ALPHA-PARTICLE RESONANT STATES IN MEDIUM WEIGHT NUCLEI

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ALPHA-PARTICLE RESONANT STATES IN MEDIUM WEIGHT NUCLEI

A. Dudek, P. Hodgson

To cite this version:

A. Dudek, P. Hodgson. ALPHA-PARTICLE RESONANT STATES IN MEDIUM WEIGHT NUCLEI.

Journal de Physique Colloques, 1971, 32 (C6), pp.C6-185-C6-187. �10.1051/jphyscol:1971636�. �jpa- 00214854�

J O U R N A L DE PHYSIQUE Colloque C6, supplt!ment au no 11-12, Tome 32, Novembre-Dkcembre 1971, page C6-185

ALPHA-PARTICLE RESONANT STATES IN MEDIUM WEIGHT NUCLEI

A. DUDEK (*) and P. E. HODGSON Nuclear Physics Laboratory, Oxford, England

Rhumb. - Une interpretation en termes d'etats de rksonance d'une particule alpha est suggkrke pour les etats a structure cc en quartet ⁾⁾ observes dans la reaction ^{('60, 12C).} IRs energies et les caracteristiques generales de ces etats resonnants ont ett calculks en utilisant un potentiel de Saxon- Woods.

Abstract. - It is suggested that the quartet states found in ( 1 6 0 , 12C) alpha-transfer reactions may also ^be interpreted as alpha-particle resonant states. The Saxon-Woods potential was used to calculate the energies of these states and the overall features of the observed resonances were obtained.

Some recent studies [I]-[3] of the ^(160,

'

We wish to suggest that these states may also be interpreted very simply as alpha-particle resonant states whose properties may be found from standard optical potentials, and that this should permit the cross- sections of the alpha-transfer reactions to be calculated.

It is well-known [4] that the total potential for alpha- particles obtained by adding the optical, angular momentum and Coulomb terms shows minima for particular values of the orbital angular momentum, as illustrated in figure 1 . For most partial waves the absorbing potential quenches the incoming wave and so no resonance can occur in these minima, but if the absorption in a particular partial wave is very small this restriction no longer applies. It has been shown that such reductions do occur in alpha-particle inter- actions because the outgoing channels cannot accept the high momenta brought in by the incident beam [5].

This note reports some preliminary calculations made to see if this can give resonances qualitatively similar to those observed.

The energies of the discrete groups of alpha-particles are shown in figure 2 for the various nuclei studied.

A theory able to account for these states in detail must presumably depend on the detailed structure of the nuclei ; the possibility studied here is that they have some systematic features that remain similar for all the nuclei and can be represented by a simple

(*) Permanent address : Institute of Nuclear Physics, Cracow, Poland.

FIG. 1. - Total optical potential as a function of radial distance.

potential. To see if this is the case it is necessary to calculate the energies of the states of the assumed alpha-particle optical potential. The results given in figure 2 show that some of the states are just bound and some just unbound. In the present preliminary calculations we'calculate the energies of the states as a function of potential depth for the bound states and at energies above the potential barrier, and inter- polated for the intervening region. As might be expected physically, the interpolation is practically linear, so the procedure gives acceptable results.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971636

C6-186 A. DUDEK AND P. E. HODGSON

eLm. 50' OUARTET STATES I KNOWN LOW-LYING STATES

"2" I

5

I . . I

e,,=35* , _I

=ON,

I

eLUl. 50' I I

"~1 e x s o _{p m m m} a s a a - # . - a a 6 : : o

,if

FIG. 2. - Diagram showing the energies of quartet states.

These calculations were made with a standard Saxon-Woods form factor for the real potential (r, = 1.15 f, a = 0.65 f) and the results for 5 8 ~ i are shown in figure 3. Several features are immediately apparent :

1. The states group into bands, and each band corresponds to the states of a particular number of oscillator quanta.

2. The orbital angular momenta of the states in each band are either all even or all odd. The band of N quanta contains states with L = 0, 2, 4, ..., N for L even and L ⁼ 1, 3, 5, ..., N for L odd.

3. The density of states is very similar to that of the observed states. This is shown in figure 3 by the superposition of the observed energy spectrum on the calculated one, a t a position corresponding to a potential of depth U z 132 MeV, which is physically very reasonable.

4. There is a tendency for one state to be rather separated from the remainder, and this is found experimentally.

5. The variation of the energies of the states with the depth of the potential is almost linear, but the rates of variation are slightly different, so that the

lines on figure 3 are not quite parallel. Subsidiary calculations showed that the ordering of the states within a band is very sensitive to the form factor chosen, particularly to the diffuseness parameter.

6 . The gaps between the bands are approximately as broad as the bands themselves. This is in accord with the experimental data for the 54Fe('60, 1 2 C ) " ~ i reaction ; the states are no longer found a t excitation energies above 12 MeV.

This comparison shows that the calculations are entirely successful in giving the overall features of the observed resonant states. To confirm the interpretation it is of course necessary to make distorted wave calculations in which the wavefunction of the captured particle is that of an alpha-particle in a potential well. The resonant structure will then appear automa- tically as the wavefunction is greater a t the resonant energies.

Comparison of the calculated and measured diffe- rential cross-sections may give the orbital angular momentum transfer, although the preliminary results give rather featureless angular distributions, and the situation may be similar in this respect to those found for the sub-Coulomb stripping of deuterons. It is a n important test of the model to determine the angular momentum transfers, because the model makes very definite predictions of the spins of these states (see 2 above). It may prove possible to determine the orbits of the nucleons contributing to the alpha- particle states by calculating the appropriate overlap integral.

If this interpretation of the quartet states is correct, it should be possible to detect them in alpha-particle elastic scattering, and experiments [6] are already under way in Oxford to investigate this possibility.

It is unlikely that the model will be able to give reliable absoIute cross-sections, particularly when the alpha-particle is captured into the lower states, as the

FIG. 3. - CaIculated energies of alpha-particle states in an optical potential with typical experimental data superposed.

ALPHA-PARTICLE RESONANT STATES IN MEDIUM WEIGHT NUCLEI C6-187 presence of other nucleons is likely t o block the the value of this parameter by a detailed nuclear available states, a n d such detailed nuclear structure model.

effects are beyond the scope of the model. It might This model was originally proposed by Dr A. M Lane however prove practicable t o represent such effects by a n d we are grateful t o him for many discussions during a single parameter for each state, a n d t o calculate the course of this work.

References [I] FAIVRE (J. C.), FARAGGI (H.), G A S T ~ O I S (J.), HARVEY

(B. G.), LEMAIRE (M. C.), LOISEAUX (J. M.).

MERMAZ (M. C.) and PAPINEAU (A.), Saclay Report CEA-N-1390, 1970.

[2] FARAGGI (H.), LEMAIRE (M. C.), LOISEAUX (J. M.), MERMAZ (M. C.) and PAPINEAU (A.). Preprint 1971.

[3] FARAGGI (H.), JAFFRIN (A.), LEMAIRE (M. C.), MERMAZ (M. C.), FAIVRE (J. C.), GASTEBOIS (J.), HARVEY

(B. G.), LOISEAUX (J. M.) and PAPINEAU (A,), Anizals o f Phvs., 1971. 66. 905.

[4] GRUHN (C. R.), WALL (N: S.), Nucl. Phys., 1966, 81. 161.

[ 5 ] CHATWIN (R. A.), ECK (J. S.), ROBSON (D.) and RICH-

TER (A.), Phys. Rev., 1970, C1, 795.

B r s s o ~ (A. E.), EBEHHAHD (K. A.) and DAVIS (R. H.), Phys. REV., 1970, C1, 539.

[6] GRACE (M. A.) and AYRES de CAMPOS (N.), private communication.