Neutron resonances in 45Sc and their relation to thermal scattering parameters

Volume 71B, number 2

PHYSICS LETTERS

NEUTRON

RESONANCES THERMAL

I N 45 Sc A N D T H E I R R E L A T I O N

SCATTERING

21 November 1977

TO

PARAMETERS*

R.E. CHRIEN and H.I. LIOU Brookhaven National Laboratory, Upton, New York 11973, USA

R.C. BLOCK Gaerttner Linae Laboratory, Rensselaer Polytechnic Institute, Troy, New York 12181, USA

and K. KOBAYASHI Kyoto University Research Reactor Institute, Kumatori-cho, Osaka.fu, Japan

Received 7 September 1977 The total neutron cross section of 45Sc from 400 eV to 22 keV has been measured. The results are shown to be incompatible with the postulate that a J= 4 bound state dominates thermal scattering.

Considerable effort has been made in the last few years to determine the properties of slow neutron interactions in the m o n o t o p e 45Sc. On the basis o f early experiments at Harwell [1 ], and at the MTR reactor [2], it was realized that the presence of a minimum in the neutron total cross section near 2 keV would make Sc useful as a transmission filter for the production of intense 2 keV neutron beams at reactor installations [3,4]. The exact position, and cross section, at this minimum is of importance in the design of a filter with a low contamination from high-energy neutron groups. On the other hand, a thermal neutron experiment using sophisticated polarization techniques [5] has purportedly established the thermal scattering parameters, including the magnitude and sign o f the difference in the J = 4 and J = 3 scattering lengths. This result was apparently confirmed in a measurement o f the magnetic form factor of scandium [6]. On the basis o f the early cross section work and the polarization experiment, an evaluation [7] was carried out which predicted a deep minimum with o T = 0.085 b at 2 keV. The present work was undertaken because a scandium beam filter installed at HFBR did not produce the * Work supported by the Energy Research and Development Administration under Contract No. EY-76-C-02-0016.

flux expected from the accepted cross section value. We consequently remeasured the total neutron cross section in the range o f 400 eV to 22 keV with energy resolution and beam intensities far superior to the early work. We also hoped to explain an anomalous primary 7-ray observed in thermal neutron capture [8]. The transition proceeds to a 1- level in 46Sc, and the observed strength is inconsistent with the accepted dominance o f a J = 4 level near thermal energy, predicted from the polarized neutron experiment. Three elements of the HFBR filter o f scandium and three thinner scandium samples from the same lot were subjected to neutron beams from the electron linac at RPI, and also to the fast chopper beams at BNL's High Flux Beam Reactor. The resolution o f 0.1/as FWHM for the RPI measurement was sufficiently good that resolution corrections near the 2 keV minimum were quite small. The samples had 2.54 cm diameter with thicknesses ranging from 0.2 to 30.5 cm. The H and O impurities (0.49 and 0.18 atom percent) were determined by the vacuum fusion method, and heavier elements by mass spectrometry at the ERDA Ames Laboratory. In addition the Ta content (0.015 atom percent) was checked by emission spectrography, X-ray fluorescence, neutron activation, and neutron time-of-flight spectrometry. Two separate 45Sc transmission runs were carried 311

Volume 71B, number 2

PHYSICS LETTERS

200

! A

5o

!t11

,oo

neutron width, and l ~ x the capture width. In the lowenergy limit, the scattering length aj is given by

iiJl ~"

/

I', i!!', ~ ;

lJ'

,t t

i:

~.o 0.5,

0.5

i.O

2.0

" 5;0

' io.o

20.0

E (keV)

Fig. 1. The total neutron cross section of scandium between 0.4 and 22 keV. The curve shows an R-matrix theory fit as described in the text. The primary interest centers on the broad minimum in the cross section near 2.0 keV, where we find a value for oT of 0.71 + 0.03 b. Two small p-wave resonances are apparent below 2 keV; these have negligible effect on the position or size of the 2 keV minimum. out at RPI. In one measurement a 10.2 cm scandium sample was kept in the beam to produce a filtered TOF spectrum peak at 2 keV; the other samples were cycled to obtain the cross section near 2 keV. The other measurement was a conventional transmission measurement on the thinner samples, and was designed to produce resonance parameters for the major s-wave resonances up to 20 keV. The first type was subsequently repeated at the HFBR. The 45Sc total cross section in the region between 0.4 and 22 keV is shown in fig. 1. The measured crosssection minimum occurs at an energy of 2.05 -+0.02 keV with a value of 0.71 -+0.03. This value is in sharp disagreement with the previously accepted value of 0.085 b. The total cross sections were fit with an approximate R-matrix formalism [9] known to be accurate for cases where Pabs/D
Uj(E)

Uj(E)],

= e-2ika [ i + ikaRj1,

Rj--R; +

r. /2ka x Ex

E-iP.yx/2'

with X denoting the resonance, ka the s-wave penetration factor, a the square well nuclear radius, PnX the 312

21 November 1977

aJ=[ R'J+ ~x

rnx/k , 2 ( E - E ~ ) +i['x-

whereR'j=a(1-R~f)"

These scattering lengths then determine the spin coherent and incoherent scattering at thermal energy. We have approximated the energy dependence of the distant level contribution, R ~ , within our energy range, by a second-degree polynomial. Bound levels below particle threshold were introduced to fit the total and coherent scattering cross sections. A single radiation width of 0.41 eV was selected to fit the capture cross section of 26.5 + l . 0 b at 0.0253 eV. The values for the thermal scattering and capture cross sections were those given in ref. [7]. The fit to the neutron total cross section, including resolution broadening and subject to these constraints, is shown in fig. 1. A satisfactory representation of the cross section is achieved in the region near 2 keV. For the constraints Oscatt. (0.0253) = 24.0 b, Ocoherent seatt. (0.0253) = 19.2 b, we can choose between two alternate sets for the thermal scattering lengths either (a) aj=4 = 0.688, aj= 3 = 1.939 × 10 -12 cm, or (b) aj= 4 = 1 . 7 8 2 , aj= 3 = 0.531 × 1 0 - 1 2 c m . We find our fit is consistent only with choice (a) and thus

aj=4 - aj= 3 = - 1 . 2 5

× 10 -12 cm.

This quantity was measured in a spin precession experiment using polarized neutrons incident on a polarized Sc target by Roubeau et al. [5]. The value they obtain for a j= 4 - aj= 3 = +1.2 X 10 -12 cm differs in sign from the present experiment. An attempt to produce a fit consistent with the sign of Roubeau et al. not only produces a significantly poorer fit to the cross section data, but requires highly spin dependent t ! R' parameters, for example, Rj=3/Rj= 4 ~ 8. This kind of spin dependence is implausible and can be rejected out of hand. The reason for the sensitivity of a total cross-section experiment to the sign of an amplitude may not be immediately obvious. The sensitivity arises from the interference between resonances of like spin. The result can be understood in simple terms: the region near 2 keV has a sizable J = 4 amplitude from the very large 4.33 keV resonance, along with a J = 3 amplitude from the neighboring 3.29 keV resonance. If a J = 4 bound state dominates thermal scattering, a rather

Volume 71B, number 2

PHYSICS LETTERS

Table 1 4SSc Resonance parameters s-wavelevelparameters:Fy =0.41eV Eo(eV)

Fn(eV)

J

Eo(eV)

rn(eV)

J

-500 -220 3295 4330 6684 8023 9092 10625 10735

4.0 (F~) 0.67 (F~) 75 340 130 145 300 10 6

3 4 3 4 3 4 3 3 4

11575 14525 14740 15560 15850 18580 18870 20500 20780

290 20 26 28 5 32 62 80 710

4 3 4 4 3 3 4 4 3

deep interference minimum would be expected near 2 keV, as the minima from the two resonances roughly coincide. If J = 3 scattering is dominant near thermal, however, the interference m i n i m m n will be less pronounced, since the minima do not coincide. Bolotin [8] has observed in his thermal (n,3') spectrum a primary transition to the 1- level at 142 keV in 46Sc with an intensity of ~ 10 - 3 photons/capture, thus implying a sizable 3 - component of the capturing state (a 4 - to 1- M3 would not be observed). In an independent capture ")'-ray experiment, we have confirmed the presence of this E2 "),-ray. The E2 width we calculate, from a photon intensity of 10 - 3 7's/capture and using our parameters of table 1 gives a value of r v x f = 1.2 meV as compared to a value of 0.2 meV derived from a single-particle estimate [10]. On the other hand, the E2 width calculated from the parameters of ref. [7] would yield I'vxf = 96 meV, some 500 times the s.p. value. Thus the capture 3,-ray data strongly support the idea that J = 3 scattering dominates near thermal. At our request, H. Marshak has analyzed transmission data for polarized neutrons on polarized scandium [11 ]. These data, taken at the Brookhaven Graphite Research Reactor, confirm our conclusion that J = 3 scattering is predominant near thermal. A re-examination [12] of the recent experiment by Koehler and Moon [6], also supports this result. Fur-

21 November 1977

thermore, the Saclay group [13] has now remeasured the spin-dependent scattering length and has confirmed our result. Thus it appears that the discrepancies for the thermal scattering parameters in scandium are now fully resolved. It is perhaps worth noting that, providing sufficiently accurate neutron resonance data over a sufficiently wide energy region are available, spin-dependent parameters can be determined in practice from total cross-section data. Thus transmission measurements with unpolarized beams and targets can, at least in some cases, compete favorably with the more difficult and elegant polarization studies. We wish to acknowledge discussions with P. Meriel, L. Passell, Martin Blume, H. Marshak, W. Koehler, S. Mughabghab, and B. Magurno. The assistance of B. Beaudry in the sample analysis is gratefully appreciated.

References [1] N. Pattenden, Proc. Phys. Soc. A68 (1955) 104. [2] W.L. Wilson, Dissertation, University of Idaho, unpublished, quoted in O.D. Simpson and L.G. Miller, Nucl. Instr. 61 (1968) 245. [3] O.D. Simpson, J.R. Smith and J.W. Rogers, Neutron standards and flux normalization, Nat. Tech. Information Service, Springfield, Virginia 22151 (CONF-701002) p. 362. [4] R.C. Greenwood and R.E. Chrien, Nucl. Instr. 138 (1976) 125. [5] P. Roubeau et al., Phys. Rev. Lett. 33 (1974) 102. [6] W.C. Koehler and R.M. Moon, Phys. Rev. Lett. 36 (1976) 616. [7] B.A. Magurno and S.F. Mughabghab, in: Nuclear cross sections and technology, vol. 1, National Bureau of Standards Special Pub. 425, 1975 (U.S. Government Printing Office, Washington, D.C. 20402) p. 357. [8] H.H. Bolotin, Phys. Rev. 168 (1968) 1317. [9] R.G. Thomas, Phys. Rev. 97 (1955) 224. [ 10] G.A. Bartholomew, Neutron capture gamma rays, Ann. Rev. Nucl. Sci. 11 (1962) 259. [ 11 ] H. Marshak, private communication. [12] W. Koehler, private communication. [ 13 ] P. Meriel, private communication.

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