Photoneutron cross sections of 208Pb and 197Au

Nuclear Physics A159 (1970) 561--576; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

PHOTONEUTRON CROSS SECTIONS OF 2°gPb AND l~Au A. VEYSSIERE,

H. BELL, R. BERGERE, P. CARLOS and Centre d'Etudes Nucl~aires de Saclay, France

A. LEPRETRE

Received 8 July 1970 Abstract: Partial photoneutron cross sections a.r. °, try. 2., try.3, and try,.4, of 2°SPb and t97Au were

measured using a monochromatic photon beam and a neutron detecting system capable of analysing directly and simultaneously interactions of the type (3', xn) in the photon energy range 6 MeV _~ E ~ 35 MeV. Nuclear information extracted from these data includes threshold values, integrated cross sections and giant dipole resonance parameters obtained by means of Lorentz line fitting. A tentative analysis of the structure observed on the rising shoulder of the giant resonance of 2°spb is presented. The level density parameters a as well as the non-statistical neutron contributions obtained from a study of the competition between the (3', n) and 0', 2n) decay modes, are also given. E

I

N U C L E A R REACTIONS t97Au, z°SPb(3', n), (3', 2n), (3', 3n), (y, 4n), E = 6--35 MeV; measured o(E); deduced integrated a. 19~Au, 2°SPb deduced giant resonance parameters.

I

1. Apparatus and experimental procedure Results presented in this paper have been obtained from experiments performed with the photon-monochromator developed by Tzara and his collaborators at the 45 MeV linear accelerator at Saclay 1). A detailed description of the measurements of the photon energy resolution AE/E and of the number of "quasi-monochromatic" photons traversing the photonuclear target has been given elsewhere 2,3). A summary of the general technique is given here. Positons are created in a gold target then deflected and energy analyzed by means of a set of three magnets and a slit of variable width. On passing through an annihilation target of lithium metal of variable thickness some of the positons are annihilated-in-flight thus creating a"quasi-monochromatic" photon beam of energyE. The remainder are swept out of the photon beam and captured in a Faraday cup 2-4). As demonstrated by a series of recent experiments using the 2SSi(v, po)27Al interaction 2), this apparatus can produce a photon beam having FWHM values AE within the following limits:

[(0005E)2+(

r)2]½ =< AE =< [(O 02E)2

r)2]~',

where (0.02E) 2 and (0.005E) 2 are terms given by the particular energy resolution of the electromagnetic deflection system for a given slit value and AEr is the energy loss of positons in the chosen Li target. 561

A. VEY,~IERE e t al.

562

For the detection o f structure in the low-energy part of the giant resonance o f 2°sPb, the F W H M o f the incident "quasi-monochromatic photon beam" was determined to be AE = 140 keV around E = l0 MeV; in this particular case, covering the energy region 7 MeV < E < 11 MeV, energy intervals of 135 keV were used. For E > 11 MeV the experimental photon resolution decreased regularly as E increased and attained approximately AE = 400 keV for E = 25 MeV.

0.6

o" b

P a r i" ia I cross-slctions

2o8pb

...... --o--

82.

0.5

~

r.z.

~.Sn

~'.4n

0.5

\

0/,

illll

-,

pe 7 8

I I i, t/~ 9 10 71 llZ "13"~z, 15 16 17 18 19 20 21 22 "Z7~4 7~" 26 27 28 ?9 50 PII~]

Fig. 1. Partial photoneutron cross sections ~7, "' cry, =o, ey, a., and (~y.4° of =°Spb. We also show the descending part o f the unique Lorentz line giving the best fit to the experimental (~y.T(E) curve.

o, b

,,:Ao

O.~ /

k

ParHal cro s s_ secHons

/

8

10

"k,

1Z

14

16

~

18

1Loreniz line

Z0

ZZ

24

Z6 PleV

Fig. 2. Partial photoneutron cross sections (~:,,., cry, =. and ~7, 3° of 19~Au. We also show the descending part of the unique Lorentz line corresponding to parameters tpven in table 3.

563

PHOTONEUTRON CROSS SECTIONS

0.6

o" b

20e~

,"~'~

0.5 ... Lorzntz. line

~~

.

0.4

0.5

0.2

0.1

6

9

I0

II

IZ

15

14

15

16

17

18 I'lcV

i

Fig. 3. Total photonuclear cross section try.r (E) of 20Spb and best Lorentz line fit corresponding to parameters given in table 3.

0..~ o - b

/ /

0.~

197

~

7sAu

\

Totol

cros._.___~ss, s s c t i . o_n

•

.Po,o,,

0.5

02

I

t I

0.I

tt t t

iiIIII ' 8

I0

li

Ik

16 lg

10 ?-/2. 14

2-6

NeV-

Fig. 4. Total photonuclear cross section (re.T(E) of ~97Auand best Lorentz line fit corresponding to parameters given in table 3. All targets were discs having a diameter of 12 cm. The lead target, m a d e of radiogenic lead, c o n t a i n e d 91 ~o of 2°Spb a n d 7 ~ of 2°TPb a n d h a d a thickness o f 3.91 g - cm - 2 whereas the gold target h a d a thickness of 5 g . cm -2. Partial cross sections

564

A. VEYSSIERE

et al.

[a~, . + a y , .p]~ a~, 2., a~, 3. and ay. 4. were measured separately and simultaneously using a m e t h o d described in ref. 4). I n figs. 1 a n d 2 we show our experimental partial p h o t o n e u t r o n cross sections for 2°spb and 197Au respectively. The corresponding total cross sections a ~ , . + % , . p + a ~ , 2 . + % . 3 . + % , 4. ~ atoll ( E ) f o r 2°spb and x97Au are given in figs. 3 and 4, respectively.

2. Giant resonance parameters and structure

2.1. THRESHOLDS Partial cross section curves ~ry.xn (E) allow us to determine the threshold values o f the corresponding reactions. Tables 1 and 2 show our experimentally obtained threshold values for 2°spb a n d 197Au respectively. A recent energy calibration o f our p h o t o n m o n o c h r o m a t o r , using well-known thermal neutron capture y-rays, enabled us to detect a non-lineaxity o f the m e a n TAnLE 1 Threshold values obtained from our z°aPb(y, xn) reactions compared with values found in the literature 2°spb

•)

Eth(Y, n) (MeV)

Refs. 6) 2°aPb 2Oypb 2°6pb

b)

7)

b) b)

a) present work

Era(7, 2n) (MeV)

Etb(Y, 3n) (MeV)

Eth(Y, 4n) (MeV)

14.110 14.194=1=0.05

22.192 22.284=1=0.12

28.926

14.01 4-0.14 14.1 4-0.1

22.5 4-0.5

304-1

7.376 7.404=1=0.028 6.7904-0.023 8.09 4-0.07 7.40 4-0.07

") Compiled from nuclear reaction Q-values. b) Experimental photonuclear results. TABLE 2 Threshold values obtained from our t97Au(y, xn) reactions compared with values found in the literature 197Au

•) b) b) b)

Refs. 6) 9) ~) present work

Eth(y, n) (MeV) 8.083 8.057±0.022 8.100-4-0.070

") Compiled from nuclear reaction Q-values.

Eth(y, 2n) (MeV)

Eta(Y, 3n) (MeV)

14.76 14.5-4-0.5

23.17

14.7=1=0.100

23.6 =t=0.5

b) Experimental photonucleax results.

PHOTONEUTRONCROSSSECTIONS

565

energy of our quasi-monochromatic photons as a function of the annihilation target thickness for energies below 10 MeV. It thus turns out that the apparent 2°spb(V, n) threshold value of 7.04 MeV published recently s) ought to be corrected to 7.28_ 0.07 MeV. Moreover if we now take the inherent width of our beam into account we find a new 2°spb(y, n) threshold value of 7.40+0.07 MeV which is in good agreement with 7.376 MeV as given by Mattauch et al. ~). The remaining threshold values for 2°spb and 197Au also agree with those given by Mattauch. 2.2. RESONANCE PARAMETERS The fitting of the total photonuclear cross section curve in the giant resonance region with a suitable mathematical expression is still an open question 10). Nevertheless a certain number of theoretical considerations concerning this problem have been developed. Danos and Greiner 11) attempted to describe the form of the absorption cross section O'fi(E) generated by the absorption of E 1 photons by a single isolated level, by means of an expression containing a Breit-Wigner term rfi/[(~,i - E) 2 + ¼r,~l1. Considering the El absorption of a photon as a doorway state whose strength is subsequently distributed through a succession of residual interactions among actual compound states in the energy interval Ffi around En, the above formalism gives results identical to those obtained by Lemmer 12) or Mahaux and Weidenmuller 13) using the "resonant scattering theory" including the existence of only a single doorway state. Then again Danos and Greiner 14,1s) pointed out that since the photon has no rest mass, time invariance considerations induce one to choose a function 0f(E) having symmetric energy poles with respect to the imaginary axis. Talcing the specific case of a single resonance f, and using some approximations such as setting Ff = constant, one is then led to adopt a so called Lorentz curve given by:

(Erfy +(Er,y"

o'f(E) ~- C ( E ~ - E 2 ) 2

(1)

This formula reminds us of the classical mathematical expression used in electromagnetism for the energy absorption by a tuned dipole antenna or the formula used to describe the classical scattering by an oscillator 16). Moreover the use of the above description technique allows Danos and Greiner to consider the photon absorption cross section as a superposition of a number of individual Lorentz lines. Furthermore, the standard assumption [see e.g. Hayward 17)] that for medium and heavy nuclei, there exists a complete overlap of the single levels in the giant dipole resonance implies that the absorption cross section can be approximated by the following Lorentz shape: E2F2 (2)

566

A. VEYSSIEREe t al.

where at is the maximal value of total cross section for E = E1 and F1 is an arbitrary parameter characterizing the decay mechanism is). Finally it should be remembered that the above approximate representation of the giant resonance for heavy spherical nuclei by a unique Lorentz line and for heavy deformed nuclei by two Lorentz lines, has generally been adopted by most authors. Harvey et al. a) used this approach in their study of the giant resonance of the lead isotopes and Fultz et al. 9) for their research on 197Au. The same point of view has also been used by Hayward xT), H u b e r t s), Davidson 19) and Spicer 20) in their review papers on the giant resonance. In this paper the best Lorentz line fits to the absorption cross sections of 2°spb and x97Au were obtained by means of a direct adjustment of the Lorentz line parameters and the results are shown in table 3. These parameters are in good agreement with the hydrodynamic model as applied to the giant resonance in heavy nuclei. This model predicts that for a spherical nucleus such as 2°apb, a single Lorentz line centered on the theoretical value of E ' = 80 A -~ = 13.5 MeV ought best to fit the giant resonance 17). Similarly, theory predicts a best fit for the 197Au nucleus at E " = 13.75 MeV. As can be seen from table 3, our experimental results are in good agreement with these values. TABLE 3 Lorentz line parameters for a°sPb and t97Au corresponding to fits shown in figs. 3 and 4

20apb 197Au

at (mb)

E, (MeV)

640 540

13.42 13.70

F'l (MeV) 4.05 4.75

The fact that we observe a t (Au) < a 1 (Pb) and r 1 (Au) > Ft (Pb) suggests a certain amount of deformation in the Au nucleus, which in turn ought to make a two-line fit possible 21). Thus a reasonable fit can also be obtained with the following two Lorentz lines: E t = 13.17 MeV,

E 2 = 14.17 MeV,

F t = 3.2 MeV,

F 2 = 5.2 MeV,

crI = 222 mb,

a2 = 367 rob.

The ratio (r2F2/crtF t --- 2.7 indicates that the 1 9 7 A u nucleus is a prolate spheroid possessing an intrinsic quadrupole moment Qo = 2.5 +__0.5 b as computed from the following relations 21): E2/E 1 = 0.911d+0.089, Qo

2

2A ~ d2-1

= 3-ZR 0

d~

2.3. S T R U C T U R E

The first experimental results for 2°apb obtained by Miller et al. 1) with monochromatic v-rays showed that a reasonable fit could be obtained with one single

PHOTONEUTRON CROSS SECTIONS

567

Lorentz line. Harvey et al. a) also working with monochromatic v-rays confirmed this result but found a small deviation in the fit at about 11.5 MeV. Using bremsstrahlung techniques, Fuller and Hayward 22) found that the rising slope of the giant resonance in 2°spb showed several discrepancies from a single Lorentz line fit at excitation energies of about 9.2 MeV and 12 MeV. Somewhat later Tomimasu 23) found indications of structure at 11 MeV but did not confirm the structure at 9.2 and 12 MeV. Goryachev et al. 24) also detected structure at roughly 9 and 11 MeV. Using bremsstrahlung photons identified in energy by means of the tagging technique, Calarco 25) also found structure in the vicinity of 11.5 MeV and 10 MeV. Our experimental results given in figs. 1 and 3 show obvious structure on the lowenergy side of the giant resonance; peaks are evident at 7.6 MeV, 8 MeV, 8.3 MeV, 9.9 MeV, 11.2 MeV and probably at 11.8 MeV. The peak at 9.9 MeV has an estimated FWHM of ~ 500 keV. Theoretical studies of electric dipole absorption in 2°spb have been made by Gillet et al. 26) and Balashov et al. 27) using the shell model and the particle-hole formalism. The results of such calculations show the typical dipole states distribution as predicted by the schematic model of Brown and Bolsterli 28), the dipole absorption strength being essentially concentrated at high energies whereas the dipole states around 8 MeV are very nearly denuded. The fact that Balashov et al. obtain a concentration of dipole states closer to the experimental value of 13.5 MeV than Gillet, who predicts them roughly 2 MeV lower, is due to the fact that Balashov assumes somewhat higher initial energies for the unperturbed particle-hole excitations and uses a different form of residual interaction. Recently Dover and Hahne 29) have shown that the coupling between lp-lh, J~ = 1- states and the continuum did not greatly alter the energies of the configurations contributing to the giant resonance formation. It thus seems as if no satisfactory explanation of the type of structure seen in our experiments has been proposed so far. It might be possible that a coupling between quasi-bound np-nh and lp-lh states would give a correct interpretation of our observed structure. Such an interpretation developed by Gillet et al. 30) was in fact shown to be correct for 1~O but has not yet been applied to 2°aPb. Nonetheless we shall examine the special case of the first structure peaks at 7.6-8 and 8.3 MeV since these can be correlated with data obtained from other types of experiments. Using bremsstrahlung photons with an endpoint energy just above the (V, n) threshold B, in the photonucleax reaction 2°spb(~, n)2°7pb, Bertozzi et al. al) and more recently Bowman et al. 32), measured the energy spectrum of the emitted photoneutrons. If one assumes that all photoneutrons are emitted directly to the 2°7pb ground state then such experiments allow a precision in the definition of the aT,, curve limited only by the precision of the method used for the neutron detection

568

A. VEYSSIEREet aL

itself. Bowman et al. a2), using time-of-flight methods with an energy resolution of A E ~ 5 keV, were thus able to observe several peaks in the ay,. (E) curve each having a F W H M of a few keV for the energy region B. ~ E < B. + 350 keV. Similarly Bertozzi et al. a 1), with an energy resolution of some 50 keV also observed several peaks in the ay.. (E) curve for the energy interval B. + 250 keV < E < B. + 1.6 MeV. These two experiments show the complicated n p - n h configurations induced L Q.U.

!0

0.2

0.~.

'

O.

r4ev

II{E,LL) O.LI.

rr

5

0

mb

-

Ji,

I

I

a

I

I

',,,

I

,

.,."

I

I

i

~

f

'i.

7.5 5n 7.5 7.7 73 6.1 6.5 0,5 ff1¢~ Fig. 5. a) Photoneutron cross sections [a~,..(E)]l and [a~,,.(E)]2 obtained by Bowman 32)and Bertozzi 31) respectively, b) Shape of our monochromatic photon beam used in these specific experiments, c) The dotted line [o'7,n(E)] 3 shows the convolution of a) with b) whereas the full line represents our experimental results aT,. (E). by photon absorption in 2°sPb, representing the long-lived states associated with Bohr's compound nucleus model. Since our experimental results were obtained with rather bad energy resolution A E = 140 keV, we could only hope to observe shortlived states, possibly lp--lh doorway states created by E1 absorption. Fig. 5 presents the essential information available for the verification of the above assumption;

PHOTONEUTRON CROSS SECTIONS

569

(i) Bowman's [a~..]l curve for B, < E < Bn+350 keV and Bertozzrs [a~.n]2 histogram for 250keV+B, < E < Bn+I.6MeV. Bertozzi's values have been approximately corrected for detector efficiency and normalized with respect to Bowman's results over their common energy interval 250 keV+B. < E < 350 keV+B,. (ii) The actual form N(E, E~) of our monochromatic photon beam, where N(E, Ei) dE represents the number of annihilation photons lying within the energy interval E and E + dE for a central photon energy E~. (iii) The dotted line represents the convolution of our monochromatic photon beam (ii) with [tr~.,]1 a,d 2. This gives us the results we ought to have observed namely;

~or?,n]3(Et) ~ f N(E E,)[o'?. nil and 2(E)dE. Taking errors due to the approximate detector correction and normalization into account we find quite good agreement between the predicted result [tr~.o]3(Ei) and our experimental results [a~.n](E~) represented by a full line in fig. 5c. In particular the position of the three peaks, which we found experimentally to be at 7.6, 8.0 and 8.3 MeV was confirmed by the [trr. n]3 (E~) curve. One should note that a few lp-lh, J~ = 1- states may be found for 2°apb in this excitation energy range. The unperturbed energies for these bound and resonant proton-proton hole configurations are: 7.69 MeV (d-~p,~), 7.70MeV (g-~h~) and 8.18 MeV (s-~rp½), 8.53 MeV (d-~p,) respectively. The energies of the bound neutron-neutron hole configurations are 7.7 MeV (h-~i~), 8.25 MeV (f-~g~) and 9.4MeV (h-~g~). Using 2°8pb(7, 7)2°8pb results for energies below the (7, n) threshold, Axel et al. 33) also found some resonance peaks at 6.72, 7.03 and 7.29 MeV. Since these peaks have roughly the same FWHM (,~ 250 keV) and the same energy interval (,~ 300 keV) as the ones observed in our experiments, we believe them to belong to the same type of structure discussed above.

3. Integrated cross sections and sum rules A precise evaluation of the different integrated cross sections and their moments requires the accurate knowledge of the absolute value of try,n (E). In table 4, which refers to 2°spb, we compare single photo-neutron cross sections obtained in several laboratories using different experimental techniques. Monochromatic photons from neutron capture were used by Hurst and Donahue 34), quasi-monochromatic photons from annihilation-in-flight of fast positons were used by Miller 1), Harvey s) and our group whereas Fuller 22), Tomimasu 23)and Goryachev ~a) used bremsstrahlung photon spectra. The original results of Fuller and Hayward corrected by 30 [ref. 35)] were subsequently republished by Danos and Fuller 36). Finally Calarco's results 25) were obtained by using an associated particle method as a means of tagging the incident photons. Table 4 shows some disagreements for the low cross-section values at 9 and 10.83

570

A. VEYSSIEREe t al.

TABLE 4 Absolute a~,,°(E) values of 2°Spb obtained from the present experiments compared with values found in the literature Photon energy refs. a4) *) n) 2 2 , as, a6) 2a) 24) 25) present work

9 MeV (mb.)

10.83 MeV (mb.)

22.6-4-11.3 35 4"10 50

2804-31 2004-20 130

100

170 300

45 4- 5

2204-10

13.5 MeV (mb.)

650-/-25 495 4-15 610 660+60 800

6504-60 6404-10

MeV where a precise comparison may be hindered by the steepness of the slope dtrr, n/dE and by the presence of structure. This could explain why we found Hurst's value of 280 mb not at 10.83 MeV but at 11 MeV. The best comparison however can be made at 13.5 MeV where a~,. has its maximum value and hence the least relative error. Five references give values converging towards 640 mb whereas refs. 8,24) give lower and higher values respectively. The maximum value of a~.. for a 9 7 A u obtained by several groups using monochromatic photons turns out to be rather consistent since Miller et al. ~), Fultz et al. 9) and our group found 480 rob, 535 mb and 540-1-10 mb respectively. TABLE 5 Integrated cross sections and sum rule values of 2°Spb and *97Au. The notation used is defined in the text Refs.

x) a) 2a) present work *) ,97Au 9) present work

2OSpb

Era

ao

ao"

aoA

ao'A

a_ x

a_ 2

(MeV)

(MeV- b)

(MeV'b)

0.06 N Z

0.06NZ

(mb)

(mb. MeV-~)

22 28 23 25 22 25 25

4.104-0.06 2.91 4-0.29 3.914-0.59 3.484-0.23 3.004-0.05 2.974-0.3 3.484-0.2

5.10 2.94 5.18 4.00 3.99 3.53 4.07

1.37 0.98 1.31 1.17 1.06 1.05 1.23

1.71 0.99 1.74 1.34 1.40 1.24 1.42

280

251 4-20 200 2384-20

20.5 14.1 4-1.4 18.64-2.4 19.1 4-2 14 15.3+!.5 17.24-2 '

Table 5 summarizes and compares the integrated cross sections, their moments and different sum rules. We used the following notation in table 5:

(i)

=

f>,

(E)dE,

where Bn is the threshold for the (~, n) reaction and EM is the upper integration limit.

P H O T O N E U T R O N CROSS S E C T I O N S

571

(ii) The quantity a~ is the area under the unique Lorentz curve from E = 0 to EM = ov which fits best our experimental curve aT(E): a~ = ½ntrlF 1. (iii) 0.06 NZ/A is the classical Thomas, Reiche and K u h n sum rule value without exchange forces and is 2.98 M e V . b for 2°spb and 2.84 MeV. b for 197Au. (iv)

(v)

a-l=

fB I?

~ °'T(E) dE. , E

°

E2

dE.

-We also note that the ay. 2n cross section was evaluated, not measured, for ref. 23) and that for ref. 1) the cross section under the sum sign was a~. n + 2 ~ . 2n rather than eT. The errors given in table 5 for our integrated cross sections include both statistical as well as photon-beam calibration errors 2). Since ao represents a low value of the integrated total cross section and a~ corresponds to a high value one can therefore try to define a mean value such that t ( e 0 ) = ½(do +do). Thus we can write: 197Au

(o'0) = (1.32+_O.08)O.06NZ/A = (I+c~)0.06NZ/A,

2°sPb

( a 0 ) = (1.25+O.08)O.06NZ/A = (I+~)0.06NZ/A.

This could indicate art average exchange-force enhancement of the dipole sum rule corresponding to ~ = 0.28+0.1, which agrees with our previous results 3s,39) but is roughly double the value extracted by Huber 37) from earlier experimental data. Theoretical calculations by Levinger 40) predict that a_ 1 = cA t where he finds c = 0.35 mb for an isotropic harmonic oscillator potential and c = 0.30 mb for a finite square potential. Our present results yield c = 0.20+0.02 mb which is in disagreement with these theoretical predictions but agrees very well with our previous results for La, Tb, Ho, T a [ref. 3s)] and I, Ce, Sin, Er, Lu [ref. 39)]. Migdal 40) derives a sum rule for a - 2 which can be expressed as a_ 2 = 2.25 A t m b . M e V - 1 and Levinger altered this expression to read ¢r_ 2 = 3.5 A t m b - M e V - 1. Table 5 shows that our experimental values of a_2 A - t = 2.61+0.2 m b " MeV -1 and 2.58+_0.2 mb • MeV -1 for 2°spb and 197Au respectively, agree rather well with Migdal's values. Furthermore these values are again in excellent agreement with our previous results 38,39) for targets mentioned above for which an average value of a_2 A-t = 2.6+_0.2 mb • MeV -1 was found.

4. Competition between (?, n) and (?, 2n) decay modes I f one supposes that all electric dipole absorptions E1 by a nucleus lead to the formation of a compound nucleus before the evaporation of one or two neutrons can occur, then several approaches exist which allow one to extract the nuclear temperature

A. VEY.~IEREet al.

572

parameter O or the nuclear level density parameter a for the target minus-one-neutron nucleus from the measured partial cross sections of the target nucleus. Hence we can write the following general expression as a function of the energy E of the absorbed photons: /.~=E-B,n ! U)ds

cry,n(E)

8p( rs=£_Bn-a*p(U)d8 J, = 0 J =o

cry.,(E) + cry.2n(E)

(3)

where U is the effective excitation energy of the ( A - I) nucleus, U = E-B~-e-~5, e is the kinetic energy of the emitted neutron, fi = pairing energy of the (A - I) nucleus, p(U ) is the level density formula stillto be determined and Bxn is the threshold value for the (% xn) reaction. If one n o w assumes that the level density form of the ( A - l) nucleus at the excitation energy U is of the type described by Blatt and Weisskopf then eq. (3) can be rewritten as follows:

CrY'2n(E)

=1-

[ 1 + E~B2n

I cxp [ E~B2n].

(4)

cry, If wc suppose that the level density in the (A - I) nucleus will be better represented by a Fermi gas type formula such as

p(U) = CU-Zexp 2 .,/aU,

(5)

then we can use expression (3) as it stands. Both formulae, however, predict the complete disappearance of the cry,n curve a few MeV above the (% 2n) threshold B2, for reasonable values of 19 and a. This prediction was verified by the results of Harvey 8) and Fultz 9) for 2°sPb and 197Au respectively but it is incompatible with our experimental data since in both cases we have clearly cry.,(E) # 0 for E = B2.+5 MeV. It follows that our experimental results imply that the classical statistical behaviour ascribed to the compound nucleus cannot be the only mechanism responsible for the emission of photoneutrons in the energy interval 14 MeV < E < 20 MeV. For (~, n) type experiments, where the energy spectrum of the emitted neutrons is examined 2s.,1-44), the following simplifying hypothesis has mostly been ack cepted. One admits that the low-energy part of the neutron spectrum can be completely represented by any of the evaporation formulae and that the residue of high-energy neutrons which cannot thus be fitted pertains to the so called direct interaction neutrons. In our specific case we assume that x % of all nuclear photon absorptions by the electric dipole process will be followed by the emission of such a direct highenergy neutron. Such a direct neutron emission towards the low-lying energy levels of the (A - 1) nucleus makes the emission of a second neutron constituting a (?, 2n) reaction impossible. Some recent experiments by Calarco 25) on the photoneutron

PHOTONEUTRON CROSS SECTIONS

573

spectrum of 2°spb (for the energy interval 12 MeV < E < 17 MeV) have shown that the fraction of "direct" neutrons is a constant and equal to nD = 0.14+0.03. This result allows us to make the additional assumption that we shall consider x to be a constant in all our subsequent calculations. Since the total cross section can be replaced by the best Lorentz line fit such that a r = aL it follows that in formulae (3) and (4) the expression [a~,. + a~, 2.] must represent the statistical contribution to the total cross section a r expressed by (1--x)aL(E). We can now fit our experimental cr~,2n(E ) points with a theoretical expression still to be derived provided we can find a suitable nuclear level density formula for 207pb at an excitation energy U corresponding to the photon energy range used in our experiments. Some recent and systematic investigations of the energy dependence of the level density by means of a study of the energy spectra of inelastically scattered neutrons have been carried out by Owens 43) and Maruyama 44). Both experiments indicate that for fairly low excitation energies (2 MeV _<__U < 7 MeV), the nuclear level densities of nuclei between the closed shells are best described by a Fermi gas formula whereas nuclei near shell closures are better described by a constant nuclear temperature formula. In our case a study of the competition between the (~, 2n) and the (~,, n) processes in 20spb implies some hypothesis concerning the nuclear level density form in 2°Tpb at an excitation energy 8 MeV < U < 13 MeV which exceeds the binding energy of a neutron in 2°7pb and corresponds to an incident photon energy of roughly 15 MeV < E < 20 MeV. This excitation energy exceeds by far the range for which the level density in 2°7pb is best expressed by means of a constant nuclear temperature form. It thus seems reasonable that for 2°Tpb we ought to use a composite level density formula with a Maxwellian shape for low-excitation energies (U < 6.4 MeV) and a Fermi gas formula for higher excitation energies as recommended by Gilbert and Cameron 4s). We therefore chose a Fermi gas type formula (5) as our basis for all subsequent evaluations. The results of such fitting processes applied to our a~,2n(E) curves for 20Spb and ~ 97Au are represented by a set of parameters x and a as shown in table 6. We also show in fig. 6 the actual result of such a procedure between our experimental points ay,2. for 2°spb and the best theoretical fit obtainable with formula (3) for x = 0.26 and a = 7.4 MeV-1 In fig. 7 we present the results obtained from another type of analysis using the neutron multiplicity defined as follows:

M(E) =

-~" * + 2(a~, 2.) 0"~,, n "~ 0"V, 2n

When using this approach, it can be shown that above the (~, 2n) threshold B2. the value of M(E) tends towards its asymptotic form: Ma =

XAOL+ 2(1 - xA)aL X A O"L "1- (1 - - XA)O" L

= 2-xA.

1 _~'~2n m b 100

75

50

o 25

-

Experimental points Calculal'ed curve

-

0 0

n

I 15

13

I

I 17

n

I 19

I

I 21

£ , MeV

Fig. 6. A c t u a l fit b e t w e e n o u r e x p e r i m e n t a l a~. 2, ( E ) c u r v e f o r 2 ° s P b a n d t h e a n a l y t i c a l e x p r e s s i o n g i v e n in f o r m u l a 3 for x = 0.26 a n d a = 7.4 M e V - 1.

zo8 Pb

8~

MultipLicity

et ee

IJ_

-

•.t. . . .

I t t mmoo

O,~ I 1Z

eeu*

I

,.

14

I

I

1G

I

I

18

I

I

20

,

,

ZZ MeV

Fig. 7. N e u t r o n m u l t i p l i c i t y M o f 2°SPb as a f u n c t i o n o f i n c i d e n t p h o t o n energy.

PHOTONEUTRON CROSS SECTIONS

575

TABLE 6 "Direct" neutron contributions and level density parameters for 2°SPb and ~9VAu obtained from the present work (undashed symbols) compared to values given by other authors (dashed symbols), where x or xA is the fraction of the total cross section responsible for the emission of a "direct" neutron, nD is the percentage of "direct" neutrons and a is the level density parameters for the target minus one neutron nucleus X

XA

nD

n' D

II"" D

Q

a'

a'"

(MeV-1) (MeV-t) (MeV-1) 2°Spb 0.264-0.05 0.274-1-0.05 0.154-t-0.04 0.144-0.03 0.18-t-0.03 7.44-1 197Au 0.314-0.05 0.35-4-0.05 0.204-0.04 0.14-1-0.04 12-4-2

11.7 16.6

8.17 19.13

The results obtained for x in the interval B2, < E < B 2 , + 5 MeV and XA for E > B 2 , + 5 MeV are in excellent agreement for 2°apb as well as for 197Au. This leads us to conclude that the contribution of "direct" neutrons n D = XA[(2--X^) is approximately 15 ~o and 20 ~ for 2°spb and 1 9 7 A u respectively. As can be seen from table 6 our values of no are again in good agreement with the n~ and n~ values (obtained from photoneutron spectra) given by Calarco 25) (12 MeV < E < 17 MeV) and Mutchler 41) (E = 14 MeV). However our a values are substantially lower than the a' values found by Buccino et al. 46) using (n, n') reactions and the a" values given by Facchini et al. 47) and calculated from slow neutron resonance data. Griffin 48) and Blann 49) have recently introduced the concept that, for (p, n) and (~, n) reactions, neutrons might be emitted before the nucleus could attain a statistical equilibrium. These so-called "precompound" neutrons would then have an energy spectrum richer in high-energy neutrons than an evaporation spectrum, and its precise shape would depend on the initial number n of excitons. The application of this "precompound" theory turns out to be extremely delicate in the giant resonance region, especially since the giant dipole states are coherent sums of lp-lh configurations 2s). Nonetheless, a tentative evaluation and fitting process using the Blann formalism for n = 2 or 4 has been applied using formula (3). The results indicate that the high-energy tail of the cry,,(E) curve for E > B2n+ 5 MeV could indeed be associated with precompound neutrons. Taking the best fit, the statistical remainder of the neutrons then yields a = (11 -I- 1)MeV- 1 and a = (21 -I-2) MeV- 1 for 2°Tpb and 196Au ' values which are much closer to the ones published by Buccino 46) and Facchini 47). We also observed that for 2°spb and I 9 7 A u the cri.(E) curve becomes tangent to the ar,2,(E) curve at about E = 23 MeV. For E > 23 MeV we have aL(E) = (or. 2n + at, an) which seems to indicate that the electric dipole absorption only causes (7, 2n) and (7, 3n) reactions in this energy interval. Moreover the disappearance of the a~.2, curve just a few MeV above the (7, 3n) thresholds in both 2°SPb and 197Au indicates that the statistical model interpretation for these decay modes is correct in this energy range.

576

A. VEY~IERE e t al.

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