FOUR-NUCLEON TRANSFERS AND LOW-LYING QUARTET STATES IN THE 1 f-2 p SHELL

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FOUR-NUCLEON TRANSFERS AND LOW-LYING QUARTET STATES IN THE 1 f-2 p SHELL

H. Faraggi

To cite this version:

H. Faraggi. FOUR-NUCLEON TRANSFERS AND LOW-LYING QUARTET STATES IN THE 1 f-2 p SHELL. Journal de Physique Colloques, 1971, 32 (C6), pp.C6-25-C6-31. �10.1051/jphyscol:1971604�.

�jpa-00214822�

JOURNAL DE PHYSIQUE Colloque C6, supplkment au no 1 1-1 2, Tome 32, Novembre-DPcembre 1971, page C6-25

FOUR-NUCLEON TRANSFXRS

AND LOW-LYING QUARTET STATES IN THE 1 f-2 p SHELL

H. FARAGGI

DCpartement de Physique NuclCaire, C. E. N. Saclay

R&ume. - Pour mettre en evidence I'cxistcnce d'etats de quartets dans le spectre de basse ener- gie des noyaux de la couche If-2p, il est possible d'utiliser Ies reactions de transfert direct d'une particule a h l'aide de faisccaux d'ions lourds, tcls que ^{1 6 0} ou ZONe, sur des cibles de noyaux pair- pairs au voisinage des cceurs fermes de 40Ca, 48Ca et 56Ni. L'ensemble des resultats obtenus, pour des energies incidentes voisines de la barriere coulombienne, sont en accord qualitatif avec les predictions d'un modkle de quartets.

Abstract. - In a search for the presence of low-lying quartet structures in the lf-2p shell, a possible experimental approach is offered by performing direct a-transfer reactions with heavy ion beams such as ^{1 6 0} or 20Ne, on doubly even targets around the 4oCa, ^48Ca and 56Ni cores.

The overall features of these reactions, for incident energies in the vicinity of the Coulomb barrier, are in qualitative agreement with the predictions of a quartet model.

The coexistence of spherical and deformed states in the 1 p and (2 s-1 d) shells is well established, and well explained, basically in terms of four particle-four hole excitations. It has been shown that as a consequence of the proton-neutron force, there exist substructures made of two protons and two neutrons in a highly symmetric state, tightly bound together, and weakly bound with the remaining nucleons, that we shall call

<(

quartets ^D. Thesc quarteting correlations, as well as

the pairing correlations of strongly interacting pairs of like nucleons, should play an important role in the understanding of nuclear structure. The

quartet

states can be found at quite low excitation energies and compete favourably with either lp-lh, 2p-2h or 3p-3h excitations. Moreover, it has been shown, either in Hartree-Fock calculations or in simple models like the aligned and stretch schemes, that the quartet configurations are deformed and give rise to multiplets of positive parity levels that behave as quasi-rotational bands [I].

As a natural development of those ideas, the ques- tion arises whether or not low-lying quartet states could be found in heavier nuclei, and particularly in the (lf-2p) shell.

For light nuclei, most of the experimental results were obtained in performing a transfer reactions with lithium ion beams [2]. But it appears impossible to reach by this way nuclei heavier than calcium-40, because the cross-section at tandem energies was found to decrease drastically with mass number. A fundamental difficulty for a direct a transfer reaction in (If-2p) shell nuclei is the predominance of j-j coupling over L-S coupling, so that a strong rear- rangement has to take place. We know now that, in spite of this difficulty, the use of ^{1 6 0} or 'ONe beams

allows to perform four-nucleon transfers in the f-p shell, although the cross sections are still quite low.

Since the last two years such experiments have been performed in different laboratories. So it seems that the time has come now to discuss in some details what is known about those states, and what remains to be understood.

Most of the results I will discuss in this talk have been already either published or presented at this Conference, and more details can be found in the literature [3], [4], [5]. I should like to limit those comments to a systcmatic survey of the results obtained for nuclei in the If-2p shell and compare them with the overall features predicted by a quartet model.

It is clear that, to make a detailed and quantitative comparison, a good model of reaction mechanism has to be obtained in order to get reliable nuclear spectroscopic amplitudes. Since this is not yet the case, my comparison will remain on a very qualitative basis, and will try to show that the systematics of the experimental results obtained up to now are in quite good agreement with what is expected by assuming the existence of low-lying quartet states in If-2p shell nuclei. I will mainly comment on the Saclay results [3], since I know them better, but very similar results have also been obtained in different labora- tories [4], [5].

Theoretical expectations. - As soon as the impor- tance of four nucleon correlation in nuclear structure is taken into account, it offers a self consistent explana- tion of different aspects of nuclear spectra. In the basic shell-model framework, the introduction of pairing and quarteting correlations as the most important residual interactions allows to understand both

:I

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971604

single particle and collective excitations, rotations and vibrations, spherical and deformed states, etc.

Thus, the quartet correlations should be present in heavy and medium-weight nuclei, as well as in light nuclei.

The presence of low-lying quasi-bands in the vicinity of one-closed shell nuclei was pointed out by Sakai a long time ago [I]. The contribution of four- nucleon correlated configurations to the structure of the first 2' levels of one-closed shell nuclei may offer an explanation of the large B(E2) strength observed experimentally. So it was quite important to obtain some direct experimental evidence for their presence.

From binding energy relationships, in the nickel isotopes for instance, these excitations are predicted between 3 to 6 MeV of excitation energies, depending upon the strength of the neglected interactions. A similar uncertainty shows up in nuclear structure calculations [I]. So it seems quite important to get experimental observations on the exact excitation energies of those states.

The best way to obtain these informations in 1 f-2 p shell nuclei will be to obtain excited states in a nickel isotope through an a-transfer reaction. However, it was known that lithium beams cannot be used for that purpose. This failure could either be attributed to the failure of the four-nucleon correlations in the f-p shell, or to the inadequacy of lithium ions as suitable projectiles. But the (160, 12C) or the (20Ne,

I%) can be used as well, and it seems worthwhile to try the a-transfer reaction with such beams. While experiments in the nickel region were under prepara- tion at Saclay, the (160, 12C) reaction was performed successfully at Argonne with a 40Ca target [4].

In principle, the best choice for a target was 54Fe, since the quartet states in 58Ni will be obtained by leaving empty two f,,, proton holes and populating the 2 p 3 , 2 , 2 p,,,, 1 f5,,, ... suborbitals of the open shell with the four nucleons. Thus an a-transfer reac- tion will selectively excite those configurations, leaving weakly excited the ground-state, since it involves the breaking of the quartet in two pairs. The basic quartet configurations should have relatively small mixing with the whole bulk of levels of other configurations ; they should extend with a relative narrow width even in the continuum, as they will form a quasi-bound structure. However, although there will be a small number of these simple struc- tures until 10 to 15 MeV of excitation energy, each of them will give rise to a multiplet of positive parity states, not following exactly the 1(1 + 1) energy sequence of a pure rotational band, ending with a possible great number of excited states. But, in an a- transfer reaction induced by heavy ions, at energies high enough to surpass the Coulomb barrier, one should expect a stronger excitation of the states with high angular momenta, so that all the members of the quartet multiplets may not be equally excited. So that, even if the energy spreading of each multiplet is such

that some overlapping between the quasi-bands is present, the states selectively excited in the a transfer will be more o r less grouped around the upper part of each multiplet ; thus one could hope that not too many states will show up with relatively enhanced cross section.

The expected signature of the quartet structure will then appear as follows : in the (160, 12C) reaction at energies low enough to avoid 12C fragments emitted by compound nucleus formation, the states below a certain excitation energy (predicted between 3 to 6 MeV) will be weakly excited. Between this threshold and the excitation energy allowed by the Coulomb effects in the exit channels, a small number of levels will be strongly excited.

However, several features may contribute to wash out these simple expectations. Break up of ¹⁶⁰ into 12C + a will result in a continuous background. In the transfer reaction, if compound nucleus formation is present, it will result as a statistical excitation of all levels, with no structure ; moreover, even in a nearly direct mechanism, the a cluster cannot be transferred as a whole, since the four nucleons in the projectile have to support a strong rearrangement to populate the shell model orbitals available in the target ; so the overlap can be quite small, and the resulting cross section quite low. In this rearrangement process, the presence of too many neutrons in the open shell may result in a splitting of the quartet configurations, so that a rather wide number of levels can be excited and the selectivity of the process will be apparently washed out. For this reason, the best choice will be target nuclei with a small number of neutrons in the open shell, which is the case of the 54Fe target, and a good resolution is needed. Thus, one can realize that there were as many hopes to see some selective quartet excitations in an a transfer reaction for 1 f-2 p shell nuclei as possible failures. But it seems worthwhile t o try and the answer was positive, as we know it now.

Experimental results. - The first successful re- sults [3] were obtained by performing the 54Fe(160, 12C)"Ni reaction at 48 MeV, as shown in figure 1 : the expected features are observed, although the spin and parity of the excited levels, or group of levels, are not already known.

The signature for selective excitation of quartet structure is given firstly by the small excitation of levels below 4 MeV of excitation energy, secondly by the presence of a small number of discrete peaks between 4 and 10 MeV, in a region where the already known level density is quite high, and thirdly by the extension of these narrow structures above the particle emission threshold. Let us recall that, according to the Nuclear Data Sheets, 70 levels are known between 5.7 and 7.9 MeV in 58Ni : only four strong groups are seen in the (160, 12C) reaction in that energy interval.

Moreover, when the same (160, 12C) reaction is

performed on 56Fe and 58Ni, the behaviour observed

FOUR-NUCLEON TRANSFERS A N D LOW-LYING QUARTET STATES IN THE If 2p SHELL C6-27

is in qualitative agreement with the predictiorl of a quartet model, as can be seen in figures 1 and 2.

100 200 300

NUMERO DU CANAL FIG. 1.

f lo.

if: I ^f ::

5 4

;... .':

I

0.

--

K O 1

622.

The ''C spectra obtained with 56Fe are very similar to the 54Fe ones, showing that the adding of a neutron pair in the 2p shell does not change the overall features of the spectra. However, with a 58Ni target, where the If,,, proton shell is filled, the whole pattern is shifted towards the ground state by about 3 MeV. In that case, there is the possibility of transfer- ring the four nucleons in the ground state of 62Zn without breaking their correlations : in fact the ground state is fairly well excited. In figure 2 one can see an overall agreement between the strongly excited groups in "Ni, 6 0 ~ i and 62Zn and the predictions of a

quartet calculation performed by Jaffrin 161, on which we shall return later on.

During the last two years, several (160, 12C) reac- tions have been performed [3], [4], [5] in nearly all even targets between 40Ca and 70Zn, at different energies between 40 and 80 MeV, so that the overall behaviour of the reactions is known, even if it is not yet completely understood. We can summarize as follows what is now established through those experi- ments.

In the overall, the cross sections are quite low, of the order of 10 to 100 pb. In order to obtain a reasonable resolution, thin targets have to be used, so that these experiments need long counting rates, of the

-...--- 203 -

40 d c g

150 - -

-

50 -- -.

P - ¹

C6-28 H. FARAGGI

order of 24 hours. If other channels are open, such as those for one or two nucleon transfers, they have in general much higher counting rates, so that a very

off of the spectra at the carbon energies given by the Coulomb barrier of the exit channel, and by the good identification system is needed. This explains

why there was little hope to obtain experimental ¹⁰ evidence about those states just by chance, and why

it was necessary to look for them on purpose, following J

Y S - ! , .

theoretical suggestions.

The incident energy must also bc chosen in the near 9 ₀

600 700 tim

CHANNEL NUflBER

(4

600 700 8 00

CHANNEL NUMBER

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- i f ^8' -

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CHANNEL NUMBER

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vicinity of the Coulomb barrier, to avoid a too great

_iv,

l;fidj',d ^{, ,}

competition with the statistical excitation of all

levels, and the increase of the breakup processes z

^o

a

contribution. As can be seen in figures 3 and 5, this

I

r;

background increases drastically with increasing 8 _w ^{30 -} I

u ^{1:. 7 .} .

energy ; however, the selectively excited peaks remain ²⁰

^:

³ r' .

-30

- 2 0

at the same excitation energy with respect to the ground

state of the residual nucleus, as long as they can be ^{l o -} observed. So, they cannot be due to some accidental

fluctuations. _{300 ma WO 0}

The reaction mechanism, as can be seen by the cut CHANNEL NUFIBER.

FOUR-NUCLEON TRANSFERS A N D LOW-LYLNG QUARTET STATES IN THE If 2p SHELL. C6-29

peaking of the angular distributions at the grazing angle of thc Coi~lomb trajectories [4], [5], is pretty well described by the semi-classical strong absorption models already known for heavy ion reactions per- formed in the vicinity of the Coulomb barrier. As a result, there is little hope to obtain informations on the spin and parities of the excited states through the shapes of the angular distributions. Only the magnitude of the cross sections may be related to spectroscopic amplitude, but we have to wait until reliable micros- copic form factors can be obtained.

The great selectivity of the (160, 12C) reactions is shown, not only through the small number of excited groups, but also through the fact that for a given residual nucleus, a very strong anticorrelation is observed between the states excited through the (160, 12C) ^CI transfer and the (160, 14C) two proton transfers (Fig. 4) [3], [4], [5]. These features cannot be explained only through the L or Q dependence of the cross sections, since the angular momentum mismatch is of the same order in both cases, and since a Q depen- dence can explain the overall shape of the continuum background, but not the presence of discrete peaks above this background.

The last general feature of the (160, 12C) reaction performed in the 1 f-2 p shell nuclei is the so-called

<(

neutron blocking effect D, which can be seen in

figures 5 and 6. In the titanium and zinc residual nuclei, where the transfer of the four correlated nucleons towards the ground states is not forbidden, the cross sections towards the ground state band decrease drastically with the neutron excess. In the same time, the number of selectively excited states increases and each of them is less strongly excited. Thus the characteristic patterns of ligure 1 are gradually washed out, for example in the 4 8 ~ i or 6 6 ~ n cases.

However, even in those cases, there remain significant dips in the spectra, showing that we still have not to deal with a statistical excitation of all the levels.

I should like to point out that this behaviour is by no means in contradiction with a quartet model. The decrease of the cross section towards the ground state of the titanium and zinc isotopes as the f,,, or 2 p,,, neutron orbitals gradually fill up with neutron excess in the target nuclei, simply means that the presence of neutron pairs reduces the possibility for the four correlated nucleons to be transferred together ; in the same way, in one-nucleon transfcr reactions, the cross section is proportional to the single particle occupation number of each orbital. On the other hand, in the middle of an open shell, there is an increasing number of possible quartet configurations among all the quasi- particle statcs available, with a resulting decrease of the cross section towards each of them and a greater numbcr of levels. Experiments with better resolution would still show a discrete structure of the spectra.

Whcn the neutron f7I2 shell is nearly filled the pat- tern became clear again, as can be seen in figure 7, where are displayed the 52Cr and 54Cr spectra obtained

L i

.:\

.

....

= ^{201. , !"#: I : ; , $'} A & &

$ ¹ " 7 , 4

C 'd 5 ²¹

]HI'/',

0 101 gLfi ^y! i i ^;. j

8 ~ i 6 2 ~ i ( w ~ , " R ~ ) ~ a ~ ~ . l ) / .,+;;:/,

T

' h ^{' 200 ' 300}

CHANNEL NUMBER.

FIG. 6 .

with 4 8 ~ i and 50Ti targets. They are vcry similar to the 58Ni and 60Ni spectra shown in figure 1 . However, with a decreasing proton number among the N ⁼ 30 nuclei, i. e. "Ni, 54Cr and 52Ti, the washing out of the pattern is also noticeable.

Another feature that is worthwhile to mention is the

increase of the cross sections towards the first 0',

2', 4' levels for N = 30, after the closure of the

f7,, neutron shell, for example between 4 8 ~ i and

52Ti (Fig. 5) or between 52Cr and 54Cr (Fig. 7). This

behaviour may be attributed to the presencemf some

admixture of quartet structures in the ground state

C6-30 H. FARAGGI

CHANNEL NUMBER

FIG. 7.

wave functions [3], obtained by leaving empty two f,,, proton holes ; such configurations could help to understand the large B(E 2) values observed for those nuclei.

To sumrnarizc the experimental results, it appears that, at energies available at the present time for oxygen beams, there is a relatively small domain of nuclei and of incidcnt energies where the low lying quartet structures are clearly seen. It might be possible to achieve more favourable experimental conditions, for example, with better resolution, possibly with higher energies [ 5 ] or other projectiles [4], where more selective reaction mechanism and more typical angular distributions might be obtained. The mode of decay of those states will also be very important to study, and some experiments are now underway to achieve it [7]. So we can hope to learn more in that field by the times to come. However, with the already available results, some systematic trends can be found.

Systematics of the quartet states in the lf-2p shell.

- The results obtained so far at Saclay for nuclei in the beginning of the I f-2 p shell are displayed sche- matically in figure 8. They show the evolution of the quartet structures with gradual proton and neutron filling between the three doubly closed shell cores of 40Ca, 48Ca and 56Ni. 111 the following, we shall try to understand this evolution in terms of quartet structures. Around the 40Ca and 56Ni cores, in the case of 4 4 ~ i and of 60Zn, the main components of the ground state bands should have (1 f7,,)4 and (2 P,,,)~

configurations, respectively. For those two nuclei it has been possible to perform exact shell model calculations [8], [9]. It has been shown [ l l ] that there is a very good overlap between the wave functions so obtained and the results of a stretch model calculation, so that in the case of more complicated nuclei, the

stretch model wave functions can be used as a valuable approach.

Around 56Ni, for 58Ni, 60Ni and 62Zn, calculations in the stretch model have been performed by Jaffrin [3]

as can be seen in figure 2. The configuration space involves a quartet and a ncutron pair that were allowed to populate the 2 p,,,, 2 p,,, and 1 f5/2 suborbitals.

The heavy stripes connect thc members of each quasi- band where protonsand neutrons populate them in pairs, whether the empty ones connect the members of the quasi bands where the protons or neutrons are separated in different orbits : as a result of the smaller overlap with the entrance channel in this last case, they will be less strongly excited in an ^cr transfer reaction. There is an overall qualitative agreement between these multiplets and the groups observed experimentally. The dominant quartet configurations that generate the stronger groups are successively, by increasing excitation energy, (2 p3/2)E - (2 p3,2)K, (2 ~ 1 / 2 ) p 2 - (2 ~3/2):, (2 ~312): - (2 ~1/2):, etc.

It is'relatively easy to track those three main groups by analogy between 66Zn and 5 2 ~ i , as indicated by the dotted arrows of figure 8. As a result, at least between the doubly closed 48Ca and 5 6 ~ i , there is a good evi- dence for the presence of three multiplets or quartet structures centered around about 4, 6 and 8 MeV, built mostly with the 2 p3,, and 2 p,,, orbitals. These are shifted by 3 MeV towards the ground states of the zinc isotopes as the f,,, shell is closed for both protons and neutrons. This 3 MeV interval is in good agreement with what is expected from binding energy relationships and for the 1 f,,, - 2 p,,, energy separation.

Now, if one likes to track down these groups between 42Ti and 44Ti, i. e. between the closed cores of 48Ca and 40Ca, the situation is less clear, but can be understood through the available results of the calculations, and simple minded considerations.

Let us start from 44Ti which is the nucleus for which

the calculations are relatively easy. In figure 9 are

presented the exact shell model calculations of Bhatt

FOUR-NUCLEON TRANSFERS A N D LOW-LYING QUARTET STATES I N THE If 2p SHELL C6-31

and Mac Grory [8] together with the results obtained by Jaffrin in the

generalized aligned scheme

model approximation [lo]. The overlap of the two sets of wave function is good enough for the first ground state band which has a dominant (f,,2)4 configuration.

Also are displayed on figure 9 the peaks obtained experimentally through the 40Ca('60, '2C)44Ti reac- tion at 48 MeV, and the whole set of levels known through the (a, y ) reactions. The selectivity of the a transfer reaction is again quite obvious. As in figure 2, there is an overall qualitative agreement, not only between the experimental peaks and the ground state calculated bands, but also with the bands of higher excitation energies calculated by Jaffrin.

Bhatt and 4 0 ~ a ( d , r ) 4 0 ~ p g60 j2c) ^{Mc Grory}

A E'(MeV) , A E '(MeV) - 4 E*(M e ~ ) AE*(MeV)

- -

2' 0

'

L o * I , .

If one looks at the components of the wave functions for the 44Ti multiplets, they show a very strong configuration mixing involving the 1 f and 2 p orbitals.

In particular, the (2 P,,,)~ configuration, that contri- butes mostly to the 4 MeV group for N > 28 isotopes, is distributed among several multiplets in 44Ti, with a

Referc [I] See, for example, GII.I.ET (V.), Proc. Intern. Conf.

Properties of Nucl. States, Montreal, 1969, p. 483, and included references (Presses de I'Universite de Montreal).

[2] BETHGE (K.), Ann. Rev. Nucl. Sci., 1970, 20, 255.

[3] FAIVRE (J. C.), FARAGGI (H.), GASTEUOIS (J.), HAR-

VEY (B. G.), LEMAIRE (M.-C.), LOISEAUX (J.-M.), MERMAZ (M. C.) and PAPINEAU (A.), Phys. Rev.

Letters, 1970, 24, 1188.

LEMAIRE (M. C.), Trieste lectures, 1971.

FARAGGI (H.), JAFFRIN (A.), LEMAIRE (M.-C.), MERMAZ (M. C.), FAIVRE (J. C . ) , GAS-~EBOIS (J.), HARVEY (B. G.), LOISEAUX (J.-M.) and PAPINEAU (A.), Ann. Phys. (N. Y . ) , 1971, 66, 905 (de Shalit Memorial) and FARAGGI (H.), LEMAIRE (M.-C.), LOISEAUX (J.-M.), ,MERMAZ (M. C.) and PAPINEAU (A.), Phys. Rev., 1971, C 4 , 1375.

greater strength above 8 MeV of excitation energies.

Thus, it can be guessed that, between 4 4 ~ i and 42Ti, the (2 p,,,)4 contribution is gradually increasing in the lowest multiplets as neutrons are added, until it became the most important term of the 4 MeV group in 52Ti, after N = 28. The pattern shows very similar features among the chromium and nickel isotopes, until it is shifted towards the ground states in the zinc nuclei, after Z = 28. Calculations for the whole set of titanium isotopes, that are now under way [I I], give preliminary results in agreement with these qualitative considerations. They also explain why there are so many weak states in the case of 48Ti.

Conclusion. - As far as we can know at the present time, it can be said that the quarteting coupling scheme, that is quite evident in light nuclei, is also present in heavier ones, at least at the beginning of the f-p shell, even if it is more diflicult to observe it in a straight- forward experimental approach. It may quite well occur that better types of experiments can be performed in a near future. At the present time, a good micros- copic model of the reaction mechanism is highly needed to be able to extract, from the already known experimental results, valuable informations about spectroscopic amplitudes. If the decay modes of the states selectively excited can be known with a sufficient degree of confidence, in order to obtain spin and pari- ties without ambiguities, it will be of paramount importance.

However, it appears that both two nucleon and four nucleon correlations are the most important residual interactions to be taken into account in the basic shell model framework of nuclear structure, and that they offer the beginning of an understanding of a large set of experimental results in a coherent way.

Acknowledgement. - All the experiments discussed here have been performed by the authors of [3], and were suggested by V. Gillet. Very enlightening discus- sions with Drs. Ripka, Jaffrin and Zuker were also of a great help at all steps of this search.

[4] FRIEDMAN (A,) et al., Proc. Heidelberg Conf., 1969, 171.

KORNER (H. K.) et al., BAPS, 1971, 16, 646 ; SIEMS-

SEN (R.) ct al., to be published.

[5] Communications at this Conference by MORRISON (G.), p. ~ ~ ; L E M A I R E (M. C.)et a]., p. 171 ; MANKO(V. I.) et al., p. 225 ; OERTZEN (W. V.), p. 233 ; P o u c r 3 ~ o ~ (F.) et al., p. 249.

161 JAFFRIN (A.), Phys. Letters, 1970, B 32,448 and ref. [3]

above.

[7] BEUZIT (P.), BALLINI (R.), DELAUNAY (J.), FODOK (I.), FOUAN (J.-P.) and GASTEUOIS (J.), this Conference.

[8] BHATT (K. H.) and Mc GRORY (J. B.), Plzys. Rev., 1971, C 3, 2291.

[9] ZUKER (A. P.), private communication.

[lo] JAFFKIN (A.), Padova Conference f 7 / 2 nuclei, 1971, and to be published.

[I I ] PASQUINI (E.), private communication.