I L NUOVO CIMENTO VOL. 19 A, N. 4 21 Febbraio 1974

Test on the S U 4 Symmetry of Nuclei.

III : Binding Energy and Many-Body Forces (').

C. MAGmN

Institut de Physique Nueldaire, Univevsitd Claude Bernard Lyon-I Institut National de Physique Nueldaire et de Physique des Particules - Villeurbanne

{ricevuto il 22 Agosto 1973)

Summary. - - A test based on three invariants of S U 4 shows that this symmetry is much better when A increases. A simpler formulation based on the first invariant alone leads to an over-estimate of the binding energy of neutron-rich nuclei such as she, nLi, X~Be. The physical meaning of the invariants shows the much greater importance of two- body forces; but small components of two- and three-body forces must be taken into account.

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

In two preceding articles noted I (1) and I I (2), the interest of using a com-

plete set of three invariants of •U 4 has been shown. We have given, in II~

the parameters fl, 7, ~ of the formula

(1) B = ~ + tiP2 + YPa + OP4 ,

which expresses the nuclear binding energy B of a nucleus in terms of the so- called generalized exchange operators P~. These parameters show a ra ther

regular behaviour, where no magic nucleus occurs.

(*) To speed up publication, the author of this paper has agreed to not receive the proofs for correction. (1) G. BtraDET, C. M~GurN and A. PA_~T~NSKY: Nuovo Cimento, 54B, 1 (1968). (3) G. BU~DET, C. IVIAGuIN and A. P~T~NSKY: Nuovo Cimento, fi4B, 263 (1969).

638

TEST ON THE S U a SYMMETRY OF I~UCLEI - I I I 639

We have reconsidered this problem for two reasons. The first one is connected to the Coulomb correction. In I we give a formula of the form A E e = = :r + �89 fl which cannot take into account the under lying shell ef- fects in Coulomb energy. Bu t JANECKE (3) has shown tha t such effects exist. I t is interest ing to see what influence a be t t e r Coulomb correct ion can have on the above results. Secondly~ P~TENSKY (~) has given a set of invariants of ve ry simple analyt ical form and to which a clear physical meaning can be given.

We want to show the consequences which can be der ived f rom them.

2 . - C o u l o m b c o r r e c t i o n .

The exact formula given in I is

--2Tz -4- 3 (2) AEc [A, Tz lTz - - 1] = 725 A A�89 1500 (keV).

I t s predict ions are verified to 1 ~/o in most eases, b u t this percentage leads to errors of about 200 keV, which appear to be impor tan t . On the other hand~ no shell effect can of com-se be seen f rom (2). Bu t in his paper (~), JANECKE gives a semi-empirical method for the calculation of AE c of light nuclei to the l/Tis-shell. He also gives three formulae very similar to (2) for heavier nuclei.

The Coulomb potent ia l can be t rea ted in the first order of per turba t ion theory ; when expanded in tensorial te rms on S U~, the applicat ion of the Wigner-

Ec ka r t theorem leads to the formula

(3) Eo(A, T, Tz) ~ E~ T ) - TzE~c(A, T) A- [3imz-- T(T + 1)]~c(A, T),

where A is the mass number, T the isospin, Tz= (N--Z)/2. ]J_ECHT (,s) has given theoret ical expressions for ~c and E~. Star t ing f rom t h e m and from the numerous exper imenta l results known in this region, JANECKE gives a set of parameters for each nuclear shell which allows the calculation of AE c with a ve r y good precision (10 to 50 keV). We shall use these predictions when necessary l a t e r on.

B u t we mus t observe tha t the AE c which occurs in the preceding discus- sion is the Coulomb difference between the ground state of a nucleus~ say (N, Z), and its analogue s ta te which is an exci ted s ta te of the ( N - - l , Z + 1) nucleus. The quan t i ty which is of impor tance in the SU4 Coulomb correction is the dif-

ference between the gound state of bo th nuclei.

(3) J. JANECXE: in Isospin in Nuclear Physics, edited by D. It. WIT.KI~SON, Chap. 8 (Amsterdam, 1969). (a) A. P~TENSXY: Thesis, University Claude Bernard of Lyon (1972). (5) K . T . HEC~T: Nucl. Phys., 102A, 11 (1967); l14A, 280 (1968).

6 4 0 c . MAGUIN

Thus~ i t is necessary to give an es t imate of the difference ~E c be tween the g round s ta te and the first exci ted s ta te of T = T z + 1 of the same nucleus.

I n order to achieve this~ we s ta r t f rom

(4) AEc = 1430 Z< + �89 992 (keV) At

g iven in ref. ('). This fo rmula reproduces ve ry well the mean behaviour of ex-

pe r imen ta l points when p lo t t ed viz. (Z< + �89 t. Such a fo rmula can be derived

f rom the Coulomb energy of the homogeneous charged sphere (with exchange

te rm)

Z ~ Z~ (5) Ec(ATT,) = oh -~ -- ~,"~ .

But according to JANECKE

1 +T (6) E~(A, T) 2T + 1 ~ Ec(A, T, T,) .

2 , z = - - ~ ,

E x p a n d i n g A E c der ived f rom (5) in t e rms of Tz/A and compar ing the resul t

wi th (4) in order to calcula te ~1 and ~,, we are led to

(7) E~(A, T) ---- 178A } + 289 T(TAt + 1) 375A - - 1 1 1 T(TA + 1)

When app ly ing (3) and (7) to the calculat ion of ~E c one gets for example the resul ts quoted in Table I . I t can be seen t h a t the differences reach a t the

mos t the order of magn i tude of errors on exper imen ta l A E c. Therefore, such

a correct ion will be ignored.

T ~ L E I. - Detailed results o/ the calculation o/ the Coulomb energy di//erenee, between thv ground state and the/irst excited T= TzT 1 state. (All results in keV.)

Nucleus ~0F 22Na 2~Al 4~Ca 4~K

A(~c) 330 321 227 264 701

--T~(E~) -- 15 0 -- 13 6 -- 5

32~(~) ~7 -- 99 -- 16 - 6 , - i s

A ( T [ T + 1]E~) - - 3 6 0 - - 2 2 8 - -207 - - 1 8 5 - -672

~E o 12 - - 6 - - 9 24 6

I n order to tes t the influence of the Coulomb correction~ we have made two calculat ions: one wi th fo rmula (4) and one wi th ei ther exper imenta l results or previsions indicated b y the J anecke method . And we h a v e made this first

T E S T O N T H ~ S U e S Y M M E T R Y O F N U C L E I - I I I 6 4 1

o n t h e s i m p l e r m a s s f o r m u l a ( F . R . ) g i v e n b y FRANZINI a n d I~ADIOATI (6) w h i c h

t a k e s i n t o a c c o u n t t h e f i rs t i n v a r i a n t o n l y :

(8) B---- ao + bo C~.

T h e i m p o r t a n c e of such a t e s t is t o s e p a r a t e t h e e x p e c t e d t h e o r e t i c a l r e s u l t

f r o m t h e e x p e r i m e n t a l ones . I t l e ads t o a v e r y s m a l l d i f f e rence b e t w e e n t h e

t w o (Cou lomb co r r ec t ed ) e x p e r i m e n t a l v a l u e s fo r e ach t r ip le t~ b u t in one case :

A = 47. Some c h a r a c t e r i s t i c r e s u l t s a r e q u o t e d in T a b l e I I .

TABLE I I . - Some characteristic results o] the in]luence o] <~ good ~ and ~ bad ~> Coulomb correction on the results o] the F.R. test.

A <~ Bad ~ value ~ Good ~ value Theoretical value

24 1.621671 1.628 359 1.5

37 3.056871 3.037030 2 �89

44 5.267 039 5.398 564 4

47 1.002018 2.766210 2

bo

12

10

8

6

x l o 3

�9 o ~ ~ J O J O J O O I ~ I O J ~ O ~ 0

el011 OeO �9 IIl--ltOllo00 OOOolo m

DOmOUO

3'0 ' s'0 ' 7'o ' ~ 0 ' ~10 ' ~0

,~ . Olol~ ~ gOloiolomom OlloooeoOoeollo j oeOlomal o ~ 3 ~ 1 7 6 ~176 e~176176176176 ~176 a l ~ 1 7 6 1 7 6 1 7 6 1 7 6

Fig. 1. - Behaviour of the coefficient b 0 in formula (8), ~/z. bad and good Coulomb correction. Errors due to exper imenta l uncertaint ies are a t least o4 the order of magni- tude of the difference between the two plots. �9 odd, o even.

(e) P. FRANZINZ and L. A. RADICATI: Phys. •ett., 6, 322 (1963).

642 C. MAGUII~T

We give in Fig. 1 the p a r a m e t e r b0 of (8). One can see some f luctuat ions in the regions where magic numbers occur. These resul ts were calculated wi th

the good correction when possible and with (4) for heavier nuclei. B u t in Fig. 2 we give a compar ison be tween the values of bo obta ined f rom the two correc-

15

13

xlO 3

[ I J I I 2O 50 A

Fig. 2. - bo-cocflicient in formula (8). Practically, the same plot is obtained for b in formula (10). o good, �9 bad.

t ions: exac t ly the same behaviour is ob ta ined (within the influence of experi- men t a l errors).

We can conclude this Section in this way : the Coulomb correct ion has no influence ei ther on the tes t or on the pa ramete r s . The f luctuat ions of bo are p robab ly due to the fac t tha t SU4 is not , for regions of magic numbers , a s y m m e t r y as good as for nuclei far f rom these regions. And this is to be con- nected to the fact t h a t magic numbers have their origin in a sui table impor- t a n t spin-orbit t e r m in the nuclear Hami l t on i an ; this t e r m is well known to be non-SU4 invar iant .

3 . - T h e n e w i n v a r i a n t s .

For one pa r t , thei r interest comes f rom their ve ry s imple analy t ica l f o rm

and, for the other pa r t , f r om their physica l meaning. P~T~ ,~SKu (4) gives

T E S T ON T H E S U 4 S Y M M E T R Y O F N U C L E I o I I I 6 4 5

thei r eigenvalue

1 (p~ C2 = ~ +/2 _{_ p,,~ + 4p + 2p')

1 Ca = ~ (p + 2)(p' + 1 ) p " ,

4 C4 = ~i {P~P'~ + P'~P"~ + 2p'(p" + / 2 ) + 4p(p,~ + p.~) +

+ p"~p* + 3p'" + 4 / 2 + 8pp' + 6p '} ,

and f rom them the very simple following values for the four different representa- t ions describing all nuclei can be deduced (Table I I I ) .

TABLE I I I . - Eigenvalue o/the three invariants given by P~.RTENSKY (4) /or the/our di/- /erent representations corresponding to the S U, symmetry, /or ground states.

(Z, N) nucleus C2 C2 C4

1 even-even T 0 0 ~ T(T -{- 4) 0 0

1 odd-odd T 1 0 ~ ( T + 1)(T+ 3) 0

3 - - (T+ I)(T+ 3) 128

( 0 I I 1 T~+4T+-2 +~(T+2) ~ T2+4T+ - even-odd T ~ + ~

3( 1 1 1 3 9 (T+2) T ~ odd-even T ~ --~ ~ -- 12-8 2-~ + 4 T - { -

Each test needs only 4 nuclei and has been formula ted so as to give theore- t ically the value 1. The F.R. mass formula has been tes ted exact ly with the same method; bo th results are given. Fig. 3 gives the F .R. results. Fig. 4: gives our results. One can make two remarks: the same general behaviour can be imn~ediately seen on the two plots, i.e. a much be t te r tes t for heavier nuclei and accumulat ion of the bad points in the magic-number regions. But the tes t based on the complete set of invariants appears to be be t t e r (the scale is the same).

Bu t if one looks in detail at the parameters of the full formula

(9) B = a + bC2 + cC3 + dC4 ,

we find t ha t e (Fig. 5) must always be taken equal to zero.

644 c. MAGUZN

{in

1 . 3

1.2

1.1

1 .0

1".I

l.O

2 1 ~ o 2 8 5 0

e o I o o o o o o o o �9

i o o o o o �9

o �9 o �9 o o o ~ 1 7 6 1 7 6 l ~ O ~ , o ' o I �9 ~ oo �9 o o O O o Oo

l~176 I~ o o o o I l o o ~ o o I i l o oio o i 0 o o . o . . . ~ o O . . . . : . , . - o , o . o ~ 1 7 6 1 7 6 1 7 6 .o. : , _,,. o �9 o - , " o" ~ l - ' _ - ' ' - - ' ' , , . , ' - ' . - , . , . O . o o ~ l o I ~ m~ mo 8 ~ o ~ ^ R o o o ~ omm o o o

o ~ 1 7 6 ~ ~ o o - - �9 �9 �9 ~ - ~ 1 7 6 1 7 6 ~ ~ 1 7 6 ~ ~

o o o

~0 ' ~'0 ' 7'0 ' 9'0 ' ,10 ' ,~0 '

o ~ o m o

o ~ o o o o ~ o ~ o ~ - ~ o ~ lOno o o o o o ~ o o o ^ o ~ �9 I)o . i o �9 o o ~ �9 o O o O " O o m m o ~ oOom- o �9 moo ~176176 oo oO m-

~ l I . . _ % . -_ -~" l o ;o ~ 1 7 6 _ . �9 " �9 l_T,m~,, .o,, .,o . �9 ,, ,_ . % �9 ~ , , ,~o l0 . j~ .o l~g l ,o .o .F t o " �9 " ~ - o ~ O - O i o " ~ o - �9 - -o o ~ . - o " - o - ~ - ;.O~oWom �9 - �9 O - o - o - O . . ~ o - ~ i o m ~ , , ~ S e ~ w ~ m o ~ o m ~ l S i 0 1 �9 o o o o o o o o o o o ~ o o o

_ -~o m Wo o o o o o o o o

,~o ' ,~o ' ,;o ' ~lo ' ~o 'A ~;o

Fig. 3. - Test of the F.R. (8) formula ( l - -k ) . The theoretical result should be one.

.U/'}

1.2

1.1

1.0

1.1

1.0

o' ,o o.o " ' : o o.OO: o . . o �9 "% o o m o �9 I ~ o ~ % o o �9 '~eooom'~ m ~ i ~

8

T I I I l ~O I 1~0 I I 4 0 ~ 0 1 8 0 A 1 4 0

e l

- o ~o or �9

1

150 170 190 210 230 A 250

Fig. 4. - Test of the complete formula (with the three invariants). Invar iants 1 - -b .

T E S T O~ THE ~ r SYMMETRY OF I~UCLEI - I I I 6 4 5

50 70 90 I

c - - x103 1 2 - -

6 - -

0 �9

! ! l l I

I

150 170

+-1

l II, +{' +l'l

190 210

110 130 A I I I I

I I ++ '~

Fig . 5. - c -coe f f i c i en t o f t h e c o m p l e t e f o r m u l a .

b u t n o t f o r n u c l e i b e l o w A = 60. I n v a r i a n t s .

'l [,t I'

1 Ir" Ill,

230 250 A

I t i s s e e n t o b e z e r o i n m o s t c a s e s

_.30 I I

d, _ x i 0 3

9 -

I ,! -I

1 I

- t

2 -- x102

_. xI02

161- |

t' f

70 90 110 130 A I I I I I I i I

+~

140 160 leo 200 220 24o A

F i g . 6. - d - coe f f i c i en t o f t h e c o m p l e t e f o r m u l a . I n v a r i a n t s .

41 - I1 N u o v o Cimen~o A .

C. MAGUIN

d (Fig. 6) is always determined with enough precision to ensm'e tha t C~ has to be taken into account , b has a behaviour (and values) ve ry similar to bo and its plot will not be given here (no great difference with Fig. 1).

F rom these results we th ink tha t one can conclude tha t :

Nuclei force us to write the S U4 mass formula as

(10) B = a + b~, + d~4.

The F .R. (8) formula is a good first approximat ion to (10), the value of dCa lying general ly around 10 to 20 ~o of bC~.

The fact t ha t the tes t gets be t t e r and be t te r with increasing A is probably due to reasons ve ry similar to the ones developed for SU~ by LA~E and SoPE~ in 1962 (7). Bu t to our knowledge, SU4 has not ye t been justified in the same way.

4. - Prediction of binding energies.

We shall not give here any paramete r for the formulat ion (1), the P~ being bui l t on the new invariants . Their values are determined with so impor tan t deviations due to the dramat ic accumulat ion of exper imenta l errors t ha t they lose any signification. We still have the choice between (8) and (10).

For our purpose, (8) has the double advantage of needing only three nuclei and of minimizing the role of exper imenta l errors. By means of (8), we have looked at the predict ion of the binding energy (and heavy-part ic le stability) of some exotic light nuclei. This can be achieved b y means of the F.R. formula

X - - B ( 3 ) C2(T,, $1, R1) - - C2(T3, $3, R3) B ( 2 ) - - B ( 3 ) c~(r, , ~ , R,) - - C~(T~, S~, R~) '

where all exper imenta l energies have been Coulomb-corrected either expeii- men ta l l y (e) or b y the Janecke calculus (v). The atomic-mass values of the 1965 table (8) have been used; (T~, S,, R~) is the representat ion corresponding to the i-th nucleus. We give some results in three tables (Table IV) and we shall then discuss them.

(7) A. M. LANE and J. SOPER: Nucl. Phys., 37, 663 (1962). (s) J. H. E. MATTAUC~, W. THIELE and A. M. WAPSTRA: Nuvl. Phys., 67, 1 (1965).

TEST ON THE ~ U 4 SYMMETRY OF NUCLEI - I I I 647

TABLE IV. - Predictions made with the F.R. ]ormula /or various exotic light nuclei.

Nucleus N Z T z B SB T S R AE o

A ~ 8 SHe 6 2 2 28 060 2000 2 0 0

SLi 5 3 1 41278.0 1.6 1 1 0

SBc 4 4 0 56497.5 0.9 0 0 0

798.5 (c)

1 458.5 (e)

Predic ted binding energy for SHe: 33700 keV

A = l l l~Li 8 3 } X ~ ~ - - � 8 9 1433 (c)

11Be 7 4 t 65475 15 ~ �89 �89 1925 (e)

11B 6 5 �89 76205.9 0.9 �89 ~ -- �89

Predic ted binding energy: 50033 keV mass excess: 36 407 keV two-neutron s tab i l i ty : 4 700 keV

A = 1 2 l~Be 8 4 2 X 2 0 0

12B 7 5 1 79574.8 1.6 1 1 0

1~C 6 6 0 92162.6 0.9 0 0 0

Predic ted binding energy : 73 963 keV mass excess: 19 766 keY oae-neutron s tabi l i ty : 8 500 keV

1943 (c)

2 521.3 (e)

5. - D i s c u s s i o n .

W e f i rs t obse rve t h a t , for 8He, t h e p r e d i c t e d b i n d i n g e n e r g y is a b o u t 4 MeV

a b o v e t h e h i g h e s t e x p e r i m e n t a l pos s ib l e va lue . S i m i l a r r e su l t s a r e f o u n d in

t h e t w o o t h e r cases . T h e h e a v y - p a r t i c l e s t a b i l i t y of 11Li is f o u n d t o b e 4.7 MeV.

This is m u c h h i g h e r t h a n t h e 2.2 MeV g i v e n b y TmBAULT-PI~LIPPE (9) w h o

uses t h e m a s s r e l a t i o n s of GA~VV.y et al. (lo). F i n a l l y , t h e 8.5 MeV of t h e n e u t r o n

s t a b i l i t y of 12Be a re to be c o m p a r e d w i t h t h e ~2B s t a b i l i t y of o n l y 3.369 MeV.

I n t h e t h r e e cases , we f ind a n exces s ive b i n d i n g e n e r g y or s t a b i l i t y . This

g ives p r o b a b l y a n u p p e r l i m i t . W e c o u l d i n c r i m i n a t e t h e Cou lomb c o r r e c t i on

b u t i t s in f luence can b r i n g o n l y some h u n d r e d s keV. W e cou ld t h i n k t h a t t h e

v a l i d i t y of t h e S U~ s y m m e t r y is worse w h e n we cons ide r nuc le i f a r f r o m t h e

(9) C. THIBAULT-PHILIPPE: Thesis, Facu l ty of Sciences, Orsay (1971). (lO) G. T. GARVEY, W. J. GERACE, R. L. JAFFE, I. TALMI and I. KELSON: Rev. Mod. Phys., 41, 81 (1969).

648 c. ~AGW~

valley of stabili ty. Bu t such an effect is never seen in the heavier nuclei, for which the tes t (~ ONE ~ is ve ry good, even for nuclei far f rom this valley. In fact, we th ink t ha t this is due to the same reason already encountered at the end of Sect. 2: magic numbers and S U4 seem mutua l ly exclusive.

6. - Physical meaning of the invariants.

We use a construct ion of U, and SU~ given by M0SmNSKY (n), based on the seeond-quant izat ion formalism. Le t b* be the creat ion Operator of a particle

/Js

in a spatial s tate labelled by #, and in a spin-isospin state labelled b y s, b v~ the corresponding almihilation operator. I t can be shown tha t the operators

[11) 8' _ _ C - - X ~ . b w'

follow the commuta t ion relations of U,, i.e.

02) _ Cs'5," i t : ' , r = " '~' ,

so tha t the 6~' are a realization of //4. The algebra of S//4 is built on the new operators

(13)

and the three invariants of SU, are in this formalism ( I ~ = ~{C,*) '= 0), $

(1t) 1~= C~= ]~ (C]:)' (C"V $1. " S k

Using the well-known commuta t ion relations of the b* and b, we can write

(15)

C2= .@ A(A -- 16)

4

A 3 C3__32--3A ~ _ _ ~ _ _ _ _ 2 A 2 + 1 5 A 4 8 '

} " " C 4 = , ~ - - ( 1 2 - - A ) ~ + AZ--5A + 43 ~ - - - ~ + . y - - 3 A 2 + 5 2 A

(11) M. M0SHINSKY: in Many Body Problems and Other Selected Topics in Theoretical Physics (London, 1966), p. 291.

TEST ON THE ~ U t SYMMETRY OF N U C L E I - I I I ~ 9

where we have noted

( 1 6 )

= ~ b* b*,,b~"~ ~' I~t~ . u s 1~14"$$"

/~t/*s/.as eZSS$/

0~: ~ b* b* b* b* bI''b~"b~''bJ"*'. pls l P~s /~s'es /.~as~,-

/~x/~s.uspa tatS#St4

There last three operators can be in te rpre ted as two-body (~) , th ree-body (5) and four-body (.~) potentials where ma t r ix elements are different f rom zero (and then equal to one) only when particles of given spin-isospin have a cyclic pe rmuta t ion of their spatial states: we th ink of generalized Majorana exchange potentials .

Going back to (10) we can now t ry to give a pondera t ion of @, ~ and .~ in B. This is due par t ly to the parameters b and d, pa r t l y to the coefficients

(depending on A) of ~ and ~ in C4. I t is found t h a t the different terms appear as corrective terms. We give below two characterist ic examples:

Nu- ~ (C .~ A Binding Coulomb cleus energy energy

lSN --14069 73 18 1 168 117981 l l000

11SAg -- 0.7 -- 16.10 -a -- 16-10 -5 696.7 953794 310 000

The terms a in (8) and (10) and A in 2 , 5 , ~ can be in terpre ted as due to Fermi two-body forces and the above two examples show tha t a plays a ve ry impor tan t role in B (giving the greater par t of it); all o ther terms can

be only considered as per turbat ions .

7 . - C o n c l u s i o n .

We have looked a t a finer Coulomb correct ion in the exper imental energies and have seen t ha t its influence is negligible.

The predict ion of binding energies for ve ry light nuclei (in the region of exper imenta l interest) shows a large majora t ion of what is known f rom either exper iment (SHe) or other theories; this is p robably due to the lack of val id i ty

of SU4 in these regions, rich in magic nuclei. The pondera t ion of Majorana two- three- and four-body forces given by

the invariants used shows the much greater impor tance of two-body forces;

6 5 0 c. MAGUII~

the two others seem to be of greater importance for lighter nuclei. All these

Majorana forces appear as per turbat ions viz. Fermi forces.

Final ly there remMns the open problem of the greater val idi ty of the S (74

symmet ry for heavier nuclei.

We wish to t hank Prof. L. A. I~ADICATI for englightening discussions and

suggestions.

@ R I A S S U N T 0 (*)

Una prova basata su tre invarianti della simmetria S/74 dimostra ehe questa simmetria migliora molto quaado A aumenta. Una formulazione pi~ semplice basata sul solo primo invariante conduce a una stima eccessiva dell'energia di legame dei nuclei ricehi di neutroni come SHe, X~Li, XZBe. I1 signifieato fisieo degli invarianti mette in luce la maggiore importanza delle forze di due corpi; ma si deve teller conto anche di piccole eomponenti dovute a forze di due e tre eorpi.

(*) Traduzione a eura della Redazione.

UlpoeepKa S U 4 en~mterpm~ a a e p . - I I I : ~ n e p r s a cen3u H M n o r o q a c r w n n a e c s m a .

Pe3ioMe (*). - - l ' IponepKa, ocaomaHHa~ Ha TpeX m ~ a p H a i v r a x 8/7 4, IIOKa3blBaCT, riTe 3Ta

CHMMCTpHR CTaHOBIiTC~I J Iyqmc , KOr}la A yBeYIHtlI.iBaeTCR. ~oJ Iee n p o c T a ~ qbopMyJIHpOBKa,

ocHoBaHHaa TOJIBKO Ha nepBOM HHBapHaHTe, np~u3omrr K nepcottemce aHeplTm CB~I3H ~LIIep C ~OYlbHI~IM qHCJIOM Hel~ITpOHOB, TaKHX KaK SHe, nLi, X2Be. {~3Hqe, CKH~ CMbIGJ1

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