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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS -1963
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NUCLEAR SPIN-PARITY ASSIGNMENTS
· FEB 2 3 1966
RELEASED FOR AİNNOUNCEMENT
IS NUCLDAR SCIGNCE ABSTRACTS
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-
INELASTIC SCATTERING AND THE DISTORTED WAVE METHOD*
LEGAL NOTICE

F. G, Perey
Oak Ridge National Laboratory
Oak Ridge, Tennessee
.
.
.
.
The subject of my talk is the determination of the spin and
parity of nuclear levels from the analysis of inelastic scat-
tering angular distributions using the distorted wave method.
The distorted wave method does not rate high, at this conference,
as a tool for determining the spin and parity of nuclear levels.
I suppose it is because the determinations are not solely based
on conservation laws. The distorted wave method is primarily
used to study reaction mechanisms, and I will make no apology
for this, but reaction mechanism is very intimately connected to
nuclear structure. In fact, it would be more appropriate to say
that a distorted wave calculation involves always two aspects:
the nuclear structure and the reaction mechanism aspect. Our
knowledge at the moment is such that we cannot yet proceed only
from "first principles" and that to remedy the situation we have
had to develop models. Some of them are based on very firm
ground; we can even prove some existence theorem. However, in
most cases, we are left with so-called adjustable parameters..
To some people this appears to be a more serious handicap than
it really is. Most distorteå wave calculations are very sensi-
tive to the spins and parities of the initial and final states,
although more often they may only be sensitive to the angular ;
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even target nucleus this enables you to determine the spin and
parity of the final state. Various mechanisms can then be
used to tie the parity of the level as well.
Let me now look at the collective model for inelastic scat-
tering as a tool for determining spin and parities of nuclear
levels. This model has been extensively tested in the last few
years for many different kinds of incident particles and has
. proved to be one of the most successful ones used in connection
with the distorted wave method. As a result, it has lately been
widely used as a tool for determining spins and parities of nu-
clear levels. The literature in this field is now too extensive
for me to hope to review it in the short time that I have.
.
R
*Research sponsored by the U. S. Atomic Energy Commission under
contract with the Union Carbide Corporation.
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NUCLEAR SPIN-PARITY ASSIGNMENTS
e
The distorted wave amplitude for the transition from an
initial state i to a final state f 18
L
Tue - dr ola)*(&por) (4/V/A>
(1),
where the 's are the so-called distorted waves and the matrix
element is a nuclear matrix element of the residual inter-
action V taken between the initial and the final state of the
target nucleus A. The idea of the collective model applied to
inelastic scattering is to identify this matrix element with a
'nonspherical part of the optical potential used to generate :
the distorted waves. Since the optical model potential used
to generate the p's is obtained from elastic scattering, we
"have very little freedom as far as parameters go to calculate
inelastic scattering.
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We consider a generalized optical model potential which
is a function of a radius parameter and assume that this radius
has a space and/or a time dependence. A multipole expansion
of the radius is made and then the generalized optical poten.
tial is expanded in a Taylor series. The monopole part of
this expansion is identified with the usual optical potential.
giving rise to elastic scattering, all the other terms in the
expansion giving rise to inelastic scattering. In this manner,
once the monopole part is known, we know all the terms in the :::
expansion and the only free additional parameter is the ampli-:::
tude of the oscillations or deformations. In the distorted
wave method this parameter is used only to determine the mag-
nitude of the cross section. Its value does not affect the
shape of the calculated cross section. Therefore, a fit to :
the elastic scattering is sufficient to give us all we need to
calculate the inelastic scattering to all the collective states.
Of course, all states do not have a collective nature and what
I am saying only applies to the collective ones. How can we
tell which ones are collective? This is rather easy because,
in the context of inelastic scattering, excitation of colle
tive states and large cross sections are synonymous. In.
practice, therefore, we take the largest cross sections..?!
in the first few Mev of excitation and try to see which ones
fit the calculated angular distributions for various multipoles
in order to determine the spins of the levels excited. As you
can see, there is very littie basic ambiguity as to what is to
be done in the calculation for inelastic scattering. One re-
markable thing about this model! 1. that despite its simplinity
it works exceedingly well. The comparison of the calcužated
cross section shape with the experimentally measured one gives;
unambiguously the spin of the final state only for even-even
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NUCLEAR SPIN-PARITY ASSIGNMENTS
Carget nuclei. For odd A nuclei you only get the angular mo-
mentum transferred in the reaction and you have in general a
choice of spins for the final states. In some cases, by con-
sidering the odd nucleon as being weakly coupled to an even-
even core and assuming that the collective excitat,icns are
those of the even-even core, the magnitude of the cross sections
can tell you the spins of the various members of the multiplets.
One disadvantage of odd A nuclei is that the strength of the
excitation is being spread among various levels for each
pole. The cross sections are then smaller and it is a little
more difficult to pick out the collective levels.
Of course, the usefulness of such a model depends to a
large degree on how different are the various angular distri-
butions for the different spin values. This is very much a
question of the kind of particle used and the energy at which
the measurements are made. So far the method has been widely
used at many different energies for neutrons, protons, deuterons,
helium-3, and alpha particles with great success and even the
magnitudes of the cross sections are given correctly for the
same deformation parameter associated with the state indepen-
dent of the projectile used for exciting the level. The well-
known diffraction-like patterns associated with a- inelastic
scattering permit usually a very good assignment of level spins,
but for all of the particles there are usually enough differences
for different spin assignments to be able to identify them
correctly.
The optical model potential has always a real and an imagi-
nary part. When incident charged particles are used, a coulomb
potential arising out of some nuclear charge distribution is
also included. For particles with non-zero spin, it is also
necessary to have a spin-orbit potential. All those potentials 4
have a radius parameter associated with them and, taking our
model seriously, we should deform them all. If one is only
interested in assigning spin and parities to nuclear levels,
vey often it is not necessary to do so and deforming the real
part only is sufficient. However, if one is also interested in
the deformation parameter, in many cases it is necessary to
deform both the real and the imaginary potential, and if the
energy is not sufficiently high above the coulomb barrier, one
should allow also coulomb excitation by deforming the charge
distribution. In particular, interference effects between
coulomb excitation and nuclear excitation can be very larg
Finally, in order to account for inelastic polarization, it
may be necessary to allow for deformation of the spin orbit
potential. Although no such calculations have been reported
yet, some are in progress."
NUCLEAR SPIN-PARITY ASSIGNMENTS
In the rest of this talk I will show you various examples
selected mostly out of recent work done at Oak Ridge. Figures
1 and 2 show for 30-MeV incident prctons the sensitivity of
the calculation to various spin assignments. The curves are:
very characteristic, and, even with data only in the range of .
30 to 100 degrees, one should be able to pick cut the spins
easily. In this calculation only the real part of the optical
model was deformed. For protons at these energies, the effect
of coulomb excitation is negligible as shown on Fig. 3,
ever, the deformation of the imaginary part of the potential
has a non-negligible effect as seen on Fig. 4. In this case,
the effect is not large but note that it goes in the right
direction to improve the fit. This example is more typical
of what is usually found but this is not always the case.
Satchler* had an interesting case dealing with optical model
parameters. The elastic data and the fits are shown in Fig. 5.
In this particular case, equivalent fits could be found to the .
elastic scattering data with two optical model potentials dif-
fering in the fact that one had a volume imaginary part (V)
and the other a surface imaginary part (S). Of course, the
real potentials were slightly different to compensate for the
change in imaginary potentials. When the two potentials were
used to calculate inelastic scattering to the 3° ievel at
-3.7 MeV and to the 5" level at -5.4 MeV, they gave different
results, The 3° level data are shown on Fig. 6 with the two i
curves. However, if one deforms both the real and the imagi-
nary parts of the potential, the very interesting results .
shown on Fig. 7 are obtained. The fits are now very good and
essentially the same for both potentials. Very similar re- .
sults were found for the 5. level. In this particular example
the model passed a very crucial test: since there are ambi-
guities in the optical model potential and our collective model
is based entirely upon it, what happens to inelastic results?
The answer in this case is: nothing if both the real and
imaginary potential are deformed. In other words, potentials
which are equivalent for plastic scattering are also equiva-.
lent for inelastic scattering.
In Fig. 3 we saw a case where coulomb excitation affected
the results very slightly. This is not always the case, par..
ticularly close to the coulomb barrier, as shown in Figs. 8
and 9. For Cd with deuteron, incident at 8 Mev, the cross
section is increased by more than a factor of two and the shape
modified also, whereas at 14 MeV the magnitude is changed by
only 25% and the shape only slightly altered. For protons on
Cd at 12 MeV, the minimum around 40 degrees is due to the in-
terference between coulomb and nuclear excitation.
-
NUCLEAR SPIN-PARITY ASSIGNMENTS

Dua
63-6934
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Fig. 1.
MeV Protons:
Inelastic Scattering of 30-
Collective Model. ..

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NUCLEAR SPIN-PARITY ASSIGNMENTS

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NUCLEAR SPIN-PARITY ASSIGNMENTS

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No such talk would be complete without some alpha scat- .
tering data. Figure 10' gives a very nice example of elastic
and inelastic scattering of 42 MeV alphas on Mg24, and Fig. 11-
is another case at the same energy but this time three in-
elastic levels have been observed. The case of inelastic
scattering of high-energy alpha particles is a little special. :
Because of the rather strong absorption of the alpha particle
as it penetrates the nucleus, it is possible to make further
approximations in the evaluation of the transition amplitude.
Our next speaker will talk on this subject.
:
Let me now show you an example with neutron inelastic
scatteringe in Fig. 12. 'Most of the data on excitation of
collective levels with neutrons is at 14 MeV, and Fig. 13 is
one more examp.le."
All the calculations I have shown you until now have con-
sidered only first-order transitions. In view 012 the large suc-
cess which this model has, it was only natural to extend it to
higher orders. It turns out that to perform such calculations it
is preferable to use a coupled channel formalism. Since the
calculations are more complex, far fewer cases have been
studied, and since the cross sections are smaller, less data
&re available. I would like to mention only that it seems a
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NUCLEAR SPIN-PARITY ASSIGNMENTS

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Fig. 6. Fit to 3* Level Deforming 'Only
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Fig. 7. Fit to 3 Level Deforming Both
Real and Imaginary Potentials for the Two Po-
tentials.
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Fig. 8. Effect of Coulomb Excitation at Lower Energy.

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Fig. 9. Effect of Coulomb Excitation at Various Energies :
for Deuteron Scattering.
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NUCLEAR SPIN-PARITY ASSIGNMENTS

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NUCLEAR SPIN.PARITY ASSIGNMENTS
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NUCLEAR SPIN-PARITY ASSIGNMENTS
very useful tool to get at some of the other levels which can
be reached by direct excitation and multiple excitation.
Finally, one should say that serious attempts are being
made to use more sophisticated models for inelastic scattering
by going to a microscopic description of the transition in
terms of a shell model description of the nuclear levels. So
far the macroscopic description in terms of the collective
model is more successful in reproducing the data as seen on
Fig. 14, but we hope to be able to understand the reason for its
successes in terms of a more fundamental microscopic description. .
To conclude I will remark that many of us doing distorted
wave analysis feel that very reliable spin and parity assign-
ments can be made using data on inelastic scattering of various
particles from levels up to a few MeV of excitation.
-
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NUCLEAR SPIN.PARITY ASSIGNMENTS
References
F. G. Perey, Proceedings of the Karlsruhe Conference on Polari-
zation Phenomena, 1965.
PR. M. Drisko, Private communication.
BM. P. Fricke and G. R. Satchler, Phys. Rev. 139 B, 567 (1965).
*K. Yagi et al., Phys. Letter 10, 186 (1964).
8J. K. Dickens, F. G. Perey and G. R. Satchler, Nucl. Phys. 23,
529 (1965).
Taro Tamura, Rev. Mod. Phys. 37, 679 (1965).
"E. Rost, Phys. Rev. 128, 2708 (1962).
ØR. H. Bassel et al., Phys. Rev. 128, 2693 (1962).
PL. Cranberg, Progress in Fast Neutron Physics, p. 204, G. C.
Philips, J. B. Marion, and J. R. Risser, University of Chicago
Press, 1963.
108. H. Stelson et al., Nucl. Phys. 68, 97 (1965).
11W. S. Gray et al., (to be published).
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END

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DATE FILMED
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