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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS -1963
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MA
ORNL. -- 2438
Conf-660906-18
:-ORNL > AEC - OFFICIAL
SEP 2 2 1966
Analysis of the Analogue state Resonaces in 208 pb (p.p.) 208 pb
and 208 Pb (p.p') 208Pb* Processes*
CESTI PRICES
Taro Tamura
Oak Ridge National Laboratory, Oak Ridge, Te LC $ 400, MN.SE
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(abstract)
.win-
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Analysis was made of the data on the analogue state
resonances in the 208 Pb (p.p.) 208pb and 208 Pb (p.p.) 208Pb*
processes in terms of an extended coupled-channel calcu-
.
lation. Rather good agreement with experiment was obtained.
The derived spectroscopic factor was also in accord....
with that obtained from a (d,p) analysis. :
RELEASED FOR ANNOUNCEMENT
' IN NUCLEAR SCIENCE ABSTRACTS
LEGAL NOTICE
This report was prepared 38 an account of Goverament sponsored work. Neither the United
States, asr the Commission, nor any person acting on behall of the Commission:
A. Makes any warranty or representation, expressed or implied, with respect to the accu-
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of any information, apparatus, method, or process disclosed in this report may not infringe
privately owned rights; or
B. Assumes any llabilities with respect to the use of, or for damages resulting irom the
use of any information, apparatus, method, or process disciceed in this report.
As used in the abovo, "per son acting on bebalf of the Commission" includes any em-
ployee or contractor of the Commission, or employee of such contractor, to the exicnt 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 lus employment with such con:ractor.

"Research sponsored by the U. S. Atomic Energy Commission under contract with
the Union Carbide Corporation.
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ANALYSIS OF THE ANALOGUE STATE RESOLIANCE IN
208Pb (p, p.) 208pb and 208Pb (p,p') 208P6 PROCESSES*
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S
by
Taro Tamura, Oak Ridge National Laboratory, Oak Ridge, Tennesse
It is known that isobaric analogue state resonances
appear in (p,p') processes as well as in (p,p.) processes”).
Analysis of the excitation functions in such resonances in
(P,P.) processes have been made, either in terms of the R-
matrix theory“) or of the coupled-channel calculations' (C.c.),
and useful spectroscopic informations were derived from such
analyses. The purpose of the present paper is to dicuss the
extention of the C.C. procedure to a combined analysis of
the (PP) and (p,p') resonances.
The coupled equations that are to be solved for that
purpose can be constructed in the following way. First we
write down the coupled equations that describe the scatter-
ing of a proton by a (core) nucleus c, chosen as a target.
We assume that the proton has an energy E. We then write
down exactly the same equation for a neutron to be bound to
a nucleus A, which is the analogue of C; A = T_C.
The energy
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"Research sponsored by the U. S. Atomic Energy Commission under contract
with the Union Carbide Corporation.
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of the neutron is given by E. = E. - A', where se is the
Coulomb energy of a proton plus the neutron-proton mass
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difference. We are interested in the case in which 4 ESO
and thus E (0. We then finall; introduce an interaction of
the form (t.T)U, (r) which couples the proton part of the
equations to the neutron part.
If these equations are solved, the cross sections for
the (P,P) and (p,p') processes are obtained. Let us assume
that we succeed in fitting the experimental excitation
functions of these prócesses in this way, and thus that
e
...
- be
appropriate values of the parameters involved in these equa-
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tions are fixed.
The next task we should do is to solve the
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neutron part of the equations, after dropping the coupling to
the proton part but keeping the above parameters as they
are. Note that the derived equations are now all in the
negative energy state, and what we shall obtain by solving
these equations is one of their eigensolutions.
Take as an example, the scattering of a proton with E ~ 15
MeV by 208Pb, and assume that the coupling of the of ground
state channel to the 3™ state (at 2.615 MeV) channel is the
only important coupling to be considered. We know that there
occurs a JT - 24 analogue state resonance in the 208 Pb + p
system for E. ~ 15 MeV. The eigensolution, that is obtained
in the last step of the calculation explained above, is nothing
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JYK-234- INYO
- 3 -
hut the eigenfunction of the + ground states of 209pb, and
at may be written as
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15/2
at = ot you in t(43-84-) ,
j=3/2
where or means the.. wave function of a state in "*°pb, '4
that of a neutron and
a vector coupling.
et suves, Y
.
If yo of (1) is normalized to unity, then
i
Bot, t - 5 y. try Par
(2)
is nothing but the spectroscopic factor, which is to have
the same meaning, and thus the same value with the spectro-
scopic factor that will be obtained from the analysis of a
208 Pb (d,p) 209 Pb (**) reaction with the angular-momentum trans-
the other hand the quantity
83-,;- - 5 43-(e)? dr
(3)
is the spectroscopic factor that is to be compared with the one
obtained from a 208Pb(3-) * (d,p) 209 Pb (at) reaction (i.e.f' an
experiment with a target in an excited state) with an angular-
momentum transfer j. Obviously the latter type of experiment:
sing
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is unfeasible, but the quantity in (3) can certainly be obtained
from our analysis.
The result of the theoretical fitting to the experimental
excitation functions,
is shown in Fig. 1, and it is seen
that the agreement is rather good. The spectroscopic factors
obtained are
Sot;2+ = 0.893,
(4.1)
83,1 = 0.027, 83-, 4- 0.0002, 83-4 = 0.004,
$3–= 0.001, 93-12 = 0.011, 93-1 = 0.009, (4.2)
$3-= 0.055.
Among the results given in (4) the value 50+,24 = 0.893 is
in very good agreement with the value S = 0.90 as obtained
in a recent preliminary analysis of a 40° Pb(d,p)
reaction®).
The reasonable fit to experiment obtained in Fig. 1, .
and the good agreement of our spectroscopic factor to the
(d,p) value seem to indicate that our approach is basically
correct, and with further more extensive calculations would
prove to be a powerful tool for the nuclear spectroscopy.
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References
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w
1.
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See e.g. G. A. Jones, A. M. Lane and G. C. Morrison,
Phys. Letters 11.,329 (1964); S. A. A. Zaidi, F. von
Brentano, D. Rieck and J. P. Wurn, Phys. Letters 19,
45 (1965).
*
2. D. Robson, Phys. Rev. 137, B535 (1965).
See e.g. T. Tamura, Proceedings of the Conference on
Isobaric Spin in Nuclear Physics, (Tallahassee, March 1966),
Academic Press, to be published.
T. Tan.ura, Rev. Mod. Phys. 37, 171 (1965).
A.M.Lane, Phys. Rev. Letters 8 171 (1962).
C. D. Kavaloski, J. S. Lilley, P. Richard and N. Stein,
Phys. Rev. Letters, 16, 807 (1.966).
.
C. F. Moor, L. J. Parish, P, von Brentano and s. A. A.
Zaidi, to be published.
.
?
G. Muehlehner, A. Poltoraki, w. c. Parkinson and P. H.
Bassel, private communication.
Captior. of Fig. 1
The 208Pb(p,p.) 208Pb and 208Pb (p,p'; 208pb* (3-) excitation
functions. The experimental data shown are part of the
data given in refs. 6 and 27. The theoretical curve is for
0 = 170°. The curve for 0 = 165° is only very slightly.
different from those for 1700.
.
2
S'+
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ORNL-DWG 66 - 6845
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208 pbt p.
O AUSTIN (470°)
• SEATTLE (4659)
ELASTIC SCATTERING
تستمتعخشمممنتنة
dolds (mb/steradian)

2.615 MeV)
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be
0.30
to
vinner 1
0.20
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0.10
ngryzatim
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13.5
14.0
15.5
16.0
16.5
14.5 15.0
ED:LAB (MeV)
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10/21 / 66



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