THE CORRELATION OF LINEAR MOMENTUM AND ANGULAR MOMENTUM TRANSFER IN THE REACTIONS OF 310 MeV 16O WITH 154Sm

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THE CORRELATION OF LINEAR MOMENTUM AND ANGULAR MOMENTUM TRANSFER IN THE

REACTIONS OF 310 MeV 16O WITH 154Sm

M. Namboodiri, R. Choudhury, Ladler, J. Bronson, D. Fabris, U. Garg, P.

Gonthier, K. Hagel, D. Haenni, Y. Lui, et al.

To cite this version:

M. Namboodiri, R. Choudhury, Ladler, J. Bronson, D. Fabris, et al.. THE CORRELATION OF LINEAR MOMENTUM AND ANGULAR MOMENTUM TRANSFER IN THE REACTIONS OF 310 MeV 16O WITH 154Sm. Journal de Physique Colloques, 1986, 47 (C4), pp.C4-101-C4-103.

�10.1051/jphyscol:1986413�. �jpa-00225777�

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JOURNAL DE PHYSIQUE

Colloque C4, supplement au n o 8 , Tome 47, aoOt 1986

THE CORRELATION OF LINEAR MOMENTUM AND ANGULAR MOMENTUM TRANSFER IN THE REACTIONS OF 310 MeV

160

WITH 1 5 4 ~ m

M.N. NAMBOODIRI(

)

, R.K. CHOUDHURY( , L A D L E R ( ~ ) , J.D. BRONSON, D. FABRIS, U. GARG('), P. G O N T H I E R ( ~ ) , K. HAGEL, D.R. HAENNI, Y.W. LUI, Z. M A J K A ( ~ ) , G. MOUCHATY, T. MURAKAMI, J.B. NATOWITZ, G. NEBBIA, R.P. SCHMITT, S. SIMON, J.P. SULLIVAN and

D.H. YOUNGBLOOD

Cyclotron Institute, Texas

A &

M University, College Station, TX 77843, U.S.A.

ABSTRACT From c o ~ n c ~ d e n c e measurements between projecttle fragments or heavy residues and thetr assoc~ated Y-rays, we ave der' ed the angular momentum transfer In the incomplete fusion reactions of 310 MeV

0 ' '

wtth '"Sm as a functton of !,near momentum transfer. The results have been compared w i t h recent model predictions.

Correlated measurements of linear momentum and angular momentum transfer in heavy i o n collisions offer the possibility of delineating the p a r t ~ a l wave dependence of domlnant reaction mechantsms such as complete and incomplete fusion. T h ~ s allows one t o test various theorettcal models which treat incomplete fusion such as the sum-rule model of Wilczynski[ll.

the geometric overlap model of Harvey

[2,3]

and the more mtcroscoplc models, based on

nucleon-nucleon ~nteractlons, proposed by Harvey [4] and by Cole [51.

EXPERIMENTS: We have deduced the correlation bet een linear momentu transfer and angular momentum transfer in the reactions of 310 MeV

' 0

projectiles with m4Sm from t w o separate experiments performed at Texas A&M University: (1) Measurements of the average total Y-ray energy (using a 76-segment NaI(TI) sum-crystal arrav) i n coincidence with

projectile-like fragments detected at 12 deg. with respect t o the beam by means of silicon detector telescopes; (2) Measurements of the average y-ray multiplicity (using an 8-element Nal multiplicity filter) in coincidence with a microchannel plate - silicon detector time-of-flight system t o measure the velocity of recoiling heavy residues. Linear momentum transfer was derived in the first experiment from the energies of the projectile-like fragments with corrections f o r missing momentum carried away by unobserved particles and in the second experiment from the residue velocities. Angular momentum transfer was derived from total gamma energy o r gamma multiplicity, respectively. These t w o measurements taken together yield data that span the full range of fractional momentum transfer from 0 t o 1. Details of the experiments will be given in a full article t o be published elsewhere.

RESULTS: (A) Ejectile-<Ey

>

Measurements: The average total gamma energies corresponding t o 10 MeV bins in the eiectile energy were extracted from the data.

Current Addresses :

("~awrence Livermore National Laboratory, Dept. of Physics, Livermore. CA 94550, U.S.A.

("~habha Atomic Research Centre, Nuclear Physics Division. Bombay 400085. India (3'~ashington University. Physics Dept.. Saint-Louis. MO 63130. U.S.A.

(4)~niversity of Notre-Dame. Dept. of Physics. Notre-Dame, IN 46556. U.S.A.

(5)~ope College. Physics Dept., Holland, MI 49423, U.S.A.

(') ~agellonian University. Institut of Physics, U1. Reylnonta 4, PL-30059 Krakow 12, Poland

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986413

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C4-102

JOURNAL

DE

PHYSIQUE

Since the gamma ray spectra indicated generally small t o negligible contributions from de-excitation of the projectile-like fragments, we have taken the observed gamma energy as representing the de-excitation of the target-like fragment. From these average Ey values, we derived average angular momentum transfer as a function of the ejectile energy using the methods given in Ref 6. The results obtained in this manner for several ejectiles are given in Fig. 1. (B)Residue

-

<Mv> Measurements: Fig. 2 shows both the residue velocity distributions and <My

>

as a functibn of residue velocity. It is seen that even the most probable momentum transfer is significantly less than full momentum transfer as i s noted by comparison with the result of a calculation using the code LlLlTA [7] (histogram in Fig 2b) assuming total momentum transfer and statistical decay of the composite system.

In Fig 3, data from both experiments are presented as a plot of the average angular momentum transfer as a function of fractional linear momentum transfer. For the E y results shown as solid circles, the ordinate is the average angular momentum transfer at the most probable ejectile energy. The abscissa ^ISthe fractional linear momentum transfer associated with the most probable ejectile energy orre ed for the missing momentum due t o particle emission using the results for the system + '"U given i n ref.

8.

The squares in Fig 3 represent the < M y > results. Here the abscissa is derived from the residue velocity assuming that any missing mass is ejected straight forward with beam velocity.

MODEL COMPARISONS: Fig. 4(a) and (b) show the 1-distributions calculated by the sum-rule model [ I ] and the geometric overlap model [21 respectively for several primary ejectile channels in our system. In general, the partial waves leading t o a given ejectile are much larger i n the overlap model than in the sum-rule model. Fig 4(b) also sh ws s arrows pointing towards the lower X-axis) the most probable initial g-values for 'He, C' and 1 4 ~ ejectiles predicted by Harvey's microscopic nucleon-nucleon collision model [4] with a nucleon mean free path of 13 fm. These R -values are, in general. similar t o those of the geometric overlap model.

The arrows along the top X-axis show the corresponding predictions made by Cole [5].

The model predictions are compared with our experimental data i n Fig 3. The sum-rule and the overlap models (curve A and 8 respectively) lead t o very similar predictions although the initial partial waves involved are very different. This is a result of the different assumptions regarding the fraction of the angular momentum carried by the captured particles. Harvey's microscopic model calculations (curve C) were done with a mean free path (mfp) f o r nucleons in the nucleus o f 13 fm. The calculated values of the R-transfer are quite sensitive t o the assumed mfp i n this model. Best agreement with our results is obtained with a m f p of 13 fm, which also gives a value of 600 m b for the fusion cross section in this system in reasonable agreement with systematics.

Finally we note that if the actual relationship between the fractional mass- and angular momentum transfers is understood, the data could be recast in terms of initial partial waves contributina t o oarticular momentum transfers. In the simolest formulation. the relation between

- .

the initial partial wave&i, and the momentum Rt may be given as re(PPi

- ^Pt)

where Pi and Pt are the initial and transferred linear momenta and re and r t are the

I

distances from the target center f o r the emitted and transferred mass. In the geometric overlap model the ratio re/rt is about 1.4 for a range of mass transfers for our system while the sum-rule model implies the assumption, re/rt = 1.

CONCLUSIONS: Models that ascribe incomplete fusion reaction channels t ver different initial values predict rather slmilar values for the !I-transfer for the system

"0

+ '54Sm at 20 MeV/u. Each model makes reasonable predictions of the observed trend of 2- transfer as a function of momentum transfer, and we cannot distinguish between them from our data alone.

However at intermediate energies where the reactions take place at a time scale comparable t o the transit times of nucleons in a nucleus, the association of the transferred nucleons with the overlap region appears reasonable. Recalling also the success of the overlap models in explaining isotope yields [4], models of this type or those treating the collision in terms Of nucleon

-

nucleon interactions may be more appropriate i n this energy range than models like the sum-rule model which use mean field considerations such as pockets i n the interaction potential and limiting angular momenta.

This work was supported b y the US Department of Energy and the Robert A. Welch Foundation, and was done in part at Lawrence Livermore National Laboratory under the ausplces of US DOE under contract No. W-7405-ENG-48.

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REFERENCES:

111 J.WILCZYNSKI et al.. Nucl. Phys. A373. 109 (1982)

[2] B.G.HARVEY and H.HOMEYER, Lawrence Berkeley Laboratory Report, LBL 16882 (1984) (31 B.G.HARVEY and M.J.MURPHY. Phys. Lett., 1303, 373 (1983)

[4] B.G.HARVEY. Nucl. Phys. A444, 498, (1985)

6 1

A.J.COLE, Z.Physik, A322, 315(1985) and private communication.

161 M.N.NAMBOODIRI et al. Phys. Rev., C20. 982 (1979)

171 J. GOMEZ del CAMP0 and R.G.STOKSTAD. ORNL Report TM 7295 (1981) [81 B.B.BACK et al., Phys. Rev.. C22. 1927 (1980)

310-MeV 160 + ' " ~ m Fragment-(E-) data

i

Rendue-(M,) data

1.0 0.8 0.6 0.4 0.2 0

Fig. 2: Residue velocity spectrum (bottom) and average y-multiplicity (top).

Fractional momentum transfer

I

310 MeV ' 6 0 + ' 5 4 ~ m - ^8,^=12" ^-

, ,

⁺

t

^-

I

30

7.5 25

22.5

-

r"

15.0 "N 1

-

5, ^7.5 "-"* ^~~ ô ^- ^~^~ ^~ ^~1 ô ô ^~^~ ô 20-

""6 ::

7 5

Fig. 3:.iAverage Qtr as a function o f momentum transfer. Experimental data compared with model predictions:

Curve A: Ref 1.6: Ref 3, C: Ref 4, D: Ref 5.

5 2 2 . 5

2 ^15.0

u 7.5 2 3 0 . 0 22.5 w 15.0

2

^7.5

W g M.0 22.5

Pi

Fig.&iModel predictions o f initial P-wave distributions for different ejectiles.

15.0 -

FRAGMENT ENERGY [MeV)

0 0.50 1.00 Fig. 1: Average total angular momentum

transfer for different ejectiles at 12 deg. Residue velocity.

cm/ns

" " " '

IZc

~ o..*-o-

- %

" " "

- :O*%wo 'IB

r

-

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