NEUTRON EMISSION FROM 14N+ 16’Ho COLLISIONS AT 35 MeV/u

Nuclear Physics A464 (1987) 133-158

North-Holland, Amsterdam

NEUTRON EMISSION FROM 14N+ 16’Ho COLLISIONS AT 35 MeV/u

F. DEAK and A. KISS

Department of Atomic Physics, Eiitviis University, H-1088 Budapest, Puskin u. S-7, Hungary

Z. SERES

Central Research Institute for Physics, H-1525 Budapest, POB 49, Hungary

G. CASKEY’, A. GALONSKY, C.K. GELBKE, B. REMINGTON’ and M.B. TSANG

National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824-1321, USA

J.J. KOLATA

University of Notre Dame, Notre Dame, Indiana 46.556, USA

Received 21 May 1986

(Revised 28 August 1986)

Abstract: Neutron emission from 14N + ‘65 Ho collisions has been studied at 25 MeV/u incident energy.

Energy and angular distributions of the neutrons were measured in coincidence with projectile-like

fragments (Li, Be, B, and C) emitted at angles of 10” and 30”. The spectra of neutrons at angles

far from the angle of a coincident fragment have been satisfactorily parameterized in terms of a

slowly moving, target-like source of temperature 2-3 MeV and a half-beam-velocity source of

temperature about 7 MeV. The latter source accounts for about 20% of the detected neutrons for

in-plane measurements. The out-of-plane cross sections are smaller. The relevant parameters of

the moving-sources parametrization suggest a simple model which qualitatively explains the data

in terms of the development of a hot participant zone and its subsequent mass exchange interactions

with spectators in the projectile and target nuclei.

E NUCLEAR REACTIONS “‘HO (14N, nX), E = 35 MeV/nucleon; measured (projectile-like

fragment)n-coin,neutronspectra,multiplicities.

1. Introduction

The study of energy dissipation processes in heavy-ion (HI) collisions around

and above the Fermi energy of nuclei (~28 MeV/u) may shed light on a transition

between different reaction mechanisms l-3 ). At kinetic energies up to about 10 MeV/u

above the Coulomb barrier the macroscopic features of nucleus-nucleus interactions

are characterized by a variety of equilibration phenomena 4-6). Reactions at relativis-

tic HI energies exhibit characteristics which may be derived from fast nucleon-

nucleon, two-body interactions: formation of hot participants and cold spectators

’ Present address: Donnelly Corp., Holland, Michigan. ’ Present address: Lawrence Livermore Laboratory.

0375-9474/87/[email protected]. (North-HollandPhysics Publishing Division)

134 F. Dea’k et al. / Neutron emission

in peripherial collisions and complete explosions in central collisions “). The investi-

gation of collisions at incident energies at which the nuclear relaxation time and

the interaction time are of comparable magnitude (-2 . 10mz2 set) may provide a

conceptual link between the low- and high-energy ranges “).

The emission of light particles (neutrons, protons, or alpha particles) is a rapid

way of de-exciting a hot nuclear system. Because the spectra of neutrons are not

perturbed by the Coulomb force they contain very direct information about the

behavior of hot nuclear systems. Their investigation has attracted much recent

interest in a variety of HI studies ‘-I’).

In inclusive light-particle spectra events with different impact parameters are

averaged ‘*). We can expect to gain more insight concerning a reaction mechanism

from results of measurements which can distinguish between processes of different

impact parameters. Since the distinction between reactions (fragmentation-like,

peripheral with binary rotation, etc.) is most likely related to an impact-parameter

selection 16), exclusive experiments, in which particles are investigated in coincidence

with PLF’s, have advantages over inclusive experiments.

The present work reports on an investigation of r4N-induced reactions on 165H~

at an incident energy E/u = 35 MeV. The particular projectile and target nuclei were

chosen because the N + Ho system is highly asymmetric (hence, neutron emission

from projectile and target-like fragments (TLF) is well separated kinematically),

the target is not highly fissionable, and there are already several reports on similar

work with a Ho target ‘,l’) (but at lower energies). This projectile+target system

was thought to be representative of a whole group of systems undergoing HI

collisions.

In the following we shall describe the details of the experiment and discuss the

phenomenological features of the neutron spectra. An attempt will be made to obtain

a comprehensive parameterization of the results in the framework of the moving

sources model 7Z11,12).

2. Experimental method

The experimental set-up, shown schematically in fig. 1, consisted of ten neutron

detectors placed around the outside of a 3 mm thick, 0.91 m diameter, steel scattering

chamber with three Si telescopes placed inside.

A beam of 490 MeV 14N5+ ions from the K500 cyclotron at Michigan State

University was used in the experiment with an intensity ~1 particle nA. The target

was a self supporting, rolled “‘Ho foil of 7.6 mg/cm’ area1 density. After the

experiment, the carbon and oxygen buildup on the target were determined in a

separate alpha back-scattering measurement. The sum of the contaminations was

estimated to be less than 20 ug/cm2 for which no correction was made “).

The PLF’s were detected at three angles by Si solid state detector telescopes (fig.

1). One of the detector telescopes was placed at +lO” and consisted of three elements

F. Dedk et al, / Neutron emission 135

0 SHAD3d BAR

Q 3oo

\o loo

8u -100

0 -300

0 -6O’=

- 900

Fig. 1. Experimental set-up. The proton veto paddles are marked by lines in front of the neutron detectors.

with 98 pm, 78 Frn and 5 mm thicknesses. The other two telescopes were at -30”

in and 30” below the plane of the beam and the neutron detectors. Each of them

consisted of two elements, a 75 km AE detector and a 5 mm E detector. The distances

of the front detectors from the target were between 10 and 18 cm, and the apertures

were 1.58 cm. Rare-earth Co magnets were mounted in front of each telescope in

order to inhibit secondary electrons knocked out of the target by the beam from

entering the Si detectors. The telescopes were calibrated using (Y-sources, the N

elastic peak and a precision pulse generator.

The neutron detectors were glass cells (12.7 cm in diameter by 7.6 cm thick) filled

with NE213 liquid scintillator. In front of them 6 mm thick, 15 cm diameter NE102A

plastic scintillators were used to veto protons and deuterons.

The neutron detectors were placed in the horizontal plane at angles of f lo”, *30“,

-45”, *60”, *90”, and -110” at distances ranging from 1.3 m to 2.0 m (see fig. 1).

The energies of the neutrons were determined by the time-of-flight method. As the

time structure of the beam was not suitable for timing the neutrons against the


cyclotron rf signal, only neutrons in coincidence with PLF’s were recorded. The start signal was given by the first element of the coincident PLF detector telescope. After event-by-event correction for the fragment flight time, the time resolution for -y-rays was about 1 ns when the threshold was set at the average 6oCo Compton edge. This allowed an energy resolution of about 10% for neutrons at the beam velocity. The anode signal from each neutron detector was fed into a pulse-shape sensitive module is) for neutron/ y-ray discrimination.

In order to determine the background contribution to the measured neutron spectra, shadow bars (brass cylinders 30 cm long by 7.6 cm diameter) were placed (as shown in fig. 1) directly between the target and the neutron detectors several times during the experiment. This background was typically less than 10%.

After PLF identification was performed r9), neutron time-of-flight spectra were constructed using the calculated PLF velocity. Each spectrum was corrected for absorption by the material between the target and the neutron detector (typical value =lO%). The neutron detector efficiencies were calculated with the Monte Carlo code developed by Cecil et al. *‘). The values agreed with efficiencies obtained with an earlier code by Kurz *I).

3. Experimental results

The results of the experiments are presented in the form of differential cross sections d4u/(df2, df2,,.F dE, dEPLF) for neutrons gated by a fragment as a function of neutron energy 15,. Such spectra were created for PLF’s of Li, Be, B and C, for each combination of PLF and neutron angle, and for each PLF energy bin (of width 7 MeV/u). In addition, the singles PLF energy spectra, dZa/(dfinpLF dE,,,), were evaluated. All these add up to about 600 different energy spectra.

Figs. 2 and 3 show typical energy spectra for individual PLF isotopes at +lO” and -3O”, respectively. At each angle the spectral shapes for other isotopes are similar to these, but the absolute values can be very different, even for isotopes of one element. The PLF spectra at 10” and 30” are, however, completely different from each other. All the 10” PLF spectra reveal a pronounced peak at 30-35 MeV/u of width several MeV/u, but varying from isotope to isotope. The peaks are asymmetric, falling slowly and exponentially on the low-energy side. At the lowest energies in fig. 2 the cross sections are either constant or decreasing with energy. Instrumental thresholds resulted in PLF energy cutoffs of 5 to 7 MeV/u.

The 10” PLF spectra reveal a special role for the incident 14N isotope. The lower-Z elements - Li, Be, B and C - could be detected quite easily, but the intensities of fragments heavier than N were negligible relative to the intensities of the lighter fragments.

The 30” PLF singles spectra (fig. 3) decrease exponentially with energy. The slope is generally steeper for the heavier elements. Furthermore, in contrast to the 10” spectra, there is no special role for the incident N isotope. The intensities of the

F. Dea’k et al. / Neutron emission

g FI 0 10 20 30 40 50

PLF ENERGY (MeV/u) Fig. 2. Energy spectra of “Be, “B and “C projectile-like fragments at 10”.

different elements decrease continuously with increasing 2. For no element could we see any cross section in the PLF energy range corresponding to the incident beam velocity.

In order to illustrate the most important features of the measured neutron spectra, we show some sets of them in figs. 4-6, where the coincident fragment is boron. The several hundred other neutron distributions have similar basic features, and so these are representative of the entire data set.

Fig. 4 displays the neutron energy spectra at 30” for all evaluated PLF energy bins of the coincident borons at +lO”. The spectra, which extend to about 70 MeV, fall rapidly at low energies to about 10 MeV and then fall more slowly. The figure shows that there is no major dependence of slope on PLF energy. Figs. 5 and 6 display energy spectra of neutrons in coincidence with 14-21 MeV/u boron PLF’s in the +lO” and -30” telescopes, respectively. For neutron detectors not colinear, or nearly colinear with the fragment detector, i.e., not within 30” of it, the spectra again appear to consist of only two components. The steepness of the spectra at low energy does not seem to change as the neutron detection angle changes. On

137


12 c I

FI III~IIIIII (1111’1’1””

0 10 20 30 40 50

PLF ENERGY (MeV/u)

m

Fig. 3. Same as fig. 2 for the -30” PLF telescope.

the other hand, there are marked changes in the slope with neutron angle for the

high energy fall-offs for both telescope positions; the slopes are steeper for larger

neutron angles. The relative importance of the high energy component is greater at

forward angles. Nevertheless, both components are present at all neutron angles.

An important phenomological feature of the neutron spectra was discussed in an

earlier paper 16). When the coincident PLF’s are at 10” and are quasi-elastic PLF’s,

there is an angular asymmetry in the distributions of the high energy neutrons; there

are more neutrons on the side of the beam opposite the PLF’s than on the side of

the beam containing the PLF’s. Neutron cross sections in coincidence with strongly

damped fragments at 10” or with fragments in either 30” telescope seem to be

completely symmetric with respect to the beam direction.

The neutron spectra, when the fragment telescope and the neutron detector are

both at the same angle, show strong enhancements around the energy of the PLF

(see corresponding spectra in figs. 5 and 6 and ref. **). The enhancements are strictly

correlated with the PLF energy, and the shape of an enhancement is different for

each coincident PLF element. When relative velocity spectra of fragment-neutron

F. Dea’k et al. / Neutron emission 139

Fig. 4. Energy spectra of neutrons at -30” in coincidence with projectile-like fragments of boron at +lO”

and within the indicated bins of energy per nucleon. The curves are results of fitting the data with two

moving sources, a target-like fragment source for the low-energy curves and an intermediate-rapidity

source for the high-energy curves. The vertical scale is correct for the spectrum gated by borons of

7-14 MeV per nucleon, but the other spectra have been scaled up by successive factors of 100.

coincidences in colinear geometry are constructed, it is found that dominating parts

of them are neutrons emitted via discrete, particle unbound states of the PLF. These

spectra are very different for different isotopes, and so most of the large enhancements

in the colinear spectra (such as those in figs. 5 and 6) are not the result of evaporation

from thermal PLF sources 22).

4. Parameterization of the data

We have shown 23) earlier that the influence of the PLF source on the neutron

spectra is limited by kinematic focusing to angles close to the coincident PLF angle.

The degree of limitation depends on parent PLF velocity and on angular distribution,

decay energy, and recoil effects. As the analysis of the PLF contributions needs a

special technique, we do not deal with them in this work.

140 F. De&k et al f Neufron emission

0 20 40 60 80 100

Neutron Energy (MeV)

Fig. 5. Energy spectra of neutrons at the indicated angles in coincidence with projectile-like fragments

of boron at +lO” and within the 14-21 MeV/u energy bin. As in fig. 4, the curves are the results of fitting

the data with two moving sources. The neutrons at the same angle as the fragments were excluded from the fit, as were the neutrons at near-colfinear angles, -10” and +3X The vertical scale is correct only

for the - 110” spectrum; successive factors of 100 have been applied to the others.

F. Dea’k et al / Neutron emission 141

Neutron Enerw INeVl

Fig. 6. The same as fig. 5 except that the coincident boron fragments are at -30’ instead of +lO”, and the data excluded from the fit are those at -3O”, -lo”, and -45” (not shown).


Monte Carlo calculations 2’) that take account of recoil effects show that if we

restrict our discussion to the spectra of the seven neutron detectors furthest from

colinearity with the in-plane telescopes and for all neutron spectra in coincidence

with the out-of-plane telescope, the PLF source has negligible effects. For these

data we obtain reasonable fits with two sources: a slowly-moving TLF source and

an intemediate rapidity source. The latter has characteristics similar to those of the

IR sources required to fit light charged-particle spectra from intermediate energy

HI collisions 24). As recoil effects do not influence the TLF and IR contributions,

in the lab. system we have ‘)

E,+ Ej-2JE,Ej cos B(r,,; uj) -

T, , (1)

where j stands for TLF and IR, Sj is the amplitude, Tj the temperature, and Ej the

kinetic energy/nucleon of the source, and 0( r,,; D.) is the angle between the neutron I

and source velocities. The source was assumed to move in the plane defined by the

beam and the PLF velocities. Hence, each source moved in the horizontal plane

when t&r was +lO” and -30” and in the vertical plane when epLF was 30” below

the beam direction.

Two-moving-source fits were made for the seven neutron spectra for each combina-

tion of PLF energy bin, element (Li, Be, B and C) and angle (+lO’ and -30”). The

fit parameers were Sj, I;, Ej and 0, for j = TLF and IR. Typical results of fitting

with a TLF and an IR source for coincident boron fragments are shown in figs. 4-6.

The curves that dominate at the lower energies correspond to the TLF source, while

the other curves represent the contributions of the IR source.

The out-of-plane spectra were also fitted with TLF and IR sources. The EIR was

held fixed and was taken to have the mean value found in the analysis of the -30”

in-plane data, viz., 7.5 MeV/u. Likewise, we took the mean IR source angle found

in the -30” case (l&l = 5”). This procedure was necessary because the source angle

is not adequately defined by fitting out-of-plane data, and the velocity and tem-

perature values are coupled. However, the assumption that the first stage of the

reaction mechanism in the in-plane and out-of-plane cases are similar seems reason-

able. For the slowly-moving TLF source the mean value (I eTLF( = 25”) found in the

-30” case was also used.

The quality of the fits was about the same for all angular distributions of Li, Be,

B and C PLF’s, in all PLF energy bins, and for all three telescopes. The value of

x2 per degree of freedom for the sums of the TLF and IR moving sources were

typically about 1.5. The fitted values of S TLF and S,, were used to determine the

multiplicity, i.e., the number of neutrons per detected PLF element.

F. Dedk et al. / Neutron emission

5. Discussion of the results

143

As the +lO” and -30” PLF spectra are very dissimilar (see figs 2 and 3), one can suppose that these in-plane events are dominated by different reaction mechanisms. Therefore, the results for each PLF telescope will be discussed separately.

5.1. EVENTS IN COINCIDENCE WITH THE +lO” PLF TELESCOPE

5.1.1. Moving source parameters. Fig. 7 shows the parameters TIR, E,, and f?rR of the IR source for each PLF element as functions of the PLF energy per nucleon. The temperature TIR does not seem to change as the PLF energy changes. Its values scatter around 7.5 MeV. The values of E,, are also constant, at about 8 f 1 MeV/u, except in the highest energy bin, where it is only about 4-5 MeV/u. The angle OIR is negative for the highest energy PLF bins. This result is the expression of the

Li @ Bex BO CO

10

5

0

10

5

0

0

-20

0 10 20 30 40

PLF ENERGY (MeV/u) Fig. 7. Fit parameters of the intermediate-rapidity (IR) source when the projectile-like fragment

(Li, Be, B, or C) is at +lO”.


angular asymmetry in the spectra of the high energy neutrons in terms of the moving

source parameters 16). The angle Or, is smaller for lower energy PLF’s and compat-

ible with zero or even small positive deflection for the lowest energy bins. At a given

PLF velocity Or, tends to be bigger for a heavier PLF.

These results are consistent with a simple explanation of the creation of the IR

source. In this explanation the experimental requirement of a coincidence with a

PLF at 10” selects events in which some nucleons of the incident 14N ion interact

with about the same number of nucleons of the 165H~ target, and a hot participant

zone is created. This zone may be heated to a temperature at which many nucleons

become unbound and leave, before the residual excitation energy can be distributed

to nucleons of the spectator parts of the colliding nuclei. The velocity of the IR

source, urR, is found to be close to half the velocity of the projectile (OSv,), especially

if we take into account its deceleration in the Coulomb field of the target nucleus

(EC = 4 MeV/u). The fact that 2)rR does not change with PLF energy is consistent

with the assumption that nucleon emission occurs at an early stage of the develop-

ment of the participant zone, whereas the EpLF is determined much later.

The properties of the angle parameter are in qualitative agreement with this

picture. When the PLF has a velocity close to ZJ~, i.e., when the event resembles

clean fragmentation 25,26), momentum conservation requires that the IR source go

to the side opposite the PLF [ref. ‘“)I. Here, the bigger the mass of the detected

PLF, APLF, the smaller is the mass of the hot zone, AIR. Consequently, there should

be a trend that OIR is bigger for higher ApLF, and according to fig. 7, there is such

a trend. For the lower PLF energies the material of the detected fragment was

obviously involved in some energy dissipating interactions. One may expect a

continuous decrease of Or, as EPLF decreases. This is also seen in fig. 7.

Fig. 8 shows the parameters TTLF, ETLF and OrLF of the TLF source for each PLF

element as functions of EPLF. The temperature TTLF decreases from about 2.8 MeV

to about 1.8 MeV as EpLF increases from 10 MeV/u to 40 MeV/u, while ETLF

decreases from about 0.07 MeV/u to about 0.01 MeV/u in the same interval. The

source angle OTLF is always negative.

The neutron multipliciies for the IR and TLF sources (pLIR and pTLF) seem to be

proportional to each other. This may be seen in fig. 9, where both multiplicities are

plotted against the square root of EPLF; but the TLF multiplicities have first been

divided by the average multiplicity ratios (4.62 for Li, 4.64 for Be, 4.33 for B, and

3.38 for C). The values of the ratios mean that about 20% of all of the neutrons

are emitted by the IR source.

51.2. Energy and momentum balances. The proportionality of the multiplicities

suggests that the TLF source develops by nuclear relaxation processes from the IR

source, which, after a short period of emitting some unbound nucleons, distributes

its energy to the neighboring nuclear matter. If this is true, one should be able to

account for the energy and momentum of the incident 14N ion in the framework of

the moving sources model.

F. l?elik et al, / Neutron emission 145

0

0.1

9

‘3: 3 0.0

;! w

0

h * 2 -50

a

C! -loo 0 10 20 30 40

PLF ENERGY fMeV/u) Fig. 8. The same as fig. 7 except that the source is the TLF instead of the IR source,

Such an energy and momentum analysis has been done in the laboratory system. We assume that the hot zone emits neutrons and {undetected) protons with about the same probability and that the kinetic and thermal energies of the hot pa~i~ipant zone are later absorbed into kinetic and thermal energies of the matter of the involved nuclei. Then the energy “seen” in the reaction is expressed as

E,,,, = &,_G&LF+ 2~& TIR + &,ind + Em) + ETLFATLF -t- ; T’&LF . (2)

where APLF amd ATLF are the mass numbers of the PLF and TLF, respectively. Here we took into account that Ebind - 8 MeV is needed to free a nucleon. The last

term estimates the excitation energy of the TLF source from the temperature parameter6). The value of ATLF was approximated by 165 in the analysis. With respect to successive neutron emissions from the TLF source, we estimated the original TLF temperature by T - #$TTLF [ref. “‘)f H ere neutron emission is expected

to be preferred among the light particles. In eq. (2) we neglected the thermal energy of the PLF and the possible rotational energy of the fragments. A simple estimate tells us that altogether these may not be larger then about 10% of the total energy.

146

E,,1/2 (M&/u) 1’2 Fig. 9. Neutron multiplicity when O,,, = +lO” versus I?$$. To demonstrate the proportionality between

intermediate-rapidity (IR) and target-like fragment (TLF) multiplicity we have divided the TLF values

by r=4.62, 4.64, 4.33, and 3.38, respectively for PLF= Li, Be, B, and C.

For the determination of the momenta in the beam direction, it was assumed that

the average momentum of the nucleons from a thermal source is equal to the

momentum/nucleon of the moving source. Hence,

PA@ = 0) = APLFV~LF cos @~LF+~CLIRVIR cos @IR

+ &FvT,_F ~0s @TLF , (3)

where vpLF, vxR and VTLF are the velocities of the PLF, IR and TLF sources,

respectively.

Eqs. (2) and (3) have been evaluated for each PLF element and energy bin

separately, always using the actual values of the parameters in figs. 7-9. The upper

sections of figs. 10 and 11 show the results in terms of the ratios of the “seen” to

incident values. Both the incident energy and momentum are accounted for by the

experimental data parameterized in the framework of the moving sources model to

better than 20% in all cases, and the average ratios are close to 1. These results

suggest that there is no other mechanism which makes a major contribution to the

F. De&k et al. / Neutron emission 147

Fig. 10. Ratio of E, the energy “seen” in the experiment, to E,, the incident energy (49UMeV), at each of the three PLF angles, +lO’, -30°, and 30’ out of the plane of the neutron detectors.

coincidences or which takes away a considerable amount of energy and/or momentum. We can conclude that the assumption about dissipation of the energy and momentum of the early hot zone into the former spectator nuclear matter is consistent with the moving sources model.

51.3. ~ec~Qn~s~ for~e~~~eru~ ~QlZ~ion~. The PLF spectra at 4-10” are dominated by fragmentation-hike peaks close to ZJ@ (fig. 2). Events with coincident PLFs on the Iow energy side of the peaks may not result from cfean f~gme~tation 25,26). For these events there has been some deceleration process. According to the conclusions drawn from the systematics of the IR parameters, this deceleration must follow hot zone formation and early nucleon emission.

We may assume that the interaction between the fragmented incident HI and the hot participant zone continues for some time in the form of a “friction” which may include the picking-up of nuclear matter from the hot zone. This kind of process could well lead to deceleration of the fragmented HI. The outgoing PLF would then be a composite of some nucleons which ~~ginally belonged to the light spectator and some of which took part in the hot zone formation. If all processes are basically

148

0.5 r 30’ out of plane 1

0.0 ~ 0

FFF ENERG (M&/E)

40

Fig. 11. The same as fig. 10, except that this figure is for momentum rather than energy.

sticking collisions, one can make a crude estimate of the mass of the participant zone by using the constraint of momentum conservation when the IR is formed

&~~R+(APLF-AA)~o= 14~0, (44

and when the PLF is formed

(A PLF - AA) vo + AAQR = -%S+LF , (4bl

where AA is the number of nucleons which were picked up from the hot zone. We note that for AA to be less than APLF, vIR -c opLF. Thus, for the mass of the early participant zone we get:

(5)

Fig. 12 shows the extracted IR neutron multiplicities as a function of the mass of the hot zone calculated according to eq. (5). There is a linear correlation between these quantities. This is consistent with the simplest idea about the multiplicity properties of an early pa~icipant zone with a given temperature, viz., the bigger the hot zone, the larger the number of the emitted nucleons. All values of PrR follow

F. Dedk et al. / Neutron emission 149

otmn ” ” ” ” ” ” ” ” ” 0 10 20 30 40

AIR

Fig. 12. Dependence of the IR multiplicity on the mass of the participant zone estimated for the indicated

PLF’s at +lO”. The values of A,, were obtained from eq. (5).

this rule independently of the PLF energy and identity. Fig. 12 summarizes the different neutron multiplicity results for different coincidence events.

According to eq. (5) and fig. 12, )(~i~‘s are expected to be linear functions of upLF, i.e. of Ebi2p Analysis of the data revealed the same relationship, as displayed in fig. 9. The agreement with the expected linear behavior is good for all PLF elements.

According to the equilibrium assumption used in testing for energy and momentum balance in figs. 10 and 11, the properties of the TLF source should be determined by the dissipation and distribution of the energy and momentum of the participant zone into the material of the target nucleus. Since figs. 10 and 11 show that the tests were successful, we may assume that the relaxation processes do have enough time to reach thermal equilibrium before the TLF neutrons are emitted. Therefore, TrLF

should be determined by the energy remaining after early emission of nucleons and transfer of mass to the PLF. In this way the residual energy that heats the TLF is

E~~~~AIR(EIR+~TIR)-~~.IR(EIR+~TIR+E~~~~)

-AA(E,,+tT,,) -&F&LF. (6)

The factor of two in the second term is present to account for fast protons. By standard thermodynamics EREs should have a linear correlation with T&. Fig. 13

shows T2 (from fig. 8) versus &REs computed according to eq. (6). The two variables are correlated, and this correlation may even be linear.

The multiplicity pTLF is influenced by multistep processes in which de-excitation by particles other than neutrons can play a role. The above model is therefore not

1.50 F. De&k et al. / Neutron emission

Li + BeX BO CO

T”“l”“l”“r”“I”‘I

0 50 100 150 200

ERES cMeV)

Fig. 13. Correlation between T* and eRES when the coincident PLF is at f10”. gpeS is the residual energy computed with eq. (6).

able to predict values of pTLF. However, supposing that the multiplicity is roughly propo~io~al to eREs, its linear dependence on AIR in eq. (6) means that , according to eq. (5), ,+,F should be a linear function of Y,,, or of E k'&. That this dependence exists may be seen in fig. 9. We cannot tell whether the additional feature of fig. 9, an empirical proportionality between plR and /JTLF, is specific to this investigation or whether it is a general property.

5.2. NEUTRONS IN COINCIDENCE WITH PLF’s AT 30”

5.21. In-plane PLF's at 30". Fig. 14 shows the temperature, kinetic-energylnu- clean, and angle of the IR source for each PLF element and energy bin. The temperatures are around 8 MeV. The kinetic energies scatter considerably, their mean value being around 6-8 MeV. The angles are slightly negative, i.e., the IR source flies to the same side of the beam as the PLF.

The temperature of the TLF source (fig. 15) decreases with PLF energy from about 2-3 MeV to 1.5-2.5 MeV, and it tends to be smaller for the heavier PLF elements. The values of ETLF are all around 0.1 MeV/u. The TLF angle scatters a lot, but its values are definitely positive. This means that the TLF source flies to the side of the beam opposite the PLF.

The in-plane data points in fig. 16 show the extracted multipliciities for the IR and TLF sources. In contrast to the multiplicities measured in coincidence with PLF’s at lo”, both multiplicity functions remain constant as the PLF energy changes. The TLF multiplicities are close to each other for all PLF elements; the average

E D&k et al. / Neutron emission 151

0 10 20 30 40

PLF ENERGY (MeV/u) Fig. 14. The same as fig. 7, except that the PLF is at -30” instead of +lO”.

value, 13*3, is near the TLF multiplicities for the lowest PLF energy bin of the +lO” telescope (fig. 9). The ratios ~TLF/~IR are displayed in fig. 17. They are between 3 and 6, which means that about 20% of the neutrons have been emitted from the IR source. The relative ~mpo~ance of the neutrons from the IR source seems to increase for heavier PLF’s. This behavior is similar to that found in the +lO” case.

The middle parts of figs. 10 and 11 show the results of the energy and momentum analyses that were made on the basis of eqs. (2) and (3). Both the incident energy and momentum are accounted for to better than 20% in all cases. One believes again that no major process has been disregarded and that energy and momentum dissipation proceeds via the formation of a partcipant hot zone.

Because of the lack of a quasi-elastic peak in the spectrum of fragments at 30” (see fig. 3), the neutrons in coincidence with those fragments must result from mechanisms other than projectile fragmentation. If we assume that they are from central collisions, the formation of hot zones which are always of about the same mass would explain why pm does not change with EptF. A slight dependence of multiplicity on the species of the coincident PLF could be imagined because cooling

152 F: De&k et al. / Neutron emission

Li * Bex BO Cfl

0 10 20 30 40

PLF ENERGY fMeV/u) Fig. 15. The same as fig. 8, except that the PLF is at -30” instead of +lO’.

of the hot zone by composite particle emission and the emission of the detected PLF might be correlated.

5.2.2. Out-of-plane PLF’s at 30”. The only parameter which was allowed to change for the IR source in this case was the temperature (see sect. 4). Fig. 18 shows the best fit values of TrR. Most of them are between 5.0 and 7.5 MeV, but there does not seem to be any systematic dependence on either the energy or the 2 of the PLF.

Fig. 19 summarizes the results for the TLF source. The value of TTLF decreases with increasing EpLF from about 2.7 to 2.2 MeV. The E,,, values have large error bars and are almost all consistent with 0.08 MeV/u.

The multiplicities are shown in fig. 16. The pLIR’s are about the same for the different PLF elements and reveal a slight decrease with EPLF. Fig. 16 also compares the multiplicities for the in-plane and out-of-plane cases. The in-plane multiplicities are always bigger, the average ratio beting about 1.3 for the TLF sources and about 2.5 for the IR sources. All these multiplicities were obtained from measured spectra assuming isotropic sources - in disagreement with the data. The ratios are still meaningful, but the pIR values used in eqs. (2) and (3) could be somewhat inconsistent.

F. Dea’k et al. / Neutron emission 153

X IN @ OUT

E PLF 1’2 ( MeV/u)l12 Fig. 16. Multiplicity of the IR and TLF sources versus Ek& when the indicated PLF is at -30” in the

plane of the neutron detectors and at 30” out of the plane.

The lowest parts of figs. 10 and 11 show the results of the energy and momentum analyses. Figure 11 shows that, to within about 10%) the incident linear momentum is accounted for in all cases, and the mean value of P/P,, is 1. However, the energy balance analysis does not account completely for the incident energy. The E/E, values are almost all around 0.8, and they do not show any significant change with either the species or the energy of the PLF. The missing 20% (i.e. ~100 MeV) cannot be dissipated by any degree of freedom which, on the average, has an important role in shaping the momentum baIance.

5.3. REACTION MECHANISM CONSIDERATIONS

Perhaps the missing energy is associated with the mechanism for emission of the coincident PLF. Neither thermal evaporation from the hot participant zone nor formation and emission by coalescence seems likely because PLF’s in this work have 6 to 14 nucleons; yet AIR = 28. Furthermore, neither mechanism would account for the in-plane to out-of plane asymmetry apparent in figs. 16 and 17.

154

10

5

0 IO

5

0 2 3 4 5 6

Fig. 17. The multiplicity ratio @-,.&P~~ versus I?;$ when the PLF is at -30” in the plane of the neutron detectors and at 30” out of the plane.

9:

% a” ~ f ; ‘s”“‘x ““‘I t I” ’ I’

0 10 20 30 40

PLF ENERGY (MeV/u) Fig. 18. T,a, obtained by fitting to the neutron spectra when the coincident PLF was at 30” out of the

plane of the neutron detectors.

A mechanism that will satisfy the momentum, energy and asymmetry requirements can be developed by extending the spectator-pickup model we used to describe the data with a PLF at 10”. For a PLF at 30” the collision is not peripheral and there will be no projectite spectator, The entire projectile wiff enter the target, setting it into rotation and creating a hot zone. But there may be target spectator which picks

Li @ Bex BO Cm 4

PLF ENERGY (MeV/u) Fig. 19. Fitted parameters of the TLF source when the coincident PLF was at 30” out of the plane of

the neutron detectors.

up AA nucems from the hot zone to form the PLF, (It is dear that to an observer at the center of mass both spectators are possible). Momentum conservation enables us to compute AA and ASPECT from

AARR = APLFQW (7a)

A PLF - - Aspect + AA . Ub)

Of course a PLF will be formed by this process only with t&F < vIR. In this model rotation absorbs energy but not momentum from the projectile.

Furthermore, the rotation favors in-plane to out-of-plane emission of the neutrons. Hence, at least qualitatively~ all three requirements are met. Using the very same arguments as in the +I@” case we can cafculate sRES from eq. (6) with A,, - 28 and again expect a linear correfation with T”. Fig. 20 shows the results. For the in-plane case the two quantities seem to correlate, and the dependence might be linear. The out-of-plane points are neither consistent nor inconsistent with a linear TZ correlation.

To account quantitatively for the missing =L: 100 MeV in the out-of-plane case, we note that the angular momentum imparted to the TLF may be as high as =BOh [ref. 28) J, corresponding to a rotational energy of a40 MeV for a rigid body, and to more if not rigid. The remainder of the missing energy must arise from neglect of rotation in ~ompu~ng neutron multiplicities i,e., from the erroneous assumption of isotropic emission in the rest frame of the sources, This assumption led to an underestimate of the energy carried away by the nuclectns, In spite of the rotation,

156 F. Dedk et al. / Neutron ~~jssion

0 0 100 200 300 0 100 200 300

GES (MeV)

Fig. 20. The same as fig. 13, except that the coincident PLF is at -30” in the plane (left side) and at out of the plane (right side) of the neutron detectors.

30”

the -30” in-plane case did not show missing energy, perhaps because the overestima- tion of the IR nucleon multiplicities was compensated by the omission of the rotational energy.

The fact that the fR source was found to move to the side of the beam with the PLF telescope for the -30” in-plane data (fig. 14) has a natural explanation in this pa~ial-orbiting model. The coincidence requirement selects those events in which some fast nucleons collectively turn in the direction of the PLF telescope, i.e., in the sense of negative angle scattering. This selection means a limited range for the impact parameters of the collision, and it defines the plane of the rotation of the

system.

6. Couc~u$i~ns

1. Neutron emission from i4N i- *@Ho collisions was studied at 35 MeV/u incident energy by measuring energy and angular dist~butions in coincidence with PLF”s of Li, Be, B and C at +lO* and at -30” in the projectile-neutron plane and at 30” out of that plane. Neutron cross sections were determined for PLF’s in energy bins of width 7 MeV/u.

2. The PLF energy distributions at 10’ are dominated by fragmentation-like peaks at velocities close to that of the incoming beam. At 30” they show only exponential fall-offs. The weak low-energy portions of the 10” spectra have similar fall-offs.

3. The coincident neutron spectra exhibit features which suggest that they have contributions from three different sources. The PLF’s emit neutrons with considerable probability via discrete, neutron-unbound states. The other two sources show

F. Dea’k er al. / Neutron emission 157

the characteristics of thermal evaporation. One of the sources has a low velocity and a temperature of about 2.5 MeV. The other one has a velocity of about half that of the beam and a temperature around 6-8 MeV.

4. The non-colinear data were successfully parametrized in the framework of the moving sources model. The neutron multiplicity shows a linear dependence on the velocity of the coincident PLF (Li, Be, B, or C) at +lo”.

5. The systematics of the fit parameters favored an explanation of the majority of the +lO” data as resulting from fragmentation-like processes in which the deceleration mechanism for the fragmented PLF was a cluster pick-up from the hot participant zone.

6. With PLF’s at 30” the data show an in-plane/out-of-plane asymmetry, there being more neutrons in the plane. The assumption of a negative angle, deep-inelastic scattering process with a limited range for the possible impact parameters qualitatively explains the data.

The support of both the Hungarian Academy of Sciences and the U.S National Science Foundation, the latter under Grants INT-80-15333, PHY-83-12245, and PHY-84-16025 is gratefully acknowledged. We thank J. Hinnefeld and J.H. Heltsley for assistance in setting up the experiment and in taking the data.

References

1) C.K. Gelbke, C. Olmer, M. Buenerd, D.L. Hendrie, J. Mahoney, M.C. Mermaz and D.K. Scott,

Phys. Reports 42 (1978) 311

2) M. Lefort, Nucl. Phys. A387 (1982) 3

3) B. Remaud, F. Sebille, Ch. Gregoire and F. Schemer, Nucl. Phys. A428 (1984) 101

4) V.V. Volkov, Phys. Reports 44 (1978) 93

5) W.U. Schrijder and J.R. Huizenga, Ann. Rev. Nucl. Sci. 27 (1977) 465

6) D.K. Scott, Nucl. Phys. A354 (1981) 375

7) D. Hilscher, J.R. Birkelund, A.D. Hoover, W.U. Schriider, W.W. Wilcke, J.R. Huizenga, A.C.

Mignerey, K.L. Wolf, H.F. Breuer and V.E. Viola, Jr., Phys. Rev. C20 (1979) 576 8) T. Fukuda, M. Ishihara, M. Tanaka, I. Miura, H. Ogata and H. Kamitsubo, Phys. Rev. C25 (1982)

2464

9) I. Tserruya, A. Breskin, R. Chechik, A. Fraenkel, S. Wald, N. Zwang, R. Bock, M. Dakowski, A.

Gobbi, H. Sann, R. Bass, G. Kreyling, R. Renfordt, K. Stelzer and U. Arlt, Phys. Rev. C26 (1982) 2509

10) A. Gavron, J.R. Beene, B. Cheynis, R.L. Ferguson, F.E. Obenshain, F. Plasil, G.R. Young, G.A.

Petitt, CF. Maguire, D.G. Sarantites, M. Jaiiskelainen and K. Geoffroy-Young, Phys. Rev. C27

(1983) 450

11) E. Holub, D. Hilscher, G. Ingold, U. Jahnke, H. Orf and H. Rossner, Phys. Rev. C28 (1983) 252

12) D. Hilscher, E. Holub, G. Ingold, U. Jahnke, H. Orf, H. Rossner, W.U. Schriider, H. Gemmeke, K. Keller, L. Lassen and W. Liicking, Coincidence particle emission from continuum states, (World

Scientific, 1984) p. 268

13) W. Liicking, R. Schreck, K. Keller, L. Lassen, A. Nagel and H. Gemmeke, Z. Phys. A320 (1985) 585

14) M. Blann, Phys. Rev: C31 (1985) 1245

15) E. Holub, D. Hilscher, G. Ingold, U. Jahnke, H. Orf, H. Rossner, W.P. Zank, W.U. Schriider, H.

Gemmeke, K. Keller, L. Lassen and W. L&king, Phys. Rev. C33 (1986) 143

16) G. Caskey, A. Galonsky, B. Remington, M.B. Tsang, C.K. Gelbke, A. Kiss, F. Deak, Z. Seres, J.J.

Kolata, J. Hinnefeld and J. Kasagi, Phys. Rev. C31 (1985) 1597

158 F. De& et al. / Ncwtron emission

17) B.A. Remington, C. Caskey, A. Galansky, C.K. Gelbke, L. Heilbronn, J. Heltsley, MB. Tsang, F. Deak, A, Kiss, 2, Seres, J. Kasagi and J.J. Kolata, Pbys. Rev. C34 (1986) 1685; B.A, Remington, Ph.D. thesis, 1986, Michigan State University

18) P. Sperr, H. Spieler, M.R. Maim and D. Evers, Nucl. Instr. Meth. 116 (1974) $5 19) T. Shimada, M. Ishihara and K. Nagatani, Nucl. Instr. Meth. 165 (1979) 261 20) R.A. Cecil, B.D. Anderson and R. Madey, Nucl. Instr. Meth. 161 (1979) 439 21) R.J. Kun, University of California Radiation Lab Internal Rep. No. UCRL-Ii339 22) A. Kiss, F. Deak, 2. Seres, G, Caskey, A. Galonsky, L. Heilbronn, B. Remington and J, Kasagi,

Phys. Lett. B, to be published 23) C. Caskey, A. Galonsky, 3. Rern~~gt~~, F. Deak, A. Kiss and Z. Seres, Pbys. Rev. C34 (1986) 506 24) G.D. Westfall, B.V. Jacak, N. Ana~tar~an, M.W. Curtin, GM. Crawley, C.K. Getbke, B.

Hasselquist, W.G. Lynch, D.K. Scott, M.3. Tsang, M.J. Murphy, T.J.M. Symons, R. Legrain and T.J. Majors, Phys. Led. 116B (1982) 118.

25) A.S. Goldhaber, Pbys. Lett. f3B (1974) 306 26) W.A. Friedman, Phys. Rev. CZ? (1983) 569 27) Kd. Le Couteur and D.W, Lang, Nucl. Pbys. 13 (1959) 32 28) S. Cohen, F. Plasil and W.J. Swiatecki, Ann, of Pbys. 82 (1974) 557

Documents

NEUTRON EMISSION FROM 14N+ 16’Ho COLLISIONS AT 35 MeV/u