NUCLEON EXCHANGE IN THE SCATTERING OF NUCLEI ON NUCLEI

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NUCLEON EXCHANGE IN THE SCATTERING OF NUCLEI ON NUCLEI

H. Bohlen, B. Gebauer, N. Marquardt, W. von Oertzen, E. Habib, B.

Kohlmeyer

To cite this version:

H. Bohlen, B. Gebauer, N. Marquardt, W. von Oertzen, E. Habib, et al.. NUCLEON EXCHANGE IN THE SCATTERING OF NUCLEI ON NUCLEI. Journal de Physique Colloques, 1971, 32 (C6), pp.C6-141-C6-143. �10.1051/jphyscol:1971622�. �jpa-00214840�

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JOURNAL DE PHYSIQUE Colloque C6, supplkment au no 1 1 - 12, Tome 32, Novembre-Dtcembre 1971, page C6- 141

NUCLEON EXCHANGE IN THE SCATTERING OF NUCLEI ON NUCLEI

H. G. BOHLEN, B. GEBAUER, N. M A R Q U A R D T , W. von OERTZEN, E. E. HABIB (*), a n d B. K O H L M E Y E R (**)

Max-Planck-Institut fiir Kernphysik, Heidelberg, West Germany

Rksume. - La diffusion elastique entre deux noyaux de la couche Ip, mettant en jeu IzC, 13C, '4C, 14N, 15N et ^{1 6 0}a ete mesurke au voisinage de la barriere coulombienne. L'analyse fondee sur la methode des Btats stationnaires perturbes donne une description consistante de la structure prononcke des distributions angulaires.

Abstract. - The elastic scattering of nuclei on nuclei in the lp-shell involving 12C, 13C, 14C, 14N, ISN and ^{1 6 0}has been measured in the vicinity of the Coulomb barrier. The analysis based on the method of perturbed stationary states gives a consistent description of the pronounced structure in the angular distributions.

In the scattering of two nuclei the density distributions of the two objects overlap and exchange of nucleons can take place which leads back to the incident channel (elastic channel) and thus to coherent contri- butions to the potential scattering. In the potential scattering the nuclei are assumed to retain their identity microscopically. T h e rearrangement of the outer nucleons in the scattering can involve exchange in both directions, the probabilities of the different amplitudes will depend on the structure of the colliding nuclei.

A systematic study of the elastic scattering of nuclei on nuclei in the Ip shell was undertaken to achieve a quantitative understanding of the transfer processes in elastic scattering of heavy ions. The experiments were performed a t the E N Tandem van d e Graaff using A E

-

^Etelescopes (proportional counters), kinematical coincidences and position sensitive surface barrier counters in a Buechner magnetic spectrometer.

The magnetic spectrometer allowed a complete sepa- ration of isotopes even at small scattering angles and allowed the measurement of extreme forward angles (and, therefore, backward angles using the recoils).

Figure 1 gives as an example the two-dimensional display ofcoincidences of the energy E deposited in the counter in the focal plane and the position (X) on the counter. The counter is 5 cm long [I]. The technique with the proportional counters was described elsewhere [2].

The incident energies were chosen in the vicinity of the Coulomb barrier. The average cross section a t these energies is not smaller than 1/10 of the Coulomb scattering cross section a t the larger angles. Spectra of

(*) On leave from University of Windsor, Canada.

( + * ) Physikalisches Institut der Universitat Marburg.

the main reaction products (if they existed) were taken and it was found that a t the energies chosen only very weak transitions to the excited states of the colliding nuclei occur, except for the maximum energies which were approximately 5 MeV above the Coulomb barrier. This choice of the incident energies assures that a two state approximation (only the two ground states of the colliding nuclei) and the method of perturbed stationary states [3], [4] can be applied to describe the exchange of the nucleons between the colliding nuclei quantitatively.

Ex-

FIG. 1. - Two-dimensional display of the events of position (x)

and energy ( E ) of particles entering a position sensitive surface barrier counter in the focal plane of a magnetic spectrometer.

In the scattering of two nuclei

A

+

(A'

+

^c)^-+ A

+

(A'

+

c ) , the exchange of particle c (elastic transfer)

A

+

^(A'

+

^{c )}-, A'

+

^{( A}

+

c ) ,

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971622

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C6-142 H . G . BOHLEN, B. GEBAUER, N . MARQUARDT ET W. VON OERTZEN

with A = A', can also be achieved by thc interchange of all nucleons in the identical cores A and A'. There- fore, the interference of the potential scattering and the elastic transfer amplitudes will be determined by a sign which depends on the number of nucleons in cores ^Aand A'. Just as in the scattering of two identical nuclei the interference structures in the angular distributions will be out of phase for fermion- and boson- cores. Figure 2 gives as an example three cases in

BOSON AND FERMlON INTERFERENCE EFFECTS IN ELASTIC SCATTERING OF NONIDENTICAL NUCLEI

FIG. 2. - Elastic scattering of nonidcntical nuclei. Pairs of angular distributions are shown which represent cases in which the mass difference is exchanged between two boson-cores (12C and 14N) or between two ferrnion-cores (13C and l5N).

which fermion- and boson-cores are involved in elastic scattering of non-identical nuclei. From the observed interference effects (and from other arguments, see below and [3], [4]) wecan conclude that the observed structure is, indeed, due to the interference of elastic transfer and potential scattering (The 12C, 13C data [5]

have been completed and remeasured using the magnetic spectromctcr). The potential scattering alone yields at these energies, close to the Coulomb

barrier, angular distributions without any structure if no strong interpenetration of the colliding nuclei is allowed (see for example ref. [6]). In view of the fact that the observed structure can be explained quantitatively with the inclusion of the exchange (see below) the strongly absorbing potentials seem to be the appropriate description of the potential scattering at these energies [7].

A particular case is the scattering of 14N on 14C where no mass difference exists. The phase of the structure agrees with that of the I4N, 12C scattering (at the same CM-energies) and the exchange of the nucleons has to occur in such a way that the 12C nucleus acts as a core. The neutron pair and the (n-p) pair in 14N and 14C are exchanged simultaneously (Fig. 3). The analysis of the data with the method of

FIG. 3. - Elastic scattering of 14N on 14C.

molecular wave functions described in refs [3] and [4]

gives a consistent description of the following data [8] : 12C

+

13C (15 and 19 MeV), 13C

+

14C (15 and 19 MeV), 14N

+

12C (20, 21.5, 23.5, 25 MeV), 14N

+

^13C(17 and 20 MeV), 15N

+

¹⁶⁰(20, 25, 27.5 MeV) and ^' ⁴

+

^~ ¹⁶⁰(20 and 25 MeV). The analysis was done using the standard parameters of ref. [7] for the core-core interaction (with 100 MeV potential depth, r, = 1.19 fm) and the parameter set given by Gobbi [9] (with 17 MeV potential depth, r , = 1.35 fm). The diffuseness of the Woods-Saxon potential was always appr. 0.5 fm. The depth of the imaginary potential was chosen to give smooth (no structure) angular distributions for the potential scattering alone. The two parameter sets have negli-

System S N e x p . Nth. S e x p . S:XP. S ~ M ...-

' 2 C I - ' 3 C 0.7 0.9 0.8 0.64 0.61

13C

+

^14C ^2.5 1.98 1.25 1.6 1.73

14N

+

^13C ^1.8 2.0 0.9 0.8 0.69

I S N .:. 1 6 0 6.6 4.62 1.41 2.0 1.5-2.0

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NUCLEON EXCHANGE IN THE SCATTERING OF NUCLEI ON NUCLEI C6-143

gible differences a t larger distances, in some cases, wave function relative to equivalent Hankel functions however, the parameter set of ref. [9] gave better fits was determined for the relevant cases, they are also to the angular distributions. The strength of the given in the table. The spectroscopic factors obtained exchange interaction induced by the exchange of the in this way are given in the table (S2), and they are in nucleons (SN), see ref. [3], [4], as obtained from the excellent agreement with those from shell-model analysis are given in table I. Using standard shell-model calculations [lo] or values determined by conventional parameters the normalisation N of the bound-state stripping reactions.

References

[I] Made by KALBITZEK (S.) and STUMPFI (M.), at MPI [6] ROBSON @.), Proceedings of Symposium on Heavy

Heidelberg. Ion Scattering, Argonne ^1971,ANL. and W. von

[2] HILDENBRAND (K. D.) et al., Nucl. Phys., 1970, A 157, Oertzen, same place.

297. [7] Voos (U. C.) et a]., Nucl. Phys., 1969, 135, 207.

[3] VON OERTZEN (W.), Nucl. Phys., 1970, A 148, 529. [8] BOHLEN (H. G.), MPI Heidelberg, Thesis 1971, to be published.

[4] VON OERTZEN (W.), Lectures at the lCTP Trieste, ₁₉₁_G~~~~(A*), lot. tit. ~ ~6. f .

and to be published. _[I01- - COHEN (S.) and KURATH (D.), NucI. Phys., 1966, 78, [5] GOBBI (A.) et a]., Nucl. Phys., 1968, A 112, 537. 409: