Giant M2 and transversal E1 resonances in light nuclei

2.A.1 : 2.L

NuclcarPhysics A338 (1980) 436-450 © North-HollandPublishing Co ., Amsardam

Not to be reproduced by phatoprint or microfilm without written permiaion from the publisher

GIANT M2 AND TRANSVERSAL El RESONANCES IN LIGHT NUCLEI R. A. ERAMZHYAN and M. GMTTRO Joint Institua forNucltar Rcstanch, Dubna, USSR

and H. R . KISSENER Zendalinstitut fïu Kemforschung, Rossendorf, DDR

Received 23 August 1979 Ahalrad: The cross section for inelastic backward electron scattering on lp shell nuclei at incident energy Ee =70 MeV is calculated in the shell model. Comparison is made with radiative pion capture and moon captuue . It is shown that the T> branch of the M2 resonance in (e, e') and the main maxima in the (a -, y) response function are formed by identical partial transitions. We consider the basic features of the M2 resonance excitation in lp shell nuclei and predict configttrational and iaoapin splitting of this mode .

1. Introdadion

Systematic studies of radiative pion capture by light nuclei show the formation of nuclear collective states 1'Z), similar to the case of photonuclear reactions, moon capture and other low-q transfer reactions at intermediate energies . In contrast to the photo giant resonance, the main contribution of the (~r-, y) yield is due to the (axial-vector) spin-multipole transitions. Earlier, clear evidence was found for the analogy between the well-resolved partial transitions at the high-energy end of the hard y-ray spectrum of (~r-, y) and the Ml resonance in lp shell nuclei 3'a). The analogy between the strong partial transitions in these reactions issupposed to extend also to higher magnetic multipoles. Atpresent, however, M2 resonances have been established in electro-excitation only for few spherical nuclei ~). Theoretical work on M2 electrcexcitation was performed systematically for medium and heavy 1zC and 160 [ref. 11 )], and 13C and 1aC nuclei 9.10 and for a few light nuclei, e.g. [ref. 1Z)]. Similar to the case of the Ml resonance s), one expects the concentration of M2 strength to decrease gradually from lighter to heavier nuclei and hence one believes the light nuclei to be particularly suitable for the experimental investigation of this mode . The purpose of this paper is: (i) to demonstrate that the main maximum in the (~r-, y) response curve for the lp shell nuclei corresponds to the same (analog) transitions which form the M2, T> resonance in electrcexcitation; 436

GIANT M2 RESONANCE

43 7

to predict the general properties of the M2 resonance in lp shell nuclei ; and (iü) based on an established analogy between the (a -, y) and (e, e') reactions to check some predictions for the M2, T, resonance in lp shell nuclei . For this reason, we calculate the inelastic electron scattering cross sections at backward angles and choose the same momentum transfer as is realized in the radiative pion capture at rest (incident energy E~ = 70 Mew. Under these conditions Ml and transversal electric dipole (Elt) and possibly electric quadrupole transitions also contribute to the (e, e') cross sections ; the latter two modes should be absent in the (~r-, y) process as follows from the structure of the elementary amplitudes . Since Ml resonances in (e, e'), (~r-, y) and (N,- , vw ) were already reviewed elsewhere 1'3'13), we shall not include them here. (ü)

2. Basic formulae Disregarding Ml terms, backward electroexcitation on light nuclei at momentum transfer q ~ m.~ is described essentially by M2 and Elt multipoles 2

\d~f1/ lso°

Ee 2J,+ 1

where

l I'LP+/~n 7i' (q)

=2M_

(2 1

~P ~n

2 T3 (~ Qlol(~ -~ Q121(q)] +Qlll(Q)~

WP+~n + %lP /~n 2 22 T3J~~

Qlwr(a) =1w(4r)La x Y~1,(F)],A,, (4) Ee being the incident energy. The nuclear radiative pion capture amplitude is described by a set of operators 1) which, after performing the multipole decom-

position, can be written as follows:

TiM(Q) =E La x Yl,,(~)lr~uF(r ; W, J); w

(5)

the function F(r; W, J) contains the pion radial wave function in the mesoatom, the spherical Bessel function from the expansion of the photon wave, and some vector coupling coefficients . The explicit expressions for the multipole terms can be found in

438

R. A. ERAMZHYAN et al.

manypapers which are quoted in ref. 1). The yield of y-quanta is expressed by matrix elements of the operators (5). For light nuclei, the first term in the sum (5), W= 0, corresponds to transitions forming the Ml resonance. The main maximum in the y-spectrum is connected with the [Q x Y1].,- terms 1). The low-energy part of the primary y-spectrum where the resonance structure practically disappears is due to the [Q x YL],` operators. In the lp shell nuclei the latter transitions do not show collectivity 1a), their numerous contributions rather add up to asmooth curve, both in the excitation and in the neutron emission spectra 1S) . The contribution of transitions with W> 2 is negligible for light nuclei. In muon capture the main contribution to the total capture rate A,~ isdue to dipole (vector current) and W= 0 and 1 spin-multipole (axial-vector current) excitation . For JA = 0+ target nuclei the transitions to states with JÉ =1- and 2- essentially account for the total rate. In the Jt =1- branch both vector and axial-vector operators are involved, whereas the 0~ ~ 2- transitions are mainly governed by the axial-vector terms (4) with a = o and W=1, see ref. la). The spin-dipole part of operator (5) which is mainly responsible for the (~rl, y) reaction on light nuclei, resembles closely the dominating term Q11a(Q) of the TZ'g operator (2). When taken in the long-wavelength limit TZ °a describes the M2 photon absorption transitions. At low q-values radial parts of these operators are also similar to each other; e.g. the F factor of eq. (5) essentially contains the same spherical Bessel functions as (2), which are only slightly weighted by the (slowly varying) pion radial wave function . Since in addition we consider the creation of the collective nuclear states to be a universal response of the atomic nuclei to the excitation agent, independently of its particular nature [photoexcitation, (e, e'), lepton- or meson-induced processes] the resonances created in the (a -, y) and (~,-, v,~) processes should be formed by the same transitions as those in the M2 excitation in the (e, e') reaction . In the present 16 1a la' 13 C, 11B, work the excitation spectra for (e, e') on 0, N, 9Be and'Li are to be s.a"1s) discussed in comparison with the earlier results for the radiative pion capture spectra and muon capture rates. The A =16 case has been considered 1a) in the np-nh (n = 0, 1, 2) shell model; we take the nuclear wave functions for the A =14, a). 13, 11, 9, 7 nuclei from ref. They were obtained by standard diagonalization of a residual force within complete subspaces of lflw non-spurious configurations. 3. Resonances in A =16 nndear system The response functions for several reactions on 160 are shown in fig. 1 as follows: (i) backward e- scattering, the M2 transitions are singled out, (ü) spin-dipole (W =1) branch of the (ar-, y) reaction (the total spectrum is shown in ref. 1s )). (iii) muon capture rate, and (iv) backward e- scattering, including both M2 and Elt transitions.

GIANT M2 RESONANCE

É

200

'° Olo,e' 1

Er 70MeV

ô 100

Y 0

6 " 180~

r`

M2

r,

30

43 9

~5

,e0,n,

rl

20

10

's ~ 400 E

M2 + E1t

Y ° 200 '3

25 T V

20

'i

' 6 01r; ~ll

15 oI . .II . .T . . .Ir .ll .l . .l . . . .l 20 25 E~1'601MQV 15

Ftg. 1 . A =16 nuclear excitation spectra in reactions (e, e~, (~, y) and (Ec - , v).

The M2 resonance is essentially connected with the p3î2 -> ds~2 transition, see table 1. The M2 strength is concentrated on the J' = 24 (19 MeV) level (the lower index indicates the item number of a state) . Two other peaks at Ex =12 and 22 MeV are excited with less intensity. Sïmilar relations can be seen in the (Tr-, y) reaction too : the relative intensity of the 2- levels in 16hT repeats the corresponding values of the (e, e') reaction to T =1 levels in'60. Therefore, these calculations demonstrate that the transitions in (~r-, y) show up oollectivity~n very much the same manneras in M2 transitions. Due to different decay channels of the systems with T3 = 0 and 1, the resonances will however be characterized by very different widths .

440

R. A. ERAMZHYAN et al. TABLE 1

Single-particle matrix elements of the operators Ti~ and 7~, eqs. (2) and (3) calculated in the harmonic oscillator basis with b =1 .67 fm

Pa/z ds/z sln ds/z

`) q `) `) q

-0 .0677 -0 .0045 -0 .0346 -0 .0524 0.0265 0.0788

Pi/z

Ps/z

Pi/z

-0.0221 +0.0040 -0.0540 -0.0725

0.0032 0.0625 0.0019 0.0335 0.0009 0.0203

-0.0028 -0.0549 -0.0003 -0.0028

`) q=20 MeV/c. ~q=100MeV/c.

In the muon capture reaction the most intensively excited states are again those 2states which form the M2 resonance. At the same time, the vector current term in the muon capture amplitude increases the strength of J~ =1 - states as compared to the (a-, y) reaction, and their contribution becomes comparable to that of JA = 2states. The transverse electric dipole (Elt) excitations in (ee') are mainly connected with the p3~2-~ d3/2 spin-füp transition (see table 1), since the Qlot(O/q) term of operator (3) dominates. Due to the dominant role of the d3î2 subshell, Elt transitions are located higher in energy than M2 transitions, the main strength is carried by the 1 s level. Similar states show up in the photoabsorption ; at such a small momentum transfer, however, the 14 level, which is built up mainly by p3~2->dsn transitions, dominates. In the (-rr -, y) reaction the 1- resonances are excited with lower intensity as compared with 1SO° electron scattering . In the latter case they are enhanced owing to the "orbital" Q~ components of the operator (3). The strongest peaks resolved 16) in the 1600-, y) experiment are located near the positions predicted in ref. 14). In the 160 (ee') reaction at E~ = 54 .3 MeV and B =165° the J~ = 2- states are seen 1') at about 20 MeV, too. The M2 excitation is split into two peaks at 19 .04 and 20.36 MeV, just in the region where our calculation locates the main M2 strength. In order to understand the structure of the giant resonance (the M2 component in particular) and to determine the microscopic structure of the coherent states forming the excitation spectrum of the nuclear system, the nucleôn decay channels should be studied. As is known, both the nucleon emission spectra from the decay of resonances to individual levels of the daughter nuclei (A-1) and the partial excitation spectra for fixed decay channels show resonance structure and reflect the parentage coupling of the giant resonance to the states of daughter nuclei. In this way, the particular states forming the resonances can be more clearly selected. For

GIANT M2 RESONANCE

44 1

1600-,

example, observing the yn) 1s Na... branch one selects the J4 = 2~ part of the M2 resonance 1s). Indeed, in both the (a - , y) and (W - , v,~) reactions on 16 0 a salient peak is seen in the neutron spectra at E =4 MeV, in full agreement with calculation 1s). In the (~,-, vn) reaction this peak is formed from the 16 N(2~)-> 1sN~ .,. and 16N(ls)-> 1sN(i-, 6.32 MeV) branches, each contributing with about equal intensity. For the M2 electro-excitation, the decay branches to the ground states of tsN and 1s0 are also expected to dominate. The experimental data for the A =16 system, just discussed, point out that in the reactions analyzed the M2 resonance states dominate both when the formation ofthe nuclear excitation and its subsequent decay are considered . It is then important to perform a unified analysis of the above mentioned low-q transfer reactions in other light nuclei as well . In this way we may obtain reasonably complete information about the M2 mode in the nuclear systems. 4. M2 resonance in non-magic N= Z nadei with l~,. ~ 0. 1`N nadeas Due to the g.s. spin 1 + the M2 resonance in 14N is formed by 1 - , 2 - and 3 excitations. The contribution of each of these groups is given in table 2. As for the gross structlue the second and third group dominate. In order to demonstrate the T.~t,E 2 Calculated M2 transitions in the 180° (e, e~ scattering and the yield of hard y-quanta in the (~r-, y) reaction on 14N E"

(14N)

(MCV)

JL

Strongest individual transitions

7.0 16.9 17.3 18.1 20.1 20.5 20.7

3233212-

(10-s fmZ/sr)

(96)

(10~)

( °~6)

62 77 118 77 64 34 20

8 10 15 10 8 4 3

11 9 12 10 8

6 5 7 5 4

10

5

Sum

58

Contributions of all nuclear states with dtfinite Jl

3210-, 4-, 5-

Total

32

419 246 100

SS 32 13

67 64 37 14

37 35 20 8

765

100

182

100

442

R . A. ERAMZHYAN tt al.

analogy of (ee') and (~r-, y) excitation we display in table 2 also the strongest individual transitions. Fig. 2 shows the calculated multipole strength distributions of the lfi~ nuclear excitations. Again, it can be seen that the same transitions build up the M2 resonance in e- scattering and the spin-dipole branch of the (Tr-, y) reaction .

Fig. 2 . 'aN nuclear excitation spectra in reactions (e, e~ and (~r - , y) . A Breit-Wigner shape of 2 MeV width was ascribed to each line .

Two groups of transitions are distinctly seen both in the M2 electroexcitation of

taN and in the laN(~-, y) reaction . The first one is connected with the Ji = 2- states

and is located at the same position as the M2 resonance in 160. The second group (3-, 2-) corresponds to somewhat lower excitation energies . The measured laN(~-, y) yield shows signs of the doubly humped structure predicted earlier a). The expected strong 3- resonance [E=( laC) = 6.73 MeV] is, 2"ts) . It contrasts with the observation of this 3- tranhowever, not yet confirmed sition in the 1a N(Ec - , v) reaction 19). laN(~-, y) was predicted a) to decay The dominating 2- resonance showing up in mainly to the lowest z- level in 13Cß .68 MeV) ; the higher-lying 3- resonance is

GIANT M2 RESONANCE

443

expected to feed mainly the i- (7 .55 MeV) above threshold of subsequent neutron emission. The M2 resonance in 14N(e, e') should decay in the same manner. Elt transitions form several distinct groups, too. The strongest peak is at the same position as in 160, another less pronounced peak at higher excitation energy is due to is ~ p liz core excitation which could not be seen in 160. Therefore, in the case of non-magic nuclei we observe the configurational splitting of the resonance which is known z°) from photonuclear reactions: the coupling between excitations from the valence shell and closed shells is not strong enough to merge these two groups of transitions. The is ~ 1p1î2 core excitation (E= z 30 MeV) should contain a larger fraction of E1 strength than the ls-> lpsn photoexcitation, due to the different p-subshell occupation. As for 160, the dominant psi2 -'dsi2 photo-dipole state (Ex x 22 MeV) is only weakly excited at q z m~ Recent 14N(e, e~ data 21) at B =180° seem to indicate M2, T =1 strength at Ex =16.1 MeV which is consistent with our calculation . The isoscalar M2 and Elt transitions are about one order of magnitude weaker than the isovector ones at the given value of q.

1?g . 3 . A =13 nuclear excitation spectra in reactions (e, e') and (a -, y) .

444

R. A. ERAMZHYAN et al. 5. Isospin splitting of M2 resonance ; ezamples : ~C and 1 `C nuclei

As in the photo-dipole excitation, an isospin splitting of the M2 and Elt (ee') resonances in N~ Z nuclei is predicted. Whereas in the photo-resonance in lp shell nuclei the T, branch usually dominates, the TS branches of the M2 resonance at tz) q x ma have comparable strength [for the exceptional cases t `C and'Li see refs . a and )] . Figs 3 and 4 show the isospin branches of the M2 and Elt excitations in t3 C and t4C. The M2, T, resonance (J=Jo +2) is concentrated around E=( 13 C)~ 21 MeV and Ex( ta C)=24 MeV, and corresponds again to the dominating (rr - , y) peaks [E=( 13 B) = 5 MeV and Ex( la B) ~ 2 MeV] . The strongest partial transitions and strength distributions over the Jt values are given in tables 3-5 . The Elt, T, resonances are again located at higher energy compared to the M2, T, ones. The available evidence for electro-excitation of t3 C and l4C in the giant-resonance region has already been discussed tz) . The new l 'C(-rr - , y) data zz)

10

fig. 4.

20

30 E'(

14 C nuclear excitation spectra in reactions (e, e') and (~r-, y) .

GIANT M2 RESONANCE

445

Tnsi,E 3 The same as in table 2, except for'3C E; (r3 C) (Me~

~i

dv/dfl (M2, T>) (10-s fm2 /sr)

Strongest indioidual T> transitons

18 .2 18 .5 20 .1 21 .1 23 .1 25 .2 26 .3

24 21 52 118 26 33 27

i+ ~+ ~+ ~+ ~+ ~+ ~+

Sum

R,,

(%)

(10 -`)

(%)

6 6 14 31 7 9 7

12 10 24 8 11 9

8 7 16 5 7 6

80 145 232

Total

(10-s fm2/sr)

(%)

49

Contributions of all nuclear stags with definite if

~+ i+ +~~+~~+

do/dI1 (M2, T~)

38 62

66 57 30

43 37 20

106 223

32 68

377

100

153

100

329

100

Tnsi~ 4 -s Total cross section (10 fm Z/sr) of inelastic electron scattering at B =180° in 14 C and yield of y-quanta (10~) in 14C (ar-, y) reaction

Elt M2 (ar-, y)

T~

T>

689 502

290 267 150

e 5 The strongest transitions which form the M2 resonance in 14C TAHr

dv/dl1 (M2, T>)

E' (14C) (Me~

(10-s fm~/sr)

(%)

(10~)

22.8 24.2 27 .4

40 170 30

15 64 11

9 53 19

R,.

446

R. A. ERAMZHYAN er al. Tnst.E 6 The same as in table 2 except for'Li

E' (~Li) (Me~

J~

do'/dI1 (M2, T>)

da/dll (M2, T<)

R,,

(%)

(10 -4)

(%)

Strongest indivudual T> transitions 20 14 .8 }+ 46 16 .7 i+ 18 26 .8 ~+ ~+ 28 31 .4 32 .7 ~+ 14

12 27 11 16 9

12 36 15 30 12

6 17 7 14 6

Sum

75

Contributions of all nutkar statu with definite J~ 30 i+ 35 }+ 86 18

18 21 51 10

33 61 89 15

100

198

Total

(10-s fm2/sr)

169

(10-s fm2/sr)

(%)

16 31 45 S

33 21 79 55

17 12 42 29

100

188

100

50

show a nice agreement with the predictions s) and support our analysis of M2 strength in the A =13 system . 6. Configaratioaal splitting of the M2 resonance; easmple: 'Li For the lightest lp shell nuclei (A = 6, 7) a considerable configurational splittingof the M2 resonance is expected between transitions p -> (d, 2s) and 1s -> p, as is indicated in the 61.,i(~r- , y) and'Li photoexcitations . Both groups (see table 6) of transitions in'Li should have about the same strength due to the shell occupation . Because of strong core excitations (Ex ;a 30 Mew the M2 resonance is shifted towards higher energy than for the heavier lp shell nuclei, cf. figs . l and 2. As a result we can see that two factors actually determine the gross structure of the M2 and Elt resonances in'Li, namely the isospin (see fig. 5) and the configurational (see fig. 6) splitting. Again, the T> branch of M2 electroexcitation is connected with the same transitions which build up the main maximum in the (-rr - , y) response curve. 7. Naclel with hailf-filled lp shell ; eznmple: 9Be With increasing lp shell occupation the role of is core excitation and, hence, the oonfigurational splitting of the multipole resonances dies off and the mean resonance energy decreases, in full analogywith the photo-resonance. The M2 resonance in 9Be is already dominated by the p3iZ -> dstz valence excitation. An analogous shift of the

GIANT M2 RESONANCE

447

b L N

10

20

30

E~I~Li I,MeV

Fig. 5 . The isospin splitting of M2 and Elt resonanoea in ~Li.

15 10

15

20

25

30

35 E ;hLill~eV

Fig : 6. A = 7 nuclear excitation spectra in reactions (e, e~ and (~, y).

448

R A. ERAMZHYAN tt al. TASLe 7 The same as in table 2 except for vBe E'. (~) (Me~

Ji

Strongtst individual tmnsilions 18 .1 ~+

19.0 19.1 20.4 20.9 21 .8 27.1

~+ i+ i+ i+ ~+ ~+

dQ/dl1(M2, T,) (10-e fm=/sr) 6

(%)

(10~)

(%)

3 9 3

2 6 4 9 5 7 5

2 5 3 7 4

19 5 35

16

21 14

6

16

Sum

7 10 54

Contributions of all nuclear states with dtfinitc h

i+

Total

R,.

6

4 31

37 38 70 72

17 18 32 33

22 28 47 22

18 24 39 19

217

100

119

100

main peak is observed in the (ar - , y) reaction 2). The Elt resonance, however, is still at.energies above 30 MeV since it still contains considerable contributions from the is core. Table 7 and fig. 7 show the strongest partial transitions forming the M2, T> resonance in 9 Be and the distribution of the transition strength over the final-state spins. The same conclusions hold for the A =11 case . S. M2 resowmce beyond the lp she0 The dominant role of M2 excitations in the (~r - , y) reaction weakens already for the 2s, ld shell nuclei [see e.g. ref. 23 )] . The pions are captured from mesoatomic orbitals with larger moments (l~ = 2, 3) and give rise to higher nuclear multipolarities . Nevertheless, one expects that the pion capture in flight and the electroand photo-production reactions should be again dominated by the low-spin transitions. By now data are already available showing the effects of giant-resonance excitation in the (e, e'~r) reaction 2`) on lp shell nuclei . The role of the giant resonances is analogous to that in the (~r - , y) process at rest . An extension of such studies should help one to complete the systematics and to understand the specific features of the M2 mode in heavier nuclei. In particular, the T> branch of giant resonances ie suppressed in the photo and low-q electrcexcitation on heavier nuclei . The (y, ~r) and (e, e'~r) processes can open the selective channels of their study.

GIANT M2 RESONANCE

449

8

b

6 4 2

~ 30 E 20

20

30 g"I9BQi,MQN

Fig. T. A = 9 nuclear excitation spectra in reactions (e, e') and (~r- , y) .

9. Condaeions The analysis performed predicts that the M2, T, branch of the giant resonance excited in the low-q backward electron scattering, the dJ = 2 branch in muon capture, and the main resonances in the radiative pion capture on the lp shell nuclei are all built out of the same transitions. It follows then that the (~r-, y) data available at present should provide evidence on the localization and the gross structure of the M2, T, resonance in backward electron scattering . From the shell model analysis, the following features of the M2 resonance are expected : (i) At the upper end of the lp shell the M2 resonance is mainly formed by lpsi~ -> ldsiz transitions and is located at Ex z 16-20 MeV. In the lightest lp shell nuclei (6~'Li) the is core and valence excitations contribute comparably to the cross section. This configurational splitting of the M2 resonance and the related shift of part of M2 strength towards higher energies decreases with increasing lp shell occupation. (ü) In nuclei with N ~ Z the M2 resonance will be isospin-split with the T, branch shifted to higher energy. The relative strengths of the T2 branches are, at q x m, on the average equal, exceptions being due to the specific structure of the target ground state ('Li, 14C). The transverse E1 excitations are connected with the spin-flip p3~Z -'d3n transitions and therefore are located at higher excitation energies than the M2 resonance.

450

R. A. ERAMZHYAN et al.

Direct tests of the predicted structure of the M2 resonance in light nuclei should be performed in the inelastic 180° electron scattering experiments and, on a complementary basis, in the study of selective decay channels of giant resonances excited in the (Tr-, y) reaction . Though experimentally more difficult, the photo- and electro-production of pious are expected to open new possibilities for studying the low-multipole magnetic modes. References 1) H. W. Baer, K. M. Crowe and P. Truöl, Advances in nuclearphysics, vol. 9, ed . M. Baranger and E. Vogt (Plenum, NY, 1977) p. 177 ; V. V. Balashov, G. Ja. Korenman and R. A. Eramzhyan, Capture of mesons by atomic nuclei (Atomizdat, Moscow, 1978) 2) J. P. Perroud in Photopion nuclear physics, ed . P. Stoler (Plenum, NY, 1979), p. 69 3) H. R. Kissener, G. E. Dogotar, R. A. Eramzhyan and R. A. Sakaev, Nud. Phys. A302 (1978) 523 4) H. R. Kisaener, G. E. Dogotar, R. A. Eramzhyan and R. A. Sakaev, Nucl . Phys. A312 (1978) 394 5) A. Richter, in Pros. 4th Seminar on Electromagnetic interactions of nuclei at low and intermediate energies (Nauka, Moscow, 1979), p. 258 6) J. Speth in Proc . Int. Conf. on Nuclear physics with electromagnetic interactions, Mainz, 1979 7) W.Knüpfer, R. Frey, A. Friebel, W. Meaner, D. Mener, A. Richter, E. Spanier andO. Titu,preprint Darmstadt 1KDA 78/9 ; Phys . Lett . 77B (1978) 367 8) S. S. Hanna, SLAC preprint 1979 9) V. O. Nesterenko, Dubna Communication P4-12513, 1979 10) V. Yu. Ponomarev, V. G. Soloviev, Ch . Stoyanov and A. I. Vdovin, Nud. Phys. A323 (1979) 446 11) J. S. Dehesa, Dissertation Jülich, Jut-1425, 1977 12) H. R. Kissener and R. A. Eramzhyan, Nud:Phys . A326 (1979) 289;in Photopion nuclear physics, ed . P. Stoler (Plenum, NY, 1979) p. 117 13) G. E. Dogotar, R. A. Eramzhyan, H. R. Kissener end R. A. Sakaev, Nud. Phys . A282 (1977) 474 14) R. A. Eramzhyan, M. Gmitro, L. A. Tosunjan and R. A. Sakaev, Nud. Phys . A290 (1977) 294 15) R. A. Eramzhyan, M. Gmitro and L. A. Tosunjan,J. of Phys . G 4 (1978) L233 ; Czech. J. Phys. B29 (1979) 370 16) G. Strassner et al., Phys. Rev. to be published 17) A. Goldmann and M. Stroetzel, Z. Phys . 239 (1970) 235 18) J. C. Alder et aL in Photopion nuclear physics, ed . P. Stoler (Plenum, NY, 1979) p. 101 19) E. Hellotti, W. Dey, R. Engfer, E. Fiorini, P . Negri, H. J. Pfeiffer and H. K. Walter, SIN Physics Report no . 1 (1976) p. 41 20) V. G. Neudachin in Pros . Int. Conf. on Electromagnetic interactions at low and intermediate energies, vol. 3 (Moscow, 1967) p. 351 21) N. Enselin, L. W. Fagg, R. A. Lindgren, W. L. Bendel and E. C. Jones, Jr ., Phys . Rev. C19 (1979) 569 22) P. Truöl, private communication 23) R. A. Eraauhyan, L. Majling, J. l~izek and R. A. Sakaev, Czech. J. of Phys . B28 (1978) 1081 24) K. Shoda, M. Yamazaki, K. Nakahara and H. Ohashi in Photopion nuclear physics, ed . P. Stoler (Plenum, NY, 1979) p. 205