is larger.
Again, data is needed over a wide range of
energy and target nuclei.
Clearly, there is need for more measurements
both at different energies and on more targets.
It goes without saying that polarization measure-
ments are a useful, indeed necessary, adjunt to
differential cross section experiments. Measure-
ments of the total reaction cross section would
also aid in pinpointing the parameters of the
potential.
Let me turn now to the elastic scattering
of more complex projectiles. The fundamental
theory for the scattering of projectiles with
internal structure is in very poor shape. In
fact, it hardly exists at all. One depends
almost entirely on a phenomenological theory
whose justification rests mainly on its success
and the smoothness of its parameters with energy
and target mass.
Another, related, topic is inelastic scat-
tering. The goals of these experiments and
theories are very ambitious. In principle, it
should be possible to learn a great deal about
nuclear structure - the detailed composition of
nuclear states - and the effective interaction
between the projectile and a target nucleon. The
theory for such a microscopic approach is only
now being developed, and is, in any case, beyond
the scope of this review. Again, we are fortunate
in that an alternative macroscopic theory has
been developed for a certain class of excited
states - the collective states. This theory is
closely related to the optical model theory for
elastic scattering. Briefly, the collective
model of nuclear structure assumes that either
a nucleus is permanently deformed, or easily
deformable. It is then reasonable to assume
that the interaction between such a nucleus and
a projectile is related to the density distri-
bution of the nucleus, 1.e., the optical model
potential is deformed. If the reaction happens
fast enough so that the excited nucleus is not
de-excited by the projectile, it is easily
demonstrated that only the spherical part of the
potential contributes to elastic scattering, since
there is no angular momentum change, while thu
nuclear excitation arises from the aspherica:
part. The measured inelastic scattering then
gives some idea of how de formed the permanently
deformed nucleus is, or, for the vibrating
nucleus, how easy it is to set into oscillation.
For a particular example, let me choose the
3He ion. This projectile is of great importance
in nuclear physics since its use allows the study
of proton single particle and hole states in the
same way that the deuteron stripping and pickup
reactions give information about single neutron
states.
The "He ion is doubly charged and relatively
easy to break up, since it takes only 5.49 MeV
to remove a proton. This latter fact suggests
that the 3He ion should be strongly absorbed at
the nuclear surface and indeed the optical model
reflects this in its parameters. The character-
istic potential has an absorptive well which is
much weaker than, and extends much further than
the real well. The success of the optical
potential for She ions is illustrated on the next
slide which shows the data and optical model fit
This model has been used, with outstanding
success, to describe the inelastic scattering of
protons, neutrons, deuterons, SHe ions, alpha
particles, and even heavy ions. A remarkable
feature is that all of chese projectiles give
essentially the same number which characterizes
the excited nuclear state.
An example of the success of the theory is
illustrated on the next slide, which compares the
collective model theory with the data for the
excitation of states in 90zr by 44-MeV SHe ions.
The data again is from Colorado. Similar studies
have been and are being conducted at ORNL and at
Los Alamos.
by the 5lv(d, 'He) 50T1 reaction. The states that
we shall consider are 0+, 2+, 4+, and 6+ states
which are assumed to be made up of two protons,
in £7/2 orbits outside a nuclear core with zero
angular momentum. That is, each of these protons
has orbital angular momentum of 3 and a total
angular monientum ot 7/2 in units of Planck's
constant divided by 26. Since Sly has 3 protons
in 67/2 orbits, these states are reached by
picking up one of them. The shell model, which
is believed to be applicable here, predicts
after dyncmical factors are removed, that the
states (0,2,4,6) should be excited in the ratio
9:5:9:13.
The theory seems to give an adequate
representation of the differential cross sec.ions.
In order to test it further and to gain more
insight into the nuclear structure and reaction
mechanism, it is necessary to devise other
measures of the amplitudes. One such, which 18
a sensitive text of the theory, is the measure-
ment of the angular correlation of y-rays
following the excitation. Another is o measure
the as yrametry of inelassically scattered
polarized protons.
This experiment has been done at Argonne
with 21- MeV deuterons, by T. H. Braid and
B. Zeidman, and repeated at Oak Ridge by
J. C. Hiebert and E. Newman using 34-MeV
deuterons from ORIC.
With 2+ MeV deuterons one finds the raw
spectrum shown on the next slide. The most
probable transition, to the 6+ state, is weaker
than the transition to the ground state (0+).
The transition to the 4+ state, which would be
comparable to the cross section for the Ot state,
if dynamical effects were unimportant, is also
weak.
The latter process has been measured by a
group at Oak Ridge, M. P. Fricke, E. E. Gross,
B. J. Morton, and A. Zucker and analyzed by
Fricke and R. M. Drisko. The next 31:de shows
the measurements for excitation of 2+ states in
2851 and 58Ni, and the preliminary analysis of
this data.
With 34-MeV deuterons the raw data for these
transitions is closer to the ratio predicted by
the shell model as shown on the next slide.
Intuitively, it might be thought that only
the real part of the potential would be de formed.
As can be seen from this slide, this form of the
theory gives a rather smooth asymmetry pattern
while the data has much more structure. What is
necessary to give reasonable agreement with the
data is to also allow the imaginary and spin-
de pendent parts of the interaction to follow
the motion of the vibrating nucleus. Even then,
for angles less than 40°, the theory misrepresents
nature. I should emphasize that the theoretical
predictions are very sensitive to the parameters
and that the best parameters haven't yet been
found. However, the failures at forward angles
suggest a more fundamental gap in the theory,
and this is being studied.
The energy difference is reflected in the
angular distributions as well. The next slide
shows the differential cross section for the
reactions initiated by 21-MeV deuterons. If the
simple shell model were perfect only : 3
transitions would be allowed to all these states.
This slide illustrates a minor breakdown in that
there is an & * 1 transition to the 2+ state. In
any case, the transitions to the Ot and 6+ states
must be pure d = 3 and this slide shows that
these two angular distributions are quite differ-
ent. However, at 34 Mev, the shapes are very
similar as can be seen in the next slide, and
orbital angular momentum transfers could be
assigned by inspection, although extraction of
magnitudes is still theory dependent.
This effect will be much more important for
higher 2 targets.
Let me turn to another topic where I think
AVF cyclotrons will dominate the field for
several years to come. This is the study of
proton hole and particle states using the
(d, 3He) and (He,d) reactions, and neutron
states in heavy nuclei with (d,p), (d,t) and
(p,d) reactions. Because of the Coulomb barrier,
these reactions are difficult or impossible to
study with low energy machines. As you know,
the shape of the angular distribution of the
outgoing particle is a measure of the angular
momentum transferred to the nucleus, while the
magnitude of the cross section is a measure of
the single particle or hole character of the
nuclear state.
Finally, I shall report on some (d,p) and
(d,c) experiments done at the University of
Michigan by two graduate students, A. Poltorak
and G. Mue lhlehner, under the direction of
Professor W. C. Parkinson. Professor Parkinson
and his group intend to investigate nuclei in the
deformed region where the spectra are complicated.
As a preliminary to this work these people thought
it advisable to study a heavy nucleus where the
structure is well known. In this way the theory
could be tested for reliability and the sensi-
tivity to deuteron energy studied. The logical
target is 208Pb since particle states in 209Pb
and hole states in 207 Pb are assumed to be pure.
An example of this, unfortunately not the
best one, is the study of states in 50Ti reached
The next slide shows angular distributions of
tritons for three incident deuteron energies.
At the lowest energy Coulomb effects úre impor-
tant for the angular distributions, although
there are nuclear effects present which show up
at forward angles. The angular distributions at
back angles differ subtly in slope for the
various b-transfer values. At the median energy,
20.3 MeV, nuclear distortions are more important
and angular distributions are shifted forward.
At 25 MeV, twice the energy of the Coulom's
barrier, the angular distributions are shiited
forward even more. At the latter two energies,
angular distributions are sufficiently different
80 that perhaps, with experience, be values
could be assigned.
The theoretical predictions, solid lines,
are in reasonable agreement with the data both
in the predicted shape and in the absolute
magnitude.
Much the same remarks can be made about
the stripping reactionis shown on the next slide.
Here, since Q values are positive, nuclear
effects set in at quite low energy. The
difference between angular distributions for
different b-transfers are not large. Compare,
for example, the d-transitions with the go
transitions. This points out the care necessary
in analyzing the data.
These results are encouraging and indicate
that meaningful spectroscopy can be done for
heavy nuclei.
Of course, I have only touched on the
experiments performed. I hope, however, that
tnis sampling has shown some of the progress
made and indicates areas of future experiments.
Research sponsored by the U.S. Atomic
Energy Commission under contract with the Union
Carbide Corporation.
** Present address: Brookhaven National
Laboratory, Upton, New York.
LEGAL NOTICE
The report was prepared u an account of Govorament sponsored work. Noltbar the United
Suatas, aor the Commission, nor any person acung oa beball of the Commission:
A. Makes any warranty or representation, expressed or implied, with respect to the accu-
racy, completened), or usofulness of the information contained in this roport, or that the wo
of any information, apparatus, molbod, or process disclosed in the report may not infringe
printoly owned righto; or
B. Assumes any liabiliuos with respect to the use of, or for damage resulting from the
um ol may information, apparatus, method, or process disclosed in this roport.
As used in the sbovo, "person acting on beball of the Commiulon" includes way on-
ployee or contractor of the Commission, or employee of such contractor, to the extent that
euch employs or contractor of the Commission, or employee of such contractor propurus,
dienominator, or provides accous to, may lalormation pursuant to klo employmont or contract
with the Commisslon, or his employment will such contractor.
ORAL-OWG 66- 482
ORNL-OWG 66-484


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Fig. 1 "Average parameter fits to 40-MeV
elastic proton scattering data.
o • DATA
THEORY
"AVERAGE"
PARAMETER
40
120
160
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Fig. 2 "Average" parameter fits to 40-MeV
elastic polarization data.

Z. POHO.HOP Izpo
E: 43.7 MOV
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Fig. 3 Optical model
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1.0
NIH HE3 ELASTIC SCATTERING
OPTICAL MODEL ANALYSIS WITH FIXED GEOMETRY
REAL POTENTIAL TO R=1.14A13 f.
0*0.723 !.
IMAGINARY POTENTIAL TO
(VOLUME FORM) adje 0.81 f.
E:22 Mev
(A.C. BLAIR et al., LASL)
E-33 Mev
(R.H. SIEMSSEN et al., ARGONNE)
E 37.7 Mev
(FRESENT WORK)
E.43.7 Mev
(PRESENT WORK)
10
20
30
40
50
60
70
80
90
100
110
120
130
140
8cm
Fig. 4 Optical model
fits to the elastic
scattering of 'He ions
from 58Ni as a function
of bombarding energy.
ro: 1.14 F.
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180
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N: 58
(MeV)
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10 20 30 40 50 60
INCIDENT ENERGY E (MeV)
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Fig. 5 Variation of
real and imaginary
well depths with ener-
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Fig. 6 Distorted-Wave
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Comparison of distorted wave
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Fig. 8 Spectrum of
He ions from the
51V(d, 'He) 50Ti reac-
tions at a deuteron
energy of 21.4 MeV.

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Fig. 9 Spectrum of
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Angular distributions of 3He ions
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at a deuteron energy of 21.4 MeV.
20
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Fig. 11 Angular distributions of 'He ions
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208Pb(d,p)207Pb
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Fig. 12 Angular distributions of tritons
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பட்டப்பட்ட டயட்டட்டாட்டப் பார்ப்பு
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Fig. 13 Angular distributions of protons
from the ePb(d,
p Pb reac -
tions as a junction of energy.
END
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