A POSSIBLE MODEL FOR MULTINUCLEON TRANSFER

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A POSSIBLE MODEL FOR MULTINUCLEON TRANSFER

C. Toepffer

To cite this version:

C. Toepffer. A POSSIBLE MODEL FOR MULTINUCLEON TRANSFER. Journal de Physique

Colloques, 1971, 32 (C6), pp.C6-291-C6-293. �10.1051/jphyscol:1971669�. �jpa-00214887�

JOURNAL DE PHYSIQUE Colloque C6, supplkment au no 11-12, Tome 32, Novembre-Dkcembre 1971, page C6-291

A POSSIBLE MODEL FOR MUILTINUCLEON TRANSFER

C. TOEPFFER

Institut fiir Theoretische Physik der Universitat FrankfurtIMain, Germany

R&um6.

-

La relation entre I'angle de diffusion et la perte d'energie dans les reactions de transfert de plusieurs nucleons est expliquke par une etude des Bl6ments de matrice de transition quasi-classiques. Pour le processus de collision conduisant au transfert de plusieurs nucleons un mecanisme est proposk dans lequel Ies collisions Clkrnentait-es ont lieu entre les nucleons dans la region de recouvrement des noyaux.

Abstract. - The dependence between the scattering angle and the energy loss in multinucleon transfer reactions is explained by a study of the quasi-classical transition matrix elements. For the collision process leading to multinucleon transfer a mechanism is proposed, in which elemen- tary collisions take place between the nucleons in the overlap region of the nuclei.

Experiments on multinucleon transfer above the Coulomb barrier, especially the recent systematic observations of the Dubna Group show a number of regularities in the angular distributions, energy loss spectra and transfer cross sections. In the reaction B(A, A') B' at a fixed energy E the various products A' = A

-

xp

-

yn have

1) angular distributions, which are

-

independent of the number of transferred nucleons

-

peaked a t the grazing angle

O,,

of the initial system A

+

B a t the initial energy E [I], [2].

2) an average energy loss - Q in the collision, which grows slowly with the number y of transferred neu- trons and strongly with the number x of protons stripped from A [2].

Qualitatively it is clear that there is a correlation between the number of transferred nucleons, the scattering angle and the energy loss : If, for example, protons are transferred t o the target, the Coulomb repulsion becomes weaker and the classical trajectories are stretched forward. This can be compensated by a loss in the kinetic energy, by which the trajectories are bended backwards. These phenomena can be studied quantitatively if one considers the dependence of the quasi-classical transition matrix elements on the distance

R

between the nuclei and on the angular momentum 1 of the relative motion.

It can be shown that favorable conditions for transfer are given, if

1) the effective interaction potentials between the nuclei (which include centrifugal terms and in the final channel also the energy of the state excited in the collision) have a crossing point a t Roy which must lie near the sum of the radii of the nuclei (Fig. I),

2) and the scattering angles of the initial and final trajectories are the same.

FIG. 1.

-

The nucleus-nucleus interaction V and effective poten- tials Uepp in the initial and final channels of rnultinucleon trans-

fer. At Ro is a crossing point.

These conditions determine the energy loss

-

^Q and the loss in angular momentum A1 = 1

-

1'.

In an actual calculation the nucleus-nucleus interac- tion of Scheid and Greiner is employed, which consists of the Coulomb and a short-ranged attractive Yukawa force [3]. Fermi-type density distributions are assumed for the nuclei and volume-conserving compound processes shall dominate in the interior region with R

<

c,

+

c,, the sum of the half-density radii of the nuclei. In the upper part of figure 2 the potential between ^{1 6 0} and 2 3 2 ~ h is drawn together with several effective potentials for EcM = 128 MeV. I n the lower part of the figure the corresponding trajectories are drawn. There exist trajectories in forward direction which lie fully outside the shaded, absorptive region, so that transfer processes on these trajectories are possible. Since the nucleus-nucleus interaction is non- monotonous one has a maximal scattering angle

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971669

C6-292 C. TOEPFFER

FIG. 2.

-

Effective potentials and classical trajectories for

1 6 0 4- 232Th at Ecm = 128 MeV.

0, x 5 6 O (rainbow effect). The observed peak in the angular distributions of the various transfer products A' lies on the bright side of the rainbow at 8 w 400.

The deflection function O(1) for this case is shown in the upper part of figure 3. For a rather extreme case of multinucleon transfer we consider the transfer of 9 nucleons, so that one has to treat the pair Be7

+

PuZ4l in the final channel. To achieve favorable conditions for transfer, i. e. similar scattering angles, and similar turning points with c,

+

^c,

<

R,,, RLi,

<

Ro in the initial and final channels, an energy loss of - Q = 62 MeV has to be assumed (Fig. 1, lower part of Fig. 3). This is in accordance to the experimental observations [2]. Also an angular momentum A1 w 35

k

has to be transferred to the interior motion.

Further observed regularities in multinucleon trans- fer reactions are :

1) the excitation spectra have a bell-shaped form with a width of AE* z 20 MeV (2) :

where f is the same function in all channels, under which the area is proportional to g(x, y). This area is just the energy-integrated cross section da/dO ;

o ~ ~ + EcM = 128 MeV T ~ ~ ~ ~

12.8 ₇₅ 13.3 ₈₀ 13.8 ₈₅ R,,, _L

-

6e7 + P" 2L1 E,, = 66 MeV

12.6 13.6 14.6 15.6 R,,,

C

35 LO 45 50 1

-10

FIG. 3.

-

Classical deflection functions for 1 6 0

+

^232Th at Ecm = 128 MeV and 7Be

+

^{Z41Pu at Ecm = 66 MeV.}

2) if one plots the logarithms of (do/dJZ) Osr=400

for the production of the various pairs A', B' as a function of the Q-values Qgg for the ground-state transitions B(A, A') B' one obtains a family of paral- lels [2], where every line is characterized by a fixed value x 2 1 of transferred protons and it is

g(x, Y ) g(Qgg ^f 8QxJ (2) where 6Q, describes the splitting between the lines for the production of the different chemical elements.

In order to develop a model which explains the linear dependence of log (do/dQ) on Q,, it is useful to notice the marked distinctions between these observations and those made in the pick-up of one or several neutrons by the light fragment. In these reactions the energy loss spectra correspond to the exci- tation spectra of the acceptor nucleus (with a width) AE* = 3

a

5 MeV) [I] and the cross sections depend on the separation energies of the transferred particles from the donator nuclei [4]. Therefore one may treat the transferred neutrons as valence particles outside of inert cores.

In contrast to that is has been argued that deep inelastic transfer reactions

-

as they are realized in the present case

-

proceed through a highly excited state, which is formed in the neck between the nuclei during the collision [5].

We want to follow this idea and notice that in the region of the overlapping tails of the mass distributions

(( elementary collisions >> can take place between the nucleons of both nuclei. These lead to 2 p-2 h states, each of which may describe as well a transfer of a

A POSSIBLE MODEL FOR MULTINUCLEON TRANSFER C6-293 nucleon or an inelastic excitation. The coupling

strength between the channels depends on the number of such elementary collisions and these in turn on the volume of the overlap region (i. e. on the classical trajectory) and on the relative velocity of the nuclei.

The transition probability depends on this coupling and the Q-value. It can be obtained by solving the coupled equations of the scattering problem in the molecular wave function method [6], [7]

-

^ZE*

d w = 4 exp ²rcR(dR/dt),, ^{8 - -}

(

^{enp ---} rcR(dR/dt),, ^x

This formula closely resembles to those for the proba- bility of Coulomb excitation. The role of the characte- ristic distance is taken here by the range rc-' of the exponential decreasing tail of the wave function of the least bound nucleon. This range is closely related to the surface thickness of the nuclei.

By comparison with the experimental energy loss spectra [2] one may extract the Qgddependent part of (3) by identifying the factor in the bracket with the bell-shaped function f , which has the same form in all channels. Integration over E* gives

w = const. exp nQ,,

.

'cfi(dRldt),,

The factor in the bracket in eq. (3) should not depend on the number of transferred particles or on Q,, : Similar scattering angles in all channels correspond to similar classical trajectories and these t o equal volumes of the overlap region. Thus the coupling between all final channels and the initial channel is expected to be the same.

Eq. (4) gives the required linear behaviour between log (doldS2) and

egg.

Inserting a value of K correspond- ing to an average separation energy of 8 MeV and taking the velocity at a crossing point R, = 12.25 fm, eq. (4) gives a slope of 0.48 for the parallels while the experimental values range between 0.40 and 0.60.

Properly not the asymptotic values Qgg have to be inserted in eq. (4) but the actual values at Ro : Q,, -+ Qgg

+

^8Q

,

which leads t o the splitting between the lines. 6Q is due to the change in the Coulomb field at

R,

when protons are transferred and also to diffe- rent nuclear polarizations of the nuclei in the initial and final channels.

The model proposed here to explain the Q,,- dependence of the cross sections still has the short- come, that the experimental evidence in the energy loss spectra is needed in order to derivate the energy- integrated transition probability (4). To improve this situation more experimental and theoretical knowledge of the states excited in such multinucleon transfer reactions is necessary.

References VOLKOV (V. V.), GRIDNEV (G. F.), ZORIN (G. N.)

and CHELNOKOV (L. P.), Nucl. Phys., 1969, A 126, 1.

ARTUKH (A. G.), AVCHEIDIKOV (V. V.), E R ~ (J.), GRIDNEV (G. F.), MIKHEEV (V. L.), VOLKOV (V. V.) and WILCZYNSKI (J.), Phys. Letters, 1970, 33B, 407 and Nucl. Phys. 1971, A 160, 51 1 . ARTUKH (A. G.), AVCHEIDIKOV (V. V.), GRIDNEV

(G. F.), MIKHEEV (V. L.), VOLKOV (V. V.) and WILCZYNSKI (J.), NucZ. Phys., 1971, A 168, 321.

SCHEID (W.) and GREINER (W.), 2. f. Physik, 1969, 226, 364.

ARTUKH (A. G.), POMORSKY (L.), TYS (Ya.) and VOLKOV (V. V.), Dubna preprint P 7-5494, 1970.

GALIN (J.), GATTY (B.), LEFORT (M.), PETER (J.),

TARRAGO (X.) and BASILE (R.), Phys. Rev., 1969, 182, 1267.

GALIN (J.), GUERREAU (D.), LEFORT (M.), PETER (J.), TARRAGO (X.) and BASILE (R.), Nucl. Phys., 1970, A 159, 461.

BASILE (R.), GALIN (J.), GUERREAU (D.), LEFORT (M.) and TARRAGO (X.), Rkactions NucMaires par Ions Lourds. Ph6nomknes Frontikres entre le Processus de Noyau Compose et les Effets Directs de Transfert, preprint, 1971, Orsay.

[6] DEMKOV (Yu. N.) in Atomic Collision Processes, p. 831, ed.

Mc DOWELL (M. R. C.), North Holland Publ. Comp., Amsterdam, 1964.

[7] TOEPFFER (C.), Dubna preprint E 2-5797, 1971, and in Phys. Rev. Letfer.~., 1971, 27, 872