PROPERTIES OF THE NEUTRON

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PROPERTIES OF THE NEUTRON

J. Byrne

To cite this version:

J. Byrne. PROPERTIES OF THE NEUTRON. Journal de Physique Colloques, 1984, 45 (C3), pp.C3- 1-C3-10. �10.1051/jphyscol:1984301�. �jpa-00224015�

JOURNAL DE PHYSIQUE

Colloque C3, supplément au n°3, Tome 45, mars 1984 page C3-1

PROPERTIES OF THE NEUTRON

J. Byrne

School of Physical and M athe m atical Sciences, University of Sussex, Brighton BN1 9QH, U.K.

Résumé - Nous passons en revue les données expérimentales récentes con- cernant les propriétés du neutron du point de vue des interactions forte, électromagnétique, faible et gravitationnelle.

A b s t r a c t - We review recent experimental data on the neutron and on i t s s t r o n g , e l e c t r o m a g n e t i c , weak and g r a v i t a t i o n a l i n t e r a c t i o n s .

1 . Mechanical P r o p e r t i e s

(1.1) Elementary nature of the neutron

An elementary quantum mechanical system i s one whose states transform according to a d e f i n i t e i r r e d u c i b l e r e p r e s e n t a t i o n of the inhomogeneous Lorentz group l a b e l l e d by the mass M and the spin J . Whether or not a p a r t i c l e i s regarded as elementary depends on the time scale over which i t e x i s t s as an i r r e d u c i b l e e n t i t y . The n a t u r a l u n i t f o r t h i s time scale i s i r / M c2 which f o r the neutron i s - l O "2" sec.

This compares w i t h it'sB-decay l i f e t i m e T - 103 sec. Thus f o r low energy phenomena a t l e a s t i t i s reasonable t o view the nefttron as an elementary p a r t i c l e .

( 1 . 2 ) Spin

That the spin o f the neutron i s J was demonstrated long ago by slow neutron s c a t t e r i n g i n o r t h o - and para-hydrogen( 1 ) . More r e c e n t l y t h i s has been confirmed d i r e c t l y from the s p a t i a l s p l i t t i n g o f unpolarized neutron beams i n a Stern-Gerlach apparatus(2)Because J = \ the neutron i s a f e r m i o n ; i f i t were not so we would not observe s h e l l s t r u c t u r e i n n u c l e i . For h a l f - i n t e g r a l spin the r e l e v a n t group r e p r e s e n t a t i o n i s diouble-valued and f o r the neutron t h i s too has been d i r e c t l y v e r i f i e d using i n t e r f e r o m e t r i c techniques ( 3 , 4 ) .

(1.3) Mass

In 1961 the I n t e r n a t i o n a l Union of Physics and Chemistry adopted as the u n i t (u) of nuclear mass one t w e l f t h p a r t of the mass of 1 2C . According to the 1973 adjustment of constants t h i s has the value i n MeV (5)

l u = 931 .5016 + 0.0026 MeV

The most accurate method f o r determining the mass of the neutron makes use of the exothermic r e a c t i o n n+p+ D+y the energy release Er. being c a r r i e d o f f by the y-ray and the r e c o i l i n g deuteron . C u r r e n t l y there are three values of En. of comparable accuracy a v a i l a b l e

En = 2.224564 + 0.000017 MeV (Greenwood and Chrien 1980) ( 6 ) E„ = 2.224568 + 0.000008 MeV (Vylov e t a l 1982) ( 7 )

E^ = 2.224575 + 0.000009 MeV (Van der Leun 1982) ( 8 )

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984301

C3-2 JOURNAL DE PHYSIQUE

These d a t a are then combined w i t h the mass d i f f e r e n c e s as determined from charged p a r t i c l e mass spectroscopy ( 9 )

'H2 - 2H = 1548.287 + 0.006 V U

'H - ^{1 = 7825.037} _- ^{0.010 UU}

t o y i e l d a value f o r the mass excess o f t h e neutron (n-1) = Eo - - ^{2 ~} + ⁾ ( I H - 1 )

The weighted average f o r the t h r e e values o f ED gives the r e s u l t

This r e s u l t may be compared w i t h t h e r e s u l t (n-1 ) = 8665.012 + 0 . 0 3 7 ~ accepted by the 1982 P a r t i c l e Physics Data Group ( 10 ). To determine t h e p h a s e space f a c t o r f a p p r o p r i a t e t o neutron 8-decay we r e q u i r e a value f o r the neutron-proton mass d i f f e r e n c e which from t h e value o f (n-1) above i s given by

(M -M ) c2 = 1.293302 + 0.000015 MeV

n P -

2 . Strong I n t e r a c t i o n s

(2.1) Strong I n t e r a c t i o n Symmetry

A d e t a i l e d d i s c u s s i o n o f the s t r o n g i n t e r a c t i o n s o f the neutron i s n o t o f immediate i n t e r e s t i n a conference devoted t o low energy phenomena and we s h a l l t h e r e f o r e o n l y summarise what i s known, o r b e l i e v e d t o be known,about t h e symmetries o f these i n t e r a c t i o n s . The p a r i t y P r e l a t i v e t o the proton i s + and the charge Q=O and baryon number B=l are a b s o l u t e l y conserved so f a r as i s known. The b e s t approximate s y m e t r y i s t h a t described by t h e symmetry group SU(2) ( i s o s p i n ) which i s extended t o SU(3) ( f l a v o u r ) t o accanmodate t h e strange p a r t i c l e s . These symmetry groups m a n i f e s t themselves as approximately degenerate m u l t i p l e t s i n t h e mass spectrum o f

hadrons g i v i n g r i s e t o t h e fami 1 ia r o c t e t s o f J=$ baryons and J=O mesons.

Since baryons o f t h e SU(3) d e c u p l e t are observed t o have J=3/2one c o n s t r u c t s the product group SU(3) ( f l a v o u r ) X SU(2) (spin) and then enlarges i t t o SU(6) t o see i f the e m p i r i c a l f l a v o u r - s p i n a s s o c i a t i o n a r i s e s n a t u r a l l y from i r r e d u c i b l e representations of SU(6) as indeed i t does.

I n the quark model baryons c o n s i s t o f three J=$ valence quarks i n t h e i r l o w e s t s p a t i a l s t a t e described by symmetric s p i n - f l a v o u r wave-functions together w i t h a small a d n i x t u r e o f quark-anti-quark p a i r s . I n t h e theory o f strong i n t e r a c t i o n s c a l l e d quantum chromo-dynamics (QCD , a gauge theory based on SU(3) ( c o l o u r ) , the quarks a r e h e l d together by exchange o f an o c t e t o f v e c t o r mesons c a l l e d gluons whose sources are the ' c o l o u r ' charges on t h e quarks.

There i s another i m p o r t a n t approximate symmetry o f the s t r o n g i n t e r a c t i o n s which emerges from t h e observation t h a t the strangelness conserving weak v e c t o r c u r r e n t i s conserved (CVC) and the a x i a l c u r r e n t approximately conserved (PCAC). The l e f t and right-handed c u r r e n t s are associated w i t h transformations o f the c h i r a l symmetry group SU(2) x SU(2) , u l t i m a t e l y enlarged t o SU(3) x SU(3) t o encompass strange- ness changi hg c u r r e n h . The crrrucial d i f f e r e n c e betheen i s o s B i n ( o r f l a v o u r ) and c h i r a l symmetry i s t h a t t h e vacuum i s n o t c h i r a l l y i n v a r i a n t and t h e r e i s no m a n i f e s t a t i o n o f the c h i r a l symmetry i n the mass spectrum. Instead the spontaneous

breaking o f t h e c h i r a l symmetry g i v e s r i s e t o a massless Goldstone boson w i t h the quantum numbers o f t h e pion. The symnetry i s n o t exact however and the p i o n i s n o t massless; i f i t were the a x i a l c u r r e n t would be e x a c t l y conserved. Extending these

ideas t o SU(3) x SU(3) t h e pseudo-scalar meson o c t e t m e r g e s as an o c t e t o f (almost) mass 1 eks olds st he ^bosons.

3. Electromagnetic I n t e r a c t i o n s (3.1 ) E l e c t r i c Charge

That the neutron i s a n e u t r a l p a r t i c l e having zero e l e c t r i c charge has been checked i n a s e r i e s o f experiments going back t o the days o f i t s f i r s t discovery. The most r e c e n t measurement o f t h i s type i s t h a t o f Gahler e t a1 ( 11 ) who searched f o r the d e f l e c t i o n o f a focused beam o f slow e l e c t r o n s i n a s t r o n g e l e c t r i c f i e l d . T h e i r resu 1 t

where e i s the charge on t h e proton, showed an improvement on t h e previous L e s t determination ( 12 ) by two orders o f magnitude.

8 7 8 7

A f u r t h e r p o i n t o f i n t e r e s t i s t h a t a r e c e n t s t u d y (13) o f t h e d e c a y R b + S r has e s t a b l i s h e d t h a t the l i f e t i m e f o r the charge-non-conserving decay n+p+

n e u t r a l s s a t i s f i e s ^T > 1.8 x 1018 y r . (3.2) Magnetic Monopole Moment

There i s no magnetic monopole term i n Maxwell'sequations o f t h e c l a s s i c a l e l e c t r o - magnetic f i e l d and indeed the presence o f such a term would v i o l a t e p a r i t y i n v a r i -

ance. However i n D i r a c ' s theory, (14,15) magnetic monopoles, i f they e x i s t , would be i n t e g r a l m u l t i p l e s o f e/2a where a i s the f i n e s t r u c t u r e constant. The i n t e r e s t i n magnetic monopoles has grown r e c e n t l y because they a r i s e n a t u r a l l y i n spon- taneously broken gauge theories; they a r e an i n t r i n s i c p a r t o f grand u n i f i e d t h e o r i e s where they a r e expected t o have masses i n the r e g i o n o f 10'' GeV, i . e . about the mass o f a l e a d p e l l e t 5~ i n diameter. There has however been one r e p o r t (16) o f the observation o f a monopole crossing the 20cm2 area o f a superconducting loop. Since o n l y one-even_; was detected i n 151 days t h i s would i m p l y a f l u x

= 2 x TO-'' sec l s r 3 i.e. approximately l o 6 times g r e a t e r than t h e Parker Parker l i m i t s e t by t h e ' 3 ~ 6 g a l a c t i c magnetic f i e l d .

To date t h e o n l y l i m i t s e t on the magnetic monopole moment (MMM) o f the neutron derives from t h e work o f Cohen e t a1 ( 17 )

qmn(l .8 x 10-15 e/2a

a1 though Ramsey (16) has p o i n t e d o u t t h a t t h i s l i m i t could be improved by a f a c t o r of ID7 u s i n g the techniques employed by GLhler e t a1 t o measure the neutron charge.

3.3 E l e c t r i c Dipole Moment

Since the existence o f a f i n i t e e l e c t r i c d i p o l e moment(EDM) i n t h e neutron r e q u i r e s the simultaneous v i o l a t i o n of p a r i t y and time-reversal invariance, i t s observation wourld s i g n i f y t h e breakdown o f CP-symmetry o f which o n l y one example i s known t o date, namely the weak decay o f the KO meson (19). L e t edn be t h e neutron EDM where d i s a s u i t a b l e d i p o l e l e n g t h f o r which t h e n a t u r a l scale i s the Compton wave- lBngth A, o f the neutron. We can then express dn i n t h e form

dn = Clp (Jt X c

where 9 - ^{5 x} represents the r e l a t i v e amplitude o f the i r r e g u l a r p a r i t y com- ponent Pn Ihe neutron wave f u n c t i o n and g i s the corresponding r e l a t i v e amplitude c h a r a c t e r i z i n g the breaking o f time r e v e k a l symmetry (20).

There are c u r r e n t l y two experiments i n progress t o look f o r a neutron ELM both o f which make use o f the Ramsey magnetic resonance technique w i t h b o t t l e d u l t r a c o l d neutrons and these have reached l i m i t s d ~ 4 ~ 7 0 - ' ~ a n ( 2 0 , 2 1 ) and d? i 4 . 8 ~ 1 0 - ~ ' ~ ~ .(?2) r e s p e c t i v e l y . There i s t h e r e f o r e no evi%ence t o d a t e f o r t h e existence o f a f i n i t e EDM although one can say t h a t the r e s u l t s r u l e o u t the e a r l y electromagnetic

C3-4 JOURNAL DE PHYSIQUE

(gt =.I) and m i l 1 iweak (gt=10-3) t h e o r i e s of CP-violation. They are however consis- t e n t w i t h superweak theory (gt=10 9 ) .

I n t h e SLi(2) x U ( 1 ) gauge theory o f weak i n t e r a c t i o n s t h e r e a r e two mechanisms f o r i n t r o d u c i n g CP-violation. I n t h e o r i e s o f the Kobayashi -Maskawa type (23) w i t h t h r e e doublets each o f the left-handed quarks and l e p t o n s the C P - v i o l a t i o n enters through the phase d i f f e r e n c e s between the v a r i o u s charged c u r r e n t s g i v i n g d i p o l e lengths dn =10-34cm o r d = 1 0 - ~ ~ c m i n the supersymmetric versions (24). I n t h e o r i e s o f the weinbergntYpe ( 2 5 ) w i t h a t l e a s t two doublets o f s c a l a r f i e l d s the C P - v i o l a t i o n i s due t o the exchange o f charged Higgs mesons r e s u l t i n g i n d i p o l e lengths o f order (2-7) x 10-25cm. Such p r e d i c t i a ~ s c o m e w e l l w i t h i n the p o t e n t i a l range o f t h e present generation o f experiments.

An i m p o r t a n t f e a t u r e o f a neutron EDM i s i t s r e l a t i o n t o the observed baryon-anti- baryon asymmetry i n the universe (26). According t o various grand u n i f i e d t h e o r i e s o f baryosynthesis the observed asymmetry sets a lower bound on the neutron EDM

where (N /N ) > 1.3 x lo-' i s the observed baryon/photon r a t i o . To disprove o r prove su!h claim would r e q u i r e an improvement i n the s e n s i t i v i t y o f the present experiments o f order l o 3 .

3.4 Magnetic D i p o l e Moment

The magnetic d i p o l e moment i s the o n l y mu1 t i p o l e moment o f t h e neutron which i s known t o be d e f i n i t e l y non-zero. The most r e c e n t measurement ( 27), c a r r i e d o u t u s i n g

the Ramsey technique o f separated magnetic resonance c o i l s , has given t h e r e s u l t

which places t h i s parameter among the most a c c u r a t e l y determined numbers i n nuclear physics. An e q u i v a l e n t r e s u l t i s the r a t i o o f neutron t o p r o t o n magnetic moments

An e a r l y success f o r t h e SU(6) model o f baryon symmetry was i t s p r e d i c t i o n p /IJ ⁼ -2/3. The MIT quark bag model n o t o n l y preserves t h i s r a t i o b u t c o r r e c t l y pPed?cts the magnetic moment f o r the A _(28). The model does n o t do so w e l l f o r the o t h e r strange baryons and g r e a t e r stccess i s obtained w i t h the c h i r a l bag model o r

' l i t t l e bag' where pions p l a y the r o l e o f Goldstone bosons. I n t h i s model where the pions e x i s t o u t s i d e the bag r a t h e r as i n the e a r l y Yukawa model (29), the magnetic moment o f t h e neutron i s p r e d i c t e d t o have t h e value pn = -1 .8%N which i s good t o 1.6% ( 3 0 ) .

(3.5) Neutron E l e c t r o n S c a t t e r i n g

Although the neutron has no n e t charge i t may have a charge d i s t r r i b u t i o n charac- t e r i z e d by an e l e c t r i c f o r k f a c t o r G n ( q 2 ) where q 2 i s the square o f the momentum t r a n s f e r . I n the same Nay the d i s t r t b u t i o n o f magnetization i s described by a magnetic form f a c t o r GM ( q 2 ) . These form f a c t o r s are s u i t a b l e f o r t h e d e s c r i p t i o n o f electron-nucleon s c a t t e r i n g a t h i g h energy since the e l e c t r i c and magnetic c o n t r i b u t i o n s do n o t i n t e r f e r e . The nucleon form f a c t o r s excluding the neutron charge form f a c t o r s a t i s f y t h e s c a l i n g law (31)

~ ~ ~G~~ ((q2)/ ( P ~ / v ~ ) ~ q ~ ) G~ ~q2)/ (un/uN) ~ (

w i t h mean square r a d i i (rE2)~ ^=(G2)P = 6 M 2 > " 2 ~ . 7 f m 2 where

Information on t h e charge d i s t r i b u t i o n within the neutron i s determined mainly from q u a s i - e l a s t i c e l e c t r o n deuteron s c a t t e r i n g and i n p a r t i c u l a r from t h e s c a t t e r i n g of slow neutrons from electron; i n s p i n l e s s atoms. For low energy phenomena i t i s convenient t o s e p ~ r a t e GEn(q2) i n t o Dirac (charge) and Pauli (magnetic rn~ment)~form f a c t o r s F, and F2 r e s p e c t i v e l y ( t h e r e i s an equivalent s e p a r a t i o n f o r GM ( q 2 ) ) . Thus we have

F, (0) = o i s t h e neutron charge and Fpn ( 0 ) = p /p i s t h e neutron magnetic moment. The experiments determine t h e s l o p e 6 1 (,? f o r which we obtain t h e r e l a t i o n N

The term ~ 2 ~ ( 0 ) / 4 f f l ~ = -0.02115 fm2 i s t h e so-called "Foldy" term ( 3 2 ) . There i s an e q u i v a l e n t term i n proton s c a t t e r i n g which i s supplemented by an a d d i t i o n a l . c o n t r i b u t i o n from the ' Carwin' term.

Data from electron-deuteron s c a t t e r i n g giwe t h e value G~ n(o) = 0.0182 fm2(33);

however t h i s r e s u l t i s hardly r e l i a b l e because of uncer\ainties a s s o c i a t e d with the deuterium t a r g e t . A more r e l i a b l e r e s u l t i s t h a t ohtainedfrom t h e long s e r i e s of experimentson neutron-electron s c a t t e r i y ( 34) f o r which t h e most recent work by Koester e t a1 ( 3 5 ) g i v e s t h e r e s u l t G' (c)=0.01999+0.003fc2. We can see then t h a t t h e Foldy term deriving from t h e Pauli Form f a c t o r c o n t r i b u t e s almost t h e t o t a l e f f e c t . This i s i n accordance with the c a l c u l a t i o n s of C a r l i t z e t a1 (36) using the quark model w i t h allowance f o r the s p i n dependence o f t h e inter-quark f o r c e s . The Dirac form f a c t o r nevertheless makes a small c o n t r i T t i o n t o t h e t o t a l s c a t t e r i n g and from t h i s residue we can compute a 'Dirac charge r a d i u s (37).

I t is not c l e a r however t h a t any c o n s i s t e n t i n t e r p r e t a t i o n can be applied t o t h i s q u a n t i t y and the whole question has been subjected t o considerable discussion i n the t h e o r e t i c a l 1 i t e r a t u r e (38).

(3.6) E l e c t r i c and Magnetic P o l a r i z a b i l i t i e s

The s c a t t e r i n g of photons by a system of charged p a r t i c l e s i s c h a r a c t e r i z e d by a s c a t t e r i n g t e n s o r which i n t u r n i s r e l a t e d t o t h e p o l a r i z a b i l i t y t e n s o r of the charge system i n an electromagnetic f i e l d of t h e same frequency. In the case of protons t h e e l e c t r i c and magnetic s t a t i c p o l a r i z a b i l i t i e s % P and %P can be determined f ran measurements on t h e d i f f e r e n t i a l s c a t t e r i n g cross s e c t i o n s of low energy ptotons. The r e s u l t s ( 3 9 ) a E P = (1.07 t 1 . l ) x fm3, F = (-0.7 t 1.6) x 10 fm a r e i n reasonable accord with t h e o r z t i c a l p r e d i c t i o n s

3

fm and %P = 3.2 x lo-' fm3 r e s p e c t i v e l y (46).

For t h e neutron t h e corresponding p r e d i c t i o n s a r e oEn = 8.5 x lo-' fm3 and ⁼ 7 . 8 x 10-*fm3 ( 2 ) . No m e a s u r e ~ e n t of onn has been reported t o d a t e and theye i s a s i n g l e r e c e n t measurement of oF 7 (13 + ^{8 )} x 1 0-3 fm3 (41). This r e s u l t was derived f r a n t h e t o t a l cross-s c t l o n f o r the s c a t t e r i n g of neutrons with energies up t o 40eV near t h e 16.83eV resonance i n l E 6 W . I t i s an o r d e r of magnitude l a r g e r than predicted.

(3.7) Neutron-Electron Bound S t a t e s

Some y e a r s ago i t was reported t h a t neutrons formed a weak bond with e l e c t r o n s trapped i n LiF a t 4°K (42) although t h e phenomenon was u l t i m a t e l y discounted(43,44) Recently t h e r e have been new r e p o r t s of n e u t r o n m a t t e r bound s t a t e s detected i~ the resonance s c a t t e r i n g of very slow neutrors i n A1 and Cu but no d e t a i l s a r e given (45).

JOURNAL DE PHYSIQUE

4. Weak I n t e r a c t i o n s

(4.1) Electro-weak U n i f i c a t i o n

The neutron p a r t i c i p a t e s in t h e weak i n s e r a s t i o n v i a t h e charged c u r r e n t s leading t o the semi -1eptonic neutron 6-decay n-t p+e + v , and v i a both charged and n e u t r a l c u r r e n t s giving r i s e t o p a r i t y admixtures inenuclear s t a t e s and p a r i t y v i o l a t i n g e f f e c t s i n neutron nucleus i n t e r a c t i o n s ( 4 6 ) . The discovery of t h e W- and Z0 (47,48) mesons i n t h e pj5 c o l l i d e r experiments a t CERN e a r l i e r this y e a r e s t a b l i s h e d beyond

doubt electro-weak u n i f i c a t i o n i n terms of a s i n g l e parameter sin2 o ² 0.21. In the corresponding SU(2) x U(1) gauge theory of Weinberg Salam and ~ l i s h o w t h e weak Fermi coupling constant G i s expressed i n terms of t h e e l e c t r i c charge by

The hadronic weak i n t e r a c t i o n s a r e renormalized by the s t r o n g i n t e r a c t i o n s a s described i n Cabibbo theory. In t h i s formulation the weak coupling constants f o r muon (purely l e p t o n i c ) , neutron and s t r a n g e p a r t i c l e decay a r e given by

where cos Oc = 0.9737 + 0.0025 (49). The vector and axial vector form f a c t o r s , g V ( o )

= gv; gA(o) = gA i n ngutron decay a r e given by

Taking t h e v$ilues (50, 51) Gy = (1.43577 + 0.00012) x lo-:' ^{e r g an3} from muon decay and G = (1.41220 + 0.00043) x e r g cmJ from 0 4 m i r r o r nuclei B-decay we f i n d g @ 1.008 + 0.005. Thus g i s not renormalized by t h e s t r o n o i n t e r a c t i o n s which i s !he s t a r t i K g p o i n t of CVC !heory.

F i n a l l y we have s t r o n g CVC theory which i d e n t i f i e s the weak vector and e l e c t r o - magnetic c u r r e n t s a s components of t h e same i s o v e c t o r c u r r e n t . This implies the

presence of a 'weak magnetism' form factor(g -gv)for t h e neutron analogous to t h e electromagnetic Paul i form f a c t o r . The verymprecise p r e d i c t i o n i s then t h a t

This form f a c t o r has not y e t been measured experimentally.

(4.2) The Neutron Lifetime

The neutron l i f e t i m e T provides a measure of t h e q u a n t i t y G 2 ( $ 2 + 3gA2) and t h r e e di r e c t measurements ofnTn of comparable accuracy a r e c u r r e n t f y avaiTable . These a r e

T , 1 918 + 14 s . (Christensen e t a1 1972) (52) 877 T 8 s . (Bondarenko e t a1 1978) (53 )

:n n 937 T ^{- 18} s . (Syrne e t a1 1980) (54 )

These r e s u l t s a r e c l e a r l y i n d i s a reement. T can a l s o be determined i n d i r e c t l y from values o f G (54.1 and h = 7gA/gv1 (54.37. The P a r t i c l e Data Group (1982) recommends t h e " f l u e ( 5 1 )

(4.3) The Axial Form Factor

The a x i a l c u r r e n t i s n o t conserved and the corresponding form-factor i s determined from t h e r a t i o A = g d g y f 7 he1$

.

A = 1.253 + 0.021 Krohn and Ringo 1975) ( 56) X = 1.263 T 0.015 [ E r o z o l i m s k i i e t a1 1979) (57) X = 1.259 E 0 . 0 1 7 (Stratowa e t a1 1978) ( 58)

The weighted mean o f these r e s u l t s i s X = 1.259 + 0.010 which would imply a value f o r the l i f e t i m e -r = 902 + 11s. On t h e o t h e r hand a r e c e n t measurement (59) gives X = 1.275 (+ 0 . 0 0 6 ~ + 0.002T g i v i n g a v a l u e T = 883 s. v e r y close t o the measured value (53) which has Feen e x p l i c i t l y r e j e c t e d By the P a r t i c l e Data Group. The s i t u a t i o n i s indeed v e r y uncertain.

The a x i a l form f a c t o r g may be c a l c u l a t e d from PCAC theory using the Goldberger Treimanrelation g F,/M w i t h c o r r e c t i o n s expressed as a value f o r A = 1-MgA/

%NN~,- Quark bae=mo%!C( are n o t very successful i n c a l c u l a t i n g A b u t a good r e s u l t A = 0.06 + 0.02 i s obtained on a l l o w i n g f o r the breaking o f c h i r a l SU(2) x SU(2)E (60,61) . n i s may be compared w i t h the experimental value A(exp) = 0.072

1

(4.4) Time Reversal I n v a r i a n c e

The weak c u r r e n t s are c l a s s i f i e d as f i r s t o r second c l a s s according as they a r e even o r odd under G - p a r i t y . If T-invariance i s v i o l a t e d we e i t h e r have ( i ) charge symmetry and second c l a s s currents (62) ( i i ) no charge symmetry and T - v i o l a t i o n i n f i r s t c l a s s c u r r e n t s . Neutron decay i s an analogue decay and o n l y the hypothesis

( i i ) can be r e a d i l y tested. This i s done by l o o k i n g f o r a non-vanishing neutron s p i n - e l e c t r o n mcmentum - n e u t r i n o tTIcXnentum c a r r e l a t i o n c o e f f i c i e n t D=2 sin4/(1+3X2).

There are two measurements a v a i l a b l e

D = - (1.1 + 1.7) x (Steinberg e t a1 1974) D = - ^(2.2 T - 3.0) x ( E r o z o l i m s k i i e t a1 1978)

D t h e r e f o r e vanishes w i t h i n experimental e r r o r corresponding t o a3phase angle 4 = (180.11 5 0.17)' and a r e l a t i v e T - v i o l a t i n g amplitude g t < 2 x 10- .

-

(4.5) The Decay n +'H + v C

This i s a r a r e decay mode f o r the neutron w i t h an estimated (65) branching r a t i o o f 4.2 x lo-'+%%. ^{I t} has never been observed. The i n t e r e s t i n i t stems from the f a c t t h a t the r e l a t i v e populations i n the s i n g l e t and t r i p l e t h y p e r f i n e l e v e l s o f the hydrogen atom a r e s e n s i t i v e b o t h t o departuresfrom (V-A) c o u p l i n g and l e p t o n number non-conservati on.

(4.6) The n-p Weak I n t e r a c t i o n

This i s a non-leptonic weak i n t e r a c t i o n and i s b e s t s t u d i e d i n t h e r e a c t i o n n + p ^-t D + y . T i s process i s governed by three weak mixing amplitudes ( 3 ~ ~ ^{/ V w l} 'P~)

(A 1=0), t l S o ] V I 'PO) (AI.0.2) and < 3 ~ 1 / ^SP,) ( A I = ~ ) . Two types o f experiment have been p e r f o h e d ( i ) measurement o f t h e y - r a y asymmetry P;y using p o l a r i z e d neutrons and ( i i ) measurement o f t h e Y - r a y c i r c u l a r p o l a r i z a t i o n PC using u n p o l a r i - zed neutrons.

Ay i s s e n s i t i v e t o the presence o f AI=l amplitude w i t h s i g n i f i c a n t enhancement from n e u t r a l c u r r e n t s . The experimental r e s u l t i s (66)

which i s t o be compared w i t h t h e o r e t i c a l p r e d i c t i o n s Ay ,<lo-'

PC i s s e n s i t i v e t o the presence o f AI=O, 2 amplitudes and i s m a i n l y a charged c u r r e n t e f f e c t w i t h t h e o r e t i c a l e x p e c t a t i o n ~ ~ = 1 0 - ~ - 1 0 - ~ . The o r i g i n a l measurement gave the r e s u l t (67)

b u t has r e c e n t l y been c o r r e c t e d t o / ~ & 5 x (6Eg.

C3-8 JOURNAL DE PHYSIQUE

A1 though PNC e f f e c t s have been observed i n "ISn(n, y)ll"Sn, ( 6 9 ) i n neutron weak s p i n r o t a t i o n ( 79 and i n neutron induced f i s s i o n Q 1 ) , f i n i t e PNC e f f e c t s have y e t t o be observed i n t h e n-p system where they would be most s u s c e p t i b l e t o d i r e c t t h e o r e t i c a l i n t e r p r e t a t i o n .

(4.7) Grand U n i f i e d Theories and nii O s c i l l a t i o n s

The u n i f i c a t i o n o f s t r o n g weak and electromagnetic i n t e r a c t i o n s i s based on t h e gauge group SU(3) x SU(2) x U(1) w i t h t h r e e ipdependent gauce couplings and tweTve v e c t o r Resons i .e. 8 gluons, 3 heavy mesons W- Z and t h e photon y. I n grand u n i f i e d t h e o r i e s the group i s enlarged, e.g. t o h ( 5 ) w i t h an a d d i t i o n a l 12 heavy mesons and a s i n g l e gauge coupling. The s t r o n g c o u p l i n g i s supposed t o decrease

l o g a r i t h m i c a l l y w i t h energy according t o the n o t i o n o f asymptotic freedom and a l l couplinas become equal a t the grand u n i f i c a t i o n mass 2 1015 GeV.

I n these t h e o r i e s p r o t o n decay ( A B = l ) i s allowed b u t n i i o s c i l l a t i o n 5 (AB=2) are forbidden. However, i t may be t h a t there i s p a r t i a l u n i f i c a t i o n a t lower masses : l o 5 GeV w i t h nii o s c i l l a t i o n s p e r m i t t e d w i t h a p e r i o d -cn6

-

observed t h a t nE o s c i l l a t i o n over t h i s time scale could account f o r the f l u x o f low energy ?j i n the cosmic r a d i a t i o n (72).

However a l l we know i s t h a t -> 1 .O x l o 6 sec; (73 ) an o s c i l l a t i o n p e r i o d - l o 8 sec would be extremely d i f f i c u l t observe u s i n g r e a c t o r neutrons s i n c e t h e number o f 5 would be extremely small w i t h E/n :10-l?

5. G r a v i t a t i o n a l I n t e r a c t i o n s (5.1 ) ' G r a v i t a t i o n a l Mass

The P r i n c i p l e o f Equivalence i n general r e l a t i v i t y a s s e r t s t h a t t h e g r a v i t a t i o n a l and i n e r t i a l masses o f any body are equal when measured i n some s u i t a b l e s e t o f u n i t s . The f i r s t t e s t o f the p r i n c i p l e f o r an elementary p a r t i c l e was c a r r i e d o u t by McReynolds (74) who observed the f r e e f a l l o f a neutron beam over a 12m. path and showed t h a t the p r i n c i p l e was v a l i d t o w i t h i n z 10%. I n the most r e c e n t s t u d i e s o f t h i s problem a neutron g r a v i t y r e f r a c t o m e t e r have been used t o t e s t the i n f l u e n c e o f g r a v i t y on s c a t t e r i n g l e n g t h measurements and t h e e q u a l i t y o f the g r a v i t a t i o n a l and i n e r t i a l masses has been v e r i f i e d t o a p r e c i s i o n o f 0.03% (75,76).

(5.2) G r a v i t y and Quantum Mechanics

The development o f t h e techniques o f neutron i n t e r f e r o m e t r y (77) has allowed a number o f many i n t e r e s t i n g s t u d i e s o f the behaviour of neutrons i n g r a v i t a t i o n a l f i e l d s t o be c a r r i e d out. For example Werner e t a1 (78) s t u d i e d the i n f l u e n c e o f the e a r t h ' s g r a v i t a t i o n a l f i e l d on the neutron phase thereby e x p l o i t i n g the i n t e r - f e r o m e t r i c technique t o t e s t the r u l e s f o r transforming a quantum mechanical Hamiltonian i n t o a n o n - i n e r t i a l reference frame. This represents the quantum mechanical analogue o f t h e o p t i c a l Sagnac e f f e c t (79). The Fizeau experiment f o r neutrons has a l s o been c a r r i e d o u t (80) w h i l e Greenberger e t a1 (81) have shown t h a t the Aharonov-Bohm e f f e c t f o r neutrons i s l e s s than t h a t f o r charged p a r t i c l e s by a f a c t o r o f 5 x 10-12. The general problem o f m a t t e r and l i g h t wave i n t e r f e r e n c e i n non-Newtonian g r a v i t a t i o n a l f i e l d s has been discussed by Stodolsky (77).

I n a d d i t i o n there have been a number o f i n t e r e s t i n g proposals. Berry (82) has p r e - d i c t e d f r e e - f a l l i n t e r f e r e n c e f r i r g e s f o r neutrons ' a f a l l i n g neutron rainbow' w i t h wavelength independent f r i n g e separation AR = 3.53897 x @2/~2g)'3 =0.026mm w h i l e Anandan (83) has proposed t o d e t e c t B and T - v i o l a t i o n (64) using neutron i n t e r - ferometry t o observe a neutron e l e c t r i c and/or g r a v i t a t i o n a l d i p o l e moment.

6. Sumary

The main neutron parameters on which experimental data i s a v a i l a b l e are sumnarized i n t h e Table below.

Mechanical J~ = $+; M = 1.008664995

+

= 939.5730 - 0.0026 MeV Strong I = L ^{2 ,} I 3 =-$, B = 1, Y = 1 , c ^{= 0}

Electromagnetic qn = -(1.5+2.2) x 1 0 - 2 0 e , qmn<l - 8 x 10-15e/2u

dn =.< 4 x 10-25cm, u ⁼ (-1.913O4308~0.O00OOo58)~~

G ; ~ ( o ) (e-D) = 0.0182fmz G ; ~ ( o ) ( n - e ) = 0.01 99+0.003fm2 a E n = (13+S) _- x 1 0 - ~ f r n ~

G r a v i t a t i o n a l M / M . = 1.00016 2 0.00025 9 '

Table 1 . Experimental Data on the Neutron

References

(1) J Schwinger Phys Rev 52 (1937) 1250.

(2) Barkan e t a l . Rev Sci Instrum 39 (1968) 101.

( 3 ) Rauch e t al. Phys L e t t A54 (1973j 425.

(4) herner e t a l . Phys Rev Lett 35 (1975) 1053.

( 5 ) E R Cohen and B N Taylor P h E Chem Ref Data 2 (1973) 663.

( 6 ) R C Greenwood and R E Chrien Phys Rev C21 (1WO) 498.

( 7 ) Vylov e t a l . Sov J Nucl Phys 36 (1982) 4 m . ( 8 ) C Van d e r Leun Nucl Phys A38U-(1982) 261.

( 9 ) A N Wapstra and K Bos N u c l . x t a Sheets 19 (1977) 177; 20 (1977) 1 . (10) P a r t i c l e Data Group Phys L e t t 811 1 ( 1 9 8 q 1.

(11) G'rihler e t a1 Phys Rev D25 (198252887.

(12) Shull e t al. Phys Rev 153-(1967) 1414.

( 1 3 ) Norman e t a1 Phys Rev-tt 43 (1979) 1226.

(14) P A M Dirac Proc. Roy Soc AT33 (1931 ) 6O;Phys Rev 74 (1948) 817.

(15) B Cabrera Phys Rev L e t t 47 -('I3821 1738.

(17) Cohen e t al. Phys Rev 1 0 4 7 1 9 5 6 ) 283.

(18) N'F Ramsey The NeutroKTnd its Applications IOP Conf S e r 64 (1982) 5.

(19) Christenson e t a1 Phys Rev L e t t 13 (1964) 138.

(20) F Boehm Comm Nucl P a r t Phys 11 ( T 8 3 ) 251.

(21) Altarev e t al. Phys Lett 117 8 ( 1 9 8 2 ) 45.

(22) Pendlebury e t a l . Phys L e K B ( t o be published).

(23) M Kobayashi and T Maskawa Prog Theor Phys 49 (1973) 652.

(24) S P Chia and S Nandi Phys L e t t B117 ( 1 9 6 2 ) 7 5 . (25) S Weinberg Phys Rev L e t t 37 (1976)-657.

(26) E l l i s e t a1 Phys L e t t 8 9 9 7 9 6 1 ) 101.

(27) Greene e t al. Phys Rev Dm (1979) 2139.

(28) De Rujula e t a l . Phys.Rei-312 (1975) 147.

(29) G E Brown and M Rho Phys Lxt 82B (1 979) 177.

(30) G E Brown and F Myrer Phys L e t t ' l 2 S B (1983) 229.

(31) Kirk e t a1 Phys Rev D8 (1973) 6 3 .

(32) L L Foldy Phys Rev 83 71951) 668; 87 (1952) 693.

(33) Trubnikov e t a l . JETP L e t t 34 (19815-134.

(34) V E Krohn and 6 R Ringo Pfis Rev. 148 (1960) 1303; Phys Rev D8 (1973) 1305.

(35) Koester e t al. Phys Rev L e t t 36 (1476) 1021.

(36) C a r l i t z e t a l . Phys L e t t B68 7J-977).

(37) T Ericson Fundamental Physics with Reactor Neutrons and Neutrinos IOP Conf S e r N042 (1978) 1,

(38) G Barton I n t r o d u c t i o n t o Dispersion Techniques i n Field Theory.

W A Benjamin (1965) 199, 218.

(39) Baranov e t a l a Phys L e t t 528 (1974) 122 (40) V E Schrijder Nucl Phys B E 6 (1980) 103.

C3-10 JOURNAL DE PHYSIQUE

(41) Yu A Alexandrov JINR P r e p r i n t E3-82-049 1982

I t

(42) T J Grant and J W Cobble Phys Rev L e t t 2 (19 4 ) 741.

(43) Krohn e t a1 Phys Rev L e t t 23 (1969) 1475;- (44) I s a a c e t a1 Phys L e t t B21 'i7970) 63.

(45) A A S e r e g r i n I N I S ATOMINDEX 13 (1982) A b s t r 643775.

(46) J Byrne Rep Prog Phys 45 (1982) 115.

(47) A r n i s o n e t a1 Phys L e t m 1 2 2 (1983) 103, 8126 (1983) 398.

(45) Banner e t a1 Phys L e t t B l r ( 1 9 8 3 ) 476. -

(49) R E Shrock and L L Mng F h y s Rev L e t t 41 (1978) 1692 (50) Duclos e t a1 Phys L e t t B47 (1973) 491. -

(51) Towner e t a1 Nucl Phys A234 (1977) 269.

(52) C h r i s t e n s e n e t a1 Phys E n 5 (1972) 1628 (53) Bondarenko e t a1 JETP L e t t (1978) 303.

(54) Byrne e t a1 Phys L e t t B92 (TV80) 274.

(55) O H W i l k i n s o n P r o g ~ a r ~ u c l Phys 6 (1981) 325; Nucl Phys A377 (1982) 474.

(56) V E Krohn and G K Ringo Phys L e t t 855 (1975) 175.

(57) E r o z o l i m s k i i e t a1 Sov J Kucl P h y s 3 0 (1979) 356.

(58) Stratowa e t a1 Phys Rev D l 8 (1978) 3-9-70.

(59) D Dubbers P r i v a t e CommuniEtion (1983).

(60) Tegen e t a1 Phys L e t t B125 (1983) 9.

(61) C A Dominquez Phys Rev ITZ5 (1982) 1937.

(62) C A Dominguez Phys Rev D20 ( 1 979) 802.

(63) S t e i n b e r g e t a1 Phys R e v T e t t 33 (1974) 41.

(64) E r o z o l i m s k i i e t a1 Sov J Nucl m y s 28 (1978) 48.

(65) L L Nemenov Sov J Nucl Phys 31 (198UJ- 115.

(66) Cavaignac e t a1 Phys L e t t B6T-(1977) 146.

(67) Lobashov e t a1 Nucl Phys A 1 T (1972) 241.

(68) E Adelberger Comm Nucl ~ a r m y s 11 (1983) 189.

(69) Benkoula e t a1 Phys L e t t B71 ( 1 9 7 n 287.

(70) Heckel e t a1 Phys L e t t B l F ( 1 9 8 2 ) 298.

(71) Petrukhov e t a1 JETP L e m 2 (1980) 300.

(72) V Krishnan and C Sivaram E t r o p h y s Space S c i 87 (1982) 205.

(73) K Green XVTT Rencontre de M o r i o n d Vol 1 Quarks, Leptons and Supersymmetry Ed Tran T h a i X T a n (1982) 397 (and P r i v a t e Communication).

(74) A W McReynolds Phys Rev 83 (1951) 172.

(75) L Koester Phys Rev 014 ( W 7 ) 907.

(76) V F Sears Phys Rev D r ( 1 9 8 2 ) 2023.

(77) U Bonse and H Rauch T e u t r o n I n t e r f e r o m e t r y Clarendon Press O x f o r d (1979).

(78) Werner e t a1 Phys Rev L e t t 42 (1979) 1103.

(79) G Sagnac C R Acad S c i P a r i s 7 5 7 (1913) 1410.

(80) K l e i n e t a1 Phys Rev L e t t 4 6 7 9 8 1 ) 1551.

(81) Greenberger e t a1 Phys R e v T e t t 47 (1981) 751.

(82) M V B e r r y J Phys A15 (1982) L385.- (83) J Anandan Phys Rev L e t t 48 (1982) 1660.

(84) P K K a b i r Phys Rev D25 - (T982) 2013.