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NATIONAL BUREAU OF STANDARDS - 1963
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i
Neutron Resonance Structure and S-Wave Strength
Function of the Even Isotopes of Zirconium*
J. A. Biggerstaff, W. M. Good, and H. J. Kim
Oak Ridge National Laboratory
Oak Ridge, Tennessee
The low values of the s-wave strength function beginning at masses Just
below mass 90 have been att:? buted, at least in part, to shell structure
effects. Lane et al. (1). and Sugie(2) :10w how the absorbtive part of the
potential can be expected to depend on the position of a given nucleus with
respect to a closed shell. In a more explicit way, Block(3) and Shakin?")
have made calculations based upon nuclear reaction theory of Feshbach and
these involve shell structure related information.
In order to furnish more detail on the role of magic number so far as
strength funci.on is concerned, we have studied the total cross sections of
the even isotopes of zirconium which have 40 protons and 50, 52, 54, 56 neutrons,
respectively. Preliminary results have been reported (5) and the present results
represent extension of the measurements to 60 keV with thicker samples. The
instrument employed is the ORNL pulsed Van de Graaff which for this type of
application operates at 1-3% energy resolution from about 2 to 60 keV. The
samples consisted of at most 12 grams at abo:at 80% purity in the case of Sozr
Research sponsored by the U. S. Atomic Energy Commission under contract with
the Union Carbide Corporation.
PATENT CLEARANCE OBTAINED. RELEASE TO
THE PUBLIC IS APPROVED. PROCEDURES
ARE ON EILE W JILE ASCOYING SECTION,
and at most 50 grams of better than 95% purity in the cases of 90,95,9*2r.
All samples were in the form of oxides.
The total cross sections versus energy in Fig. I show the resonance spectra
obtained. From the corresponding absorption spectra the level wiáths were
derived by area analysis, and the s-wave strength functions and mean level
spacings of Table I deduced. Here we have treated all resonances as s-wave
2010

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2p94
TOTAL CROSS Koton
2*
фик ооз кето
Fig. 1. Total neutron cross sections of the even isotopes oz
zirconium.
which is justified on the basis of the resonance shape up to something like
20 keV, but is not justified at the higher energies. Table I shows good
agreement between the present measurements and those of Moskalev et al.''
Table I also shows an increase in what is arbitrarily interpreted as s-wave
strength function at energies above, say, 20 keV. Angular distribution
measurements at 75 kev() show a ratio 012602 = 1.2 establishing the
0(90°)
existence of other than s-wave interactions. Fig. 2 is taken from the
2-
Teble I
Sunrary of effecti'a s-wave strength functions and average level
spacing of the even isotores of zirconium
EMO
Isotope
JE
(kev)
sa -
(20-4)
Ref. 6
Escp.
. (kev)
Present
Present
Exp.
Ref. 6
GOZI
0.85 + 0.65
4.5 $ 1.6
0.28
28 - 70
0.70
1.01 + 0.7
2.46 £ 1.2
1.82 $ 0.9
5.0 $ 1.0
9-ах
1.2 $ 0.8
1.2 $ 0.4
oto
1.20 $ 0.9
1.82 $ 0.9
1.75 $ 0.8
3.3 $ 0.7
.
gtrza
1.1 I 0.8
2.4 $ 0.9
0 - 21
21 - 44
0 - 44.
1.18 $ 1
2.84 £ 1
2.24 + 1
1.7 $ 0.3
9621
0.9 $ 0.6
0 - 5.8
5.8 - 58
058
1.0 $ 0.3
1.28 + 1
2.93 + 1
2.79 #1
0.750 £ 0.2
4.12 $ 0.8
measurements of average cross sections by

11. i
Newson et al.10) and the ORNL data show sub-
046
xhustru
stantial agreement up to 60 keV. The question
is what exactly causes the rise in average cross
section? If the p-wave is assumed to be about
the optical value of 5 x 10-4, then the rise is
substantially due to energy dependence of the
s-wave strength function. If-the s-wave strength
function is taken to have the value of about
1 x 10-4 which is predicted by the optical
model and which agrees with the experiment below
20 keV, then the p-wave strength is of the order
of 40 x 10-4. The question is essentially un-
settled but the presence of what may be p-wave


_
20 40 60 80 100 420 140
Elkev)
Fig. 2. Dnergy dependence of
the assumed s-wave strength :
function.
-3-
resonances in Fig. 1 may provide a clue.
The three resonances in
Zr that
might be said to ve most probably p-wave give for the 9-20 keV interval in
which they appear a strength function value of (75 + 65) x 10".
References
1. A. M. Lane, J. E. Lynn, E. Melkonian, and E. R. Rae, Phys. Rev. Letters 2,
424 (1959).
2. A. Sugie, Phys. Rev. Letters 4, 286 (1960).
3. B. Block and H. Feshbach, Ard. Phys. 23, 47 (1963).
4. C. Shakin, Ann. Phys. 22, 373 (1963).
5. J. A. Biggerstaff, W. M. Good, and H. J. Kim, Bull. Am. Phys. Soc. 2, 167 (1964).
6. S. S. Moskalev, H. V. Muradian, Yu. V. Acamchuk, Nuclear Phys. 53, 667 (1964).
7. R. C. Block, W. Haeberli, H. W. Newson, Phys. Rev. 109, 1620 (1958).
8. H. W. Newson, R. C. Block, P. F. Nichols, A. Taylor, A. K. Furr, and
E. Merzbacher, Ann. Phys. 8, 211 (1959).

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