Angular distribution of the protons from 5Lig.s. decay in the 6Li(3He, α)5Li → α + p reaction

Nuclear Physics A480 (1988) 51-61 North-Holland, Amsterdam

ANGULAR

DISTRIBUTION OF THE PROTONS FROM IN THE 6Li(3He, a)5Li + a + p REACTION

S. BURZYNSKI,

J. TURKIEWICZ, Institute

K. RUSEK,

forNuclear

Studies, Hoia

I.M.

TURKIEWICZ

69, 00-681

5Li,.,. DECAY

and

P. kUPRAkSK1

Warsaw, Poland

Received 23 July 1987 (Revised 23 October 1987) Abstract:

The 6Li(3He, cy)‘Li + a + p reaction has been studied at energies of 1.5, 1.73, 3.0 and 3.5 MeV. From the measurements of the alpha-proton coincidences the angular distribution of protons from the decay of the particle unstable 5Li nucleus have been derived. They are asymmetric relative to the ‘Li recoil momentum, in agreement with earlier experiments. A possible explanation of this asymmetry is given in terms of a strong polarization of the ‘Li as is expected in an angular momentum mismatched transfer reaction.

E

NUCLEAR

REACTIONS v(f3,,

6Li(3He, a), E = 1.5-3.5 MeV; measured ~(0,, 5Li decay; deduced reaction mechanism.

B(‘Li), E,),

0,) following

1. Introduction The unbound the sequential

‘Li nuclear reaction

system

(1.25 MeV and 1.54 MeV) energies 5Li decay relative

can be formed

6Li(3He, cy)‘Li+ cy+p.

to its propagation

le3) have revealed direction.

as an intermediate

The studies

a cylindrical

The observed

product

of this reaction asymmetry

of

at low of the

effect was explained

in the simple semiclassical model ‘) as a result of the short lifetime of 5Li and the memory retained by the proton of its strong localisation at the time of the formation of 5Li. Following this model, more protons should always be emitted in the direction nearer to the incident 3He beam than in the opposite direction (in agreement with the experimental results reported in references “)). Another interpretation of the observed asymmetry was based on the assumption of a strong influence of a 9B compound nucleus level, in analogy with the explanation of the asymmetry observed in 5He decay in the reaction ‘Li(d, an)4He [ref. “)I. With the objective of understanding better the origin of this asymmetry, the ‘Y-P angular correlations in the 3He + 6Li = (Y+ (Y+ p reaction were measured at several 3He energies. The low energy (1.5 MeV and 1.73 MeV) measurements provide a comparison with the earlier studies. They also permit an estimate of the possible influence of the compound nucleus, because an incident 3He energy of 1.5 MeV corresponds to the known, narrow (70 keV) level of the 9B nucleus at 17.64 MeV, 0375-9474/88/%03.50 @ Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

52

while

S. Burzyriski et al. / 6Li(3He,

1.73 MeV falls between

provide explained

asymmetry assuming

the levels.

data at higher energies. the polarization

a)‘Li+

a +p

The measurements The experimental

of the intermediate

at 3.0 and 3.5 MeV results are successfully

‘Li nucleus.

2. Experiment The measurements of the 6Li(3He, a)‘Li reaction were carried out using the Van de Graaff accelerators at the Institute for Nuclear Studies in Warsaw (1.5 and 1.73 MeV) and at the Joint Institute for Nuclear Research in Dubna (3.0 and 3.5 MeV). The target was a 100 kg/cm* thick LiF (enchired to 95% 6Li) layer evaporated onto a 10 kg/cm* carbon foil. The Rutherford cross section for the elastic scattering of the 3He+ 19F measured simultaneously with the reaction on 6Li, was used to obtain the absolute normalisation of the cross section. The energy of the incident 3He beam in the target varied from 75 keV to 125 keV with the energy. The particles emerging from the target were detected by two detectors in incidence. Because of favourable kinematical conditions (the Q-value for

loss 3He cothe

reaction under study is 16.87 MeV) no identification of particles was necessary. One detector, a lithium-drifted silicon detector of a depth of 2.5 mm, was covered by aluminium foil thick enough to stop all particles but protons with energies above 2.5 MeV. The second detector had the depletion layer thickness adjusted to transmit protons but stop alpha particles in the investigated energy range. It was shielded with a thin aluminium foil against low energy 3He and 6Li from elastic scattering. The energy spread in these foils together with the target thickness resulted in a final total energy resolution of 200 keV for forward angles of proton detection, and up to 400 keV for large angles. The alpha particle detector was kept fixed was set in the reaction plane defined by the a-particle. Its laboratory angle was varied opposite side of the 3He beam; i.e. on the

at 90” to the beam. The proton detector incident 3He beam and the registered from 30” to 130” in 10” steps, on the side of 5Li recoil. Coincidences were

recorded on a magnetic tape as 3-fold events: the energies of the alpha-particle (E,), the proton (,I$), and the time difference between them. The time resolution of the prompt peak in the TAC spectrum was typically 50 ns. Random coincidences, monitored by recording events over a wider time range, were negligible. Signals were processed by a Nuclear Data 4420 computer, which controlled the writing of the data on tape and provided for several on-line control displays. Off-line analysis proceeded in the following order: (i) Event-by-event recorded data were sorted to produce two-dimensional spectra in the (E, - EJ plane, gated by a TAC window. (ii) Projection of the kinematical contours onto the E, axis, with the window condition on E, + E2 to select the region of interest, yielded the one-dimensional alpha particle spectra.

53

S. Burzyn’ski et al. / 6Li(3He, a)‘Li + a +p

(iii)

Alpha particle

transition

energy spectra in the range corresponding

were integrated

to obtain

the angular

distributions

to 6Li(3He, a)‘Li gs of protons

from 5Li

decay. 3. Energy spectra When two particles are detected in a particular coincidence geometry, their energies E, and E2 lie on a well determined contour in the El - E2 plane, as a result of energy and linear momentum conservation. In our experiment only one contour was observed for a Q-value of 16.87 MeV, with a width determined by the total energy resolution. Along this locus, enhancements were observed corresponding to sequential

processes proceeding through these intermediate unbound states: 5Li, ground state, $-, E = 1.5 MeV [ref. “)J from the reaction 6Li(3He, cu)‘Li; *Be, 11.4 MeV, 4+, r = 3.5 MeV [ref. “)I from the reaction 6Li(3He, p)*Be. On some contours, e.g. from the proton registration angles 30”-50” and loo”-130”, these groups were well separated. At these angles the ‘Be” contributions were found to be quite important (contrary to the suggestions formulated in ref. I)). For this reason, at those angles where for kinematical reasons both groups of events overlapped the procedure of decomposition was applied by fitting the energy distributions of alpha particles in the frame of final state interaction theory, as explained below. The triple differential cross sections d3u/d0, dfi2, dE, (alpha particle spectra) were obtained by projecting the kinematic contour corresponding to the Q-value onto the alpha particle energy axis E,. They 6Li(3He, cy)5Li,.,. reaction were transformed to the “sequential decay” relative coordinate system d3a/dE’kM dR, d~‘Li defined by Ohlsen ‘). Our indices are related to those of Ohlsen in the following way: EzM = Eymx3, l2, = Ll_23, and ~SLi = 0n2_3, where the detected alpha particle is labeled Some of the spectra are peaks, the higher energy one from the 8Be (11.4)

by 1, the proton by 2, and undetected alpha particle by 3. shown in figs. 1 and 2. They mainly contain two broad one being a contribution from the ‘Li g.s. and the lower MeV state. The shape and position of the second peak

depends very much on the proton registration angle. Our experimental geometry was designed to fix the directions of the ejectiles of the two-body reaction leading to (Y+ 5Li. When the reaction first emits a proton, the accompanying alpha particle comes from the ‘Be recoil;

thus its energy depends on both the kinetic energy of energy from the decay ofthe 3.5 MeV broad level.

‘Be and on the relative alpha-alpha

The cross section for a three-body reaction proceeding through an intermediate unstable state can be factorized into the amplitude M of the first reaction step and the final state interaction enhancement function Fr( E2_3) [ref. ‘)I:

(1) where formula

K is the phase space factor. of Ohlsen

It is calculated

‘) and is proportional

from the three-body

to [E,_23(ET-

El_z3)]“2.

kinematics

S. Burzytiski et al. / 6Li(3He, a)‘Li + a +p

54

The amplitude which

an unstable

dependence compound

M is determined nucleus

is produced.

of M on the reaction nucleus

by the mechanism

mechanisms

However,

products “). Taking

of the two-body

for a given incident

reaction energy

in the

energy is very slow for both direct and this into account,

one can assume

the

amplitude M to be constant over the range of the unstable state width in the intermediate nucleus, as is done in the present analysis. The final state interaction enhancement function F,-(E,_,) usually is taken as a state density function pr of an unstable nucleus ‘). This function influences very strongly energy spectrum of particles in the vicinity of a residual nucleus resonance. To calculate the pr function for ‘Li we have chosen from among several final state interaction

models the R-matrix

theory. This model is particularly

useful in a vicinity

of a resonance and is also convenient for including Coulomb effects. Following the R-matrix formulation given by Lane and Thomas lo) the density of states in the one-level approximation is given by: 4Y2&(K a) Pf=[E-Eo-y2{SL(E,a)-S,(Eo,a)}]2+y4P2,(E,.)’

(2)

where y* and E. are the reduced width and energy of the level respectively, Q is the channel radius and Pi_ (penetration factor of the Coulomb barrier) and S,_ (level shift) are combinations of regular FL and irregular G, Coulomb functions as defined in ref. lo). Formula (2) was applied to calculate the density of states function for ‘Li,,,. and ‘Be( 11.4 MeV) states. The parameters characterizing intermediate levels were obtained from a fit to the available experimental phase shifts for p + KY[ref. “)I and (Y+ (Y [ref. “)I elastic scattering corresponding to the levels under study:

where the symbols are the same as in formula (2). An example of a fitted energy spectrum is shown in fig. 1. It displays a typical result obtained in our analysis using R-matrix: the shape of the peak corresponding to ‘Be decay is described correctly, but the calculated

peak

corresponding

to ‘Li decay

is shifted

to lower energy

in

comparison with the experimental one and has a long low energy tail not observed in the experiment. A similar problem was encountered in the analysis of the p-alpha final state interaction in the 3He(3He, pp)4He reaction 13) using R-matrix theory. The failure of the final state interaction theory to describe the energy spectra can be explained, for example, by the distortion of the 5Li wave function by the first alpha-particle. Without entering into the details of energy spectra analysis, which is used here only to separate the contributions from the two considered processes, we say in summary that the Breit-Wigner parametrization was used to compute the contribution from the channel a + 5Li, while the R-matrix description was employed for the

55

S. Burzytiski et al. / 6Li(‘He, ol)‘Li + (Y+p

6

7

8

9

10

11

EC&“IMeVl

Fig. 1. Energy spectrum of alpha particles detected at 90” in coincidence with protons detected at 40” at Ei,,=3.5 MeV. The curves represent consistent R-matrix theory predictions. Dashed curve is the the dot-dashed curve is that for 3He+6Li + contribution of 3He+6Li+ CY+~L~,$.+ (Y+ (Y+p, p+8Be ,,,4 MeY+ (Y+ (Y+p and the solid one is their sum.

p + ‘Be contribution,

The parameters 0, E. and the relative ‘Be contribution A/C were fitted using x2 test for cases when both peaks were separated. For other spectra these parameters were obtained from an interpolation between the values for neighbouring spectra. Examples of the fits are shown in fig. 2. It is seen that this parametrization successfully decomposed the contributions from the two sequential processes.

4. Angular distribution The measured proton

angular

distributions

a-p angular distributions

in the reaction

correlations

from the 5Li decay were transformed

in the rest frame plane

of 5Li decay into

of the 5Li. As these are the angular

it was convenient

to use the coordinate

system

with a positive polar angle 0 for C$= 0” and negative for C#J = 180”, where 0 are measured to the left and to the right, respectively, from the direction of 5Li. The positive angles 0 correspond to the emission of protons in the direction nearer to the direction of the incident 3He beam. The angular distributions are shown in fig. 3. Error bars contain both the statistical errors and the uncertainties resulting from ambiguities in energy spectra separation. All the presented angular distributions are evidently asymmetric in respect to the direction of emission of the ‘Li, denoted by 0” on the angle axis. The asymmetry observed at 1.5 MeV and 1.73 MeV is similar to that observed by Livesey and Piluso ‘) at 1.25 MeV, shown also in fig. 3 for comparison. One must comment on a close similarity of the angular correlations measured at 1.25 MeV, 1.5 MeV and 1.73 MeV, because the energy 1.5 MeV (corrected for energy loss in

56

S. Burzyri’ski er al. / “Li(3He, a)‘Li+

a +p

E~(MeVl I .-i :,

0.6 .

7o”

73

6 I

7

8

3

‘0 ” c

(MeVl

0.6 c

Fig. 2. Alpha particle spectra acquired at 90” in coincidence with protons registered at 40”, 70” and 110 at 0 He= 3.5 MeV, fitted with mixed Breit-Wigner and R-matrix description (eq. (4)). Dashed line indicates contribution from “He+&Li + CT+‘Li p,,i,+ a t a +p, the dot-dashed curve is that from ‘He+ ‘Li+p+‘Be 1, 4MeY+ cz + CI+ p, and the solid line is their sum.

the target) corresponds to the 17.64 MeV level of the 9B compound nucleus while other two energies do not coincide with any known level. It could mean that the process is not affected by a single excited level of the compound nucleus, contrary to the interpretation suggested in ref. “>. Rather, the smooth change of the measured anguiar distributions with the 3He beam energy indicates that the reaction mechanism is a direct process.

57

S. Burzyriski et al. / 6Li(3He, a)% + a + p

.6 .4 .2_ 3.5 MeV .o

I

1 -80

I

,+ I -LO

0, b

,

,

40

,

,

00 8,

[degl

Fig. 3. Angular distributions of protons from the 3He+hLi+ LY+‘Li g b,+ (Y+ 01 + p reaction in the rest frame of the ‘Li nucleus. Data at I+ He = 1.25 MeV are from ref. ‘). Empty arrows indicate directions of the transferred neutron momenta and solid arrows indicate directions of the transferred deuteron momenta.

The angular distribution measured at 3.0 MeV is rather flat. At 3.5 MeV the asymmetry is again quite pronounced, but in this case more protons are observed at negative proton emission angles than at positive angles - just opposite to that at lower energies. The cylindrical asymmetry of the ‘Li decay can be understood if one assumes that 5Li is formed during the first stage of the reaction in a polarized state. The angular distribution for the particle with spin s to decay into two particles with spins s1 and s2 is described in the rest frame of the decaying particle by the general

S. Burzyn’ski et al. / 6Li(3ffe,

58

a)‘Li-s

a +p

expression given e.g. by Simonius 14):

(5) Here, tkq are the spherical polarization tensors of rank k, which describe the polarization of the decaying particle, k = 0, 1, . . .2s, -k s q G +k, and (0, 4) are the angles defining the direction of the emission of one of the decay products. Ak, the decay amplitudes, are reai and q-independent. Parity conservation in the decay implies Ak = 0 for odd k. Thus the decay of the ‘Li ground state of spin 3 into an alpha particle and a proton is completely determined by the polarization tensors t,,, tzO, fzl and tzz. Assuming a, equal to 1 according to the usual convention ‘“) one can calculate a2 = -1. Using the coordinates in which the experimental angular distributions are presented, the angular distribution (5) for the particular case of 5Li can be written in a form: W(O)=

t,,-$tz0(3

cos* @-1)+&r,,

sin 0 cos 0-Sf22sin2

0.

(6)

From this expression one can see immediately that the asymmetric angular distribution results from the term containing the tZ1component of the 5Li tensor polarization. To describe the measured proton angular distributions this formula was transformed into W(O)=A-BCOS~{O-@~),

where A, B and O0 are the following functions of the tensor components:

B=&t2,,--J;t22)2+6t;,

,

They were treated as free parameters in fitting to the experimental angular distributions. The solid curves presented in fig. 3 are the results of these fits. The best fit parameters are smoothly dependent on the incident energy, which indicates that the correct description of the experimental data is not fo~uitous. Parameters A and B determine the overall normalization and anisotropy of the distribution. The asymmetry is related to O,,, where 00, arctangent function of all three tensor polarization components, depends very strongly on their relative signs and magnitudes. Thus the experimentally observed change of the position of the minimum in the proton angular distributions should reflect the energy dependence of the tensor polarization of 5Li. In fact it contains also a hidden angular dependence on the energy-dependent ‘Li emission angle kinematically coupled to a fixed (90”) alpha-registration angle.

59

S. Burzyn’ski et al. / 6Li(3He, a)‘Li + a +p The

tensor

polarization

of the ‘Li in the 6Li(3He, a)‘Li

reaction

was calculated

in finite range DWBA using the code DWUCKS ‘j). As was already mentioned, a rather monotonic behaviour of the angular distributions as a function of the incident energy

suggest

that a direct

mechanism

is mainly

responsible

for the reaction

in

this energy range. The two simplest one step direct processes which can be involved are transfers of either a neutron or a deuteron from 6Li to 3He. The transferred orbital angular momentum in both processes is equal to 1 (neglecting a contribution from the D-state in 6Li). A large positive Q-value for this reaction results in a strong mismatch of angular momenta in entrance and exit channels: (I& - Lr( > 1). It makes DWBA hardly applicable for the studied reaction. Additionally the optical model potentials

are not known,

especially

for the (Y+unbound

‘Li channel.

Having

these

shortcomings in mind we nevertheless attempted the calculation using in the entrance channel a Coulomb potential and a real optical potential with V = 50 MeV. In the exit channel a potential for 6Li+alpha from the Perey compilation r6) was taken. The calculations were carried out for a transfer of a neutron and of a deuteron. From the calculations the tensor polarization components t,, of the 5Li in the usual Madison coordinate frame with the z-axis along the momentum of the incident 3He have been obtained. These components were then transformed into the coordinate system with z-axis along the momentum of 5Li and y-axis perpendicular to the reaction plane and used to calculate the angular distributions of protons using formula (6). The calculated proton angular distributions are shown in fig. 4. The curves calculated for a neutron transfer are flat and do not change considerably with energy. These

for a deuteron

transfer

and show a tendency observed.

Because

bear some resemblance

to change of the

the position

shortcomings

to the experimental

of the minimum

of the

DWBA,

shapes

as experimentally

we did

not

search

for

parameters to get a better description. These calculations nevertheless illustrate the influence of the ‘Li polarization on the asymmetry of its decay. The source of this strong polarization can be found in the dynamic conditions of the reaction. It is well known that a strong angular momentum mismatch forces the transfer

to occur

in the reaction

plane

(see e.g. von Oertzen

I’)). Thus

the

transferred angular momentum 1 is perpendicular to the reaction plane (having a z-component m = 0). The polarization of the transferred orbital angular momentum is transmitted to the total angular momentum transfer and hence to the polarization of outgoing particles through the coupling between Z-transfer and spins of the participating nuclei given by an appropriate Clebsch-Gordan coefficient I*). The 5Li nucleus, being the product of a very mismatched reaction, should then have very large vector and tensor polarization. Our measurements of the angular correlations are sensitive only to the second rank polarization 14) as explained above. The DWBA calculations carried out for the reaction under study are not reliable enough to permit conclusions concerning the preferred transfer mechanism. Another attempt was done to obtain such conclusions from the analysis of the proton angular

S. Burzytiski et al. / 6Li(3He, a)‘Li+

60

a +p

d .

~--C

R/

-

‘-,__n

E4=3.5 e

t--

MeV

Fig. 4. Results of calculations of the decay angular distributions of the ‘Li nucleus produced in the 3He+6Li+o+5Li g,s reaction. Angular distributions are calculated using the t,,, tzo, t,, and tZ2 tensors obtained from code DWUCKS and transformated to the helicity system of the 5Li nucleus. The curve marked with n is for an assumed neutron transfer, and the curve marked with d is for a deuteron transfer mechanism.

distributions in terms of the dispersion theory 19). Using the formula given in ref. 19) we have calculated the directions of the linear momenta of the transferred deuteron or neutron accordingly to the assumed reaction mechanism. These directions are shown in fig. 3 as solid arrows for a transferred deuteron and as empty arrows for a transferred neutron. One sees, that all the angular distributions of 5Li decay are approximately

symmetric

about

the momentum

of the transferred

deuteron,

while

the direction of the neutron momentum is far from the symmetry axis. From this observation one can conclude that the reaction 6Li(3He, c~)~Li,,,. proceeds rather through the deuteron transfer. The procedure applied here is a method of investigating of the reaction mechanisms using the angular correlations introduced by Treiman and Yang 20). The Treiman

and

Yang

test can be applied

particle is not polarized and initial and final state interactions in plane wave approximation. However the strong correlation of the ‘Li decay with the deuteron indication that a deuteron transfer

momentum

direction

when

the transferred

can be neglected, i.e. of the symmetry axis

for all 3He energies

is an

is favoured. 5. Conclusions

In the present paper we have presented the in-plane correlations of alpha particles with protons from the 6Li+3He+ (Y+ (Y+ p reaction. Our experimental results support earlier findings, that the reaction proceeds sequentially through intermediate unbound states of 5Li and ‘Be. The angular distributions of protons from the ‘Li,.,

S. Burzydski

decay show an asymmetry of the observed

relative to the direction

asymmetry

first step of the sequential momentum the interaction by the

mismatch.

can be explained reaction,

The supposed

of the incident

symmetry

of the

c~)-~Li+

et al. / 6Li(iHe,

which

by the polarization

The origin

of the 5Li in the

in turn comes from the strong

mechanism angular

61

of the 5Li propagation.

angular

of the first step of the reaction

3He with the deuteron proton

a +p

is

cluster in 6Li, which is suggested

distribution

relative

to the

deuteron

momentum. The assistance of Dr G.M. Osjetinskij out in Dubna is gratefully acknowledged.

during

the part of the experiment

carried

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20)

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