fulltext

Observation techniques and properties of



-cluster states

at high excitation in

A=16

–

40

nuclei

( 

)( 

)

T. L¨ONNROTH

Department of Physics, ˚Abo Akademi Porthansgatan 3, FIN-20500 Turku, Finland

(ricevuto il 26 Luglio 1997; approvato il 15 Ottobre 1997)

Summary. — Groups of narrow states with seemingly rotational-like structures are

observed in-particle elastic scattering from the Coulomb barrier up to excitation en-ergies of about 35 MeV. These states are best studied in28

Si, but similar states are observed in nuclei ranging from16;18

O to36;38

Ar. For each`-value some 10-15 states with narrow widths,20 – 80 keV, are observed in

28

Si and apparently in other mid-sd-shell nuclei, but the properties of these states are not yet fully understood. Existing models, mostly based on rotation-vibration molecular arguments are not able to ex-plain the experimental findings in a consistent way. Non-linear models, interpreting the alpha-particle as a soliton on the nuclear surface, provide a sufficient number of states with the desired properties. Their microscopic interpretation, however, because of the non-linearity, has not yet been made physically clear. In addition to conventional scattering experiments, using-particle beams on solid targets, we have developed a “thick-target” method which makes the data acquisition much faster, and gives contin-uous energy spectra. We further develop an inverse-geometry method, impinging vari-ous heavy ions on helium gas in a target chamber with variable pressure, also providing continuous excitation-energy spectra. This method saves enormously beam time, but has some disadvantages which are being studied.

PACS 25.55.Ci – Elastic and inelastic scattering. PACS 29.25 – Particle sources and target. PACS 01.30.Cc – Conference proceedings.

1. – Introduction

We discuss the results of experimental investigations of



-particle elastic scattering on a number of nuclides. The most comprehensive data is from scattering on28

Si using a

( 

)Paper presented at the 174. WE-Heraeus-Seminar “New Ideas on Clustering in Nuclear and Atomic Physics”, Rauischholzhausen (Germany), 9-13 June 1997.

(  

)Work supported in part by the Academy of Finland and Nordisk Forskeruddannelse Akademi (NorFA).

Fig. 1. – Example of reverse-geometry spectrum for32

S+forEexc 12.5 – 16.0 MeV. Further details are found in [8]. Note, that the narrowest structures have widths of only30keV.

thick-target method developed in our laboratory. A new method, using reverse geometry impinging heavy ions on a helium gas target is shown to be powerful. Narrow states, which seem to form a rotational structure, are observed from the Coulomb barrier up to an excitation energy of about 35 MeV.

Cluster models have been applied to light nuclides, i.e. for

A

 40, see e.g. [1] for a

comprehensive review. The experimental features are quite well discribed within these models near the doubly magic 16

O. However, we will point out, that these approaches rather fail to describe the wealth of structures we observe in mid-sd-shell nuclei.

2. – Experimental methods

The original bulk of experimental data of elastic



-particle scattering was obtained with the MGC-20 cyclotron of the Accelerator Laboratory at ˚Abo Akademi. The main part of the experiments, and the methodical development, was performed based on the “thick-target method” [2]. For general presentations see, e.g., [3-5]. New experimental techniques in reverse geometry, originally proposed by the Moscow group, see [6] and references therein, are being developed at the Cyclotron Laboratory of Jyv¨askyl¨a Uni-versity. We want to call this new method “the Goldberg method”. Powerful tools to obtain intense beams of all elements, also their less abundant isotopic species, e.g. the MIVOC method [7], have been developed by that laboratory.

We have checked the inverse-geometry method against known excitation functions obtained with Tandem machines, and we are in progress to obtain new data. Figure 1 shows a partial spectrum of32

S+



in the excitation energy range

E

exc

12.5 – 16.0

MeV. Note especially that the good energy resolution is retained despite a thick entrance window (see [9]b for a discussion). One may compare fig. 4 of [10], bottom panel and text, where they measured the excitation function of



+

20

Ne using800 beam energy

settings, whereas our method gives the same spectrum with one setting [8].

The angular distributions are fitted to Breit-Wigner expressions on-peak: d

=

d = 1 k 2 (2

`

+1) 2 (, 

=

,) 2

P

2 `

(cos



)

;

giving the

`

-value and, 

=

,. Note that for the inverse

ge-ometry the following relation holds: tan



Lab = sin



CM

=

(

x

+cos



CM ), where

x

is the mass ratio

x

=

m

ion

=m

targ. For sulphur on helium

x

=8and consequently the laboratory



In our set-up, using helium gas in a chamber with an entrance foil, the scattered



-particle is detected at 0

, or generally at small angles with respect to the incoming beam in the laboratory, and the beam energy itself is continuously degraded down to zero (see [8]). The path length of the heavy-ion beam is some tens of cm, depending on the pressure, which is calculated to stop the beam before the detector. Scattering at 0

thus corresponds to backward scattering at 180

in the conventional thick-target set-up.

3. – Results

The following thick-target experiments have been performed: the most comprehensive data is for



+28

Si, further we also have data of alpha-particle scattering on14

C, 27

Al,

29;30

Si and32;34;36

S, the latter using the stepping method. Tests have also been performed on evaporated KCl, providing35;37

Cl and39;41

K. For the case of



+28

Si the data is continuous in energy, and the angle data with 14-21 points, quasi-continuous in angle. When the energy pieces are ’glued’ together, taking into account the differential stopping power (see [2]) and likewise the angular parts, one obtains an energy-angle cross section matrix which can be analyzed subsequently. This is, in fact, a unique kind of data.

The data on29;30

Si are virtually identical to that of28

Si, however, there are large differ-ences in the cross-section mean values. For28;29;30

Si they vary as 8:1:3, and for32;34;36

S the ratios are 5:4:1 [11]. This data will be extended and improved in future experiments using the Goldberg method. At present we have used the inverse method with beams of12

C, 16;18

O,20;22

Ne and32;34

S, albeit with rather thin detectors. A drawback of the method is the need for thick (up to 5 mm) detectors because of large laboratory energies of the



-particles.

We notice an important spin-off of the Goldberg method: the method was used to deter-mine properties of the g.s. and excited states in the particle-unstable nucleus11

N, using the reaction10

C+p (methane gas target) at LISE3-GANIL [12]. States in this nucleus can apparently also be interpreted as dimers with additional “covalent-binding” protons,

i.e. a 2



+3p configuration [13].

4. – Discussion and outlook

When the centroids of groups of states with the same angular momenta in32

S are plotted against

`

(

`

+1), one obtains a straight line. This linear behaviour vs.

`

(

`

+1)

indicates a rotational behaviour in the



+ 28

Si system. The moment of inertia can be obtained as

I

=4

:

85

h

2

MeV,1

, which indicates an object slightly more extended [14, 15] than the ”ground-state band”. Further, experimentally the so-called parity splitting is absent — in serious conflict with most potential-scattering model predictions.

Below we mention some theoretical approaches, but it will be seen that none of the models is able to fully explain the experimentally observed features:

– Classical potential descriptions with e.g. a Dunham-type shape [16] is not able to produce a sufficient number of vibrational states without being unphysical, i.e. too shal-low [17]. These rotation-vibration approaches of [18, 19] cannot explain the multitude of states with same

`

-value in our



+28

Si rotational structure (see fig. 11, right panel, of [5]): translating the classical vibrational amplitude

A

to a quantum energy gives the semiclassical expression

A

2 = 2(

n

+ 1 2 )

h

2

=m

(

h!

) ,1



h!

 0

:

23MeV (

m

is the reduced mass of the



-particle). This gives

A

 6

:

5fm for

the zero-point vibration,12fm for

n

=1, etc., which clearly is completely unphysical!

This is in accordance with the unphysical potentials obtained by Kato and Abe [17]. Our preliminary results on32

S+



show very similar structures.

– A soliton approach is, indeed, the only description so far that can give a suffiently large number of states [20]. It has, however, problems with a physical interpretation be-cause of the non-linear approach and bebe-cause of the excitation of the soliton (“orbiting alpha particle”) itself.

– Algebraic models, not based on bosons like in [21], which have basically the same problems as the rotation-vibration model [17], but a Semimicroscopic Algebraic Cluster Model [22] may be able to explain this multitude.

– Microscopic shell model calculations can, in principle, give all the states that can be constructed of the nucleonic orbitals, but it is not evident that the residual interaction is able to create the correct alpha-cluster correlations. These calculations would also need very large bases, and this is a well-known problem. A serious attempt should be made to improve the microscopic descriptions, e.g. along the lines of [23], starting from16

O and working up into more complex cases [24] with larger number of nucleons.

For example, can the ”cut-off ” in the excitation function of32

S at32 MeV be

ex-plained as running out of valence-particle spin? The

sd

-space configuration

d

2 3=2

d

3 5=2

s

1=2

has a maximum spin of 14

h

, whereas

d

2 3=2

d

4 5=2

has 12

h

. One can conclude that the

forth-coming theories must be able to explain at least the following experimentally observed features:

– There are a large number of states with the same

`

-value which seem to be grouped in energy regions of some few MeV, and no parity-splitting is observed.

– The observed states have narrow widths, ranging from some 20-50 keV at

`

 4

h

and increasing to about 100 keV at the highest spins. This implies that the lifetimes of the observed states are100 times larger than what is anticipated from transit-time

ar-guments or calculations of resonance widths. Consequently this quasiboundedness has to be explained by some attractive interaction, or by a hindrance mechanism of the decay.

– The summed alpha-particle widths of angular-momentum groups seem to nearly ex-haust the Wigner limit up to i.e. 60,100% [9]. This means that the effect may have

the microscopic behaviour of alpha particles retaining the identity/structure for ”50-100 revolutions” of the system, i.e. they are quasi-bound.

  

The presentation is an account of a collaborative work with several persons and in-stitutions: K.-M. K¨ALLMAN, M. BRENNER AND P. MANNG˚ARD( ˚Abo Akademi), P. O. LIPAS, T. SIISKONEN and W. H. TRZASKA(Jyv¨askyl¨a), M. GRIGORESCU, A. LUDU

and A. S˘ANDULES¸CU(Bucures¸ti), V. Z. GOLDBERG, V. I. DUKHANOV, A. E. PAKHO

-MOV, V. V. PANKRATOV, G. V. ROGACHEV, M. G. RUTCHKOV, I. N. SERIKOVand V. A. TIMOFEEV(Moscow), and the “11



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