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Title: Spallation-Fission Competition in Heaviest Elements; Helium Ion-Induced Reactions in Uranium Isotopes Author: Vandenbosch, R. Thomas, T.D. Vandenbosch, S.E. Glass, R.A. Seaborg, G.T. Publication Date: 11-01-1957 Permalink: http://escholarship.org/uc/item/1j7140x5 Copyright Information: All rights reserved unless otherwise indicated. Contact the author or original publisher for any necessary permissions. eScholarship is not the copyright owner for deposited works. Learn more at http://www.escholarship.org/help_copyright.html#reuse
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UNIVERSITY O F CALIFORNIA
I
EK LOAN COPY This is a Library Circulating Copy which may be borrowed for two weeks. For a personal retention copy, call Tech. Info. Division, Ext. 5545
BERKELEY, C A L I F O R N I A
UNIVERSITY OF CALIFORNIA Radiation Laboratory Berkeley, C a l i f o r n i a Contract
NO.
W-7405-eng-48
SPALLATION-FISSION COMPETITION I N HEAVIEST ErnMENTS ; HELIUM 2,.
I O N -INDUCED RE.! C'.LIIOIJ S I1 UR !1 IIUAI ISOTOPES
"
by R . Vandenbosch
t , T. D. Thomas, S. E. Vandenboscht , R . A . Glass, + and G. T. Seaborg
November
1957
P r i n t e d f o r t h e U. S. Atomic Eaergy Commission
SPALLATIOI1'-FISSION COMPETITION I N HEAVIEST ELJBBNTS; HELIUM I O N -INDUCED
by
t , R. A . , ~ l a s s l , I
Thomas, S. E . Vandenbosch and G . T. Seaborg
Radiation Laboratory and Department of Chemistry U n i v e r s i t y of C a l i f o r n i a , Berkeley, C a l i f o r n i a November 3C
1957
This work was performed under t h e auspices of t h e U. S. Atomic Energy Com-
mission.
It i s based i n p a r t on t h e Ph.D. t h e s e s of R . Vandenbosch, U n i v e r s i t y
of C a l i f o r n i a , J u l y ,
1957, and T. D. Thomas, U n i v e r s i t y of C a l i f o r n i a , J u l y ,
1957, and on t h e M.S. t h e s i s of S. E. Vandenbosch (nee ~ i t s e m a ) ,U n i v e r s i t y of C a l i f o r n i a , January, 1956. 'present
address :
*present address:
Argonne National Laboratory, Lemont, I l l i n o i s . Stanford Research I n s t i t u t e , Menlo Park, C a l i f o r n i a . ABSTRACT
A radiochemical study of f i s s i o n and s p a l l a t i o n products produced b y bombardment of
u
~ u ~ ~ and ~ ~ U238 , ~
with ,
18-46 Mev helium ions has been made.
As i n the case of s i m i l a r s t u d i e s using i s o t o p e s of plutonium a s t a r g e t s , m o s t of the r e a c t i o n cross s e c t i o n i s taken up by f i s s i o n .
Also, t h e pronounced
increase of t h e t o t a l cross s e c t i o n f o r (a,xn) r e a c t i o n s with i n c r e a s i n g mass number of t h e t a r g e t t h a t was observed f o r plutonium t a r g e t s i s observed f o r uranium t a r g e t s . E x c i t a t i o n functions f o r ( a , 2 n ) , ( a , 3 n ) , and (a,4n) r e a c t i o n s a r e i n t e r p r e t e d i n terms of compound nucleus formation and f i s s i o n competition at the various s t a g e s of t h e neutron evaporation chain.
The importance of neutron
binding energies on t h e competition between f i s s i o n and neutron emission i s stressed.
An e x i s t i n g model f o r nuetron evaporation following compound nucleus
formation has been extended t o include t h e e f f e c t of f i s s i o n competition.
Re-
s u l t s of c a l c u l a t i o n s based on t h i s model show good agreement with those f e a t u r e s of t h e (a,xn) e x c i t a t i o n f u n c t i o n s b e l i e v e d t o r e s u l t from compound nucleus formation.
These c a l c u l a t i o n s a l s o show t h a t f i s s i o n u s u a l l y procedes
u~~~ and U235 , + a , d ) , (a,p2n + a , t ) ,
neutron evaporation f o r helium-ion-induced r e a c t i o n s of
The
e x c i t a t i o n functions f o r t h e ( a , n ) , ( a , p ) , (a,pn
and
(a,p3n
+ a,tn)
r e a c t i o n s a r e discussed i n terms of d i r e c t i n t e r a c t i o n mecha-
nisms involving l i t t l e competition from f i s s i o n . F i s s i o n shows an i n c r e a s e i n symmetry with energy and becomes symmetric a t about 40 Mev energy of t h e helium i o n s .
There i s no s i g n i f i c a n t d i f f e r e n c e
i n the asymmetry of f i s s i o n f o r t h e t h r e e uranium i s o t o p e s . Tokal r e a c t i o n cross s e c t i o n s , including those f o r both f i s s i o n and s p a l l a t i o n r e a c t i o n s , i n d i c a t e a nuclear r a d i u s parameter r
0
s l i g h t l y l a r g e r than 1 . 5 x 10-'~crn.
COMPETITION I N HEAVIEST ErnMENTS; HELIUM
++
ION-INDUCED mACTIONS I N URANIUM ISOTOPES
R. Vandenbosch
t , T. D. Thomas,
S o E. Vandenbosch
t , R. A. Glass
*
and G. T. Seaborg Radiation Laboratory and Department of Chemistry University of C a l i f o r n i a , Berkeley, C a l i f o r n i a November
1957
*
This work was performed under the auspices of t h e U. S. Atomic Energy Commission. It i s based i n p a r t on the Ph.D. theses of R. Vandenbosch, U n i v e r s i t y of C a l i f o r n i a , July, 1957, and T. D. Thomas, U n i v e r s i t y of C a l i f o r n i a , J u l y , 1957, and on t h e M.S. t h e s i s of S. E. Vandenbosch (nee ~ i t s e m a ) ,U n i v e r s i t y of C a l i f o r n i a , January, 1956.
'present
address :
*present address:
Argonne National Laboratory, Lemont
, Illinois.
Stanford Research I n s t i t u t e , Menlo Park, C a l i f o r n i a .
I.
INTRODUCTION
This paper extends t h e i n v e s t i g a t i o n s of t h e p r e s e n t s e r i e s s i o n and s p a l l a t i o n r e a c t i o n s i n t h e h e a v i e s t element region.
1-4
on f b -
Spallation r e -
a c t i o n s i n t h e h e a v i e s t elements a r e p a r t i c u l a r l y i n t e r e s t i n g because t h e f i s s i o n process provides a prominent competing r e a c t i o n ( n o t found i n l i g h t e r elements a t high e x c i t a t i o n energies) which can have e f f e c t s on t h e c r o s s s e c t i o n s of t h e other r e a c t i o n s .
I n a d d i t i o n , t h e f i s s i o n process i s i n t e r -
e s t i n g i n i t s own r i g h t . The i n v e s t i g a t i o n s which a r e being pursued i n t h e present program a r e p r i m a r i l y of t a r g e t nuclides of atomic number g r e a t e r than o r equal t o 88, vhere f i s s i o n threshold energies are roughly comparable t o nucleon binding energies.
We have been concerned p r i n c i p a l l y with nuclear r e a c t i o n s induced
by p a r t i c l e s of l e s s than about 50 Mev energy, with t h e hope t h a t a t these r e l a t i v e l y low energies t h e compound nucleus theory can be used a s a s t a r t i n g point i n describing t h e c h a r a c t e r i s t i c s of the nuclear r e a c t i o n s .
Previously r e p o r t e d work
1-4 has indicated, f i r s t , t h a t f i s s i o n compete a
s u c c e s s f u l l y with s p a l l a t i o n r e a c t i o n s t h a t proceed by t h e formation of a compound nucleus, and, second, t h a t r e a c t i o n s involving t h e emission of charged p a r t i c l e s proceed by d i r e c t
i n t e r a c t i o n mechanisms.
In particular, fission
competes with neutron emission a t every stage of t h e neutron evaporation chain, 1 There has been noted, however, a s t r i k i n g e f f e c t of t h e mass number of t h e t a r g e t on t h e r e l a t i v e p r o b a b i l i t i e s of f i s s i o n and neutron emission: neutron emission competes more s u c c e s s f u l l y a s t h e mass number of t h e t a r g e t i s i n The s u r p r i s i n g l y l a r g e c r o s s s e c t i o n s f o r t h e production of t h e
creased.
nuclide correspbnding t o t h e (a7p2n) r e a c t i o n have been shown t o be due t o t h e
3),~ i n which a t r i t o n r a t h e r than t h r e e s e p a r a t e p a r t i c l e s , i s reaction ( a , emitted.3
Furthermore, it has been suggested t h a t an a p p r e c i a b l e f r a c t i o n of
the ( a 7 x n ) r e a c t i o n s a r e produced by d i r e c t i n t e r a c t i o n mechanisms. 1 I n t h e f i r s t paper of t h i s s e r i e s , t h e v a r i a t i o n i n t h e f i s s i o n mass y i e l d d i s t r i b u t i o n with bombarding energy of helium ions was r e p o r t e d f o r plutonium isotopes.
It was found t h a t t h e t r a n s i t i o n from predominantly
asymmetric t o symmetric f i s s i o n occurred a t helium-ion bombarding e n e r g i e s between 30 and 40 Mev. This paper w i l l r e p o r t cross-sections f o r helium-ion-induced r e a c t i o n s of
u
~ lJ235, ~ and ~ IJ2380 ,
The study of these i s o t o p e s was undertaken t o d e t e r -
mine t h e e f f e c t of changing t h e atomic number and mass of t h e t a r g e t nucleus, t o compare with t h e work on t h e plutonium isotopes, and a l s o t o see i f t h e s t r i k i n g mass e f f e c t on t h e s p a l l a t i o n r e a c t i o n s i n t h e plutonium i s o t o p e s i s apparent f o r uranium i s o t o p e s .
It was a l s o hoped t h a t a comparative s t u d y of
t h e f i s s i o n mass y i e l d d i s t r i b u t i o n i n l i g h t on f i s s i o n asymmetry.
u
~ u ~ ~ and ~ ~ U238 , ~
would , shed some
11. EXPERIMENTAL PROCEDURES Preparation of t a r g e t s The
u~~~ used
i n these bombardnents had an i s o t o p i c p u r i t y of approxi-
96%. There was about 3% U238 and l e s s than 1% U234 p r e s e n t i n t h e m a t e r i a l . The u~~~ g e n e r a l l y had an i s o t o p i c p u r i t y of g r e a t e r t h a n 99.9%. The U238 a l s o had an i s o t o p i c p u r i t y of g r e a t e r than 99.9%. The techniques
mately
used i n these experiments were g e n e r a l l y those described b y Glass et al.
1
Most of t h e t a r g e t s were prepared by e l e c t r o d e p o s i t i o n of 0 . 1 t o 2 mg of hydrated uranium oxide over an a r e a of about 1 cm2 on a dish-shaped aluminum disk.
The amount of m a t e r i a l deposited, which was of uniform t h i c k n e s s , was
determined by d i r e c t alpha counting, weighing, or both.
These t a r g e t s were
then mounted i n a water-cooled m i c r o t a r g e t holder5 which a l s o served a s a Faraday cup f o r beam i n t e n s i t y measurements. Bombardments Aluminum or platinum f o i l s of measured thickness were used t o degrade t h e helium ion beam t o t h e d e s i r e d energy.
6 The i r r a d i a t i o n s were f o r a
period of two t o t h r e e hours f o r each t a r g e t , with beam c u r r e n t s of 5 t o 10 micro-amperes.
Because of t h e f a c t t h a t o n l y moderate amounts of a c t i v i t y
were produced, the chemical s e p a r a t i o n s of t h e various f i s s i o n and s p a l l a t i o n products were g e n e r a l l y performed on t h e whole t a r g e t . periments were performed i n which 1 - m i l m e t a l l i c
However, t h r e e ex-
u~~~ f o i l s
(- 93% i s o t o p i c
p u r i t y ) were bombarded and one experiment was performed i n which a 1 - m i l m e t a l l i c U238
f o i l (>
9%) was bombarded.
This procedure r e s u l t e d i n t h e production of
s u f f i c i e n t a c t i v i t y t o permit a l i q u o t s t o be taken f o r t h e various f i s s i o n produ c t elements, making possible a study of a wider s e l e c t i o n of f i s s i o n - p r o d u c t elements and a more complete determination of t h e mass y i e l d curve.
The p r i n c i -
p a l disadvantage of t h e use of uranium f o i l s was t h a t t h e uranium f o i l reduced t h e helium-ion beam energy by 3 t o
5 Mev, r e s u l t i n g i n a range i n energy of t h e
helium ions which caused t h e r e a c t i o n s . Chemical procedures The usual chemical procedure7 involved dissolving t h e t a r g e t , backing p l a t e , and aluminum cover f o i l i n a c i d i c s o l u t i o n containing known amounts of
f i s s i o n product c a r r i e r s and r a d i o a c t i v e t r a c e r s ( s p a l l a t i o n products.
N and ~ ~
~ u f o~r ~t h e~ ~
F i r s t t h e neptunium, aLd then t h e plutonium, was r e -
moved from t h e t a r g e t s o l u t i o n b y c o p r e c i p i t a t i o n i n the I V o x i d a t i o n s t a t e with zirconium phosphate under t h e proper o x i d i z i n g or reducing c o n d i t i o n s , The neptunium f r a c t i o n was f u r t h e r p u r i f i e d by c o p r e c i p i t a t i o n w i t h lanthanum f l u o r i d e and conversion of t h e f l u o r i d e s t o hydroxides,
followed b y d i s -
s o l u t i o n i n a c i d and t h e e x t r a c t i o n i n t o benzene of a neptunium (IV) thenoylt r i f l u o r o a c e t o n e c h e l a t e complex. The plutonium was p u r i f i e d by s i m i l a r f l u o r i d e and hydroxide
preci-
p i t a t i o n s followed by an ion-exchange column s t e p , i n which t h e plutonlum I V was f i r s t adsorbed on Dowey A - 1 anion exchange r e s i n from concentrated hydroc h l o r i c a c i d and then reduced t o t h e I11 oxidation s t a t e and e l u t e d from t h e resin.
The neptunium and plutonium were e l e c t r o d e p o s i t e d
8
onto platinum
The f i s s i o n products were p u r i f i e d by t e c h i q u e s adopted 10 from those described i n t h e compilations by bIeinke9 and L i n b e r . counting p l a t e s .
Detection of r a d i a t i o n s The f i s s i o n products were mounted on previously weighed alum'rnum p l a t e s f o r weighing and counting.
The d i s i n t e g r a t i o n r a t e s were determined
using end-window "Amperexf' geiger counter t u b e s , factors1'
ing r a t e s .
Appropriate c o r r e c t i o n
were applied t o o b t a i n d i s i n t e g r a t i o n r a t e s from t h e measured countThe i n t e n s i t i e s and energies of alpha-emitting s p a l l a t i o n prod-
u c t s were measured by use of multichannel alpha-pylse analyzers.
The countfng
r a t e s of s p a l l a t i o n products which decay by negatron emission o r e l e c t r o n capture were determined with a methane-flow windowless p r o p o r t i o n a l eounter. Counting e f f i c i e n c i e s f o r t h i s counter have been measured o r e s t i m a t e d f c ? each p a r t i c u l a r isotope involved.
Table I l i s t s the nuclides produced by
s p a l l a t i o n r e a c t i o n s , t o g e t h e r with t h e i r n u c l e a r p r o p e r t i e s and counting e f f i c i e n c i e s used i n t h i s work.
~
)
Table I NUCLEAR PROPERTIES AID CC I
Isotopes
Principal mode of decay
t 1/2
Pu232
Dl
E.C.
20 m
E.C.
9h
E.C.
26 m
E. C.
2.7 yr 44 d 89.6 yr 35 In 4.4 d
a
36
Percent alpha emission 12
Source
counter counting efficiency (percent)
Source
a
E.C.
a E.C. E.C.
410 d
E.C.
22 h
E.C.,
B-
p-
2.1d
Estimated from the alpha systematics.
I. Perlman and J. 0. Rasmussen,
1957. Thomas, Vandenbosch, Glass, and Seaborg, Phys. Rev. 106, 1228 (1957). P r i v a t e communication, R , W e Hdf f and F. Asaro (1957).
Handbuch der Physik ( s p r i n g e r - ~ e r l a g , ~ e r l i n )VqL. 42,
Estimated by authors. By "milkingn daughter U234 and determining i t s alpha d i s i n t e g r a t i o n r a t e , see Reference 12. This work, mass spectrometry. This work, by "milking" daughter Pu236 and determining i t s alpha d i s i n t e gration r a t e .
Percent negative b e t a decay from T. 0. P a s s e l l , Ph.D.
thesis,
1954 (unpublished); a l s o U n i v e r s i t y of C a l i f o r n i a Radiation Laboratory Report UCRL-2528, March 1954 (.unpublished).
University of C a l i f o r n i a , June
This work, by "milking" daughter Pu238 and determining i t s alpha d i s i n t e gration r a t e . This work, by 4fi-counting t o determine absolute d i s i n t e g r a t i o n r a t e . This work, by 431-counting and by counting K x-rays. !The number of K x-rays p e r d i s i n t e g r a t i o n was taken a s 0.55, from Rasmussen, Canavan, and Hollander, Phys. Rev. 107, 1 4 1 ( 1957)
.
111. RESULTS S p a l l a ti o n r e a c t i o n s The cross-sections cbtained at each energy f o r t h e s p a i i a t i o n 7~eactior.s of t h e various uranium i s o t o p e s a r e shown i n Tables I1 t o I V .
Ine
spallation
c r o s s - s e c t i o n s have been p l o t t e d a s a l'unction of helium-ion energy 4n F i g s . 1to
5.
The product which was observed i s i n d i c a t e d i n t h e t a b l e s ,
I n the
was t h e product, only the 22-ham i s m e r was cbsezve5. 240 f o r t h e 60-minute isomer was t h e product only t h e S i m i l a r l y , when Np cases where
was measured,
The standard deviation due t o random e r r o r s i s b e l i e v e ? t o be
about f 10% f o r most of t h e s p a l l a t f o n c r o s s s e c t i o n s . e r r o r s r a i s e t h e t o t a l e s t i m a t e s standard I n t h e case of t h e N~~~~
u~~~
Estimated systematic
d e v i a t i o n t~ between
+ 15%
and f 25$,
(a,pn) and (a,kn) r e a c t i o n s , t h e y i e l d s of t h e p r c d u c t s
and ~u~~~were d i f f i c u l t t o measure, and t h e l i m i t s of e r r o r may be a s
much a s f 50%. Fission yields The measured cross-sections f o r t h e fsrmation of various f i s s i o n prodlwt i s o t o p e s a r e shown i n t h e l e f t - h a n d columns of Tables V t o V I I . c r o s s - s e c t i o n s were not measured i n t h e bombardments of
u~~~ and
Since a b s o l u t e
U238 m e t a l l i c
f o i l s , it was necessary t o normalize t h e s e r e s u l t s i n some way t o t h e a b s o l u t e cross-sections obtained from other bomb-dments.
This was done by t a k i n g t h e
average of normalization f a c t o r s obtained b y i n t e r p o l a t i o n of smooth excsitaticn f u n c t i o n curves f o r t h e absolute f i s s i o n y i e l d s of s e v e r a l i s o t o p e s , l3 The median energy of the helium ions inducing t h e f l s s i o n i n t h e foil bombardments was a l s o c a l c u l a t e d from t h e s e curves. Gibson, Glass, and Seaborg
4 have
d i s t r i b u t i o n i n medium energy f i s s i o n .
made a p r e l i m i n a ~ ystudy of t h e charge Their conclusion i s t h a t t h e chazge
d i s t r i b u t i o n i n f i s s i o n a t t h e s e energies i s n o t completely described e i t h e r b y t h e equal charge displacement noted a t low energies l4,15 o r by t h e c o n s t a n t charge t o mass r a t i o which has been suggested t o be occurring i n v e r y h i g h 16 However, t h e l a t t e r p c s t u i a t e appears t o give a b e t t e r c o r energy f i s s i o n . relation.
A few primary y i e l d s measured i n t h i s work plus t k e primary y i e l d s
measured by Gibson have been used t o c o n s t r u c t a charge d i s t r i b u t i o n curve which i s s l i g h t l y d i f f e r e n t from t h a t of Gibsor,
et ,1.,bxt
l i k e -ckeTrs, i s
based on t h e p o s t u l a t e of e q u a l charge t o mass r a t i o . 4 ~ 2 0 This curve was used t o c o r r e c t t h e observed f i s s i o n product c r o s s - s e c t i o n s f o r t h e l o s s of y i e l d s of members of the same mass chain with higher atomic number, and t h e c o r r e c t e d cross-sections are shown i n t h e right-hand columns of Tables V t o V I I .
The
mass number of t h e apparent f i s s i o n i n g nucleus used i n a p p l i c a t i o n of t h e curve was es,timated from t h e b e s t values f o r t h e c e n t e r of symmetry of t h e f i s s i o n y i e l d curves.
Additional discussion of t h e problem of n u c l e a r charge d i s t r i -
bution i n medium energy f i s s i o n w i l l be given b y Gibson, Glass, and Seaborg, and t h e problem w i l l not be discussed f u r t h e r h e r e .
6 to
Mass y i e l d curves f o r r e p r e s e n t a t i v e e n e r g i e s a r e shown i n Figs.
8. The l i m i t s of e r r o r a r e estimated t o be about chains reported.
+
15% f o r most of t h e mass
However, a t higher energies, p a r t i c u l a r l y f o r
u
~
t h e~ chain ~
y i e l d c o r r e c t i o n s became q u i t e s i z e a b l e , and t h e e r r q x s may be somewhat g r e a t e r . The number of neutrons emitted a s e s t i m a t e d from t h e c e n t e r of symmetry of t h e f i s s i o n mass y i e l d curve i s i n d i c a t e d i n Figs. l a s t row of Tables V t o VII.
6 t o 8 and i n t h e next t o
It should be emphasized t h a t t h e r e f l e c t i o n of
mass y i e l d curves does not give any information as t o whether t h e neutrons a r e emitted before or a f t e r t h e f i s s i o n process t a k e s place b u t includes c o n t r i butions from
both sources.
However, some information on t h i s s u b j e c t implied
by o t h e r types of d a t a w i l l be discussed l a t e r . The t o t a l f i s s i o n cross-sections obtained by i n t e g r a t i o n of t h e f i s s i o n mass y i e l d curves a r e shown i n t h e l a s t row of Tables V t o V I I .
The t o t a l
f i s s i o n cross-sections a r e compared with t h e summed s p a l l a t i o n c r o s s - s e c t i o n s i n Figs.
9 and 10. No f i g u r e i s shoWl f o r IJE38, a s it was impossible t o meas-
ure y i e l d s f o r most of t h e (a,xn)r e a c t i o n s because of t h e long h a l f l i v e s of the products.
The importance of t h e f i s s i o n process i s r e a d i l y apparent from
these f i g u r e s . Total cross sections The t o t a l r e a c t i o n cross-sections a s obtained from t h e sum of t h e experimental f i s s i o n and s p a l l a t i o n cross-sections a r e shown i n Figs, 11 t o 13. Theoretical cross-sections f o r compound nucleus formation a s given by B l a t t and ~ e i s s k o ~ fare ' ~ shown f o r two values of t h e n u c l e a r r a d i u s parameter,
r
0
= 1 . 3 ~ 1 0 - ~ ~ c r n a n= d 1r . 5 x 1 0 -13 cm. 0
Theseexperimentalresults in-
d i c a t e a value of t h e nuclear r a d i u s parameter s l i g h t l y g r e a t e r than r x 1 0 - lcm. ~
0
=
1.5
,
IV. DISCUSSION The general f e a t u r e s of t h e e x c i t a t i o n f u n c t i o n s f o r s p a l l a t i o n r e a c t i o n s i n t h e uranium i s o t o p e s a r e i n many ways q u i t e s i m i l a r t o those t h a t have been determined f o r o t h e r v e r y heavy elements.
he cross-sections
f o r t h e ( a , n ) and (a,p) r e a c t i o n s do not v a r y much with energy and are seldom more than a few m i l l i b a r n s i n magnitude.
The e x c i t a t i o n functions f o r t h e
(a,xn) r e a c t i o n s ( f o r x g r e a t e r than 1) have peaks which decrease i n magnitude a s x increases. a c t i o n s of
u~~~
The c r o s s - s e c t i o n s f o r t h e (a,2n), (a,3n), and (a,4n) r e a r e considerably smaller than those f o r U 235 A s i m i l a r mass
e f f e c t occurs i n t h e plutonium i s o t o p e s .
The c r o s s - s e c t i o n s f o r r e a c t i o n s i n
which charged p a r t i c l e s a r e emitted a r e q u i t e l a r g e compared t o the (a,xn) reaction cross sections.
I n order t o e x p l a i n t h e r e l a t i v e l y low c r o s s - s e c t i o n s f o r t h e s p a l l a t i o n r e a c t i o n s of t h e plutonium isotopes, Glass and co-workers have prcposed t h a t both f i s s i o n and t h e major p a r t of t h e (a,xn) r e a c t i o n s involve compound nucleus formation and t h a t i n t h e break-up of t h e compound nucleus f i s s i o n competes more s u c c e s s f u l l y than does s p a l l a t i o n t o claim t h e l a r g e r share of 1 the t o t a l cross-section. The decrease i n t h e peak h e i g h t s f o r t h e successive
(a,xn)r e a c t i o n s has been i n t e r p r e t e d t o mean t h a t f i s s i o n i s competing succ e s s f u l l y a t each s t a g e of t h e evaporation chain i n a compound nucleus r e a c t i o n . Thus t h e peak c r o s s - s e c t i o n of t h e (a,3n) r e a c t i o n i s lower than t h e peak c r o s s s e c t i o n of t h e (a,2n) r e a c t i o n because i n t h e former case f i s s i o n has had t h r e e chances t o compete w i t h neutron emission compared with two chances i n t h e l a t t e r case.
The long " t a i l s " on t h e (a,xn) e x c i t a t i o n f u n c t i o n s and t h e r e l a -
t i v e l y high c r o s s - s e c t i o n s f o r t h e r e a c t i o n s involving t h e emission of charged p a r t i c l e s suggest d i r e c t i n t e r a c t i o n s of t h e p r o j e c t i l e w i t h a few nucleons on t h e nuclear s u r f a c e .
If a d i r e c t i n t e r a c t i o n occurs i n which one o r more
nucleons a r e emitted without leaving much e x c i t a t i o n energy i n t h e nucleus, then t h e r e s i d u a l nucleus may n o t be s u f f i c i e n t l y e x c i t e d t o undergo f i s s i o n . Thus t h e products of t h e d i r e c t i n t e r a c t i o n type r e a c t i o n s o f t e n survive f i s s i o n , whereas t h e products which a r e formed by evaporation of neutrons from a compoimd nucleus tend t o be eliminated by f i s s i o n .
This means t h a t e x c i t a t i o n f u n c t i o n s
f o r r e a c t i o n s i n t h e v e r y heavy elements o f t e n s t r i k i n g l y demonstrate t h e
importance of d i r e c t i n t e r a c t i o n mechanisms even a t r e l a t i v e l y low bombarding energies.
Most of t h e r e s u l t s r e p o r t e d h e r e can be explained i n t h e framework
of t h e ideas mentioned above. Compound nucleus s p a l l a t i o n r e a c t i o n s The cross-sections r e p o r t e d f o r t h e (a,xn) r e a c t i o n s i n d i c a t e t h a t f i s s i o n i s competing more e f f e c t i v e l y i n t h e bombsrdments of of Pu239.
u~~~ t h a n
i n those
I f one considers j u s t t h e difference i n f i s s i o n a b i l i t y p r e d i c t e d
through use of t h e parameter
z - , this
A
curium isotopes produced from pua3'
observation i s s u r p r i s i n g because t h e z2 have l a r g e r values f o r - than do t h e
corresponding plutonium isotopes from
u~~~
A
However, i f we consider t h e
neutron binding energies of t h e intermediate n u c l e i and of t h e products formed i n t h e (a m ) r e a c t i o n s of u~~~ and Pu239 we see t h a t t h e neutron b i n d i n g
18 a r e energies
,
higher f o r t h e plutonium i s o t o p e s produced i n
u~~~ bombardments
than f o r t h e corresponding curium i s o t o p e s p r o d u c e d i n Pu239 bombardments. This has two e f f e c t s .
The f i r s t e f f e c t i s on t h e r e l a t i v e p r o b a b i l i t y f o r
From a s t a t i s t i c a l p o i n t of view a neutron w i t h a low
neutron emission.
binding energy i s e a s i e r t o evaporate t h a n a neutron with a higher b i n d i n g energy, and thus neutron emission w i l l t e n d t o be more probable i n t h e plutonium r e a c t i o n s than i n t h e uranium r e a c t i o n s .
A c o r r e l a t i o n of t h e r e l a t i v e prob-
a b i l i t y of neutron emission and f i s s i o n i n terms of neutron binding e n e r g i e s and f i s s i o n thresholds
-
n2
closely related t o
-A &-
i n d i c a t e s t h a t neutron emission
v i l l compete more favorably with f i s s i o n i n t h e r e a c t i o n s of ~u~~~ t h a n i n t h e
.
r e a c t i o n s of U 233 l9 The second way by which higher neutron binding e n e r g i e s favor f i s s i o n i n t h e r e a c t i o n s of uranium i s r e l a t e d t o t h e f a c t t h a t f i s s i o n thresholds a r e lower than neutron binding energies i n the elements considered. Therefore a nucleus t h a t has survived f i s s i o n long enough t o evaporate a l l of t h e neutrons t h a t t h e o r i g i n a l e x c i t a t i o n energy would allow may s t i l l have s u f f i c i e n t r e s i d u a l e x c i t a t i o n t o undergo f i s s i o n . Z0
Thus f i s s i o n has an
a d d i t i o n a l chance t o occur when neutron emission can no longer compete,
The
higher t h e neutron binding energy t h e l a r g e r w i l l be t h e e x c i t a t i o n energy range i n which such f i s s i o n can occur, i f one neglects t h e v a r i a t i o n i n t h e f i s s i o n threshold.
Although no f i s s i o n t h r e s h o l d s have been measured e x p e r i -
mentally f o r elements heavier than plutonium, i t i s l i k e l y t h a t t h e v a r i a t i o n i n f i s s i o n thresholds between t h e plutonium and curium n u c l e i w i l l c o u n t e r a c t t h i s e f f e c t t o a c e r t a i n extent. 19
The strong e f f e c t of the mass number on the r e l a t i v e p r o b a b i l i t y of neutron emission and f i s s i o n observed i n both the reactions of t h e uranium isotopes and the reactions of t h e plutonium isotopes can a l s o be explained by arguments along similar l i n e s .
The e f f e c t appears t o be much greater than
the e f f e c t due t o 1 / A predicted on the b a s i s of the f i s s i o n a b i l i t y parameter z2 l9 Therefore it seems quite l i k e l y t h a t the most important f a c t o r i s the A * e f f e c t of the neutron binding energies on t h e probability f o r neutron emission.
It i s well known t h a t there i s a general t r e n d f o r neutron binding energies t o %s one decrease with increasing mass number, f o r a given atomic number. can a t t r i b u t e the higher cross sections f o r the (a,xn) r e a c t i o n s f o r the heavier isotopes of a p a r t i c u l a r element p r i n c i p a l l y t o t h e g r e a t e r ease with which neutron-rich isotopes can evaporate neutrons. 22 Jackson has devised a schematic model f o r (p,xn) r e a c t i o n s i n heavy elements.
I n h i s treatment he combines the r e s u l t s of Monte Carlo calculations
f o r t h e p r o b a b i l i t y af the various prompt processes with the r e s u l t s of a simplified evaporation model.
H i s c a l c u l a t e d cross s e c t i o n s show reasonable
8
agreement with the experimental r e s u l t s of B e l l and ,SkarsgardZ3 and Kelly
f o r ( p , ~ reactions ) of l e a d and bismuth i n the energy range up t o 100 Mev. The evaporation model devised by Jackson has incorporated i n t o it the following assumptions: ( 1 ) the neutron energy spectrum i s given by E exp
(-'/T)
where
6
i s the k i n e t i c energy of the neutron and T i s the nuclear
temperature, ( 2) neutron emission occurs wherever it i s e n e r g e t i c a l l y poss i b l e , (3) proton evaporation i s neglected, and (4) the nuclear temperature T i s independent of e x c i t a t i o n energy.
This l a s t assumption i s contrary t o
what one would predict *an most nuclear models.
However, it i s doubtful t h a t
any large e r r o r s are introduced by t h i s approximation.
According t o Jackson,
the probability t h a t a nucleus with i n i t i a l e x c i t a t i o n energy E w i l l evaporate exactly x neutrons i s then given by
1 " n -x where I (z,n) i s Pearson's incomplete gamma function, I (z,n) = 1 x e dx n: 0 X and ax = (E $. / T. Bi i s t h e binding energy f o r t h e i t h neutron and -, B ~ ) T i s the nuclear temperature.
-
ZL
I f we wish t o extend t h e model given b y Jackson t o helium-ion induced r e a c t i o n s of f i s s i o n a b l e elements, two d i f f i c u l t i e s a r i s e .
The f i r s t i s t h a t
no Monte Carlo c a l c u l a t i o n s have been made f o r t h e case where t h e p r o j e c t i l e i s a helium ion.
Thus t h e c o n t r i b u t i o n of d i r e c t i n t e r a c t i o n s o r s i m i l a r
prompt processes w i l l f o r t h e p r e s e n t have t o be ignored i n t h e c a l c u l a t i o n . On t h e other hand, comparison of t h e c a l c u l a t e d p r o b a b i l i t i e s f o r evaporation with t h e experimental r e s u l t s can be used t o e s t i m a t e t h e c o n t r i b u t i o n of direct interactions.
Secondly, we must make a modification t o include t h e
e f f e c t of f i s s i o n competition. The f i s s i o n competition w i l l be considered i n t h e framework of compound nucleus formation followed b y competition between neutron emission and f i s s i o n a t each stage of t h e evaporation chain.
There a r e two e f f e c t s t o consider:
f i r s t , f i s s i o n occurs while neutron emission i s e n e r g e t i c a l l y p o s s i b l e , t h u s destroying n u c l e i during t h e e a r l y s t a g e s of t h e evaporation chain, and, second, some f i s s i o n occurs a f t e r a l l of t h e p o s s i b l e neutrons have been evaporated, thus destroying n u c l e i whose e x c i t a t i o n energy i s l e s s than t h e b i n d i n g energy of t h e l a s t neutron, and which would otherwise have de -excited by gamma emission. The p r o b a b i l i t y t h a t an e x c i t e d nucleus w i l l emit a neutron i s given b y n' / i t s branching r a t i o a 4 ( l e v e l width r a t i o ) f o r neutron emission
/$*
ri -
(henceforth designated a s ~ n ) . S i m i l a r l y t h e branching r a t i o f o r f i s s i o n i s
n,
given by
' /
/$. fi,o r
IS
P
.
Gf,
and t h e branching r a t i o f o r gamma r a y d e - e x c i t a t i o n
r
lor G m e denominator, H contains terms f o r a l l t h e i r : i' I p o s s i b l e modes of decay of t h e compound nucleus. However t h e assumptions w i l l
by
I
be made t h a t the widths f o r proton evaporation and f o r gamma-ray d e - e x c i t a t i o n a r e n e g l i g i b l e wherever neutron emission o r f i s s i o n i s e n e r g e t i c a l l y p o s s i b l e . However t h e gamma-ray branching r a t i o i s taken as u n i t y wherever n e i t h e r f i s s i o n nor neutron evaporation i s e n e r g e t i c a l l y p o s s i b l e .
When t h e e x c i t a t i o n
energy i s g r e a t e r than t h e f i s s i o n t h r e s h o l d and l e s s than t h e binding energy of t h e l a s t neutron, G
f
i s taken t o be u n i t y .
Hence t o t a k e i n t o account t h e
f i s s i o n competition along t h e evaporation chain, we m u l t i p l y t h e p r o b a b i l i t y , P (E,x),
defined above, by terms, G t o give a new p r o b a b i l i t y t h a t t h e ni' o r i g i n a l compound nucleus w i l l not only evaporate x neutrons b u t w i l l a l s o survive f i s s i o n during t h e evaporation process.
A f t e r a l l of t h e neutrons have been evaporated, t h e r e s i d u a l nucleus may e i t h e r undergo f i s s i o n o r may de-excite b y gamma emission.
We make t h e
somewhat a s b i t r a r y assumption t h a t i f t h e r e s i d u a l nucleus has an e x c i t a t i o n energy g r e a t e r than t h e a c t i v a t i o n energy f o r f i s s i o n it w i l l undergo f i s s i o n and t h a t i f t h e nucleus has an e x c i t a t i o n energy l e s s t h a n t h e a c t i v a t i o n energy f o r f i s s i o n it w i l l de-excite b y gamma emission.
I n Jackson's model,
t h e f i r s t incomplete gamma f u n c t i o n gives t h e p r o b a b i l i t y t h a t t h e o r i g i n a l compound nucleus w i l l emit a t l e a s t x neutrons; t h e second t h e p r o b a b i l i t y t h a t t h e r e s i d u a l nucleus w i l l have an e x c i t a t i o n g r e a t e r than t h e binding energy Therefore, t o account f o r f i s s i o n competition a t t h e
of t h e l a s t neutron.
f i n a l s t a g e , we replace t h e l a s t incomplete gamma f u n c t i o n of Jackson by one giving t h e p r o b a b i l i t y t h a t t h e r e s i d u a l nucleus w i l l have an e x c i t a t i o n g r e a t e r than t h e a c t i v a t i o n energy f o r f i s s i o n .
The r e s u l t i s a narrowing of t h e peak
of t h e t h e o r e t i c a l e x c i t a t i o n f u n c t i o n s , i n b e t t e r agreement with experiment. Using these considerations, one can e x p r e s s t h e c r o s s s e c t i o n f o r a r e a c t i o n following compound nucleus formation as
where
A,
f
=
(E
- 2Xi
Bi
-E
~ / T~.
)
i s t h e a c t i v a t i o n energy f o r f i s s i o n f o r t h e r e s i d u a l nucleus. The subEth s c r i p t s 1, 2 - - X on t h e Gn f a c t o r r e f e r t o t h e branching r a t i o f o r emission o f t h e l s t , 2nd,
--,x
t h neutron from t h e compound nucleus,
cr
C
i s the c r o s s
s e c t i o n f o r t h e formation of t h e compound nucleus a t t h e p a r t i c u l a r energy considered.
The neutron binding energies were taken from Hyde and Seaborg,
18
and t h e f i s s i o n a c t i v a t i o n e n e r g i e s were c a l c u l a t e d from a semi-empirical equation r e l a t i n g f i s s i o n thresholds t o spontaneous f i s s i o n r a t e s . 19
It i s necessasy t o evaluate t h e G q u a n t i t i e s and t o choose a value of n t h e n u c l e a r temperature. Not a g r e a t d e a l i s known about t h e v a r i a t i o n of In/ w i t h e x c i t a t i o n energy and nuclear type (2, A, even-odd c h a r a c t e r , e t c )
rf
The following ass ( 1 ) /'
p t i o n about rnj
r,
rf w i l l b e made:
i s independent of e x c i t a t i o n energy.
..
(2)
r "/ r
f o r even-even n u c l e i i s twice a s g r e a t a s
f o r even-odd n u c l e i .
l'n
/rf (1t w i l l not be n e c e s s a r y t o consider
odd-odd products i n t h e p r e s e n t c a l c u l a t i o n s . )
(3) Aside from even-even and even-odd e f f e c t s , t h e r e i s a general trend f o r
n/
rf
t o vary with mass number.
The f i r s t assumption a s a f i r s t approximation o b t a i n s support from t h e shape of e x c i t a t i o n functions f o r f a s t neutron-induced f i s s i o n and a l s o from an a n a l y s i s by Batze12' of high energy s p a l l a t i o n e x c i t a t i o n f u n c t i o n s . conclusion was reached by Glass and co-workers from a n a l y s i s 1 c i t a t i o n functions. There i s , however, some evidence t h a t
The same
s p a l l a t i o n ex-
/rf i n c r e a s e s
with i n c r e a s i n g e x c i t a t i o n s Z 6 The second assumption a r i s e s from t h e b e l i e f t h a t t h e odd-mass product of t h e evaporation of a neutron from an even-mass nucleus has a higher l e v e l d e n s i t y than t h e even-mass product from an odd-mass nucleus; t h e f a c t o r of two used was taken from an e s t i m a t e b y Weisskopf. 27 The v a r i a t i o n of
Pn
/
rf
w i t h mass number has been evaluated from a p l o t of
t h e neutron t o f i s s i o n width r a t i o s a c t i o n s i n various uranium isotopes. increase by a f a c t o r of 1.3 per u n i t increase of mass number A. Using t h e above considerations, one needs t o choose o n l y two parameters t o c a l c u l a t e e x c i t a t i o n f u n c t i o n s f o r a l l of t h e p o s s i b l e
a,xn) r e a c t i o n s .
These a r e t h e nuclear temperature T and a mean value f o r
"/
have been made f o r t h e (geometric) value f o r
o
0 6 fir u2j3
and
Calcul~tions and U 235 A mean
u~~~ 0.29 ro; u~~~ and
a,xn) r e a c t i o n cross s e c t i o n s of
In/Vf
rf.
nuclear
temperatures of 1.41 Mev and 1.35 Mev r e s p e c t i v e l y were found t o give t h e b e s t f i t t o t h e exper' e n t a l data. mean values of
/'
rf
The neutron branching r a t i o s aerived from t h e
a r e i l ~ s t r a t e di n Table V Y I I I ,
i n Figs. l k and l j t h e
c a l c u l a t e d curves a r e compared with the experimental p o i n t s .
Considering t h e
s i m p l i c i t y of t h e model, t h e agreement with those f e a t u r e s of t h e e x c i t a t i o n functions believed t o r e s u l t from compound nucleus formation i s good. agreement with t h e peak c r o s s s e c t i o n values f o r t h e (a,2n), r e a c t i o n s supports t h e assumed v a r i a t i o n of rn/
rf
The
(a,3n), and (a,4n)
with mass number and nuclear
I n view of t h e success i n reproducing c e r t a i n f e a t u r e s of t h e s p a l l a t i o n e x c i t a t i o n functions using t h e branching r a t i o s shown i n Table V I I I ,
it seems j u s t i f i a b l e t o use t h e s e branching r a t i o s t o c a l c u l a t e t h e f r a c t i o n of t h e f i s s i o n t h a t occurs before t h e emission of v a r i o u s numbers of neutrons. Given an i n i t i a l e x c i t a t i o n energy of t h e compound nucleus, we can a l s o calcul a t e t h e average e x c i t a t i o n energy a t which f i s s i o n occurs.
It i s assumed
t h a t t h e average e x c i t a t i o n energy of a r e s i d u a l nucleus a f t e r t h e emission of a neutron i s given by
t h e i n i t i a l e x c i t a t i o n energy minus t h e binding energy
of t h e neutron and minus 2 T, where t h e nuclear temperature T has been taken a s 1.41Mev a n d 1 . 3 5 M e v f o r U 235
for^^^^
.
I n Table I X t h e percentage of t o t a l f i s s i o n s o c c u r r i n g a f t e r t h e evaporation of various numbers of neutrons a r e l i s t e d f o r t h r e e helium-ion bombardment energies.
The second row gives t h e i n i t i a l e x c i t a t i o n energy
corresponding t o t h e helium ion energy.
The l a s t row g i v e s t h e average ex-
c i t a t i o n energy a t which f i s s i o q i s occurring f o r each of t h e t h r e e i n i t i a l
excitation energies i n t h e ease of each isotope.
C a l c u l a t i o n s by Coffin and
Halpern give r e s u l t s which a r e i n s u b s t a n t i a l agreement w i t h those reported -
here
.26
It can be seen from Table IX t h a t most of t h e f i s s i o n prekedes neutron evaporation f o r h e l i m - i o n induced f i s s i o n of u~~~and U 235 This conclusion i s i n apparent disagreement with t h e observations of Harding and ~ a r l e who ~ , ~ ~ measured t h e angular d i s t r i b u t i o n of neutrons from t h e bombardment of n a t u r a l uranium w i t h
147 Mev protons.
They concluded t h a t t h e g r e a t e r p a r t of t h e
neutron emission occurred before f i s s i o n , with only 2.5 emitted from t h e moving fragments.
+
1 neutrons being
Although it i s p o s s i b l e t h a t a t high energy
the p r o b a b i l i t y f o r neutron emission i n c r e a s e s f a s t e r t h a n t h e p r o b a b i l i t y f o r f i s s i o n , t h e l a s t 3 o r 4 s t a g e s o f t h e evaporation chain should occur a t exc i t a t i o n energies comparable t o those of t h e n u c l e i i n t h i s work; t h a t i s , a t energies such t h a t f i s s i o n w i l l be followed by t h e emission of from 5 t o 7 neutrons.
However Marquez has pointed out t h a t had Harding and F a r l e y assumed
what appears t o be a more reasonable value f o r t h e average energy of t h e emitt e d neutrons, t h e y would have found t h e i r r e s u l t s c o n s i s t e n t w i t h t h e neutrons' being emitted a f t e r f i s s i o n . 30
Direct i n t e r a c t i o n s
14 and 15 shows t h a t almost a l l of t h e ( a , n ) e x c i 2n) e x c i t a t i o n f u n c t i o n c m t a t i o n functions and t h e high energy p a r t of t h e (a, Examination of Figs.
not be accounted f o r by a compound nucleus model.
It has been mentioned e a r l i e r
that d i r e c t i n t e r a c t i o n mechanisms must be important i n t h e s e r e a c t i o n s .
In
general, however, it has been expected t h a t t h e e f f e c t s of d i r e c t i n t e r a c t i o n would be seen only a t p r o j e c t i l e e n e r g i e s
above 50 Mev.
I n t h e r e a c t i o n s of
non-f i s s i o n a b l e n u c l e i , t h e prominent compound-nucleus - s p a l l a t i o n r e a c t i o n s u s u a l l y mask out any small e f f e c t s due t o d i r e c t i n t e r a c t i o n .
The region of
f i s s i o n a b l e n u c l i d e s i s , t h e r e f o r e , a p a r t i c u l a r l y good place t o s t u d y t h e
direct-interaction-spallation r e a c t i o n s with f a i r l y low energy p a r t i c l e s b e cause t h e r e a c t i o n s which involve compound nucleus formation a r e l a r g e l y elimi n a t e d by f i s s i o n competition. One reasonable mechanism f o r t h e (a,n) and ( a , p ) r e a c t i o n s i s a "knockon" r e a c t i o n i n which t h e h e l i m ion s t r i k e s a nucleon, which i s then emitted. The product of t h e (a,2n) r e a c t i o n can be formed i n t h e following t h r e e ways: (1)by evaporation of two neutrons from t h e compound nucleus and ( 2 ) by e j e c -
t i o n of t h e f i r s t neutron by a d i r e c t i n t e r a c t i o n mechanism followed by evaporation of t h e second neutron, d i r e c t i n t e r a c t i o n mechanism.
and (3) by e j e c t i o n of both neutrons b y a
The " t a i l " of t h e e x c i t a t i o n f u n c t i o n f o r t h e
(a,2n) r e a c t i o n i s v e r y l i k e l y due t o an i n i t i a l knock-on followed b y t h e evaporation of t h e second neutron.
Many of t h e d i r e c t i n t e r a c t i o n s i n which
one neutron i s knocked out w i l l leave t h e nucleus with enough energy t o evaporate a second neutron.
F i s s i o n tends t o c u t down t h e products, b u t n o t s o
severely a s it c u t s down t h e products from t h e r e a c t i o n involving t h e evaporation of two neutrons, s i n c e i n t h e l a t t e r case f i s s i o n has two chances t o compete w i t h neutron emission whereas i n t h e former it has only one. on the (a,2n) e x c i t a t i o n function f o r
u~~~
The f a c t t h a t t h e " t a i l " i s lower than t h a t f o r u~~~and Pu239
i s consistent with increased f i s s i o n competition a t t h e evaporation s t a g e s of
u~~~~ A comparison of t h e (a,2n) e x c i t a t i o n functions of U 233 , ~ and~ ~u~~~ ~ w, i t h those of l e a d shows t h a t t h e peaks have been c u t down b y
the r e a c t i o n s of
u
f i s s i o n more than have t h e " t a i l s " , an observation t h a t lends f u r t h e r support t o the idea t h a t t h e peaks, being due t o i n i t i a l compound nucleus formations, s u f f e r from f i s s i o n competition twice, whereas t h e t a i l s , being due p a r t l y t o
d i r e c t i n t e r a c t i o n , s u f f e r from f i s s i o n competition a t most only once.
The
c o n t r i b u t i o n of d i r e c t i n t e r a c t i o n s t o t h e e x c i t a t i o n f u n c t i o n s f o r t h e (a,3n) r e a c t i o n appears t o be f a i r l y small.
S e a c t i o n s proceeding by d i r e c t i n t e r a c t i o n
mechanisms probably c o n t r i b u t e t o t h e peak i n t h e curve r e p r e s e n t i n g t h e ( a , ~ n ) cross s e c t i o n s and p o s s i b l y t o t h a t i n t h e curve r e p r e s e n t i n g t h e (a,3n) c r o s s sections.
It i s l i k e l y , however, t h a t t h e observed products of t h e (~11,411) r e -
a c t i o n a r e due almost e n t i r e l y t o r e a c t i o n s going b y a compound nucleus mechanism. There i s l i t t l e doubt t h a t t h e products of t h e (a,p2n) r e a c t i o n of t h e heavy elements a r e produced almost e n t i r e l y by t h e d i r e c t emission of high energy t r i t o n s , without t h e formation of a compound nucleus .3 The y i e l d of tritium from helium-ion bombardment of has been measured3 and found t o be s l i g h t l y l a r g e r than t h e amount t h a t would be expected i f t h e e n t i r e c r o s s s e c t i o n f o r t h e (a,p2n) r e a c t i o n
-
a s measured radiochemically through t h e y i e l d of t h e
product nuclide i n t h i s work
- was
due t o t h e (a,t) r e a c t i o n .
The c r o s s s e c t i o n
f o r t h e production of t h e nuclide corresponding t o t h e "(a,p3n) r e a c t i o n " i s probably due t o t h e r e a c t i o n ( a , t n )
.
Thus t h e y i e l d of tritium would be expected
t o be higher than t h e radiochemical y i e l d of t h e product due t o t h e (a,t) r e a c t i o n because of t h e contribution of ( a , t n ) and (a,t f i s s i o n ) r e a c t i o n s . observation t h a t t h e y i e l d f o r t h e product of t h e includes t h e c o n t r i b u t i o n of t h e
u~~~
u~~~ (a,p3n)
The
r e a c t i o n (which
(0,411) r e a c t i o n ) i s much l e s s t h a n t h e
y i e l d f o r t h e product of t h e U238 (a,p3n) r e a c t i o n i n d i c a t e s t h e i n c r e a s e d f i s s i o n competition i n t h e neutron d e f i c i e n t i s o t o p e s . A simple c l a s s i c a l model can be used t o show t h e p l a u s i b i l i t y of t h e
i d e a t h a t a d i r e c t i n t e r a c t i o n between a helium ion and a nucleus can r e s u l t i n t h e emission
of a high energy t r i t o n w i t h t h e nucleus l e f t with a low
e x c i t a t i o n energy.
Since such a r e a c t i o n probably occurs a t t h e s u r f a c e of t h e
nucleus, t h e predominant force
i n determining t h e t r a j e c t o r y of t h e i n c i d e n t
and emitted charged p a r t i c l e i s t h e coulombic f o r c e .
It i s assumed t h a t t h e
helium i o n approaches t h e nucleus along t h e hyperbolic p a t h t h a t i s tangent t o t h e nuclear s u r f a c e .
A t t h e nuclear s u r f a c e , t h e helium s p l i t s i n t o a t r i t o n
and a proton, both moving with the same v e l o c i t y a s t h a t of t h e helium ion a t t h a t point.
The proton i s absorbed b y t h e nucleus and t h e t r i t o n moves away
from t h e nucleus along a hyperbolic p a t h tangent t o t h e nucleus a t t h e same
p o i n t t h a t t h e helium i o n path was tangent.
Calculations based on t h i s model
show t h a t a 4O-~evhelium ion i n c i d e n t on a U238 nucleus can cause t h e emission of a 2 4 - ~ e vt r i t o n , w i t h about 2 Mev of e x c i t a t i o n given t o t h e nucleus. Although t h e r e i s no d i r e c t evidence t h a t deuterons a r e e m i t t e d i n t h e "(a,pn)" r e a c t i o n , t h e r e i s other evid-ence t h a t t h i s i s l i k e l y t o be a cont r i b u t i n g process. n
I.
I f one remembers t h a t t h e y i e l d r e p o r t e d here f o r t h e U 238
A
(a,pn) IYpLW
r e a c t i o n i s t h a t f o r one isomer only, a comparison of t h e e x c i ~ U238,~ and ~ Pu , 238 1 show t a t i o n functions f o r t h e (a,pn) r e a c t i o n s of u t h a t t h e y a r e a l l of about the same magnitude, although t h e t a r g e t n u c l i d e s vary greatly i n f i s s i o n a b i l i t y . functions
The d i f f e r e n c e s i n shapes of t h e e x c i t a t i o n The f a c t
f o r t h e (a,pn) r e a c t i o n s are not understood completely.
t h a t t h e product of t h e
u~~~ (a,pn)
r e a c t i o n i s long-lived N~~~~
d i f f i c u l t t o i d e n t i f y and t h a t only one isomer of t h e U238 a c t i o n was observed somewhat complicates t h e p i c t u r e . t h e e x c i t a t i o n functions f o r the
u~~~
(a,pn) and t h e
which was 240 (a,pn) Np re-
However, b y comparing
u~~~
(aj2n) reactions?
one can f i n d a t l e a s t p a r t i a l evidence f o r d i r e c t emission of deuterons.
If
t h e " ( ~ l , ~ nr e) a c t i o n " took place by t h e emission of a s e p a r a t e proton and neutron, e i t h e r by formation of a compound nucleus o r b y d i r e c t i n t e r a c t i o n , a s i m i l a r mechanism should a l s o cause t h e emission of two neutrons with a t l e a s t equal frequency, w i t h the r e s u l t t h a t t h e c r o s s s e c t i o n f o r t h e (a,2n) r e a c t i o n would be a t l e a s t a s l a r g e a s t h a t f o r t h e (a,pn) r e a c t i o n . a c t u a l f a c t , t h e cross s e c t i o n f o r t h e (a,2n) r e a c t i o n of than t h a t f o r the ( a J p n ) r e a c t i o n of U 233
.
u~~~ i s
In
much smaller
The (a,m) r e a c t i o n was t h e most promSnent s p a l l a t i o n r e a c t i o n observed i n t h e bombardment of U238 with helium ions.
It i s doubtful t h a t compound
nucleus formation accounts f o r much of t h i s c r o s s s e c t i o n since t h e coulomb b a r r i e r would make it v e r y d i f f i c u l t t o evaporate an alpha p a r t i c l e .
This
view i s supported b y t h e low y i e l d s of (d,an) r e a c t i o n s observed i n t h e bombardment of u~~~ and Pu239 l2 S e v e r a l p o s s i b l e mechanisms remain. One
.
mechanism f o r t h i s r e a c t i o n i s a d i r e c t i n t e r a c t i o n of t h e bombarding p a r t i c l e with a neutron i n t h e d i f f u s e rim of t h e nucleus, r e s u l t i n g i n t h e neutrons being knocked out without t h e capture of the bombarding p r o j e c t i l e , -.
With t h i s type of mechanism t h e c r o s s s e c t i o n f o r t h e ( a , a p ) r e a c t i o n should a l s o be f a i r l y prominent.
Another p o s s i b i l i t y i s i n e l a s t i c s c a t t e r i n g of t h e
incident alpha p a r t i c l e , with the excited t a r g e t nucleus evaporating a neutron. With t h i s type of mechanism, the cross s e c t i o n f o r the
(a,-) r e a c t i o n should
be much l e s s than t h a t f o r the (a,m) r e a c t i o n because of coulomb b a r r i e r d i s crimination against charged p a r t i c l e evaporation.
Unfortunately, no c r o s s
sections f o r (a,ccp) reactions have been studied i n t h e heavy elements so t h a t
it i s not possible t o choose between the two mechanisms on t h i s b a s i s .
Still
a t h i r d p o s s i b i l i t y i s a coulomb e x c i t a t i o n process, but the p r o b a b i l i t y f o r t h i s does not seem t o be large enough t o account f o r the observed cross s e c t i o n . ~ e r k l e has ~ l measured a cross section of 70 mb f o r the (a,m) r e a c t i o n of ~u~~~a t
46 Mev, which i s quite comparable i n magnitude t o t h a t found f o r
the ( a , m ) reaction of U238.
,is
would i n d i c a t e t h a t the l a s t two mechanisms
are not very l i k e l y , f o r i n those cases one would expect t h a t f i s s i o n would compete with the neutron emission and the (a,an)r e a c t i o n would be l e s s probable f o r U238 than f o r Au197
.
One i n t e r e s t i n g consequence of t h e l a r g e contribution of a d i r e c t i n t e r a c t i o n mechanism i n s p a l l a t i o n reactions f o r highly f i s s i o n a b l e n u c l e i i s i l l u s t r a t e d i n Figs. 9 and 10. The curves showing the percent of t o t a l reaction cross section due t o s p a l l a t i o n r e a c t i o n s i s seen t o decrease with increasing energy f o r highest energies.
u~~~ and
~
u while ~ f o~r
u~~~ ~ t h e, curve
r i s e s a t the
This i s a t t r i b u t e d t o the prominence of compound nucleus
type s p a l l a t i o n reactions a t the lower energies with increased chances f o r
u~~~ and reactions. r e a c t i o n s i n u~~~ proceed through
f i s s i o n competition a t the higher energies i n the However, t h e major p a r t of the s p a l l a t i o n
d i r e c t i n t e r a c t i o n mechanisms and these become more probable a t higher energies. This does not imply t h a t there i s a l a r g e r amount of d i r e c t i n t e r a c t i o n taking place f o r
u~~~ than
for
u~~~ and
but t h a t the f r a c t i o n
l a t i o n reactions t h a t go by d i r e c t i n t e r a c t i o n i s l a r g e r f o r pu239 and U 235
.
of the s p a l -
u~~~ than
for
Fission The mass y i e l d d i s t r i b u t i o n s of t h e f i s s i o n products are shown f o r d i f f e r e n t helium ion energies i n Figs. 6 t o 8.
It i s seen t h a t f i s s i o n i s predomin a n t l y asymmetric a t low energies and appears t o become more symmetric as t h e e x c i t a t i o n energy i s increased, i n agreement with previous work. 1,4,32
However, it should be noted t h a t t h e increased symmetry i s not due t o t h e asymmetric peaks moving t o g e t h e r , b u t r a t h e r t o an apparent i n c r e a s e i n a symmetric mode causing t h e v a l l e y t o r i s e up f a s t e r than t h e wings.
Com-
parison of t h e f i s s i o n y i e l d curves, and p a r t i c u l a r l y t h e v a l l e y t o peak r a t i o s ( r a t i o of t h e c r o s s s e c t i o n a t t h e minimum i n t h e y i e l d d i s t r i b u t i o n t o t h e cross s e c t i o n a t t h e asymmetric maxima) i n d i c a t e s t h a t t h e r e i s no s i g n i f i c a n t difference i n t h e f i s s i o n asymmetry i n t h e t h r e e uranium isotopes studied. As i s seen i n F i g s .
9, 10, and 13, t h e t o t a l f i s s i o n c r o s s s e c t i o n s
f o r t h e t h r e e isotopes a r e a l l approximately t h e same and account f o r most of t h e t o t a l cross s e c t i o n .
Comparison of t h e f i s s i o n c r o s s s e c t i o n s determined
i n t h i s work f o r helium i o n induced f i s s i o n of
u~~~ and
U238
with the r e s u l t s
determined b y ~ u n ~ e r m ausing n ~ ~ an i o n i z a t i o n chamber show good agreement between t h e two methods.
We wish t o acknowledge h e l p f u l discussions with Drs. W. M. Gibson, B. G. Harvey, and W. H. Wade.
The cooperation of t h e l a t e G. Bernard Rossi,
and of W. B a r t Jones and t h e crew of t h e Crocker Laboratory 60-inch cyclotron i s appreciated.
The Health Chemistry Group of t h e Radiation Laboratory a s -
s i s t e d i n minimizing t h e hazards i n wocking with r a d i o a c t i v e m a t e r i a l s . Two of t h e authors (R.v.
and T.D.T.)
wish t o acknowledge t h e support
of t h e National Science Foundation i n t h e form of Predoctoral Fellowships
(1955 -57 and 1954-57, r e s p e c t i v e l y )
.
This work was performed under t h e auspices of t h e U. S. Atomic Energy Commission.
Table I1 S-p a l l a t i o n cross s e c t i o n s (mb ) f o r helium-ion induced r e a c t i o n s of U233
Table 111 S-p a l l a t i o n c r o s s s e c t i o n s (mb ) f o r helium-ion induced r e a c t i o n s of U235
Product
,238
,237
,236
,235
PU234
Np238
Np236
Table I V
S p a l l a t i o n cross sections ( m b ) f o r helium-ion induced r e a c t i o n s of U238
Product
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