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THE EFFECT OF THE ELECTRIC
POLARIZABILITY OF THE NEUTRON ON NEUTRON-NUCLEUS SCATTERING
H. Leeb, G. Eder, H. Rauch
To cite this version:
H. Leeb, G. Eder, H. Rauch. THE EFFECT OF THE ELECTRIC POLARIZABILITY OF THE NEUTRON ON NEUTRON-NUCLEUS SCATTERING. Journal de Physique Colloques, 1984, 45 (C3), pp.C3-47-C3-50. �10.1051/jphyscol:1984310�. �jpa-00224024�
JOURNAL DE PHYSIQUE
Colloque C 3 , supplement au n ° 3 , Tome 4 5 , m a r s 198^ page C3-47
The electric and magnetic polarizabilities of the nucleon together with mass, charge and magnetic moment describe the response of a neutron or proton on an external electromagnetic field. The polarizabilities reflect the internal structure of the particle and hence they are interesting quantities in the context of the quark model. But the knowledge of these structure constants is also desired from the nu- clear physics point of view, since scattering processes /!/, hyperfine splitting of atomic states /2,3/ and energy shifts of hadronic atoms /4,5/ are influenced.
Due to experimental difficulties the polarizabilities are presently known rather poorly. This is particularly true of the electric polarizability of the neutron a.
Since laboratory electric fields are too weak to obtain measureable effects it has been suggested by Aleksandrov /6/ to extract a from neutron scattering on heavy ele- ments. Unfortunately, the interpretation of these experiments is rather hard and has
led to contradictory results /6-8/ ranging from a = 0.26 fm3 to a = lO-1* f m3. Theoretical estimates based on meson theory /9/ or on the quark model picture /10/
as well as semi theoretical derivations from photo-neutron processes /11,12/ favour a value a 'v 1Q~3 fm3 but model dependence and systematic errors do not allow a clear decision.
Neutron-nucleus scattering gives a nearly model independent way to determine a.
Corresponding experimental data have been obtained a couple of years ago. In the meantime not only considerable improvements in the experimental techniques have been achieved but also intense neutron beams in energy ranges not accessible before exist at spallation facilities. Considering these developments it seems worthwhile to think about whether modern neutron-nucleus experiments can give new information on a. In the present contribution we study some possibilities to extract a from the elastic differential cross sections.
Due to the finite electric polarizability an electric dipole moment of the neutron is induced in the electric field £ of the target nucleus. In static approximation
THE EFFECT OF THE ELECTRIC POLARIZABILITY OF THE NEUTRON ON NEUTRON-NUCLEUS SCATTERING
H. Leeb, G. Eder and H. Rauch
Institut fiir Kernphysik, Technische UniversitSt, A-1020 Wien, Schiittelstrasse 115, Austria
Résumé - En utilisant une distribution de charge schématique pour l'atome il est montré que la polarisabilité peut être extraite de l'analyse des sections efficaces différentielles de la diffusion n-Pb à des énergies avoisinant 100 eV. Une augmentation de l'effet de polarisation dans la distribution angulaire est trouvée aux directions avant pour lesquelles l'interaction de Schwinger domine la diffusion.
Abstract - Using a schematic charge distribution of the atom it is shown that the polarizability can be extracted by analyzing differential cross sections for n-Pb at energies about 100 eV. An increase of the polarization effect in the angular distribution is found at forward directions, where the Schwinger interaction dominates the scattering.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984310
C3-48 JOURNAL DE PHYSIQUE
t h i s e f f e c t can be described by t h e p o t e n t i a l
P + 2 -+
V ( r ) = - ~ I T E ~ c ~ E ( r ) . ( 1
Assuming reasonable values a < lo-' f m 3 t h i s term represents o n l y a small f r a c t i o n o f t h e nuclear i n t e r a c t i o n which dominates t h e neutron-nucleus s c a t t e r i n g . C o n t r i - b u t i o n s o f t h e same o r d e r as vP a r i s e due t o electromagnetic i n t e r a c t i o n s , namely the Schwinger term /13/ which gives r i s e t o a s p i n o r b i t i n t e r a c t i o n and t h e Foldy term /14/. While the Schwinger term i s w e l l determined by t h e anomalous magnetic moment o f t h e neutron t h e r e a r e some doubts concerning the p r e c i s e value o f t h e electron-neutron s c a t t e r i n g l e n g t h an, /8,15/ which c h a r a c t e r i z e s t h e Foldy term.
Hence, an, has t o be determined from neutron-nucleus s c a t t e r i n g experiments, too.
The s c a t t e r i n g amplitudes o f t h e various terms can g i v e us a f e e l i n g where p o l a r i - z a t i o n e f f e c t s should show up. I n f i r s t Born approximation which i s s u f f i c i e n t f o r these p o t e n t i a l s we o b t a i n f o r a schematic charge d i s t r i b u t i o n o f t h e t a r g e t
t h e s c a t t e r i n g amplitudes
- -i bF { s i n ~ R o - qRa cos qRo -
f ~ c h w i n g e r - ( qRo l 3 I ) c o t + s . 1 , ( 3 )
1 + (qR1)' m s i n qRo - qRo cos qR, -
fFoldy = Z ane - { 3 1
mn 1 ,
( qRo I3 1 + ( ~ R I ) ~
2 m c 1
f, = z af a - [ ( 6 q ~ o - q3~!) cos qRo + ( 3 q 2 ~ f - 6 ) s i n q ~ 3 (qR0
Here, Z i s t h e p r o t o n number o f t h e t a r g e t nucleus, b~ = -1.4681 fm i s t h e Foldy s c a t t e r i n g l e n g t h , q i s t h e t r a n s f e r r e d momentum, mn i s the mass o f the
Fig. 1 - The q-dependence o f t h e s c a t t e r i n g amplitudes f p and I f F o l d y l assuming an,=-1 .4681-10-3 fm and a=10-3 f m 3 . The energy corresponds t o maximal momentum t r a n s f e r a t 5=180°.
neutron and m i s t h e reduced mass o f t h e neutron-nucleus system. I n Eq. ( 3 ) fi de- notes the s c a t t e r i n g plane and 3 i s t h e s c a t t e r i n g angle. For t h e c a l c u l a t i o n o f t h e s c a t t e r i n g amplitudes f o r n-'08pb which a r e shown i n Fig. 1 t h e values R o = 7.41 fm and R1 = 49310 f m have been taken i n o r d e r t o reproduce t h e charge r a d i i o f t h e nucleus and t h e atom, r e s p e c t i v e l y . Yet i t should be mentioned t h a t Eq. ( 5 ) i s obtained by n e g l e c t i n g t h e e l e c t r o n charge d i s t r i b u t i o n which i s de- s c r i b e d by t h e second term o f Eq. ( 2 ) . This approximation i s j u s t i c i e d since t h e i n f l u e n c e o f t h e e l e c t r o n s on Eq. ( 5 ) i s o f t h e order R o / R 1 ?. 10- . The comparison i n F i g . 1 i n d i c a t e s c l e a r l y t h e p o s s i b i l i t y t o disentangle t h e d i f f e r e n t c o n t r i b u - t i o n s v i a t h e i r d i f f e r e n t angular d i s t r i b u t i o n s . The optimal energies t o separate a a r e between 100 eV < E < 10 keV which i s i n agreement w i t h t h e estimates o f Bernabeu and Ericson /16/. A t energies below 1 eV t h e angular d i s t r i b u t i o n becomes s e n s i t i v e on an,.
Now we w i l l focus our a t t e n t i o n on t h e determination o f a from t h e e l a s t i c d i f f e r - e n t i a l cross sections. For s i m p l i c i t y we assume ane = b ~ and t h a t t h e nuclear i n t e r a c t i o n p o t e n t i a l i s a square w e l l o f depth V o = 48.296 MeV and range
R o = 7.41 fm. Then t h e experimental t o t a l cross s e c t i o n f o r n-208Pb i s w e l l r e p r o - duced. The t o t a l s c a t t e r i n g amplitude i s then given by
where fr i s t h e p a r t i a l wave s c a t t e r i n g amplitude o f t h e nuclear i n t e r a c t i o n . I n the case of 2 0 8 ~ b the f i r s t known resonance l i e s a t about 80 keV and can be neg- l e c t e d i n our q u a l i t a t i v e considerations. Therefore fv i s given o n l y by t h e square a e l l p o t e n t i a l described above. The phase s h i f t q1 i s due t o t h e p o l a r i z a t i o n
Fig. 2 - The cross s e c t i o n r a t i o R ( 3 , a ) f o r p o l a r i z e d and u n p o l a r i z e d neutron beams and the s e n s i t i v i t y o f the angular d i s t r i b u t i o n A($) on a . For t h e parameters o f t h e c a l c u l a t i o n see t e x t .
1.5 1.4.
- 8 1.3 1.2.
*-
-
-, 1.1-
- 2
.--__ - . '.
unpolarized E=lOeV
- a= lob2
1
._---
E=lOeV - unpolar~zed
--- polar~zed -
1.004 - ..
--- a.0
polarized
E= 1 keV --- - unpolar~zed polar~zed
a
' 3 2
--- ''. 0
R(J,.)=~(~,.)PPI~:~I d~ dn
1
'-
___---0 60 120 0 60 120 180 0 60 120 180
--- 4 (degree) unpolarized
E=l keV - .=,0-2
C1
- 0 2
n(y)= 2 R(J..I- R(~.a=OI a R(3,=1+ R(*,.=OI -
,---
1 0
C3-50 JOURNAL DE PHYSIQUE
p o t e n t i a l and t h e Foldy term. F i g . 2 shows t h e d i f f e r e n t i a l cross s e c t i o n c a l c u l a t e d f o r u n p o l a r i z e d neutrons as a f u n c t i o n o f energy and a. The peak a t forward d i r e c - t i o n s i s caused by the Schwinger i n t e r a c t i o n . I f one uses, however, a neutron beam which i s p o l a r i z e d i n t h e s c a t t e r i n g plane t h e Schwinger term disappears. The c o r r e - sponding c r o s s sections, shown i n F i g . 2, r e f l e c t t h e i n t e r f e r e n c e between t h e nu- c l e a r i n t e r a c t i o n and t h e p o l a r i z a b i l i t y e f f e c t d i r e c t l y . The r i g h t s i d e o f F i g . 2 shows t h e q u a n t i t y A which i s a measure f o r t h e s e n s i t i v i t y o f angular d i s t r i b u t i o n s on t h e p o l a r i z a b i l i t y . I n p a r t i c u l a r we see t h a t a t E = 1 keV f o r a = f m 3 cross s e c t i o n v a r i a t i o n s o f t h e order o f 10-4 have t o be detected. The s e n s i t i v i t y A i n - creases an order o f magnitude a t forward angles, where t h e Schwinger i n t e r a c t i o n dominates t h e s c a t t e r i n g . However, the n u c l e a r i n t e r a c t i o n has very s t r o n g i n f l u e n c e on R(8,a) i n t h i s angular range, too, thus reducing t h e p o s s i b i l i t y t o separate a.
Nevertheless, t h e d e t e r m i n a t i o n o f R(3,a) a t forward angles i s very u s e f u l since i t o f f e r s a n o r m a l i z a t i o n f r e e q u a n t i t y which i s very s e n s i t i v e on a.
Our c a l c u l a t i o n s i n d i c a t e c l e a r l y t h a t p o l a r i z a t i o n e f f e c t s o f t h e neutron should show up i n t h e angular d i s t r i b u t i o n s between 10 eV and 10 keV. A l l measurements so f a r have been made a t lower energies E < 5 eV /6,7/ o r a t t o o h i g h energies /8/. A t lower energies t h e energy dependent e f f e c t s a r e very small and can be detected hardly. On t h e o t h e r hand a t h i g h energies t h e p o l a r i z a t i o n e f f e c t s a r e concentrated a t very small angles thus causing experimental d i f f i c u l t i e s , too. These shortcomings of previous experiments e x p l a i n t h e ambiguous r e s u l t s obtained up t o now. F i n a l l y i t should be mentioned t h a t t h e r e are i n h e r e n t assumptions i n t h e ansatz ( 1 ) which might l e a d t o systematic e r r o r s . F i r s t l y , a l l dynamical e f f e c t s have been neglected.
This should be a good approximation a t low neutron energies. A more c r u c i a l p o i n t i s t h e assumption about t h e i n t e r p l a y between t h e nuclear f o r c e and t h e e l e c t r i c f i e l d . I n Eq. ( 1 ) i t i s assumed t h a t the e l e c t r i c d i p o l e moment induced i s unchanged i n t h e presence o f t h e nuclear force. I t can be estimated t h a t t h e systematic e r r o r made by t h i s assumption i s l e s s than 5%. Concluding o u r c o n s i d e r a t i o n s i t can be s t a t e d t h a t new neutron-nucleus s c a t t e r i n g experiments u s i n g i n t e n s e neutron beams from s p a l l a t i o n f a c i l i t i e s w i l l reduce t h e bounds f o r t h e e l e c t r i c p o l a r i z a b i l i t y o f the neutron.
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