Neutron energy determinations

X&%rr Physics A134 (I 969) 361-368;

@ ~o~~~-~o~ta~d ~~lis~iag

Co., Amsterdam

Not to be reproduced by ph~toprint or microfilm witbout written permission from the publisher

LUMEN

ENERGY DE~R~A~ONS

J. C. DAVIS and F. T. NODA Universify of Wisconsin, Madison, Wisconsin t Received 19 June 1969 Abstract: Neutron energies in the range 3-8 MeV were measured to 0.1 % accuracy. The effects of energy losses in targets and gas cell entrance windows were investigated. Narrow resonances in the interaction of fast neutrons with light nuclei were located with neutrons from the 3H(p, n), ‘Li(p, n) and 2H(d, n) reactions.

E

1. Introduction Neutron energies above 3 MeV at which structure in neutron cross sections has been reported differ in some cases by amounts which are several times the uncertainties quoted for the energy determinations. Neutron energies may be calculated either from the kinematics of the source reaction used or from the measured neutron time of flight. Discrepancies occur both between measurements using the same method of energy determination and between measurements using the two different types of energy determination. An example of such discrepancies is shown in fig. 1. Three measurements ‘-‘) of the neutron total cross section of “C between 7 and 8 MeV are shown. In the experiments of refs. 1, 2), the ‘H(d, n ) reaction served as the neutron source, while the results of ref. “) are based on neutron time-of-flight measurements using a neutron source which produces an energy continuum. Although some of the difference in structure positions might result from the differences in energy resolution in the various experiments, the 80 keV shift between the results of refs. X*“)is larger than the quoted uncertainties. In the present investigation, an attempt was made to improve the determination of neutron energies above 3 MeV by using mono-energetic neutrons from the following three source reactions: 7Li(p, n), “H(pp n> a nd ‘H(d, n>. For a11three reactions, the Q-values are well enough known that their uncertainty does not contribute significantly to the uncertainty in the calculated neutron energy. Errors in neutron energy then result from uncertainties in the energy of the bombarding charged particfes and in the properties of the target. A particularly important cause of uncertainty t Work supported in part by U.S. Atomic Energy Commission. 361

362

1. C.

DAVIS

AND

F. T. NODA

is the energy loss in the foils used to separate gas targets containing the hydrogen isotopes from the vacuum system. All these effects which may cause errors in energy determinations

were studied

in the present

.-.--0.5-

7.0

I

Fig. 1. Values of the total cross

’

’

section

work.

Fosson et ol.,Wisconsin Moncro et al, tiarwcll GlosgawFostcr.Hanford

’ ’ 7.5 N@utron Entrqy

’

’ 8.0

’

’

-

of 12C between 7 and 8 MeV determined at various laboratories.

2. Experimental 2.1. DETERMINATION

’ tUrV)

OF CHARGED-PARTICLE

procedure ENERGIES

A calibration factor may be determined for the analysing magnet which serves to measure charged-particle energies by locating accurately known reaction thresholds. For a threshold of energy E observed at NMR frequency f, the calibration factor is given by k

(f)

=

m,E(1+Wmoc2)9

f2q2

where m, and q are the rest mass and charge of the bombarding particle. Since the Wisconsin EN Tandem was installed shortly after the first tandem at Chalk River and since the design of the analysing magnet and nuclear magnetic resonance probe was the same for the two machines, it was assumed that the two magnets would have similar calibrations. The calibration factor reported “) for the Chalk River magnet was (2.008 &0.002) x IO-’ MeV - amu/(MHz)’ independent of field. A check of the 13C(p, n) and the “Al(p , n) thresholds at this laboratory “) yielded the same calibration factor. This field-independent calibration had been assumed for the Wisconsin magnet for many years. However, currently recommended threshold energies “) differ somewhat from the values used in the Chalk River calibratioo (particularly for the r60(d, n) threshold), and their use makes it somewhat doubtful that the calibration factor determined at Chalk River was actually independent of the field. The analysing magnet of the Wisconsin accelerator was, therefore, recalibrated over the equivalent proton energy range 2-25 MeV by locating the thresholds of the

NEUTRONENERGY

363

DETERMINATIONS

(p, n) reactions on ‘Li, 13C, “F, “Al, 54Fe and ‘*Ni and the ‘H(160, n) threshold for oxygen charge states -t 3 and +4. The threshold of the 160(d, n) reaction was also located to see if it gave a result consistent with the low-energy (p, n) thresholds. All data were taken with analyser entrance and exit slit separations of 0.06 cm. Before taking data, the analysing magnet was run through several current cycles to eliminate differential hysteresis effects. Table 1 lists the values of the calibration factor determined for each threshold. The threshold energies used in all calculations were those recommended by Marion 6). TABLE

Calibration Reaction

‘Li@, n) ‘WP, n) 160(d, n) “F(P, n) “Al(p, n)

S4Fe(p, n) 58Ni(p, n) ‘H(r60, n) q = +4 4= +3

Threshold energy (keV)

Threshold frequency (kHz)

1880.06&0.07

3235.7 1829.2 4234.3 5796.9

1

points

kO.7 ho.6 *0.8 k3.8

9738* 12760& 13560+ 14598& 17072f 17069+

Radiation detected

2 2 3 2 5 4

neutrons neutrons neutrons neutrons

9202.7 k4.8 9515.2 12.9

21494& 2 218601 3

511 keV gammas positons positons

14525.4 14.8 14525.9 h4.8

26832f 8 35754f15

neutrons neutrons

W) (10v2MeV u/MHz’) 1.9996f0.0008

2.0058f0.0008 2.0041 kO.0012 2.0061 f0.0006 2.0098~0.0018 2.0104f0.0014

2.0179f0.0014 2.0203 +0.0018

Fig. 2 shows the calibration curve for the analysing magnet. The curve was obtained by fitting a straight line through the points from the (p, n) reactions and then drawing a smooth curve from that line through the ‘H(160, n) points. All points except that from the 13C(p, n) reaction lie within kO.05 % of the resulting curve. This uncertainty is consistent with the value expected from the analyser slit settings and is taken to be the accuracy with which charged-particle energies can be determined with the present equipment. The previously used calibration is shown by the horizontal dashed line in fig. 2. The dependence of the calibration factor on field strength probably results from the location of the NMR probe near the edge of the pole pieces. The new calibration removes some inconsistencies previously observed in measurements at this laboratory. Hardie et al. ‘) first observed two narrow isospin forbidden resonances in the scattering of protons from 160 at energies of 12.671 and 13.215 MeV. Subsequent measurements at Rutgers “) and at the California Institute of Technology ‘) reported the lower of these resonances to be about 45 keV higher in energy. The new calibration changes the energies of the resonances observed by Hardie et al. to 12.732 MeV and 13.280 MeV. Since Hardie et al. did not attempt precise measurements of the resonance positicns, the adjusted value for the position of the lower resonance is consistent with the other determinations.

364

J.

C. DAVIS

AND

F. T. NODA

Another inconsistency was observed at this laboratory in measurements of neutron total cross sections lo). Structure in the energy dependence of the cross sections near 6 MeV appeared to occur 20 keV higher in energy when the neutrons were produced by the “H(d, n) reaction than when the 3H(p, n) reaction was used. The new calibration reduces this apparent difference to 10 keV which is within the uncertainty of the energy determinations in the cross-section measurements. 2.2. RESONANCE

PEAK DETERMINATIONS

Neutrons from the ‘Li(p, n), 3H(p, n) and ‘H(d, n) reactions were used to locate sharp resonances in the 12C and I60 neutron total cross sections and in the 20Ne(n, a) cross section. Lithium metal targets were evaporated onto tantalum backings inside the beam tube. Targets of tritium absorbed in a thin layer of titanium evaporated

Fig. 2. Calibration

curve for the analysing magnet. The previously calibration is shown as a dashed line.

assumed field-independent

onto a copper backing were obtained commercially +. Gas target assemblies similar to those described by Fowler and Brolley 11) were used to contain deuterium or tritium. Thicknesses of the lithium and T-Ti targets were determined from the 0” neutron yield above threshold. The possibility of non-uniformity of tritium within the titanium layer was investigated by locating narrow resonances in the 160 total cross section below 2 MeV with neutrons from this target. The resonance positions obtained agreed to 2-3 keV with the results of high-resolution measurements at Oak Ridge 12), thus indicating that there was no significant non-uniformity in the distribution of tritium through the titanium. Target thicknesses for the gas cells were calculated from the pressure of deuterium or tritium used, usually less than 0.2 atm. Energy lost by the beam in the 0.76 i.rrn Ni foils used as entrance windows on the gas cells was determined by observing the t Purchased from the Radiochemical Centre, Amersham, Buckinghamshire,

England.

NEUTRON

ENERGY

365

DETONATIONS

shift in the 0” neutron yield curve from the ‘Li(p, n) reaction at threshold when the foils were placed in the proton beam. The energy loss at Ep 2 MeV was scaled to the desired proton or deuteron energy using tabulated 13) values of stopping power. The average energy lost by the beam in the foils was found to be IO-20 % greater than the values calculated using the nominal foil thickness and the stopping power taken from Janni’s tables 13) or calculated from the Bethe-Bloch formula. Energy straggling in the foils was 20-40 y0 greater than expected, probably because of variations in foil thickness, The energy spread of neutrons from the ‘Li(p, n) reaction was kept below 10 keV by proper choice of target thickness. Neutrons from the 3H(p, n) reaction on the T-Ti target had an energy spread of about 12 keV between 4 and 7 MeV. For the gas targets, the energy spread was 20 keV for 3H(p, n) neutrons and 25 keV for ‘H (d, n) neutrons. 3. Results 3.1. TOTAL CROSS-SECTION

RESONANCES

Resonant structure in the lzC and 160 neutron total cross sections was observed with neutrons from the different sources by measuring the transmission of graphite and Be0 sampIes to better than 1 y0 statistical accuracy over the resonance regions. Resonance peak positions determined from these measurements are shown in table 2. The standard error listed for each determination is a quadratic sum of uncertainties in charged-particle energy, target and foil thicknesses, counting statistics and alignment at 0”. Determinations with different sources are consistent within the stated errors. TABLE 2 Resonance peak positions with different sources (keV)

‘Li(p, n)

gas target

‘Wd, u) gas target

4934+6 5369f6 6291&7 775.518

7763&S

5914&6 6394&7 6801 Ifr7 7196&S

6397&10 6811& 9 7204f 9

‘WP, n) T-Ti carbon

4935&4 5369&S 6297&S

493415 536635 6293&6 oxygen

3764*3 5123f4

3766&4 5120*5 5914f5 6394&-7 6808 f7

Table 3 compares the rest&s of this work with the earlier measurements performed at this laboratory “) both as originally reported and after correction for the change in

J.

366

C. DAVIS

AND

F. T. NODA

analysing-magnet calibration. Also shown are results of recent high-resolution total cross-section measurements performed at Karlsruhe 14), where neutron energies were determined from time of flight over a 57 m path. Peak positions were taken from a listing of the cross-section data. No energy uncertainty is quoted for these measurements, but the FWHM resolution of the spectrometer varied from 14 to 36 keV between 4 and 8 MeV. As the sources of error are entirely different for the Karlsruhe results and this work, the good agreement between the two sets of determinations is particularly significant. Values of the excitation energy of the compound nuclei 13C and I’0 corresponding to the energies determined in this work are also shown in table 3. TABLE

3

Resonance peak position determinations Wisconsin *)

This work

original

(keV)

Karlsruhe “)

shifted

4935 f4 5368&5 6294&5 7759&g

4930 5360 6270 7730

carbon 4940 5370 6290 7750

4935 5369 6293 7755

9499 9899 10753 12104

3765&3 5122&4 5914*5 6395 f7 6807&7 7200&8

3770 5110 5900 6390 6790 7180

3770 5120 5915 6410 6810 7190

3764 5119 5909 6390 6804 7203

7684 8960 9705 10158 10545 10915

“) Ref. I). b, Ref. 14).

Fig. 3 shows the results of a new measurement of the 12C total cross section between 7 and 8 MeV. The earlier results obtained at this laboratory ‘) have been corrected for the calibration change, and the results of the Karlsruhe measurements have been included. Although the neutron energies were carefully determined in the present study, no attempt was made to determine the cross sections accurately. The agreement with the energies determined in the previous Wisconsin measurements is satisfactory. Good agreement is obtained with the Karlsruhe results, but there is a 4-8 % difference in the magnitude of the cross section. The present energy determinations and the Karlsruhe measurements, however, disagree with the results obtained at Harwell “) and Hanford “). 3.2. RESONANCES

IN *ONe(n, c()

In previous measurements at this laboratory 1‘), sharp resonances in the “Ne(n, LX) reaction had been found between 6 and 10 MeV. Positions of the two most prominent

NEUTRON

ENERGY

367

D ETERMINATIONS

2.0 -

0 - -.-.------

bti 1.0 -

45

Present Work Fossan et al, Wisconsin Manero et al.. Howell Glas9or 6 Foster, Hanford Clerjacks et al., Karlsrune

1.5

NEUTRON

ENERGY

IMeW

Fig. 3. Total cross section of “C between 7 and 8 MeV. The results of the present work and of measurements at Karlsruhe a*) have been added to the data shown in fig. 1.

0 ‘H

l0.n)neutrons

6.0

NEUTRON

Fig. 4. Count-rate curves for *ONe(n, ao+a,)

ENERGY

( MeV)

taken with the ‘H(p, n) and ‘H(d, n) source reactions

Fig. 5. Count rate curve for ‘ONe(n, a) taken with ‘Lib,

n) neutrons.

368

J. C. DAVIS

AND F. T. NODA

resonances near 6 MeV gas targets. In fig. 4 the section are shown. The 6289-&6 keV and 6552

were determined with 3H(p, n) and ‘H(d, n) neutrons using counting rates observed for the 20Ne(n, a0 + ar) partial cross resonance positions obtained with the 3H(p, n) neutrons were +6 keV, while measurements with 2H(d, n) neutrons gave 6286+9 keV and 6554f 9 keV, respectively. Shamu ’ ‘) reported energies of 6.3 1 and 6.58 MeV for the resonance positions. Correction for the calibration change would raise these energies 5 keV, but 10 keV should be subtracted because of the large halfangle subtended by the gas scintillator for Shamu’s measurements. The agreement of our determinations and Shamu’s results is satisfactory as his data were taken with a 60 keV energy spread and wide analyser slit settings. A “Ne(n, a) resonance near 3.2 MeV was used as a neutron energy standard in the measurement of the n-p total cross section performed at Columbia 16). The resonance was located with ‘Li(p, n) neutrons at 3184f3 keV in disagreement with the Columbia result of 3200+6 keV. The target used was 6 keV thick for the incident protons. A count-rate plot is shown in fig. 5. Our value for the resonance position is in better agreement with an earlier measurement at Rice “) that gave 3190 keV. The effect of this change in energy upon the n-p singlet effective range deduced from the cross-section measurement has been discussed in a previous note la). References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18)

D. B. Fossan, R. L. Walter, W. E. Wilson and H. H. Barschall, Phys. Rev. 123 (1961) 209 F. Manero, B. H. Armitage. J. M. Freeman and J. H. Montague, Nucl. Phys. 59 (1964) 583 D. W. Glasgow and D. G. Foster. Jr., Bull. Am. Phys. Sot. 8 (1963) 321 H. E. Gove er al., Phys. Rev. Lett. 1 (1958) 251 P. Dagley, W. Haeberli and J. X. Saladin, Nucl. Phys. 24 (1961) 353 J. B. Marion, Rev. Mod. Phys. 38 (1966) 660 G. Hardie. R. L. Dangle and L. D. Oppliger, Phys. Rev. 129 (1963) 353 R. Van Bree and G. M. Temmer. Bull. Am. Phys. Sot. 12 (1967) 518 J. R. Patterson, H. Winkler and C. S. Zaidins, Phys. Rev. 163 (1967) 1051 A. D. Carlson and H. H. Barschall, Phys. Rev. 158 (1967) 1142 J. L. Fowler and John E. Brolley, Jr., Rev. Mod. Phys. 28 (1956) 103 C. H. Johnson er al., National Bureau of Standards Publication 299. Washington, D.C., 1968, Vol. II, p. 851 Joseph F. Janni. Technical Report No. AFWL-TR-65-150, Clearinghouse for Federal Scientific and Technical Information (1966) S. Cierjacks er ul., EANDC (E) - 11I “U” (1968) R. E. Shamu, Nucl. Phys. 31 (1962) 166 C. E. Engelke. R. E. Benenson, E. Melkonian and J. M. Lebowitz, Phys. Rev. 129 (1963) 324 E. J. Bell, T. W. Banner and F. Gabbard, Nucl. Phys. 14 (1959) 270 J. C. Davis and H. H. Barschall. Phys. Lett. 27B (1968) 636