The 7Li+d → α+α+n reaction

1 ~

Nuclear Physics 81 (1966) 305--321; ( ~ North-Holland Publishing Co., Amsterdam N o t to be reproduced by p h o t o p r i n t or microfilm without written permission from the publisher

T H E 7Li+ d --~ ~ + ~ + n R E A C T I O N

P. A. ASSIMAKOPOULOS, hi. H. GAhiGAS and S. KOSSIONIDES t Nuclear Research Centre "Democritus", Aghia Paraskevi, Attikis, Greece Received 27 December 1965 Abstract: The reaction cLiq-d ~ ,,q-uq-n is studied at deuteron bombarding energy 0.380 MeV.

The SBe compound nucleus is formed with an excitation around 17 MeV. The two u-particles are detected in coincidence by two solid state detectors. Thus, the kinematics of the reaction are completely determined and discrimination between sequential two-body decay and direct three-body decay is possible. The reaction mechanism is found to be sequential two-body decay involving the ground and broad first excited states of 5He. Contributions from the direct three-body decay and the sequential two-body decay involving the SBe, J- = 4+ second excited state, if at all present, are not more than a few percent of the total reaction output. Kinematically possible contributions from the SBe ground, J~ = 0+ and. the 2.9 MeV, j,t = 2+ excited state fall within the energy region excluded by the apparatus.

EI I

NUCLEAR REACTION 'Li(d, 2u)n, E = 0.380 MeV; measured o'(Eal, Ea,, 0a, 0s). SBe deduced cluster configuration. Natural target.

[

I

1. Introduction

The aim of the present experiment is the observation of possible cluster configurations of the 9Be nine-nucleon system at an excitation of around 17 MeV. Similar investigations 1, 2), in the frame of the cluster model of the nucleus 3), have been undertaken in recent years by a number of investigators. This has been due to the apparent success of the cluster model in describing properties of light nuclei. Phillips et al. 4, 5) have presented a two-body cluster model of the nucleus in terms of coupled SchrOdinger equations. The basic assumption in this model is that three- or morebody cluster configurations are not important for the description of a light nucleus. A direct way to test the validity of the above assumption is to investigate how the nucleus under study decays into clusters or into particles which compose these clusters. The natural experimental approach, therefore, is to investigate in a nuclear reaction the correlations of the decay products of the nucleus to be studied. The information that can be gained from the investigation of such nuclear reactions by multiparameter experiments has been presented in the works of Phillips 6,7) and others 8, 9) and is briefly developed in sect. 2. For the purpose of the present experiment, the 7 L i + d - ~ ~ + ~ + n reaction is selected, allowing the investigation of the 9Be cluster configuration at an excitation energy around 17 MeV for the available deuteron bombarding energy. This reaction * Now at Physics Department, the University of Manchester. 305

306

1,. A. ASSIMAKOPOULOS et aL

has been studied by several investigators for various purposes and employing different techniques. Experiments i o, 11) in which the vector momentum of only one of the particles in the final state has been measured, lead to inconclusive results due to incomplete definition of kinematics and the broad excited states of the intermediate nuclei involved (SHe and/or aBe). However, their results show that 9Be at this excitation energy decays more frequently into an alpha particle and a 5He nucleus than into a neutron and a aBe or into two alphas and a neutron produced directly. The results from experiments 12-14) in which two particles were observed in coincidence by measuring the vector momentum of the one particle while specifying crudely the energy and direction of the other, show also a preference for the 0t-SHe configuration and estimate the contribution to the spectra from the n-aBe and the ~ + ~ t + n configuration to be less than 10 ~oIn the present experiment the mechanism of the 7 L i + d ~ ct+ct+n is studied at 0.380 MeV bombarding energy by measuring the vector momenta of the two alphas and thus defining completely the reaction kinematics. It is shown that out of the four energetically possible cluster configurations, i.e. 0t-SHe J~ = ½-, ct-SHe J'~ = ½-, n-aBe J~ = 4 + and ct + c t + n , which could be investigated by our experimental apparatus, the first two are the predominant ones.

2. Reaction Dynamics The final state of a three-body decay is completely specified by giving Pl, P2, P3 the laboratory momenta of the final state particles, i.e. by giving nine scalar parameters. These nine degrees of freedom are, however, readily reduced to five by imposing energy and momentum conservation. For instance an experiment on a threebody decay would completely determine the final state by measuring the momentum of one particle, while specifying the direction of emission of a second. However, in actual practice, it is customary to measure the vector momenta of two particles and use this overdetermination of the final state for elimination of background effects. The cross-section dependence on the kinematic variables of an n-body reaction with particles A and B in the initial state and particles a I , a2 . . . . . a~ in the final state, has been treated in an exact way by Zupan~i~ 15). This treatment is based on the assumption that the energy-momentum shell formed by the coordinates of the events in p h a s e space is uniformly populated. We note that this assumption leads only to "invariant" phase space predictions for the reaction cross section, i.e. it takes into account only energy and momentum conservation. Deviations from uniform population will appear along the phase space shell due to other dynamical effects, e.g. angular momentum conservation. It is therefore desirable to define ad hoe as "dynamical effects" all causes for deviation from a uniformly populated energy-momentum shell and examine them after the invariant phase space normalization has been carried out. For a three-particle final state (n = 3) we may express the probability density dP(p, U, Pl, P2, a3) for the final state leaving particle al with momentum between

?Li+d

~ 0t+¢+n

307

REACTION

Pl and p~ + dp~ and particle a 2 with momentum between P2 and P2-t-dp2 by

dP(p, U,p,,p2,a3) ~ U-T,-T2-2(~-~_mI~-~m2) j

dap,dap2,

(2.1 /

where T t and T2 are the kinetic energies of particles al and a2, respectively, U the

7

~///~

'Li o d - - Q - a *

/

/

6

5

.n

/

'Li (d ,=)'Be l: 2.90 MeV

/ / ' L i (d , o)'He /1 o : ground

l J, V

~'4

f-

n:

6 MeV

3

T, • 0 . 3 8 0 M e V

®, = 9 0 " ®~ = 77.5 °

2

1

/ / o

I

I

I ~-

,'-"J"~l

I

2

3

4

/ /

'

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5

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7

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I 7

I $

T, ( M e V )

(a) 200

lOO

0

I ,-7"-I-'-1 2

J

I 3

J I 4

I 5 T, ( M e V ) (b)

Fig. l. (a) Calculated, two-dimensional plot for the 7Li+d reaction. The solid line represents contributions from the direct process. The symbols for contributions from sequential processes for the different excitation levels of the various intermediate nuclei are shown. The deuteron bombard3ng energy and the two angles of detection for which the calculations were carried out are also indicated. The dashed line denotes the region of the kinematic locus eliminated due to the exclusion of events with alpha particles of energies less than 1.5 MeV by the apparatus. (b) Calculated one-axis spectrum of coincident counts received at the detector placed at 90 °. Contributions from the direct 7Li+d -+ ct+~t+n have only been considered and a uniform population on the kinematic locus in (a) has been assumed. The dashed line indicates contributions from the experimentally realizable locus (solid line in (a)).

308

P.

A. A S S I M A K O P O U L O S

al.

et

total energy

U = TA+Ta+ Q,

(2.2)

P = PA + PB,

(2.3)

the total momentum p is Q is the Q-value of the reaction. For the purposes of the present experiment the discussion is restricted on the reaction plane with polar angles of detection O1 and 02 for the two detected particles a I and az, respectively, and O12 = O1+O2 the angle between Pl and P2. The probability density will give contributions for the poles of the expression (2.1). In terms of the kinetic energies T1 and T2 of the two detected particles, the contributions will occur for T 1 and T 2 satisfying the relation Q=

ml 1+~33:TI+

1+~33

T2-

1 - ~33

TA--2 COS O1

m3

- 2 c 0 s 0 2 x/mAm2TAT2 +2c0s012 x/mlrn2TIT2 Itl 3

(2.4)

WI 3

For a given bombarding energy T A and two angles of detection O 1 and 02, eq. (2.4) is the equation of a closed curve in the (T1, Ta) plane. A typical example of such a curve is given in fig. 1(a). From the nature of the derivation 15) of eq. (2.4) and the initial invariant phase space postulate, a uniform population on the curve described by eq. (2.8) is also assumed. For a two-particle final state (n = 2), a probability density similar to the one in eq. (2.1) may be constructed, so that contributions from intermediate states in a threebody final state reaction can be taken into account. In this case the probability density will be given by dP = dP 1 • dP2, (2.5) where dP~ is the probability density for the initially formed compound nucleus to decay into a final state particle and an intermediate cluster and dP2 the probability density for the intermediate cluster to decay into two final state particles. The locus of contributions from intermediate states in a three-body final state decay will again be given from the poles of dP1 and dP2 in eq. (2.5). Since the kinematics of a threebody process have been given in detail elsewhere 16) only the final results are given here in table 1. The notation involved is also summarized in the same table. These results are presented in a convenient form for their employment in a Fortran code. The reaction channels open to the 7Li+ d reaction are

_ 7Li+d

I

, ~ + c ~ + n + 15.122 MeV

(2.6)

, a + S H e * + 14.165 MeV I , e + n + 0 . 9 5 7 MeV ~n+SBe*+15.027 MeV

(2.7)

!

~ + ~ + 0 . 0 9 5 MeV.

(2.8)

309

7Li+d ~ ~+~z+n REACTION

TABLE 1 Kinematics of the process ~_~ a l . + a 2 + a R A+B aI-~-*C(2R), *C(2R) ~ azq-a R aR+*C(12), *C(12) ~ at-{-a 2 Symbols

(I)

(2) (3)

Definition i,j=A,

A B

al, a l aR

*C0, j) mi

Pi

T~ Q

m0, j) 0,, 0, 0,2 Qo, J)

B, 1, 2, R projectile target nucleus detected particles particle escaping detection cluster (i-q-j) at an excited level mass of particle i momentum of particle i kinetic energy of particle i Q-value of the direct process mass of cluster ( i + j ) kinetic energy of cluster (i-t-j) polar angles of detection angle between Pt and P2 excitation level of cluster ( i + j ) Q-value from initial state to cluster ( i + j ) at ground state Kinematics

Process (1)

Process (2)

F--B:E(B,--4AC)½1 , T'+ =

L

~

J

X

A = m,+m R

T2+ satisfying both

7"1 = £ T B

for each T, ~ 0 satisfying B 2 - - 4 A C ~ 0 where

EcosO,+ ( D - - s i n ' O , ) ' l ' ] ' mt T~2R)/cos

7"2+

m--~2R) ~

-t- V(m' 2R) --1) Q2 - - t_ ,---~-2 T(2R--" ~

C = (m,+mR)T ,

--sine (Oa--0,)] ½}'

-q- ( m A - - m R ) T A - - m R Q

F--B:h(B'--4AC)½1~' 7-,+ = t. -~ ,

and (O3-- 0,)

B = 2 cos O,,(mxm, T,)½ --2 cos 02(mZmATA)½ -- 2 cos O1(mA TArn1Tx)'t"

Process (3)

F--bq-(b'--4ac)~.q z Tz+ = L' ~a "_l

where A, B and C are the same as in process (1), and a = m(12)--m2 b = --2 cos Oxs(mxm~Tl)~:

where Q1 = Q ( 2 R ) - - E ( 2 R )

Q2 = Q--Q(2R)-~-E(2R) ET = TA+QI B=

mA ml TA/ET

(mA+mB)'*

mA Q*) mBm(2R) D = (I + - (mA+mB)' \ mB ET T(2R) = T A + Q I - - T t O3 = arc sin

rg,d) sined

c = (mo2)--ml)T 1

--(E(12)--Q(12))m(12)

310

p.A.

ASSIMAKOPOULOS el al.

The calculated contributions from sequential processes (2.7) and (2.8) are indicated in fig. l(a). It is noted that intermediate state contributions, when plotted on the (T1,/'2) plane, are contained in the kinematical locus of the direct three-body process. This is a result of the overall energy-momentum conservation. It is thus seen that when sequential processes are considered, invariant phase space calculations predict a deviation from uniform population on the kinematic locus of a three-body final state process. By studying this deviation from uniform population on the experimental spectra, information on the mechanism of the reaction can be drawn. When analysing experimental results, it is more convenient to study projections of the kinematic locus on a single energy axis. In order to extract information on nonuniformities caused by dynamical effects, a projection of experimental data on a single energy axis has to be compared with the evaluated structure of the projection of a uniformly populated kinematic locus. In the particular example of fig. 1 the single axis projection of the kinematic locus in fig. 1(a) is given in fig. 1(b). As expected, the projection shows a marked increase in population at energies above which the kinematic locus has a vertical tangency.

3. Experimental Apparatus The experimental set-up is shown schematically in fig. 2. A 0.380 MeV monatomic deuteron beam from the "Democritus" Van de Graaff accelerator is selected through a 90 ° deflection in the coupled magnetic analyser. The beam is further defined by three collimating slits S t, $2, $ 3 , 2 mm in diam, placed at the entrance of the reaction chamber R. The reaction chamber consists of an iron cylinder 35 cm in diam and 10 cm in height. An iron rod R 1 along the axis of the cylinder allows the adjustment of the target height and orientation with respect to the beam. The target holder T, fixed at the top of rod R~, consists of a 6 cm x 6 cm x 1 cm solid copper frame, grounded through its supporting rod to avoid heating and charge accumulation. The reaction chamber top plate, apart from the four BNC-plugs for the electrical connections, bears at the periphery a movable metallic scale which is marked at 1° intervals and a sliding rod R2 along the cylinder axis. Rod R3 serves as an angle indicator on the above scale and is fastened to rod R2. Inside the chamber, runner R4 is also fastened on rod R2 and moves parallel to the angle indicator R 3 . As it is described below, the scale is adjusted so that the angle indicator reads the angle between the direction of the beam and the direction of the moving runner R4. The two alpha particles are detected by two Surface Barrier ORTEC detectors of 25 mm 2 surface. One detector assembly CF is fixed at 90 ° with respect to the beam direction and at 10 cm distance from the target while the second detector assembly CM is attached on runner R4 and is allowed to cover a 180 ° range with respect to the beam direction. Each assembly consists of a plexiglass base on which a solid state detector is mounted. To reduce interference from Coulomb scattered deuterons, collimators C1, C2 have been placed in front of each detector. These collimators are

?Li+d --* a+at+n REACTION

311

5 cm long cones with front apperture of 1 cm in diam. With the introduction of the collimators the angular definition is improved to better than +2.5 °, depending on the particular setting of the moving detector. The beam, the fixed detector, the centre of the target and the moving detector are made complanar by adjusting the sliding rods R 1 and R2. These are secured in position after the adjustment by the stops ST1 and S T 2 . The target is placed at a 45 ° angle with respect to the beam when the moving detector angle is less than 90 ° and at a 135 ° angle when the moving detector angle is greater than 90 °.

AF

CF

~

MO D IGIED L A B E N-512

SCALER l

Fig. 2. E x p e r i m e n t a l a p p a r a t u s e m p l o y e d a n d block electronic diagram. T h e v a r i o u s s y m b o l s are explained in the text.

A block diagram of the associated electronic circuitry is also shown in fig. 2. The detector gives a fast output for timing purposes and a slow output for the energy measurement 17). The fast signal is driven through a tunnel diode discriminator and triggers a coincidence unit (~ = 50 nsec) whose output signal gates the Laben 512 modified is) multi-channel analyser. The discriminator trigger level is set at 1.5 MeV. The two slow energy outputs through two identical charge sensitive amplifiers are fed into the X and Y inputs of the multi-channel analyser. The fixed detector spectrum,

P.A. ASSIMAKOPOULOS

312

et aL

in parallel to the X-input of the analyser, is also fed to a single-channel analyser, whose output triggers a scaler. The scaler indication serves to monitorize the coincident spectra obtained for different ~9~ settings. A 40 x 40 channel representation in the analyser has been used. 7

x

I

8

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7

--

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ODDIOIIOOXOX O O Q O el Q II II I1@ II O X . . . . . oo.... . . . . oox xx x x oxoo OQOIBIIQX

x

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xxx

o o o @ ill III o x xooOlJllO O xoxrTonllo x • Ill II III O 0 OOOII&AX O ool&lx OXQA&O xo 0 &lllO X O&Ao X OEIIX XXOAeX

6

E i-

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Y I

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ounx x:

3-5

o o

,o'"

O: 6 - 9 D: 1 0 - 1 4 e: 15-20

2 11:21-29

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1

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OF

I

I

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4:30--45

I

20O

COINCIDENCES

I

I

I

I

I

1

I

1

2

3

4

5

(5

7

Tf

(MeV)

W 7 U,J

7 Li (d.n)2a T, = 0 . 3 8 0

e = g0" 65"

MeV

-

U 7 hi (3 Z

100

U h 0

8 .~

200

e=

•

xxoOx xxxx x o xx x x

3

100 NO.

4

--

+

JJ

16

10 8

7

O

0

Fig. 3. Coincidence spectra in a two-dimensional form for the reaction ~Li+d ~c<+~-I-n. The lab bombarding deuteron energy and the detection angles together with the various symbols fo~ population densities are indicated. The axes Tt and Tm in the upper right hand two dimensional plots represent the energy coordinates of the coincident c(-particles received in the fixed and moving detectors, respectively. The observed counts are projected onto the T-axes and presented as a histogram on the left and below. The calculated curves Elx, E12 and E(xt) relate the energy Tt of an event to the excitation energy (on the right hand energy scale) or the intermediate nucleus 5He (E~x and E~z) or aBe (E~I~). The branches of these curves marked by a dashed line indicate a nonrealizable region due to the elimination of alpha energies less than 1.5 MeV by the apparatus.

The energy calibration for both counters is made with the help of the 5.3 MeV ~-line of a thin 21°Po source and the alphas from the reaction 6Li(d, c()4He. The resolution for the 5.3 MeV line is 0.7 ~o at the output of the amplifiers. The adjust-

"¢Li+d --* a t + a t + n

313

REACTION

ment of the scale for the angle measurement is achieved with the help of the alphas from the 6Li(d, ~)4He reaction in the following way. It is calculated that, for the particular bombarding energy of the experiment, when the first alpha from this twobody reaction is emitted at 90 ° (fixed counter), the second alpha will be emitted at an

xx~ xxoeoe

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xxx &ooeoex

XOXOOOXX OXOOXX xooxx xoooxx xooeo

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:Oo':g XOII

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x: 3 - 5

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o:

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A:20-35

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200

I

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I

I

I

I

1

2

3

4

5

6

7

8

NO. O F C O I N C I D E N C E S

Tt ( M e V ) )19 nbJ Z W 16

200

'Li (d,n)2= T, = 0 . 3 8 0

E,~

MeV

14

e. = 9 0 " 0.72"

12

100

10 8

./

@ 4 2 0

Fig. 3(b).

angle of 82.5 °, with energies E(90 °) = 11.280 MeV and E(82.5 °) = 11.474 MeV respectively. The rate of coincident alphas of the above energies is determined experimentally as a function of the angle of the moving detector. At the position of the maximum coincidence rate the scale is set so that the angle indicator is pointing to 82.5 ° .

314

P.A.

ASSIMAKOPOULOS

eta[.

4. Experimental Results The 7 L i + d ---, ~ + ~ + n reaction is studied at 0.380 MeV deuteron energy. Due to the appreciable dE/dx losses of the deuteron in the natural Li target employed, 9

1

x x x x x x x x x x x x x x x x x x x x x x x x xxxoooox x x x x x x xx x x x x o e o e x x x xx xxxooxx xxoxeox xxxoeo xxxeex xoo x xxxex xxxx xxxx xxxxx xx x x xxx xxx xxx xxox xxox x: 3 - 1 g x x x xxxx o: 2 0 - 3 5 x

1 J 7

I

T 6

5

4

3

m

2

m

e:36-60

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I

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100 NO

OF

I

I

I

I

I

I

200

-I _

I 1

2

--

COINCIDENCES

I 3

I 4 Tf

I 5

I 6

I 7

1 8

(MeV)

v 2 0 0

W Z hl "tLi (d,n)2a Td = 0 3 8 0

16

-

MeV

14

e.=9o" Q=775"

12 .

-

100

10 8 6 4 -

2 0

Fig.

3(c).

the 9Be compound nucleus is formed with a virtual excitation in the region o f 16.97 MeV to 17.07 MeV. Data were collected in the reaction plane with the fixed detector placed at O f = 90 ° and with the moving detector placed successively at ~9m = 65 °, 72 °, 77.5 °, 80 °, 90 °, 97.5 ° and 100 °. Due to the 512 event maximum capacity of the modified Laben analyser, four runs were taken for each setting of the moving detector, collecting thus a total o f approximately 2 000 events. In fig. 3, the results obtained are plotted in a (T e, Tin) representation. In this representation it is observed that the events are spread around

315

"tLi+d ~ c t + c t + n REACTION

the kinematical locus. This is due to the strong angular dependence of the locus and to the dE[dx losses of the alpha particles in the target. The projection of the events at the three-body locus on the Tr-axis is given also in fig. 3 for each (Of, Or,) pair. The curves E l l , Ex2 and E(x2) plotted with the xxoxxxxxoxox

xoeooxxxxxxoeeeeo

F

x

J

x

xeAo

°:::

I___.

xxoe xoeo

rJ

I 1

x:

xxox oo xx xxx xx xx xx xoo ex oox oo x x

3-g

o" I 0 - 1 g

e: 2 0 - 3 4 A: 3 5 - 5 0

I

I

I

O

I

I

I

I

100 N O OF"

I

I

I

[

200

I

I

I

I

I

I

I

I

1

2

3

4

5

6

7

8

A

Tf ( M e V )

COINCIDENCES

$ 200

o

W

? L i (d,n)2ct "f= = 0 3 8 0 ~, = gO °

16

MeV

14. (J Z

® = 80"

12 10

100

8

Z

6

U

~

_

../~"

O

2

o Z

4

O

0

Fig. 3(d).

projections of the spectra relate the observed alpha-particle kinetic energy Tf to the excitation energies of the two possible intermediate state nuclei SHe and abe; Ell and E12 give the excitation of 5He when the first or second alpha respectively from reaction (2.7) is detected with kinetic energy Tr by the fixed detector; E(12) gives the excitation of aBe when either alpha of reaction (2.8) is detected by the fixed detector with kinetic energy Tf. These curves indicate that the 5He J" = ½- and abe J~' = 4 + states may contribute to the spectra of all measured (Of, Ore) pairs, while the 5He J" = } - state may only contribute to the spectra with Om = 72 °, 77.5 °, 80 ° and 90 °.

316

P. A. ASSIMAKOPOULOS e t

al.

The aBe J= 0 + and 2 + states, although energytically possible, will give contributions for either Tf or Tm less than 1.5 MeV not detected by the apparatus. The monitor scaler counts (see fig. 2) are employed for the normalization of the Traxis projections which are collected on a three dimensional Tf-Om-d3tr/dTfdDfdf2m isomeric histogram in fig. 4. =

- - ]

k

x112 I

J

8

-

7

"-

6

-

x xxxxxx xooeeoleo@eAe&eo xoxxooxxxoooole&elx

r--

I

x

xxoeeex

)

xoeox xoeeAo xoooo xoAe xeel oel o@ oox oeo olx xex oex oex eel ox x x

5

x:

4

i-

5-9

o" 1 0 - 1 g

f

e:20-34

3

A:35-50

2

_1

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2

3

4

5

6

7

8

COINCIDENCES

Tf

(MeV)

20O x1/2 'Li

( d , n )2a.

® = 90"

U z bJ C~

(D= 9 0 "

U Z

T= 0.380

MeV

bJ Z W 15

14 12 100

I(>

U h 0

8 6.

oz

4 2 (3"

F;g. 3(e).

The three-dimensional spectra as well as the Tr-axis projections show clearly contributions due to SHe formation at the intermediate state according to reaction (2.7). In the (Tt, Om) plane of this plot the kinematical loci for the ground state and the 5.2 MeV excited state 19) of 5He are also drawn. From the nomograms drawn with the Trprojections, contributions for the energetically possible 8Be intermediate states (process (2.8)) are seen to overlap with 5He contributions. The realizability

7Li+d

~ ~z+a+n

317

REACTION

of process (2.8) will therefore be determined from the relative heights of the 5He peaks. 5. Discussion The experimentally obtained spectra (figs. 3 and 4) show a marked predominance of reaction (2.7). Reactions (2.6) and (2.8), if at all realizable, contribute to no more than a few percent of the total yield of the 7Li-I- d ~ ct + 0t+ n reaction.

----I

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8

x314

xx xx ooooeoooox xxooxQoeAImllllooxx

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oxxo

x

x

x x

xoo

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xoomoQ

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5; ~

ooloo xomBox xoomQ

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3-5

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--

1:21- 29

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3

4

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6

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COINCIDENCES

_

u

T f (MeV)

Ix7

200

hd

Z Ix/

'Li (d.n)2a To = 0 3 8 0 e,= 90" e:

975.

MeV

u z w 121

16

-_<

0 Z

u b.. 0

oZ

14 12

io0

10 8

•/"

~

/

2,,;,

6 4 2 0

Fig.

3(f).

The 9Be compound nucleus, for the bombarding energy available in the present experiment, is formed with an excitation energy just below the 17.28 MeV, F = 200 keV level. At 16.97 MeV a J~ = ½- level has been recently identified 2o.21). This level, however, has small alpha and neutron reduced widths, due to isobaric spin conservation. Since no other level in the vicinity of 17 MeV is known, it is assumed

318

•

P.A.

et al.

ASSIMAKOPOULOS

in what follows that the formation and decay of 9Be* in the reaction studied goes through the lower tail of the 17.28 MeV level. It is furthermore assumed that, due to the low bombarding energy, only s-waves are important in the entrance channel. Hence the possible values for J~ of abe* are ½-, { - and { - .

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Reactions (2.6), (2.7) and (2.8) are the energetically possible particle decay modes of 9Be at art excitation around 17 MeV. For this excitation energy and the apparatus employed in the present experiment, reaction (2.7) may contribute for SHe formed with an excitation energy in the range of 0 to 12 MeV, while reaction (2.8) for 8Be formed with an excitation energy in the range of 8 to 16 MeV. The former range contains the 5He ground (J~ = ½-) and first excited (J~ = ½-) state, while the latter range contains only the aBe second excited (J~ = 4 +) state. In the shell-model picture for 9Be*, however, angular momentum conservation inhibits the occurrence of reaction (2.8) through the J~ = 4 +, 11.7 MeV level of 8Be. A contribution from reaction (2.8), if at all, present in our results, will be probably small. The kinematic locus

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320

P.A. ASSIMAKOPOULOSet al.

population from reaction (2.6) is also expected to be small since calculations 22) in the frame of the cluster model show that 9Be is not well described by the picture of two alphas, which do not interact with the neutron. A qualitative analysis of the experimental results shows in fact, that the contributions in the spectra obtained lead in a kinematically consistent way to the conclusion that reaction (2.7) is the predominant channel for the reaction 7 L i + d ~ ~ + ~+ n. This is in agreement with previous experiments io to 1,) as well as with the preliminary results of a similar experiment by ffones et al. 2a). In order to test further the above qualitative results, a theoretical reconstruction of the spectra obtained has been undertaken. Assuming that the reaction studied proceeds through compound nucleus mechanism 2,) for the formation of 9Be* and its sequential decay according to reaction (2.7), the following three-body reaction amplitude is formed for a given d ~ of the compound nucleus: J+s, +ax

S,,.;,m, =

(t. s. 0. t=l'-sl,m.=-•

x (1, ½, r n , - rn,, m,[sm,)Y~. = _=~(2)(1 - Sx,(2)), where J and mj is the 9Be* compound nucleus spin and its z-axis projection, respectively, and s and m s the SHe nucleus spin and its z-axis projection. The arguments 1 and 2 of the spherical harmonics Y~.,, and the scattering matrices S~,;oa and S,, indicate each of the two alpha particles in the final state. After symmetrization of this amplitude with respect to the two alpha particles, the cross section d3a/dTrdKatdfa= has been derived for each possible J= of 9Be*. In this derivation cross terms of the matrices have been omitted. Thus, interference terms resulting from the order of emissions of the two alphas are not taken into account. The cross section for the decay of 9Be* with J= = ½- through the J= = ½first excited state of SHe leads to isotropy. However, this prediction is not consistent with our results as well as with those of Farley et al. 1 a). Therefore, the theoretical spectra resulting from J= = ½- and { - only have been attempted. For the evaluation of the cross sections the Breit-Wigner form for S~; oJ has been substituted, while for St, the =-n scattering phase shifts 6+ and fi_ given by Seagrave 25) have been used * The theoretically predicted cross section may be expressed as d3a(J~) - G(J')+E(J~), dTf dQfd[2 m where G(J ~) and E ( J ~) contain the contributions from the SHe ground and first excited state respectively. For the two 9Be* total spins considered E('t- ) = E ( { - ). • A generalized density of state analysis for the decay of the 5He .In = ½- state has not been successful in describing the general features of the experimental spectra.

7Li+d ~ ~t+a+n REACTION

321

In G(½-), the predominant term contains l --- 0 dependence, leading to isotropy, while in G(~k-) an l = 2 dependence is predominent. It follows that the theoretical spectra will differ in the O m range (70 ° < O m < 95 °) for which 5He ground state contributions are kinematically possible. It turns out, however, that the Legendre polynomial associated with l = 2 varies very slowly for Om in this region, so that the assignment of either compound nucleus total spin leads to very simila~ spectra for the angle range scanned in the experiment. Although a 9Be* jn _- ~- assignment seems to be in a slightly more satisfactory agreement with the data (fig. 4), an attempt to identify the 9Be* state has led to inconclusive results. This may also be due to the. approximation mentioned earlier, namely the omission of cross terms in the calculation of the cross sections. It is possible that interference terms are important and the deviation for O m = 72 °, 80 ° and 90 ° in fig. 4 is due to such terms. Contributions from reaction (2.6) are also seen to be small, if at all present. The spectrum from this reaction will have the general form of fig. I (b). If such contributions are added to the theoretical spectra from reaction (2.7), large discrepancies with the experimental spectra occur when contributions to the total reaction cross section from reaction (2.6), exceed a few percent of the total. The authors wish to thank Professors Th. Kanellopoulos and Th. Ypsilantis for fruitful comments. Ch. Mantakas and L. Papadopoulos for their help with the electronics and B. Katselis, P. Nikolaou and S. Valamontes for their help in obtaining the data. Thanks are also extended to Professor K. Pezopoulos and K. Genidounias of the Athens Polytechnic and to Professor I. Anastassiades of the University of Thessaloniki for their assistance in the computational work by making available the computers of the above Institutes. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25)

E. H. Beckner, C. M. Jones and G. C. Phillips, Phys. Rev. 123 (1961) 255 J. D. Bronson, W. D. Simpson, W. R. Jackson and G. C. Phillips, Nuclear Physics 68 (1965) 241 K. Wildermuth and Th. Kanellopoulos, Nuclear Physics 7 (1958) 150 G. C. Phillips and T. A. Tombrello, Nuclear Physics 19 (1960) 555 T. A. Tombrello and G. C. Phillips, Nuclear Physics20 (1960) 648 G. C. Phillips, lectures on few nucleon systems, Hercegnovi (July 1964) G. C. Phillips, Revs. Mod. Phys. 36 (1964) 1085 P. A. Assimakopoulos, DIC-Thesis (1964) unpublished C. Zupancic, Revs. Mod. Phys. 37 (1965) 330 G. Weber, Phys. Rev. 110 (1958) 529 P. Paul and D. Kohler, Phys. Rev. 129 (1963) 2695 A. C. Riviere, Nuclear Physics 2 (1957) 81 F . J . M . Farley and R. E. White, Nuclear Physics 13 (1957) 561 P. Fessenden and D. R. Maxson, Phys Rev. B133 (1964) 71 C. Zupancic, N.I.J.S., Report R - 429 (1964) P. A. Assimakopoulos, Program, No. 3, N.R.C.D. Internal Distribution Report (1965) L. Papadopoulos, Nucl. Instr., to be published N. H. Gangas, B. Katselis, N. Kouvaras and S. Kossionides, Nucl. Instr. 36 (1965) 341 P. A. Assimakopoulos, N. H. Gangas and S. Kossionides, Phys. Lett. 19 (1965) 316 J. W. Woods and D. H. Wilkinson, Nuclear Physics 61 (1964) 661 W. L. Imhof, L. E. Chase Jr. and D. B. Fossan, Phys. Rev. B139 (1965) 904 Th. Kanellopoulos, private communication C. M. Jones et al., Revs. Mod. Phys. 37 (1965) 437 M. Manalis and J. E. Heukel, Phys. Rev. B136 (1964) 1741 J. D. Seagrave, Phys. Rev. 92 (1953) 1222