Photoneutrons from 13C at photon energies up to 14 MeV

]

2.1

1

Nuclear Physics Al56

(1970) lo-

18; @ North-Holland

Publishing

Co., Amsterdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

PHOTONEUTRONS

FROM

13C AT PHOTON

ENERGIES

UP TO 14 MeV

K. FUKUDA Radiation

Center of Osaka Preflcture,

Sakai,

Osaka, Japan

Received 5 May 1970 (Revised 3 August 1970) Abstract: The photoneutron yield of 13C was measured as a function of the maximum bremsstrahlung energy up to 14.5 MeV. The cross section for the r3C(y, n)W reaction was obtained by using the inverted matrix method of Penfold and Leiss. The integrated cross sections from threshold to 10 MeV and to 14 MeV are 2 and 16 MeV . mb, respectively. These values are in agreement with earlier experiments. The cross-section curve shows peaks at 6.2, 7.5,8.2, 9.1, 11 and 13 MeV, the last two being in the pygmy resonance energy region. The angular distributions of photoneutrons were measured at different values of Eym.x. The data were analyzed for the distribution of neutrons from each peak. The significant features of the cross-section curve and the angular distributions of neutrons from the peaks are discussed and compared with the theoretical ones reported by several authors. The integrated cross section from the threshold to 10 MeV is much smaller than those calculated on the basis of a pure single-particle model. The neutrons in the pygmy resonance energy region follow a 1+0.46 sin2 8 angular distribution, while a 1+ 1.5 sin* 19distribution is expected from the single-particle picture of the pygmy resonance. These discrepancies are interpreted in terms of the mixing of core excitations and single-particle excitations.

E

NUCLEAR

REACTIONS rsC(y, n), E $ 14 MeV; measured u(E; 8); deduced integrated o. Enriched target.

1. Introduction Photoneutron disintegration of 13C has been investigated by several authors both experimentally 1 - “) and theoretically 5 -I “). The 13C(y, n)12C cross section was first reported by Cook I), who found the cross-section curve to have a secondary peak at about 13.5 MeV on the lower side of the usual giant resonance. This secondary resonance was named the pygmy resonance. Fujii “) explained the peak at 13.5 MeV on the basis of a valence neutron model. The valence neutron model has already been postulated by Guth and Mullin 11) to explain the ‘Be(y, n)aBe cross section near threshold. However, it was shown that this model was not applicable to 9Be in the higher y-ray energies above several MeV [ref. “)I. Francis, Goldman and Guth “) calculated the electric dipole transition probabilities in 13C and ‘Be at energies below 10 MeV on the basis of the similar pure single-particle model. The cross sections calculated for the 13C(y, n)12C reaction at 6.4 MeV y-ray energy, with popular nuclear potential parameters, were 3 times as large as the experimental values by Edge ‘). Those of the ‘Be(y, n)‘Be reaction 10

-C

11

PHOTONEUTRONS

were larger than the experimental values even near the threshold energy region. Several authors assumed that the core deformation or the core excitation’“2 ’ 3- ’ “) for 13C and 9Be explained the discrepancies between and the theoretical ones obtained on the basis of Barker ‘) and Aurdal lo) calculated in l’C(y, n)i3C energies below the giant resonance energy region. section curve would have several peaks in this energy

the experimental cross sections the pure single-particle model. cross section in detail for the They predicted that the crossregion. It is interesting to deter-

NEUTRON DETECTOR

MAGNET

-

LI AC

MAGNET

Fig. 1. Block diagram of the experimental

arrangement.

mine the 13C(y, n)% cross section and the angular distribution of emitted neutrons for the purposes of comparison with the theories given above. Few experimental studies on the 13C(y, n)12C reaction have been reported. Edge “) and Green and Donahue “) determined cross sections at several discrete photon energies below 10 MeV. Bertozzi et al. “) measured differential cross sections at angles of 77” and 157” for energies below 13 MeV. In the present work, the photoneutron yield from the 13C target and the angular distribution of emitted neutrons were measured for incident bremsstrahlung energies up to 14.5 MeV using a 15 MeV linear electron accelerator. A direct neutron detection system 1“) was employed. The cross sections were obtained from the yield curve by the inverted matrix method of Penfold and Leiss 17).

2. Experimental arrangement 2.1. ELECTRON

BEAM

The block diagram of the experimental equipment is shown in fig. 1. The electron beam was obtained from a 15 MeV linear electron accelerator through an analyzing system comprised of twin 70” deflecting magnets and slits. Quadrupole magnets focused the beam on the target. The beam spot was maintained within 3 mm in diameter. The energy scale of the analyzing system was calibrated to within an error of 1 % by measuring the conversion electrons of 13’Cs and photoneutron thresholds of

12

K. FURmA

bismuth and copper. The energy spread AE/E was kept to within I % throughout the experiment. 2.2. CARBON TARGET

Carbon powder of 1.45 g enriched in W, supplied from Isomet Co., USA, was sealed in a thin walled aluminium cup 2 cm in diameter by 2 cm long. The enrichment

H.T. AND SIGNAL

PARAfftN

SCATTERER

Fig. 2. Schematicdiagram ofthe neutron detector. Iwo targets. 13C target and natural carbon target% are placed in the target chamber” They move up and down in a verticaf line on the plane ofthe diagrams A part of the shield in the front face which is shown by a broken line is taken away for the measurement of angular distributions.

was proved to be 48 yi by using our mass s~ctromet~. A nickel plate 0.5 cm thick and 2 cm in diameter was used as an X-ray targe& which was followed by the carbon sampie. They were inserted in an a~urn~n~~~ cup 4 cm in diameter by 4.5 cm long. A target assembly which curtained the equivalent weight of natural carbon inst~d of 13C was also used to estimate the background counts. These two targets were set in a target chamber on a simpfe target changing device, which enabled irradiatibn of only one of them by remote control, The target chamber was set on the center of a turntable. The beam was determined to be in the center of the target by viewing the beam spot on a zinc sulfide screen with an ITV. 2.3.

NEUTRON

DETECTOR

The ~h~to~e~tr~~ yield was measured by means of a thermalized neutron detector. A schematic diagram of the counter assembly and the target chamber are shown in fig. 2. The details of the construction of the detection system have been previously reported 16). The variation in the efficiency of the detector with neutron energy was

13C

PHOTONEUTRONS

13

experimentally checked. The efficiency for random neutrons plotted as a function of neutron energy is shown in fig. 3. It was flat to within 10 oAover the range of slow neutron energy up to 5 MeV. The efficiency was 2.1 x lo- ’ counts per source neutron, when the neutron source was 15 cm from the front face of the counter assembly.

j

,k______+L+

Cl

E

yo* :

23456 1 NEUTRON ENERGY

(MeV)

Fig. 3. Efficiency of the neutron detector as a function of neutron energy in terms of counts per neutron emitted from a source 15 cm from the front face of the detector.

The neutrons from the target were counted for 900 gsec after a delay of 80 ,z+ecfollowing each beam pulse. A delay of 80 ,usec was found necessary to allow the counters and their associated circuit to recover from the effects Is) caused by an X-ray burst, and 900 psec was enough to count the diffuse neutrons. The mean life of the thermal neutrons in this setup was experimentally determined as 155 psec, hence the initial delay of 80 psec represents a counting loss of 40 %_ A Ra-cl-Be neutron source was used to check the stability of the efficiency of this detection system. The individual measurements were corrected for any variation of the efficiency from the nominal value. The counter assembly was mounted on a turntable to rotate around the target. The distance between the target center and the front face of the detector was 5 or 15 cm for the measurement of neutron yield and 15 or 20 cm for the measurement of the angular distribution. The detector used in this experiment was able to measure the neutron yield at various angles. The total neutron yield was obtained by integration. 3. Results 3.1.

CROSS SECTIONS

The neutron yield curve was measured with the detector at an angle of 90” with respect to the incident electron beam. The electron beam current was measured by using a current integrator. The neutron yield per 240 +L&was determined for the “C and natural carbon targets at 0.12 MeV intervals for maximum bremsstrahlung energies in the range 7 to 10 MeV. The maximum bremsstrahlung energy was increased successively, and this procedure was repeated 10 times. In the other energy region, the measurement was made by the same procedure at 0.25 MeV intervals. In fig. 4, the yield, counts per 234 ,uC, is plotted as a function of the maximum energy of the bremsstrahlung, and a smoothed curve is drawn through these plots. Each plot is an average

14

K. FUKUDA

neutron count of the individual measurements. The plots are normalized to the neutron counts measured with the detector set at a distance of 15 cm from its front face to the target. Errors on the yield points are less than 2 % except near the threshold energy region.

maximum

ENERGY

OF BREM~TRAHLuN~(M~v)

Fig. 4. Neutron yield curves from “C target measured with and without the X-ray target as a function of the maximum energy of bremsstrahlung spectrum. Plots on the yield curve from 7.5 to 12.5 MeV are measured without the X-ray target. A dotted line from 10 to 13 MeV shows the neutron yield resulting from photons below 10 MeV.

To calculate the net bremsstrahlung contributions, the neutron yield was also measured without X-ray target at 0.25 MeV intervals from 7.5 to 12.5 MeV. The results are also shown in fig. 4. The net bremsstrahlung contributions are calculated by the following formula: Y(E) = Y,(E)-- Y&z-LIE>,

(1)

where Y(E) is the neutron yield per electron due to photons produced in the X-ray target, E is the incident electron energy, Y,(E) and Y,(E- AE) are neutron yields measured with and without the X-ray target, respectively, and AE is the energy loss of electrons in traversing the X-ray target. The energy loss AE was estimated from the following experiment: The yield for the 63Cu(y, n)62Cu reaction was measured by the stacked foil method. The experiment was performed in two stages, as described by Barber lp). In the first stage, the target was a copper foil, and in the second the target was a stacked foil of 0.5 mm thick nickel radiator followed by a copper foil. This procedure, therefore, was the same for the measurement of the photoneutron yield of 13C. The reaction yields Y,(E) and Y,(E) were determined at 0.5 MeV inter-

‘k

15

PHOTONEUTRONS

vals for incident electron energies from 10 to 14 MeV. On the other hand Y(E) calculated using the thick target bremsstrahlung spectrum 20) and known cross tions of the 63Cu(y, n)62Cu reaction 2’). The energy loss AE was estimated from (1) to be about 0.6 MeV. This value might be considered as an effective energy in traversing the X-ray target. --

-

6

7

a

9

PHOTON

10 ENERGY

loss

COOK

GREEN

5

was seceq.

PRESENT

11

12

AND DONAHUI EXPERIMENT

13

14

(Mei’)

Fig. 5. Photoneutron cross sections for 13C. The solid line is the cross-section curve determined in the present experiment. In addition to the present data, the results of Cook I), Edge ‘) and Green and Donahue 3, are shown for comparison.

The differential cross section at an angle of 90” was calculated using the thick target bremsstrahlung spectrum and the inverted matrix method of Penfold and Leiss “). It was calculated at 0.25 MeV intervals with a bin width of 0.5 MeV. The cross section resulting from the combination of the differential cross section at 90” and measured angular distribution is plotted in fig. 5. In addition to the present data, the results of Cook I), Edge “) and Green and Donahue “) are shown for comparison purposes. 3.2. ANGULAR

DISTRIBUTIONS

The angular distributions were measured with bremsstrahlung of maximum energies of 6.8, 8.7, 10.1, 12.0 and 13.1 MeV with and without the X-ray traget. These energies were chosen as they were between the pronounced peaks of the differential crosssection curve at 90”. The neutron yield was measured at angles from 130” to 50” in 10” intervals. The angular distribution of neutrons measured at each energy could be fitted with a curve of the form a+b sin’ 0. The angular distribution of the bremsstrahlung and the scattering of neutrons in the target tend to make the observed distribution more isotropic than it actually is. Approximate corrections were made for these effects; they amounted to less than 13 %

16

K. FUKUDA

attenuation in the anisotropy coefficient of the distribution function for the worst case. The angular distribution observed is a superposition of neutrons resulting from photons of all energies up to the maximum energy of bremsstrahlung. The angular distribution of the neutrons corresponding to each peak has been calculated from extrapolated yield curves. One of the extrapolated yield curves is shown in fig. 4 by a dotted line from 10 to 13 MeV. This extrapolated curve represents the neutron yield resulting from photons below 10 MeV. The extrapolation was made by assuming that all the peaks in the differential cross-section curve have the shape of a BreitWigner resonance. For example, the angular distribution of neutrons has been found to be 1+0.43 sin ‘8 for the bremsstrahlung spectrum of 13.1 MeV maximum energy. The neutrons resulting from photons below 10 MeV is calculated to be 33 % of the total neutron counts and follow a 1 +OSl sin’ 0 angular distribution. Then, the distribution of neutrons in the pygmy resonance is calculated to be 1+0.46 sin’ 8. The angular distributions measured without the X-ray target were found to be of the same form as those measured with the X-ray target within the experimental errors, and therefore the distributions of neutrons corresponding to the Y,(E) and Y,(E-LIE) yields might be the same form. The angular distribution calculated in the aforementioned example takes no account of the contribution from Y,(E- dE) yield. Table 1 shows the observed peaks, their integrated cross sections and the angular TABLE1 Observed peaks, integrated cross sections and angular distribution

6.2 7.5 8.2

0.02 0.3 0.6

9.1 13

1.2 14 “)

functions

1+(1.7

+1.7) sir? 8

1+(1.5

hO.4) sin’ 0

1+(0.00~0.30) 1+(0.46&0.20)

sin* 0 sin’ 6

“) Integrated cross section from 10 to 14 MeV.

distributions of neutrons corresponding to the peaks. In the second column, the probable error is calculated to be 30 %, in which 10 % comes from the statistical error of the yield data, and the other 20 ‘A comes from the estimation of the photon spectrum. In the third column, the errors come from the statistical error of the yield data and the extrapolation of the yield curve. 4. Discussion In fig. 5, the cross section integrated from the threshold to 10 MeV is 2 MeV * mb. This value is much smaller than those calculated by Francis et al. “) and Aurdal lo). The increases of the cross-section curve at 7.5 and 8.2 MeV are in agreement with the predictions by Barker ‘) and Aurdal lo). The integrated cross sections of the peaks

I36

PHOTONHJTRONS

17

are in agreement with their calculated values. The neutrons from the peaks follow a 1+ 1.5 sin2 Q angular distribution, This distribution is compatible with an electric dipole transition to a d-state. These peaks are mainly due to the 3’ levels of 13C at 7.68 and 8.2 MeV [ref. ““)]_ The admixture of the ground 0’ and first excited 2’ 12C core states probably reduces the photoneutron cross sections calculated on th.e basis of the pure single-particle model where the valence neutron is coupled to the ground state of 12C. Kurath and Lawson ‘“) calculated the similar admixture using a weak coupling of a valence neutron to a deformed *2C core. The angular distribution of the neutrons from the peak at 9.1 MeV is nearly isotropic. It is inferred that this peak is mainly due to a magnetic dipole excitation of the &- level in 13C at 8.85 MeV [ref. “)], In fig. 5, the cross-section curve shows no pronounced~ak just above the threshold energy region, which was observed in the ‘Be@, n)*Be reaction. The corresponding peak in the 13C(y, n)‘%J reaction may be found to scattering cross sections for p-rays below the (y, n) threshold. The cross-section curve shows a broad peak at about 13 MeV with a shoulder at about 11 MeV; this broad peak is called the pygmy resonance. The integrated cross section from the threshold to 14 MeV is 16 MeV * mb. The neutrons in the pygmy resonance energy region follow a l-+-O.46 sin2 0 angular distribution, while a 1 + 1.5 sin2 @ distribution is expected from direct interaction calculations “*). The main part of the pygmy resonance has been assigned to a group of positive parity levels at about 13 MeV which are excited by electric dipole absorptions ‘-‘*). The shape of the cross-section curve is in agreement with those theoretical calc~ations. The angular distribution observed can be explained by the contributions from the neutrons which are produced through decays of the +* levels to the first excited 2” state of 12C! There is a level in 13C at 11.0 MeV [ref. ““)I, whose spin-parity is assigned to be Q’. The neutrons from the 3’ level follow an isotropic distribution. This level will contribute to an increase of the cross-section curve at 11 MeV. In this energy region, theoretical calculations ‘-lo ) aIso predicted the appearance of 8’ levels, which decays by neutron emission leaving 12C in its first excited state. The comparison of the experimental and the theoretical results suggests that the main part of the pygmy resonance may be explained in terms of the mixing of core excitations and valence neutron excitations, The mixing probably reduces the photoneutron cross section below 10 MeV calculated on the basis of a pure single-particle model, l

The author would like to express his cordial thanks to Dr. K. Kimura and Dr. T. Azuma for their advice and encouragement throughout the course of this work. He would also like to thank Dr. S. Okabe for his advice, and Mr. Y. Sato for his assistance in performing the experiment. He is also greatly indebted to members of the linear accelerator group of this laboratory for their valuable help in operating the machine.

18

K. FUKUDA

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24)

B. C. Cook, Phys. Rev. 106 (1957) 300 R. D. Edge, Phys. Rev. 119 (1960) 1643 L. Green and D. J. Donahue, Phys. Rev. 135 (1964) B701 W. Bertozzi, P. T. Demos, S. Kowalski, F. R. Paolini, C. P. Sargent and W. Turchinetz, Nucl. Instr. 33 (1965) 199 S. Fujii, Prog. Theor. Phys. 21 (1959) 511 N. C. Francis, D. T. Goldman and E. Guth, Phys. Rev. 120 (1960) 2175 F. C. Barker, Nucl. Phys. 28 (1961) 96 B. R. Easlea, Phys. Lett. 1 (1962) 163 D. F. Measday, A. B. Clegg and P. S. Fisher, Nucl. Phys. 61 (1965) 269 T. Aurdal, Z. Naturf. 24a (1969) 461; 24a (1969) 1361 E. Guth and C. J. Mullin, Phys. Rev. 74 (1948) 833; 76 (1949) 234 J. H. Carver, E. Kondaiah and B. D. McDaniel, Phil. Mag. 45 (1954) 948 J. S. Blair, Phys. Rev. 123 (1961) 2151 T. Aurdal, Z. Naturf. 24a (1969) 1188 S. Boffi, F. D. Pacati and J. Sawicki, Nuovo Cim. 52B (1967) 244 K. Fukuda, S. Okabe and Y. Sato, Nucl. Instr. 60 (1968) 297 A. S. Penfold and J. E. Leiss, Phys. Rev. 114 (1959) 1332 K. Fukuda, S. Okabe and Y. Sato, Nucl. Instr. 50 (1967) 150 W. C. Barber, Phys. Rev. 111 (1958) 1642 A. S. Penfold, University of Illinois report, unpublished (1954) S. C. Fultz, R. L. Bramblett, J. T. Caldwell and R. R. Harvey, Phys. Rev. 133 (1964) Bi149 Nuclear Data Sheet, compiled by K. Way er al. (US Government Printing Office, National Academy of Sciences National Research Council, Washington 25, DC, (1961) NRC 61-5,6-161) D. Kurath and R. D. Lawson, Nucl. Phys. 23 (1961) 5 E. D. Courant, Phys. Rev. 82 (1951) 703