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514
Papor to be presented at German Physical Society Meeting, Düsseldorf,
Gornjov, October 5-10, 1964.
ORNLP-514. DET
ce1f-724-3
UCI 31964
NUCLEAR REACTIONS WITH HEAVY IONS
A. Zuckor
Oak Ridge National Laboratory
1. Introduction
At this writing the field of heavy ion nuclear physics is just a
little over ten years old. This period, which has witnessed striking
developments in so many branches of nuclear physics, has seen
heavy ions used for the study of nuclear physics in many diverse ways
and for many reasons. We should note at the outset that the field owes
a great debt to several now accelerators, cyclotrons, and linear
accelerators which were developed specifically for heavy ions in the
carly 1950's, and to other electrostatic accelerators that were later
adapted for this use.
Currently many species of heavy ions are available, from
lithium to argon ions, with energies from 1 to 15 MeV/amu, in various
laboratories throughout the world. We will outline very briefly some
of the more common uses to which heavy ions have been put",2,3,4.
Elastic Scattering. Elastic scatt:ring experiments have been
carried out as research problems in their own right as well as to
gain an understanding of incoming and outgoing channel phenomena
when applied to other reaction studies. In general it was found that
semiclassical approximations are very useful and give good agreement
with the data, which is not surprising since for heavy ions n = 2,2,2“/Xv
is normally much larger than unity. Results of the se investigations
show that the nuclear radius parameter r. = 1.5 F fits the data, that
* Research sponsored by the U. S. Atomic Energy Commission under
contract with the Union Carbide Corporation.
VH-*
the nuclear surface is probably about 2F thick, and that the optical
model gives good agreement with the scattering data. Wo might
note, here, that one of the semiclassical theories which is used to :
interpret the elastic scattering of heavy ions derives directly from
the work of Airy on the scattering of light from raindrops to explain
the occurrence of rainbows5,6,7.
Inelastic Scattering. This field, which strictly speaking,
includes Coulomb excitation, has on account of the classical nature
of the interaction, contributed much to our understanding of nuclear
structure. Coulomb excitation with heavy ions has revealed the
existence of very high-spin rotational states, and been very useful
for the study of second-order effects such as multiple excitation,
and reorientation of static quadrupole moments. Besides the
classical nature of the interaction to make the interpretation simple,
a further advantage is derived from the fact that heavy ions can
carry large amounts of energy, tens of MeV, and may still be well
below the Coulomb barrier for many nuclei, thus minimizing
competing y-rays from reactions which might obscure the effects
of Coulomb excitation. Other particularly characteristic effects
obtained with heavy ions include mutual excitation in inelastic scattering
whereby both participating nuclei are left in some excited state.
Transfer Reactions. The transfer of a nucleon or group of
nucleons from one nucleus to another is characteristically a field
which originated with the advent of heavy ions. Here the hope is that
some secrets of the nuclear surface will be revealed -- for example,
if the transfer mechanism is well understood, neutron reduced widths
may be extracted from single neutron transfer experiments. Many
.
pussles, especially insofar as multinucleon and complex transfers
are concernnd still remain oven after several years of study. For
example, the angular distributions for transferi of more than one
particle are strongly poaked in the forward direction, whersas
· nucleon transfers at the same energy may have a very pronounced
· maximum at about 30°.
Statistical Model. Heavy ions are useful for the study of the
formation and subsequent de-excitation of highly excited complex
nuclei for two principal reasons: a) it is easy to disentangle direct
and statistical effects, and b) heavy ions bring in large amounts of
angular momentum and thus enable us to investigate the role of
angular momentum in the statistical model of nuclear reactions.
Fission, with heavy ions, for example, clearly reveals the importance
of angular momentum in this process'. Fluctuations in total or
differential cross sections have also been investigated with heavy
ions, thus providing a measure of the lifetime of the compound
nucleus.
Lithium Reactions. These fall generally into two classes:
low energy (1-4 MeV) and high energy (20-70 MeV). In the first
category, Li ions have been used to identify and study energy levels
in very light nuclei such as B", Be®, etc., and to elucidate the cluster
structure of nuclei in the vicinity of Li. Experiments of the second
category have been used as a possible tool for nuclear spectroscopy
in analogy with stripping reactions. They show, for example, that
w can break up into He* + H3 when passing close to a heavy target
aucleus.
...
T.
Production of Radioisotopes. On account of their short
range and consequently low yield heavy ions are in general not very
useful for the production of isotopes either for practical application
or for the study of the isotopes themselves. Two exceptions to
this must be noted: in some instances vory neutron deficient
isotopes can be made with heavy ions and in no other way. Trans-
uranic elements seem to be produced most successfully by the transfer
of nucleors from a complex projectile to a heavy element target.
The problem here is that a highly excited compound nucleus of a
very heavy element will invariably fission with much greater
probability than it will decay by neutron emission. If, however,
neutrons or protons are added to the target nucleus by a transfer
process, the resulting nucleus may be only slightly excited, and
decay by y-emission followed by B-decay to a heavy isotope of
sufficient half-life to be detected by some of the very sophisticated
apparatus that the transuranium hunters employ.
We cannot in this review cover all the areas in which heavy
ions nre used for the study of nuclei. Instead we shall limit
ourselves to two topics which may illustrate some of the virtues
and disadvantages of heavy ion reactions: a) neutron transfer
reactions, and b) the effects of angular momentum on the statistical
decay of excited nuclei.
II. Neutron Transfer Reactions
Very soon after heavy ion reactions began to be studied in
a systematic way, nucleon transfer reactions were identified
An example of such a reaction (and we shall henceforth, for
simplicity, limit ourselves to neutron transfors) is
A12? + N24 - A128 + Nd3 .
Here a neutron is transferred from the nitrogen nucleus to the
aluminum; and frequently the reaction proceeds to the ground
states of both residual nuclei. Such reactions have been extensively
studied and have the following characteristics: Above the Coulomb
barrier the excitation functions are flat, levelling off between 10
and 20 mb. Below the barrier the cross sections drop off more
gently than is the case for the reactions in which the participating
nuclei fuse. As we shall see, the reaction N14 + x14 - 113 + 15
has a measurable cross section of 4 Mb even at 4.7 MeV in the
center-of-mass system. This energy is less than half the Coulomb
barrier energy E. = 9.8 MeV, as calculated for a black nucleus with
r. = 1.5 F, and E. = 2,220'/R.
Transfer reactions exhibit very characteristic angular
distributions consisting of a single peak which appears at small
angles at high energies and at large angles at or just above the
barrier, Fig. 1. In a classical collision picture we may imagine
that the transfer always takes place at a certain closest internuclear
distance Romin. If the nuclei approach more closely fusion takes
place; while at larger distances there is no nuclear interaction
whatever and we get pure Rutherford scattering. The angle 8 at
which the peak in the angular distribution appears is related to
Rmin by
2,2262
Rmin
(1 + csc 012).
20
.
.
.
It turns out that if Rimin is expressed in terms of r., the nuclear
radius parameter, in the usual fashion Rimin = r. (A," + A,"",
that the value of r. is about 2.0 F for light nuclei such as boron,
nitrogen, or aluminum, and about 1.6 F for heavy nuclei such as
gold. The reason for this difference in r, is not at all clear nor
has it been investigated in sufficient detail.
So much for general properties of transfer reactions. We
turn now to the interesting question: whether we can learn anything
about the nuclear surface from them.
For this.a reaction theory is needed -- and the most complete
is the one developed by Breit and his collaborators" for the transfer
of a neutron, well below the Coulomb barrier where all competing
reactions can be neglected, with a Q-value close to zero to make the
kinematic problem simpler. This theory has gone through many stages
of sophistication; we will examine it here at its semiclassical stage
wherein the orbits of the heavy ions are treated in a classical fashion
and the neutron is considered as tunneling from one nucleus to the
other. The transfer cross section is given by the following formula
Iſ R, Rzg2 x
8a 1, dz 111 + a R,) (1 + a Rz!
In this expression
· = reduced wavelength of the transferred neutron h/Mv.
a is proportional to the separation energy of the transferring
neutron in the original and final nucleus.
(R, + R2 = R are the radii of these nuclei) a = (2M E 112,112.
The exponent X contains the tunneling probability
x=27[x 2,12 ,1 - _121].
Horo, for simplicity, the neutron separation energy is taken to be
the same in the donor and acceptor nucleus. In fact this is usually
not the case, but aside from complicating the formulao introduces
· no additional difficulty. These factors are all calculable, so that
the formula for the cross section contains now the interesting
product 1/, 12, where , is the probability of finding the neutron
in the donor nucleus and 1, in the acceptor nucleus.
Several possibilities emerge from this treatment. First
we must ascertain whether the theory fits experimental data.
Since the expression for the total cross section contains a product
of a's, we may take ratios of reaction cross sections which
eliminate all factors except the reduced width 6. For example,
N 4,113 and F9F18 transfers have been measured on six targets,
then the ratio of o(N24, n°3,70(F19, F18) should be the same in all
the barrier where the theory is expected to hold.
..
"..
.
Table I. Ratios of Reduced Width:
A(N 4,/91F9
2.5
Reaction PAL
BONA, AND
B20(829, 718,81
Nday , ints
Na23, Na24
A127, , A128
V517 , 1952
Mn55, Mn56
1.5
2.0
1. 2
2.0
The agreement is remarkably good considering that no nuclear structure
information is used in the theory. Additional confirmation comes
from the excellent agreement between theoretically predicted angular
distributions for the reaction N 4(N4, n n ) and recent measure-
ments at Oak Ridge, Fig. 2.
By fitting the excitation function, Fig. 3, the product 1, 1,
is then evaluated. If it is assumed that the reduced width for the
neutron is equal in N°4 and in N's, the value for the spectroscopic
factor o? = .046. This may be compared with ? = .040 for plane
wave and .052 for distorted wave analysis from the (dp) reaction
N.*id, p)N"5. We thus have in heavy ion transfer reactions a very
powerful tool for the measurement of spectroscopic factors so
essential to the nuclear shell model.
III. Angular Momentum and the Statistical Model
Heavy ion reactions in which most of the nuclear matter fuses
can be used to great advantage to study the statistical model of nuclear
roactions, and in particular to investigate the offects of angular
momentum on the de-excitation of a compound nucleus. Before we
proceed I would caution the reader that the term "compound nuclou."
in this case is used somewhat losely and docs not have the precise
mathematical meaning that was given to it by Breit and Wigner".
One of the virtues of heavy ion reactions is that it is easy to
some evaporative process. This is especially true at low energy,
2 to 5 MeV/amu where fragmentation of the projectile or the target
has not been observed to be a likely process. For example, while
(p, n) or (a, p) reactions have both direct and statistical components
with different admixtures at different angles, a (Nº4, a) or (C2, p)
reaction must proceed through a compound nucleus since direct
reactions in this case are of the (N 4, NS) type. This fact not
only lessens the confusion but also permits the study of angular
distributions of such reactions 5, 16; a matter which is very difficult
5. 16
with light projectiles.
Before launching into the effects of angular momentum, we
will list here some conclusions which have been drawn from previous
heavy ion experiments:
1) The spectra of light particles from heavy ion reactions
show a statistical shape, and do not have a high-energy
tạil.
10
2)
The level density of light nuclei measured in this way is
roughly in agreement with the formula 1 = elab
and a ~ A/10. This is an average behavior and deviations
on account of nuclear structure are observed.
The probability of evaporation of various particles,
protons, deuterons, tritons, or a-particles is equal.
That is, the preformation coefficient which was postulated
for this case is unity for all particles to within the
accuracy of the evaporation theory and our knowledge of
nuclear level densitie 8.
We now turn to a more detailed consideration of the effects
of angular momentum in the statistical de-excitation of compound
nuclei produced by the bombardment with heavy ions. The level
density of a nucleus with spin į can be approximated as
PIE*, ;) = P(E*, 0) (21 + 1) e-j|j + 1)/202.

It is clear that the level density cannot increase without limit,
as (2j + 1), since the rotational energy of a nucleus may not exceed
its excitation energy. The exponential term in the above equation
takes care of that, and remembering that ple*, 0) ~exp (E* (T) where
T is the nuclear temperature, we can write
: PIE*, j) = (2j +1) 6
(E* - Exot)/T
From the usual definition of the rotational energy E = 1 jbj + 1)/23,
where J is the moment of inertia, we may express o as
· (2 = 0T*?.
.
11
The limitation of high-spin states is thus due to a reduction of the
thermal excitation energy on account of the energy which is tied up
in rotation.
There are several effects which are the result of the
.
limitation of angular momentum:
A. Compound Nucleus
1. Reduced thermal excitation
2. Nonformation of compound nucleus
B. Residual Nucleus
1. Forward-backward peaking
2. Evaporation spectrum changes with angle
3. Excitation functions changed - Ghoshal breakdown
4. High-spin isomers favored
5. Evaporation spectrum shifted in energy
6. Reduced cross section for particle emission
7. Enhanced cross section for y-decay
Nuclear reactions with light particles do not reveal any of
these features because the orbital angular momenta are of the same
order as the intrinsic spins of the nuclei involved. With a-particles
as projectiles, these effects become observable, and with heavy
ions where 20 to 50 units of angular momentum may be brought in,
these effects become very pronounced.
The effects on the compound nucleus are: reduced thermal
excitation due to the fact that energy is tied up in the rotation of
the compound nucleus and is thus 'not available as kinetic energy of
the nucleons. In extreme cases where 80 or 90 units of orbital;
12
· angular momentum are involved in a collision, the formation of a
compound nucleus itself is forbidden, simply because no stable body
of the proper size can exist.
The effects on the residual nucleus are more easily observed:
1) The cause of forward-backward peaking is easily explained
in the classical case of a spinless particle with momentum p; and
orbital angular momentum T; impinging on a spinles: target to produce
a compound nucleus of spin I = , Fig. 4. Particles of momentum
Ps are emitted from the compound nucleus isotropically in 8. If we
average over all łwe get the well known result that the differential
cross section do ~ do w dn/ sin 8, and do / d = K/ sin 8. If the residual
nucleus has spin ja small compared to ī, the plane of emission can be
moved around 1 since I = i + ], within an angle ~ jil. This results
in an isotropic angular distributiun from 0” to e, and from (- ) to
1. Thus we see that the shape of the angular distribution depends not
only on the spin of the compound nucleus but also on the spin of the
residual nucleus. From this it follows that evaporation particle
The third point -- that excitation functions for reactions are
not independent of the mode of formation -- is illustrated in Fig. 6.
We see that the nitrogen induced reaction has a peak in the cross section
at higher energy than the proton induced reaction. This follows from
the hypothesis that not all the energy is available for thermal
excitation when high angular momenta are involved, and also results
in a shift of evaporation spectra (point 5).
It is natural to expect the fourth point, which is indeed borne
out by experimental observation.
13
..
Because evaporation protons and neutrons can, on the average,
carry away only a few units of angular momentum even at high kinetic
energies, the compound nucleus may find itself at some stage of
evaporation with a great deal of angular momentum and relatively
little excitation energy. This condition was named by Fļerov as
neutron-metastable, and requires the emission of y-ray cascades.
The observed result is a reduced cross section for particle emission:
(point 6) and a consequent enhancement of y-ray de-excitation.
Although several experiments seem to confirm this prediction, much
quantitative work still remains to be done.
The parameter o which characterizes the limitation of
angular momentum in the level density is thus of considerable interest.
We will show that angular distributions from heavy ion experiments
. provide one of the very few methods of investigating it.
We may write the differential cross section for the probability
of the evaporation of a given particle v
k
and the theoretical expression for the expansion coefficient is
21 + 1) T.
21
*****
riy wagte". więcern gezonde a diversameling
whore
(24 + 1) T
Loni
14
First we note that decay is no longer independent of formation, i.e.,
we cannot separate the last equation into two independent factors.
Then it is apparent that the calculation is a very complicated one
wherein angular distributions are fitted by a least squares method
with even Legendre polynomials, and the parameter o is extracted
with considerable uncertainty.
. Figure 7 shows the a-particle angular distributions for the
reactions A127(N14, a)Ar 37 and Na23(N14, a)333 and the Legendre
polynomial fits. We list in Table II the values of o from three
experiments with 28 Me V nitrogen ions:
Table II
Residual
Nucleus
Target
Range of E*
(MeV) :
uld gigid
E-
m
4126
4 to 12
2.7 + 0.6
0.8 * 0.4
6 to 18
3.0 + 0.6
0.9 + 0.3
ail
A12?
A 27
6 to 20
3.5 + 0.4
0.9 + 0.2
It is clear that the data show the moment of inertia to be
approximately that for a rigid body.
These experiments are very difficult and time consuming to
do and to analyze. Nevertheless, it would be most interesting if they
were extended to other parts of the periodic table to get information
about the variation of o with nuclear structure properties such as
shell effects and deformations. .
15
...
.
-
-
REFERENCES
..
-
..
.
Proc. of Second Conference on Reactions Between Complex
.
.
:
.
,
2.
4.
5.
6.
Nuclei, ed. by A. Zucker, E. C. Halbert, and F. T. Howard
(John Wiley and Sons, 1960).
A. Zucker, Annual Review of Nucl. Science 10, 27 (1960).
Proc. of Third Conference on Reactions Between Complex
Nuclei, ed. by A. Ghior so, R. M. Diamond, and H. E. Conzett
(University of California Press, 1963).
G. N. Flerov, Proc. of the Paris Conf. on Nucl. Physics,
(1964), in press.
G. B. Airy, Proc. Cambridge Phil. Soc. 6, 379 (1839).
K. W. Ford and J. A. Wheeler, Annals of Physics 7, 287
(1959).
M. V. Goldman, ORNL report 3025 (1961), unpublished.
T. Sikkeland, E. L. Haines, and V. E. Viola, Jri, Phys. Rev.
125, 1350 (1962).
M. L. Halbert, F. E. Durham, C. D. Moak, and A. Zucker,
Nucl. Physics 47, 353 (1963).
H. L. Reynolds, D. W. Scott, and A. Zucker, Proc. Nat'l.
Acad. Sci. U. S. 39, 975 (1953).
K. F. Chackett and J. H. Fremlin, Phil. Mag. 45, 735
(1954).
J. A. McIntyre, T. L. Watts, and F. C. Jobes, Phys. Rev.
119, 1331 (1960).
9.
10.
11.
16
12.
13.
G. Breit, Handbuch Der Physik XLI/1, Springer, Berlin
(1959), p. 367 et seq.
G. Breit, J. A. Polak, and D. Torchia, Proc. of Paris Conf.
on Nuclear Physics (1964), in press.
A. Zucker, Proc. of the Conf. on Direct Interactions and
Nuclear Reaction Mechanisms (Gordon and Breach 1963),
p. 860.
G. Breit and E. P. Wigner, Phys. Rev. 49, 519 (1936).
T. Ericson, Advances in Physics 9, 425 11960).
F. E. Durham and M. L. Halbert, Nucl. Physics, in press.
14.
.
.
.

г тттттт
- E(CM):133 Mer
.
- E(CM):126 Mev
n
E(CM):120 Mev
- E(CM):110 Mev
dolda IN 10-27cme
-TTTTT
FIGURES
E(CM):102 MOV
17
E(CM):90 Mev
E(CM)* 82 Mev
E(CM): 77 MOV
co مع
20
30
50
60
70
80
90
100
110
120
Figure 1. Angular distributions of N13 from the reaction Au97(N14, NS) Au"98
as a function of incident N14 energy.
18

Om -
.tror

- WMN.
fam. 6.99 More
.
Naarmt to the KOMI
.
?.
.
0;
10
20
30
40
$0
0
10
0
MO
180
Figure 2.
Angular distribution of the transfer reaction
Nl4in14, N13)15 at 6.55 MeV c. m. The solid
line is the result of a theoretical calculation.

am)
THEORY
SM
.
IOWY
Figure 3.
Excitation function of the transfer reaction
Ni4in14, n13)N15. The Coulomb barrier is
at 9.8 MeV.
19
2.
Cowouto matus
THAL SYSTEM,
MENO
promote maten, arom
-
-
-
-
-

vn
SvTT, NONATO
MENAGE oven 7
ONECTION
o
i.
.
-
Figure 4.
Schematic description of the effect of angular
momentum on the emission of particles in
statistical decay.

Nm. a) 4,25
lain
scene
.co....
Figure 5.
Variation of level density parameter, a 48 a
function of angle for the reaction o16 N14. a)A126.
..
6
.
.
.
-
-
-
-
...
..
20

52.5
o(mb)
Cu 560,3n) x-177
VSI(N14,3n) -
52
53
50
.65
E*(Mev)
Figure 6.
Excitation functions for the reactions Cu°(p, 3n) Znºs
and V51(N14, 3n) Zn63.
T
*
21
V
ENET -.
.
.

.
Am
- anau
.
.......
1:1
.
CUL UNEI
.....
-
---
Ull
--
-
---
.
. .
.
. .
Figure 7.
Alpha particle differential cross sections from
the reactions A127(N14, a) Ar37 and Na23(N14, a)533
at various energies of excitation in the residual
nucleus.
?
2
2.1
EV
DATE FILMED
12/ 17 /164





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-
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LEGAL NOTICE

.
.
-
.
-
.'
This report was prepared as an account ol Government sponsored work. Neither the United
States, nor the Commission, nor any person acting on behalf of the Commission:
A, Makes any warranty or representation, expressed or implied, with respect to the accu-
racy, completeness, or usefulness of the information containod in this report, or that the uso
of any information, apparatus, method, or procoss disclosed in this report may not infringe
privately owned rights; or
B. Assumos any liabilities with respect to the use of, or for damages resulting from the
use of any information, apparatus, mothod, or process disclosed in this report.
As used in the above, "porson acting on behalf of the Commission” includes any on-
ployee or contractor of the Commission, or employee of such contractor, to the extont that
such employee or contractor of the Commission, or employee of such contractor prepares,
disseminates, or provides access to, any information pursuant to his employment or contract
with the Commission, or his omployment with such contractor.
L:
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"
. .
Mr.
,-
tri.
--
ni
arm,
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FYW
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12,
.
END