Photonuclear reactions in Pr141

Nuclear Physics 10 (1959) 422

i28;@.~North-Holland PublishingCo., Amsterdam

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

PHOTONUCLEAR F. F E R R E R O ,

REACTIONS

I N P r t't

R. M A L V A N O a n d E. S I L V A *

Istituto di Fisica dell'Universit& di Torino Istituto Nazionale di Fisica Nucleate, Sex. di Torino, J. G O L D E M B E R G

a n d G. M O S C A T I

Universidade de S. Paulo R e c e i v e d 16 J a n u a r y 1959 A b s t r a c t : T h e (7, n) a n d (7, 2n) r e a c t i o n s in P r x'x h a v e b e e n s t u d i e d u p to 30 M e V b y t h e m e t h o d of residual a c t i v i t y . A c o m p a r i s o n is m a d e w i t h t h e s t a t i s t i c a l t h e o r y of n u c l e a r r e a c t i o n s f i n d i n g a partial d i s a g r e e m e n t a t h i g h energies. T h e t o t a l p h o t o a b s o r p t i o n c r o s s s e c t i o n is e v a l u a t e d a n d t h e i n t e g r a t e d v a l u e is f o u n d to be g r e a t e r t h a n t h e t h e o r e t i c a l predictions. T h e b e h a v i o u r of t h e a b s o r p t i o n cross s e c t i o n in t h e region a b o v e t h e g i a n t r e s o n a n c e is discussed.

1. I n t r o d u c t i o n

Many experiments concerning (7, 2n) reactions have been carried out using the X-rays produced with electron accelerators, but only for F x9 and Cu e3 were the (7, 2n) excitation curves detected b y means of the residual activity technique. The difficulty is to find elements that, irradiated with X-rays, present a residual activity of convenient half-life:actually this is the case of P r m . The Pr 142 disturbing/~--activity (19.3 h half-life) that could be formed by neutron capture in Pr m , is in our case avoided b y counting the 0.51 MeV 7-rays from the ~+-annihilation: indeed, the Prm(7, n)Pr 14° and Prm(7, 2n)Pr 189 reactions give rise to/~+ residual activities of 3.4 min and 4.5 h respectively. The evaluation of the (7, 2n) yield is usually made b y subtracting the (7, n) yield from the total neutron yield, measured by residual activity, and dividing the result by two. The difference between the two yields is in general very small in comparison with the total neutron yield: the (7, 2n) activation curve is therefore affected by much greater errors than the (7, n) yield curve. The Prm(7, 2n)Pr 1~9 reaction is particularly interesting because Pr m is magic in neutrons and in these cases it seems that an appreciable part of the absorption cross section is beyond the giant resonance. From this point of view one m a y clearly expect a rather strong (7, 2n) process. The independent t Fellow of t h e N a t i o n a l Council of R e s e a r c h of Brazil. O n l e a v e of a b s e n c e f r o m t h e U n i v e r s i t y of S. Paolo, Brazil. 423

424

F. FE~m~RO et al.

measurement of the two cross-sections, (7, n) and (7, 211), allows us to build up the complete absorption cross section in the energy region beyond the giant resonance and to evaluate its integrated value.

2. E x p e r i m e n t a l Procedure One gram powder samples of high purity (99.99 ~ ) Pr e 011 were irradiated b y the X-ray beam of a 31 MeV Betatron. The distance of the sample from the internal target of the Betatron was as small as possible ( ~ 20 cm) in order to increase the incident dose. The PreOll powder was enclosed in a small aiuminium container which did not affect the measurements in view of the counting schedule. The activities were measured b y detecting the 0.51 MeV annihilation radiation from the fl+-conversion in a convenient absorber placed around the samples. The NaI(T1) well type (2"×2") crystal was looked b y a 6292 Dumont photomultiplier. A one channel pulse height analyser, set on the 0.51 MeV line, with a channel width of 10 %, allows only the annihilation radiation to be counted. The relative dose was measured b y an aluminium ionization chamber and in the (7, n) reaction measurement the electrometer was matched with a time constant equal to the mean life of Pr ~4°. The two yield curves of the (7, n) and (7, 2n) processes were independently measured: the difference between the two half-lives is so great that one can obtain the best data for the short lived activity b y irradiating the samples for a time comparable to the half-life with a consequent better evaluation of the effective dose. Although the samples contain oxygen, this does not appreciably affect the measurements because the oxygen activity will be a few per thousand of the total short lived praseodimium activity.

3. Results In fig. 1 are plotted the yield curves for the two processes; the absolute value of the disintegrations/mole, lOOr has been obtained b y comparison with the (7, n) activity in copper 1); the ratio of the two activities, Pr xo and Pr 189 was obtained in a single irradiation. The ratio ~+/(p++E.C.) is 0.54 for l:'r 13' and 0.06 for Pr 14° and has been taken into account 3,8). The Prm(7, 3n)Pr I~ reaction (~+, T½ = 2 h) has a threshold of approximately 24 MeV; this process, if important, could give an undesirable contribution very difficult to separate from the 4.5 h activity. In order to evaluate this contribution, we tried to separate it b y analyzing the decay curves but we did not succeed to detect any appreciable distorsion of the 4.5 h half-life even at the maximum available energy. A trial to detect the 0.8 and 1.05 MeV 7-rays belonging to Pr ls8 4) also failed. These measurements prove that

PHOTONUCLEAR

I

1"

REACTIONS

I

IN

425

P r 141

I

i

x 101

-t

(Y. 2n)

..,.._..,,..-.-.,--" 10.5

15.5

Fig. 1. E x c i t a t i o n functions for

I

I

25.5

2Q5

1:~"4t(7,

I

e'. v (MeV) 30S

n ) P r .4° a n d Pr1'1(7, 2 n ) P r * " reactions.

I

i

I

=o ~00

L "-,?, 500

= o400

300

200

....... .:........].,.....~......~ "'"'" ~ ............... ~"--'-1.......~ ......

I0C

I

I

I0

I

r- - - } - - - r - - ~ - ' ~ - - ~ - "

I

,

t~

20

"t. ~ - - ~ - "

25

Fig. 2. Cross sections v e r s u s energy: pr141 (y, n ) P r " 0 ; Pr141 (y, 2n)Prt~0; . . . . . .

s u m of t h e t w o a b o v e processes.

_ _

-t. - -

hv

- - -

~MeV)

30

49.6

F,

FERILERO

8t

~.

the (7, 3n) contribution, if it exists at these energies, is extremely small. The Penfold-Leiss method 5) was used to analyze the two yield curves of fig. 1 and the obtained cross sections are shown in fig. 2 *. 4. D i s c u s s i o n

The possibility to compare these results with the statistical model of nuclear reactions is quite good, since the (7, n) and the (7, 2n) reactions are probably the only important processes from 16 to 30 MeV, because of the high Coulomb barrier for-proton emission and of the experimental evidence on the weakness of the (7, 3n) reaction. Following Blatt and Weisskopf e) we have 0(7, 2n) __ ~ a(7, n ) + a ( 7 , 2n) -- 1-- ( 1 + O ) exp ( - - -~) where eo is the excess energy over the threshold of the (7, 2n) reaction (16.5 MeV); O = (E'/a)t is the temperature of the intermediate nucleus ~PrZ4°; E' is the excess energy over the (7, n) threshold (9.5 MeV) and a is a function of the mass number A (in our case a = 9). This ratio, together with that obtained experimentally, is plotted in fig. 3. A disagreement between the I |

.

I .

.

I .

.

.

.

.

.o --- .......

"l'l'~or'fticol

sS D 4-

sS /

~

/

Z // =

I

0.5--

o

o

/( 17

I

I

20

25

E n e r g y (MeV) 3 0

Fig. 3. Comparison between the statistical theory of nuclear reactions (theoretical) and the experimental ratio O(y, n)/[o~, n ) + o ( y , 2n)].

two curves is apparent and is supposed to be due to an appreciable direct photoneutron component that affects the (7, n) process. t O. Borello of the University of S. Paolo recently measured the total absorption coefficient of P r x4z using threshold detectors, and on subtracting the electronic absorption obtains results for the nuclear absorption which agree with the present work. i

PHOTONUCLEAR REACTIONS IN Px"141

427

The integrated absorption cross section up to 30 MeV is evaluated as follows: the sum of the two measured processes (7, n) and (7, 2n) is 3.3 MeV- b; to this figure we must add at least 0.1 MeV. b for the (7, P) process, because, taking into account the data for the (7, P) reaction found in the literature, we see that a reasonable value of the integrated (7, P) cross section is about 3 % of the correspondent (7, n) integrated cross section. Neglecting the unknown contributions of the (7, i~p), (7, ~) etc. processes, we obtain for the integrated cross section 3.4 MeV. b. The Levinger and Bethe (L.B.) dipole sum rule t

7'), (7,

fadE

= 0.06 - ~ (l+0.8x)

gives, for an exchange force fraction x = 0.5, a value of 2.88 MeV. b; we see, therefore, that the experimental result strongly exceeds the L.B. prediction *. This experimental result is not, however, peculiar to P r m : in fact, in Ta lsx Whalin and Hanson 9), taking into account only the (7, n) and (7, 2n) processes, found a value of 3.6 MeV- b for the integrated cross section up to 22 MeV, and for the same element, Jones and Terwillinger lo) found 5.1 MeV - b by integrating up to 80 MeV. The agreement with the L.B. prediction seems to be very difficult to obtain. For a detailed discussion on this point we refer to a paper b y Levinger 11). Another expression for the integrated cross section, that is not confined to dipole transitions, is that of GeU-Mann e t a / . x~):

/0~'a(E)dE

NZA e'?~Mkl 0; a,,/aN = 1.3

// dE(1--R(E))[Zaj'(E)WNctN(E)]"

Taking R ( p ) = and the experimental behaviour of a~ versus energy, this relation becomes #

NZ

A s

fo a(E)dE = 0.06-~- (1+0.1~--~). Now, the above expression, which takes into account higher order multipole transitions also, nevertheless gives nearly the same value as the L.B. formula with z = 0.5. This seems very peculiar and it lies outside the purpose of this paper to discuss t h e validity of the above expression. One thing, however, is certain: the experimental integrated cross section is greater than both the above theoretical predictions, even if one extends the integration only to 30 MeV and not up to the meson threshold. t E v e n if, for t h e calibration, we h a d used t h e d a t a o n c o p p e r given in ref. 8), which axe m u c h smaller t h a n t h o s e usually employed, we would still get a value t h a t exceeds the L. B. prediction b y a t least 0.3 MeV. b.

428

F. ~ERRERO ~t ~ .

Danos and Steinwede118) have pointed out that the hydrodynamical model of Jensen and Steinwede114) would predict an absorption for quadrupole transition with a peak located at an energy 1.6 times the energy of the dipole one. The maxima for quadrupole and dipole absorption cross sections are correlated by the following relation ares.ares"d.qU"__ 0 . 2 1

\~q/

•

Taking into account the experimental data we get Eq --~ 24 MeV and therefore ares.qu. = 43 mb. Fitting a Lorentz line to the experimental values of the dipole resonance curve we get a contribution to the dipole tail of 20 mb. The difference from the experimental value is 100 mb and this last figure could be compared with the value of Danos and Steinwedel's calculation. Considering the uncertainty in the cross section values the results are not in contradiction with the quadrupole absorption mentioned above. We thank Prof. M. Mandb, of the University of Florence, who kindly supplied pure praseodimium oxide, and Miss S. Menardi for computation work. One of us (E.S) wishes to express his gratitude to Prof. G. Wataghin, for the kind hospitality in the University of Turin. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14)

L. C. B. T. A.

Katz a n d A. G. W. Cameron, Can. J. of Phys. 29 (1951) 518 I. Browne, J. O. Rasmussen, J. P. Suris and D. F. Martin, Phys. Rev. 85 (1952) 146 J. Stover, Phys. Rev. 81 (1951) 8 H. Handley and E. L. Olson, Phys. Rev. 96 (1954) 1003 S. Penfold and J. E. Leiss, Analysis of photo-cross-sections (Phys. Res. Lab., University of Illinois, Champaln, II1., May 1958) J. M. Blatt and V. F. Weisskopf, Theoretical Nuclear Physics, (John Wiley & Sons, New York, 1952) p. 379 J. S. Levinger and H. A. Bethe, Phys. Rev. 78 (1950) 115 A. I. Berman and K. L. Brown, Phys. Rev. 96 (1954) 83 E. A. Whalin and A. O. Hanson, Phys. Rev. 89 (1953) 324 L. W. Jones and K. M. Terwillinger, Phys. Rev. 91 (1953) 699 J. S. Levinger, Annual Rev. of Nuclear Science 4 (1954) 13 M. Gell-Mann, M. L. Goldberger and W. E. Thirring, Phys. Rev. 95 (1954) 1612 M. Danos and H. Steinwedel, Z. Naturforschg. 6 a (195I) 217 H. Steinwedel and J. H. D. Jensen, z. Naturforschg. 5a (1950) 413