TWO-NUCLEON TRANSFER REACTIONS AMONG HEAVY IONS

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TWO-NUCLEON TRANSFER REACTIONS AMONG HEAVY IONS

R. Broglia, T. Kammuri, R. Liotta, A. Winther, B. Nilsson

To cite this version:

R. Broglia, T. Kammuri, R. Liotta, A. Winther, B. Nilsson. TWO-NUCLEON TRANSFER REAC- TIONS AMONG HEAVY IONS. Journal de Physique Colloques, 1971, 32 (C6), pp.C6-151-C6-153.

�10.1051/jphyscol:1971624�. �jpa-00214842�

J O U R N A L DE P H Y S I Q U E

Colloque C6, supplkment au no 1 1 - 12, Tome 32, Novembre-Dkcembre 1971, page C6-15 1

TWO-NUCLEON TRANSFER REACTIONS AMONG HEAVY IONS

R. A. BROGLIA, T. KAMMURI, R. LIOTTA (*) and A. WINTHER The Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

and B. NILSSON

NORDITA, Copenhagen, Denmark

Resum@.

La theorie du transfert de deux nucleons entre ions lourds dans I'approximation de Born avec ondes deformks est present&. Les effets

portee finie sont traites dans l'approxima- tion

Buttle-Goldfarb. Nous discutons a titre d'exemple les reactions AZr(lG0,

80)A-*Zr.

Abstract. - The

theory of two-nucleon transfer reactions between heavy ions is present- ed. Finite-range effect is taken into account by means of the Buttle-Goldfarb approximation.

As an example, we discuss the "Zr(160, I80)A-zZr reactions.

The (t, p) and (p, t) reactions have been extensively two-nucleon transfer reactions developed [3] to deal used in recent years and have provided specific with light projectiles to the case when the reaction information on the pairing correlation present in takes place among heavy ions.

nuclei. This picture is being substantially enriched We consider the reaction A(a, b) B when B

A + ²

with the data on two-nucleon transfer among heavy and a

b + 2. The effective matrix .element ions [I], [2], in particular with the proton transfer data. < Bh I V I Aa > appearing in the DWBA transfer

In the present contribution we extend the theory of amplitude can be written as

< Bb I V I Aa >

< $1,~,,(5A, r ~ ,

C I , a,) $,,,,(5b), V$,,M,(~A) I)s,,n,(cb, r l ,

>

=

1 (I, MA jm I I, M,) (I, M a 1,

Mb I ^sm,) (lml sm, I jrn) (- l)lb-M"-l

Isj

n K )

(1)

where

The wave functions $ describe the internal degrees spectroscopic information. To evaluate it we expand of freedom of systems A, a, B and b. The matrix the functions and I),,,,, in terms of the corres- element < Bb 1 V ] Aa > contains all the nuclear ponding two-nucleon spectroscopic amplitudes

The spectroscopic amplitude Azsj(ic1) is given by

(*)

Supported

Consejo Nacional dc ~nvcstigaciones Cientificas

Tecnicas, Argentina.

On leave from Universidad de Rosario, Rosario, Argentina.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971624

C6-152

K.

R .

B.

The function

is the overlap of the harmonic oscillator wave functions of the relative motion of the two particles with different size parameters and

The function

is equal to

frs,,,,(R,

ti')

g , ( ~ , K') hjl)*(ilif R ) K;,(R) , (5) where for the case of neutron transfer g,(ti,

6(ti - I;'). For proton transfer one finds [4]

\ ^{0 for}

^<

1 + 1,

I , n' + ^1, -

f o r

>

(6) In deriving expression (5) for protons use has been made of the expansion

where W is the Whittaker function and

This allows us to apply the Buttle-Goldfarb expan- sion [5] to the proton case, to obtain a finite range form factor. Because of relation (7) it is not possible for protons to attain a complete separation of G as the product of the spcctroscopic amplitude and the form factor.

Note that a similar type ofcoherence as the one found in the spectroscopic amplitude for (t, p) or (3He, n) reactions also appears in (3) though in the present case the summation over the two-particle configurations appears twice. This is because the reaction that takes place between heavy ions can be interpreted as a simultaneous and coherent pick-up and stripping of two nucleons.

By means of this method, and the DWBA code DWUCK [6], we are presently treating two-proton and two-neutron transfer reactions. As an example we

show thecalculational result on the AZr(160, 1 8 0 ) A - 2 ~ r ( A

92, 94, 96) ground-state reaction induced by 60 MeV

[I].

The Zr ground states are assumed to be superfluid.

The wave function for

is taken from Federman and Talmi [7], but the contribution from the deformed component has been neglected. The optical parameters are those given by Becchetti et al. [ l ] in their analysis of the elastic scattering of 60 MeV

on Zr isotopes, and have the following values :

V

40 MeV, W

15 MeV, r ,

1.285 fm,a

0.5fm.

The calculated angular distribution shows a single peak near the grazing angle. As can be seen from the table, the decrease of a(0obs) with decreasing A corresponds to the sharp damping of the cross section for the scattering angle smaller than the peak angle, due to the reduced tunnelling probability. We can compare the relative peak cross section with the results of (t, p) reaction at 38 MeV [8]. In both cases, the peak changes rather mildly, in contrast to a(0obs).

The cross sections for AZr(160, 180)A-2Zr g. S. at 60 MeV and AZr(p, t)A-2Zr at 38 MeV (in mb/sr)

(*)

normalized.

TWO-NUCLEON TRANSFER REACTIONS AMONG HEAVY IONS

References

[I] NICKLES (R. J.), MANKO (V. I.), CHRISTENSEN (P. R.) [S] BUTTLE (P. J. A.) and GOLDFARB (L. J. B.), NucI. Phys., and BECCHETTI (F. D.), Phys. Rev. Letters, 1971, 1966,

409.

26, 1267, and private communication. [6] KUNZ (D.), DWBA code DWUCK (unpublished).

LEMA'p~~,",i,"'~~p'~~~~R,",~ ~ . ~ [7] FEDERMAN ~ $ (P.) and TALMI ~ ' (I.), Phys. Letters, ~ ~ 1965,

Letters, 1971,

490.

[3] GLENDENNING (N. K.), Phys. Rev., 1965,

B 102. [8] BALL (J. B.), AUBLE (R. L.) and Roos (P. G.), Phys.

141

WINTHER (A.), unpublished note. Rev., 1971, C 4 , 196.